Addition and Subtraction Basic Math Packet 2009-2010

Washington County Public Schools 2009‐2010

Office of Elementary Education 1 DRAFT

Addition and Subtraction

Basic Fact Strategies Office of Elementary Education

Draft 2009-2010



Table of Contents Page Numbers

Basic Fact Philosophy 3-6 Description of Addition Math Fact Strategies 7

- Parent Letters: Description of Addition Math Fact Strategies

9-12

Classroom Math Fact Assessments 13-25 Grade Level Expectations 26-27 Roll Out of Strategies in the Primary Grades 28-29 Roll Out of Strategies in the Intermediate Grades 30-35

Addition Strategies One-More-Than and Two-More-Than Facts 36-76

- Drill of Efficient Methods and Strategy Selection 77 - Use of Flash Cards 78-80 - Turn Around Facts 80-87 - Beginning Exploration of Subtraction as Think Addition 88-90

Facts with Zero 91-99 Doubles 100-132 Doubles + 1 133-152 Inside Doubles 153-179 Make-Ten Facts 180-214 Strategy Selection/Strategy Retrieval 215-228

Subtraction Strategies Strategies for Subtraction Facts 229-242 Triangular Relationship Cards 242-243 One-More-Than and Two-More-Than Subtraction Facts (Think Addition) 244-249 Doubles Subtraction Facts (Think Addition) 250-256 Doubles + 1 Subtraction Facts (Think Addition) 257-261 Inside Doubles Subtraction Facts (Think Addition) 262-267 Make Ten Subtraction Facts (Think Addition) 268-276 Additional Strategies for Subtraction Facts 277-281 Center Bag Support 282-293 Washington County Public Schools Monthly Fact Program 294-301



Basic Fact Philosophy



Basic Fact Philosophy Mastery of basic facts means that a child can give a quick response (in about 3 seconds) without resorting to non-efficient means, such as counting. All children are able to master the basic facts—including children with learning disabilities. Children simply need to construct efficient mental tools that will help them. Development of Efficient Strategies An efficient strategy is one that can be done mentally and quickly. The emphasis is on efficient. If drill is undertaken when counting is the only strategy available, all you get is faster counting. Two Approaches to Fact Strategies You need to plan lessons or short activities in which specific strategies are likely to be developed. There are two basic types of lessons suggested for this purpose. The first is to use simple story problems designed in such a manner that students are most likely to develop a strategy as they solve it. These are worthwhile tasks that do not require a full period to do and discuss. Rathmell, Leutzinger, and Gabriele (2000) suggest a simple story problem and discussion in a 5 to 10 minute period to start every day. Their teachers report that students develop and use a variety of effective strategies for mastering basic facts. In the discussion of these solution methods, you can focus attention on the methods others have developed. A second possible approach is a bit more direct. A lesson may revolve around a special collection of facts for which a particular type of strategy is appropriate. You can discuss how these facts might all be alike in some way, or you might suggest an approach and see if students are able to use it on similar facts. There is a huge temptation simply to tell students about a strategy and then have them practice it. Though this can be effective for some students, many others will not personally relate to your ideas or may not be ready for them. Continue to discuss strategies invented in your class and plan lessons that encourage strategies. Drill of Efficient Methods and Strategy Selection It is important here to make a distinction between drill and practice. Practice refers to problem-based activities in which students are encouraged to develop (invent, consider, try—but not master) flexible and useful strategies that are meaningful. The types of lessons just described can be thought of practice lessons. Whether from story problems



or from consideration of a collection of similar facts, students are wrestling with the development of strategies that they can use themselves. Drill refers to repetitive non-problem-based activity. Drill activity is appropriate for children who have a strategy that they understand, like, and know how to use but have not yet become facile with it. Drill with an in-place strategy focuses student’s attention on that strategy and helps to make it more automatic. Drill plays a significant role in fact mastery, and the use of old-fashioned methods such as flash cards and fact games can be effective if used wisely. Avoid Premature Drill It is critical that you do not introduce drill too soon. Suppose that a child does not know the 9 + 5 fact and has no way to deal with it other than to count fingers or use counters. These are inefficient methods. Premature drill introduces no new information and encourages no new connections. It is both a waste of time and frustration to the child. Drill should only be used when an efficient strategy is in place. Overview of the Approach For each particular strategy, from development to eventual drill when the strategy is well understood, the general approach for instruction is very similar. Make Strategies Explicit in the Classroom As has been discussed, your students will develop strategies as they solve word problems or as they investigate a category of facts you present. When a student suggests a new strategy, be certain that everyone else in the room understands how it is used. You can ask another student to explain what the student has just shared with the class. This requires students to attend to ideas that come from their classmates. Then, explore with the class to see what other facts would work with the student’s suggested strategy. Don’t expect to have a strategy introduced and understood with just one word problem or one exposure such as this. Try on several successive days problems in which the same type of strategy might be used. Children need lots of opportunities to make a strategy their own. Many children will simply not be ready to use an idea the first few days, and then all of the sudden something will click and a useful idea will be theirs. It is a good idea to write new strategies on the board or make a poster of strategies students develop. Give the strategies names that make sense. (Doubles and add on more set. Helen’s idea. Use with 3s. Include an example.)



No student should be forced to adopt someone else’s strategy, but every student should be required to understand strategies that are brought to the discussion. Drill Established Strategies When you are comfortable that children are able to use a strategy without recourse to physical models and that they are beginning to use it mentally, it is time to drill it. You might have as many as ten different activities for each strategy or group of facts. File folder or boxed activities can be used by children individually, in pairs, or even in small groups. With a large number of activities, children can work on strategies they understand and on the facts that they need the most. Flashcards are among the most useful approaches to fact strategy practice. For each strategy, make several sets of flash cards using all the facts that fit that strategy. On the cards, you can label the strategy or use drawings or cues to remind the children of the strategy.

Teaching Student Centered Mathematics K-3 John Van De Walle

Pages 94-98



Math Strategy Descriptions



Description of Addition Math Fact Strategies One-More-Than and Two-More-Than Facts This strategy is used for facts that have a 1 or a 2 as one of it’s addends (example: 8 + 2). Out of the 100 addition facts students will learn, 36 fall under the one-more-than and two-more-than facts. In these situations, students simply count up 1 or 2 from the greatest addend. This should be the only situation where students “count” to find their answer. Facts with Zero 19 facts have zero as one of the addends. Although these facts seem to be the simplest of all, some students will overgeneralize the idea that answers to addition are bigger. Putting these facts into real life situations oftentimes help the students to reinforce the zero rule. Doubles There are only 10 doubles facts. These facts are relatively easy to learn and become a powerful way to learn many other facts. Examples of double facts include: 5 + 5, 3 + 3, 6 + 6. Dice from board games are good visuals to use to help students remember their double facts. Near Doubles Near doubles are also called the “doubles-plus-one” facts and include all combinations where one addend is one more than the other. There are 18 of these facts. When students realize that these are facts that have addends with a difference of 1 (1 + 2), (3+ 4), (5 + 6) etc. they simply double the smaller addend and add 1. Inside Doubles Inside doubles or “doubles plus two” facts focus on facts that have 2 addends that are separated by 2 numbers. Some examples are: (5 + 7), (4 + 6), (7+ 9). Once the students are able to recognize these facts, they are able to look at the number that falls between the 2 addends and double it to find the answer. For example: 5 + 7, the number that comes between the 2 numbers is 6. The student doubles the number to find the answer (6 + 6 = 12).

Make-Ten Facts These facts all have at least one addend of 8 or 9. One strategy for these facts it to build onto the 8 or 9 and up to 10 and then add on the rest. For 6 + 8, start with 8, then 2 more makes 10, and that leaves 4 more for 14. Information gathered from Teaching Student Centered Mathematics Grades K-3, John Van De Walle The attached parent letters can be used to communicate with parents about the various strategies. The second letter can be sent home with students as a homework guide. The first column can be used to show the level at which the child is currently working. Centers can be sent home as homework to support that particular strategy.



Dear Parents, In the weeks to come, our class will be focusing on learning our addition and subtraction math facts. I wanted to make you aware of some of the strategies we will be using so that you can help to reinforce these same strategies at home. 1. One-More-Than and Two-More-Than Facts This strategy is used for

facts that have a 1 or a 2 as one of it’s addends (example: 8 + 2). Out of the 100 addition facts students will learn, 36 fall under the one-more-than and two-more-than facts. In these situations, students simply count up 1 or 2 from the greatest addend. This should be the only situation where students “count” to find their answer.

2. Facts with Zero 19 facts have zero as one of the addends. Although

these facts seem to be the simplest of all, some students will overgeneralize the idea that answers to addition are bigger. Putting these facts into real life situations oftentimes help the students to reinforce the zero rule.

3. Doubles There are only 10 doubles facts. These facts are relatively

easy to learn and become a powerful way to learn many other facts. Examples of double facts include: 5 + 5, 3 + 3, 6 + 6. Dice from board games are good visuals to use to help students remember their double facts.

4. Near Doubles Near doubles are also called the “doubles-plus-one”

facts and include all combinations where one addend is one more than the other. There are 18 of these facts. When students realize that these are facts that have addends with a difference of 1 (1 + 2), (3+ 4), (5 + 6) etc. they simply double the smaller addend and add 1.

5. Inside Doubles Inside doubles or “doubles plus two” facts focus on

facts that have 2 addends that are separated by 2 numbers. Some



examples are: (5 + 7), (4 + 6), (7+ 9). Once the students are able to recognize these facts, they are able to look at the number that falls between the 2 addends and double it to find the answer. For example: 5 + 7, the number that comes between the 2 numbers is 6. The student doubles the number to find the answer (6 + 6 = 12).

6. Make-Ten Facts These facts all have at least one addend of 8 or 9.

One strategy for these facts it to build onto the 8 or 9 and up to 10 and then add on the rest. For 6 + 8, start with 8, then 2 more makes 10, and that leaves 4 more for 14.

Subtraction facts prove to be more difficult than addition. This is especially true when children have been taught subtraction through a “count-count-count” approach; for 13 – 4, count 13, count off 5, count what’s left. 1. Subtraction as Think-Addition The main strategy that will be used

with subtraction facts is subtraction as “think addition”. When done in this think-addition manner, the child uses known addition facts to find the answer. When your child sees 9 – 4, you want them to think spontaneously, “Four and what makes nine?”

If you have any questions, please feel free to contact me. I look forward to working with you and your child on this new and exciting adventure!

Sincerely, *Information gathered from Teaching Student Centered Mathematics Grades K-3, John Van De Walle



Dear Parents, We are continuing to practice our addition and subtraction math facts. Your child will be bringing home activities to help reinforce their current focus. Your child has mastered the following strategies (M). Your child is currently working on this strategy (C). (M) Mastered (C) Currently Working On

Strategy and Description

One-More-Than and Two-More-Than Facts This strategy is used for facts that have a 1 or a 2 as one of it’s addends (example: 8 + 2). Out of the 100 addition facts students will learn, 36 fall under the one-more-than and two-more-than facts. In these situations, students simply count up 1 or 2 from the greatest addend. This should be the only situation where students “count” to find their answer.

Facts with Zero 19 facts have zero as one of the addends. Although these facts seem to be the simplest of all, some students will over generalize the idea that answers to addition are bigger. Putting these facts into real life situations oftentimes help the students to reinforce the zero rule.

Doubles There are only 10 doubles facts. These facts are relatively easy to learn and become a powerful way to learn many other facts. Examples of double facts include: 5 + 5, 3 + 3, 6 + 6. Dice from board games are good visuals to use to help students remember their double facts.

Near Doubles/Doubles + 1 Near doubles are also called the “doubles-plus-one” facts and include all combinations where one addend is one more than the other. There are 18 of these facts. When students realize that these are facts that have addends with a difference of 1 (1 + 2), (3+ 4), (5 + 6) etc. they simply double the smaller addend and add 1.

Inside Doubles Inside doubles or “doubles plus two” facts focus on facts that have 2 addends that are separated by 2 numbers. Some examples are: (5 + 7), (4 + 6), (7+ 9). Once the students are able to recognize these facts, they are able to look at the number that falls between the 2 addends and double it to find the answer. For example: 5 + 7, the number that comes between the 2 numbers is 6. The student doubles the number to find the answer (6 + 6 = 12).



Make-Ten Facts These facts all have at least one addend of 8 or 9. One strategy for these facts it to build onto the 8 or 9 and up to 10 and then add on the rest. For 6 + 8, start with 8, then 2 more makes 10, and that leaves 4 more for 14.

Subtraction as Think-Addition The main strategy that will be used with

subtraction facts is subtraction as “think addition”. When done in this think-addition manner, the child uses known addition facts to find the answer. When your child sees 9 – 4, you want them to think spontaneously, “Four and what makes nine?”

Thank you for your support in this area.

Sincerely, *Information gathered from Teaching Student Centered Mathematics Grades K-3, John Van De Walle



Math Fact Assessments

Developing fact fluency and quick recall of basic facts is very similar to being on a successful dieting program. In order to lose weight, you need to eat healthy, exercise

regularly and assess your progress through weighing yourself on the scale. The same is true for developing fact

fluency! Extensive amount of time needs to be spent working with and applying basic fact strategies, as well as

reasoning and mental strategies. In order to determine the effectiveness, assessment plays a key role. In contrast,

assessing continuously without more time spent developing strategies is ineffective. That is like a person who knows

about the dieting program, doesn’t eat healthy or exercise, but constantly weighs themselves and wonders why they

are not losing weight.



Fact Strategy Assessments The attached fact strategy assessments and student tracking chart were developed so that teachers can diagnose which strategies the students have mastery of and which strategies still need to be explored. These assessments should not be used as practice sheets. They should be used sparingly only to diagnose the strategies that students have and have not mastered. There are two sets of assessments included in this packet. The first set focuses on one strategy per page. The second set includes all strategies in order starting with the most basic of strategies and working up to the most complex. To determine time limits for each assessment, teachers should calculate 3-4 seconds per fact. “If there is any defensible purpose for a timed test of basic facts it may be for diagnosis—to determine which combinations are mastered and which remain to be learned.”

Teaching Student Centered Mathematics

John A. Van De Walle Page 119



Name _____________________________

One More Than Write the answers as fast as you can.

5 + 1 = ____ 4 + 1 = ____

2 + 1 = ____ 1 + 1 = ____

1 + 8 = ____ 1 + 7 = ____

6 + 1 = ____ 3 + 1 = ____

1 + 3 = ____ 1 + 9 = ____

Name_______________________


5 + 1 = ____ 4 + 1 = ____

2 + 1 = ____ 1 + 1 = ____

1 + 8 = ____ 1 + 7 = ____

6 + 1 = ____ 3 + 1 = ____

1 + 3 = ____ 1 + 9 = ____

Name_______________________


5 + 1 = ____ 4 + 1 = ____

2 + 1 = ____ 1 + 1 = ____

1 + 8 = ____ 1 + 7 = ____

6 + 1 = ____ 3 + 1 = ____

1 + 3 = ____ 1 + 9 = ____

Name_______________________


5 + 1 = ____ 4 + 1 = ____

2 + 1 = ____ 1 + 1 = ____

1 + 8 = ____ 1 + 7 = ____

6 + 1 = ____ 3 + 1 = ____

1 + 3 = ____ 1 + 9 = ____



Name_______________________

Facts with Zero Write the answers as fast as you can.

5 + 0 = ____ 0 + 1 = ____

0 + 2 = ____ 0 + 5 = ____

8 + 0 = ____ 0 + 8 = ____

4 + 0 = ____ 7 + 0 = ____

0 + 6 = ____ 1 + 0 = ____

Name_______________________


5 + 0 = ____ 0 + 1 = ____

0 + 2 = ____ 0 + 5 = ____

8 + 0 = ____ 0 + 8 = ____

4 + 0 = ____ 7 + 0 = ____

0 + 6 = ____ 1 + 0 = ____

Name_______________________


5 + 0 = ____ 0 + 1 = ____

0 + 2 = ____ 0 + 5 = ____

8 + 0 = ____ 0 + 8 = ____

4 + 0 = ____ 7 + 0 = ____

0 + 6 = ____ 1 + 0 = ____

Name_______________________


5 + 0 = ____ 0 + 1 = ____

0 + 2 = ____ 0 + 5 = ____

8 + 0 = ____ 0 + 8 = ____

4 + 0 = ____ 7 + 0 = ____

0 + 6 = ____ 1 + 0 = ____



Name_______________________

Two More Than Write the answers as fast as you can.

4 + 2 = ____ 1 + 2 = ____

2 + 6 = ____ 2 + 2 = ____

8 + 2 = ____ 2 + 3 = ____

3 + 2 = ____ 7 + 2 = ____

2 + 4 = ____ 2 + 9 = ____

Name_______________________


4 + 2 = ____ 1 + 2 = ____

2 + 6 = ____ 2 + 2 = ____

8 + 2 = ____ 2 + 3 = ____

3 + 2 = ____ 7 + 2 = ____

2 + 4 = ____ 2 + 9 = ____

Name_______________________


4 + 2 = ____ 1 + 2 = ____

2 + 6 = ____ 2 + 2 = ____

8 + 2 = ____ 2 + 3 = ____

3 + 2 = ____ 7 + 2 = ____

2 + 4 = ____ 2 + 9 = ____

Name_______________________


4 + 2 = ____ 1 + 2 = ____

2 + 6 = ____ 2 + 2 = ____

8 + 2 = ____ 2 + 3 = ____

3 + 2 = ____ 7 + 2 = ____

2 + 4 = ____ 2 + 9 = ____



Name_______________________

Doubles Write the answers as fast as you can.

2 + 2 = ____ 4 + 4 = ____

5 + 5 = ____ 0 + 0 = ____

1 + 1 = ____ 3 + 3 = ____

6 + 6 = ____ 9 + 9 = ____

8 + 8 = ____ 7 + 7 = ____

Name_______________________


2 + 2 = ____ 4 + 4 = ____

5 + 5 = ____ 0 + 0 = ____

1 + 1 = ____ 3 + 3 = ____

6 + 6 = ____ 9 + 9 = ____

8 + 8 = ____ 7 + 7 = ____

Name_______________________


2 + 2 = ____ 4 +4 = ____

5 + 5 = ____ 0 + 0 = ____

1 + 1 = ____ 3 + 3 = ____

6 + 6 = ____ 9 + 9 = ____

8 + 8 = ____ 7 + 7 = ____

Name_______________________


2 + 2 = ____ 4 +4 = ____

5 + 5 = ____ 0 + 0 = ____

1 + 1 = ____ 3 + 3 = ____

6 + 6 = ____ 9 + 9 = ____

8 + 8 = ____ 7 + 7 = ____



Name_______________________

Doubles Plus One Write the answers as fast as you can.

5 + 6 = ____ 6 + 7 = ____

5 + 4 = ____ 6 + 5 = ____

8 + 7 = ____ 9 + 8 = ____

7 + 6 = ____ 4 + 5 = ____

8 + 9 = ____ 7 + 8 = ____

Name_______________________


5 + 6 = ____ 6 + 7 = ____

5 + 4 = ____ 6 + 5 = ____

8 + 7 = ____ 9 + 8 = ____

7 + 6 = ____ 4 + 5 = ____

8 + 9 = ____ 7 + 8 = ____

Name_______________________


5 + 6 = ____ 6 + 7 = ____

5 + 4 = ____ 6 + 5 = ____

8 + 7 = ____ 9 + 8 = ____

7 + 6 = ____ 4 + 5 = ____

8 + 9 = ____ 7 + 8 = ____

Name_______________________


5 + 6 = ____ 6 + 7 = ____

5 + 4 = ____ 6 + 5 = ____

8 + 7 = ____ 9 + 8 = ____

7 + 6 = ____ 4 + 5 = ____

8 + 9 = ____ 7 + 8 = ____



Name_______________________

Inside Doubles Doubles +2 Write the answers as fast as you can.

5 + 7 = ____ 6 + 8 = ____

5 + 3 = ____ 6 + 4 = ____

8 + 6 = ____ 6 + 8 = ____

7 + 9 = ____ 4 + 6 = ____

3 + 5 = ____ 7 + 5 = ____

Name_______________________


5 + 7 = ____ 6 + 8 = ____

5 + 3 = ____ 6 + 4 = ____

8 + 6 = ____ 6 + 8 = ____

7 + 9 = ____ 4 + 6 = ____

3 + 5 = ____ 7 + 5 = ____

Name_______________________


5 + 7 = ____ 6 + 8 = ____

5 + 3 = ____ 6 + 4 = ____

8 + 6 = ____ 6 + 8 = ____

7 + 9 = ____ 4 + 6 = ____

3 + 5 = ____ 7 + 5 = ____

Name_______________________


5 + 7 = ____ 6 + 8 = ____

5 + 3 = ____ 6 + 4 = ____

8 + 6 = ____ 6 + 8 = ____

7 + 9 = ____ 4 + 6 = ____

3 + 5 = ____ 7 + 5 = ____



Name_______________________

Making Ten Write the answers as fast as you can.

9 + 5 = ____ 8 + 5 = ____

4 + 8 = ____ 4 + 9 = ____

9 + 4 = ____ 9 + 6 = ____

8 + 4 = ____ 5 + 9 = ____

6 + 9 = ____ 5 + 8 = ____

Name_______________________


9 + 5 = ____ 8 + 5 = ____

4 + 8 = ____ 4 + 9 = ____

9 + 4 = ____ 9 + 6 = ____

8 + 4 = ____ 5 + 9 = ____

6 + 9 = ____ 5 + 8 = ____

Name_______________________


9 + 5 = ____ 8 + 5 = ____

4 + 8 = ____ 4 + 9 = ____

9 + 4 = ____ 9 + 6 = ____

8 + 4 = ____ 5 + 9 = ____

6 + 9 = ____ 5 + 8 = ____

Name_______________________


9 + 5 = ____ 8 + 5 = ____

4 + 8 = ____ 4 + 9 = ____

9 + 4 = ____ 9 + 6 = ____

8 + 4 = ____ 5 + 9 = ____

6 + 9 = ____ 5 + 8 = ____



Student Tracking Chart



Name ______________________________ (1)

Write the answer as fast as you can.

9 + 1= 1 + 5=

2 + 4= 2 + 6=

3 + 2= 1 + 4=

1 + 8= 2 + 9=

0 + 2= 7 + 2 =

Name ______________________________ (2)Write the answer as fast as you can.

1 + 1= 8 + 8=

4 + 4= 5 + 5=

9 + 9= 7 + 7=

6 + 6= 2 + 2=

3 + 3= 0 + 0

Name ______________________________ (3)


6 + 7= 4 + 5=

5 + 6= 6 + 5=

8 + 7= 8 + 9=

7 + 8= 5 + 4=

7 + 6= 9 + 8=

Name ______________________________ (4)


5 + 7= 6 + 8=

5 + 3= 6 + 4=

8 + 6= 7 + 9=

4 + 6= 3 + 5=

7 + 5= 1 + 3=



Name ______________________________ (5)


5 + 8= 9 + 5=

9 + 6= 8 + 4=

4 + 9= 9 + 2=

3 + 8= 6 + 9=

4 + 9 = 9 + 3=

Name ______________________________ (6)


10 – 1 = 6 – 5 =

6 – 4 = 8 – 6 =

5 – 2 = 5 – 4 =

9 – 8 = 11 – 9 =

2 – 2 = 9 – 2 =

Name ______________________________ (7)


2 – 1 = 16 – 8 =

8 – 4 = 10 – 5 =

18 – 9 = 14 – 7 =

12 – 6 = 4 – 2 =

6 – 3 = 10 – 5 =

Name ______________________________ (8)


13 – 7 = 9 – 5 =

11 – 6 = 11 – 5 =

15 – 7 = 17 – 9 =

17 – 8 = 9 – 4 =

13 – 6 = 15 – 8 =



Name ______________________________ (9)


12 – 7 = 14 – 8 =

8 – 3 = 10 – 4=

14 – 6 = 16 – 9 =

10 – 6 = 8 – 5 =

12 – 5 = 4 – 3 =

Name ______________________________ (10)Write the answer as fast as you can.

13 – 8= 14 – 5=

15 – 6= 12 – 4 =

13 – 9 = 11 – 2=

11 – 8 = 15 – 9=

13 – 9= 12 – 3=



Grade Level Expectations



Grade Level Expectations for Facts

Kindergarten

Kindergarten students begin to explore addition and subtraction during Unit 3 instruction. There should be no formal instruction with fact strategies. However, if a strategy emerges, teachers should openly discuss the strategy with the group.

Grade 1

Students continue to develop meaning for addition and subtraction. Specific addition and subtraction strategy instruction begins during

Unit 2. A focus on strategies continues throughout the remainder of the year. Students use strategies to solve basic addition and subtraction facts.

Grade 2

Students should be proficient with basic addition and subtraction facts by the end of the 2nd grade.

Students are introduced to basic multiplication at the end of 2nd grade. By the end of Grade 2, students should have mastered levels 1-5 of the

basic math fact assessments.

Grade 3

Addition and Subtraction fact remediation/intervention begins with Unit 1 instruction. Third grade students are not formally introduced to multiplication and division facts until the beginning of December. This provides an opportunity for teachers to focus on addition and subtraction facts before students are formally introduced to multiplication and division.

Students continue to explore and gain proficiency with multiplication and division facts throughout the remainder of the year.

Grade 4

Students devote time to reviewing the basic multiplication and division facts.

Students should be proficient with basic multiplication and division facts by the end of the year.

By the end of Grade 4, students should have mastered levels 6-10 of the basic math fact assessments.

Interventions should be made for students still struggling with the basic facts.

Grade 5 Interventions should be made for students still struggling with the

basic facts.



Addition and Subtraction Math Facts Roll Out in the Primary Grades (1-2 Grade) This lesson was used with grade 2 students. This is an example of how teachers can work with students in the early grades to develop fact strategies. Doubles + 1 TSW indentify efficient ways to solve addition facts. Curricular Connection:

6.C.1.a (1st Grade) Develop strategies for addition and subtraction basic facts such as: counting on, counting back, making ten, doubles, and doubles plus one

6.C.1.a (2nd Grade) Demonstrate proficiency with addition and subtraction basic facts using a variety of strategies.

Materials: Linker Cubes (1 base taped together for each child plus 20 additional cubes) Number Cube Train Story Problem Sheet Number Cube Train Response Sheet (3 half sheets stapled together) Number Cube Exit Slip Variety of addition fact cards Marker Chart Paper Tape Let’s Practice the Facts Center Activity

Procedures:

1. Introduce the students to the objective: Today we are going to look for easy ways to solve addition facts.

2. Display a variety of math fact cards for the students to view. Ask the students to choose a card and have them explain how they would solve that particular fact. Chart this information.

3. Tell the students that they will explore new strategies by solving story problems and looking for connections among the facts.

4. Students will choose 3 story problems to solve, build the number train to represent the number expression, and think of a way that that you could easily solve these facts.



5. When they finish this exploration time, the partners should record how they would solve these facts on a sentence strip.

6. Bring the students back together. Collect 1 of their pictorial representations of their number train. Talk about what all the number trains have in common. Display the sentence strips. Engage students in conversations about how they would easily solve these facts.

7. Exit Ticket Assessment and Evaluation:

Teacher Observation Evaluation of partner work and exit slip

Fast Finishers: Let’s Practice the Facts Center Activity



Addition and Subtraction Math Facts Roll Out in the Intermediate Grades (3rd Grade) The following pages include notes and insights from a teacher’s experience with addition and subtraction math facts in the third grade setting. This account provides insight to intermediate teachers for how to address addition and subtraction facts in grades 3 – 5.



Addition and Subtraction Math Facts Roll Out in the Intermediate Grades (3rd Grade)

Date Description

Early September

I decided I needed to take some time to work with the addition and subtraction fact program outside of the primary setting. In the primary grades students were beginning to explore with these strategies and so the explorative lessons provided in the packet for each strategy proved to be a good starting point. However, I realized that by the time students reached the 3rd grade many students had a familiarity with the strategies but still struggled with fluency of the basic facts. So, I contacted a willing 3rd grade teacher and began to think about how things would roll out in a 3rd, 4th, or 5th grade classroom. I consider this approach to be more of an intervention with facts considering the expectation is that 2nd graders maintain fluency of the basic facts (+/-) by the time they leave 2nd grade. When I began my work with the 3rd grade my goal was to have all students fluent by the time they began Unit 3 instruction (November 22nd) the multiplication/division unit. I was even hoping to have some students beyond +/- and moving into beginning explorations with x/ .

Tuesday September 9,

2008 (approximately 30

minutes)

I decided the first thing I needed to do with the group of students was to assess their level of fact fluency. Perhaps I would be surprised at the level of fluency they maintained. So, although not a “set the world on fire-get to know the class activity” I decided to make a packet of mini assessments to test the entire group on specific strategies (See Appendix). I labeled each assessment with a number instead of the strategy:

(1) one more than two more than (2) doubles (3) doubles + 1 (4) inside doubles (5) making ten (6) think-addition, one more than two more than (7) think-addition, doubles (8) think-addition, doubles + 1 (9) think-addition, inside doubles (10) think addition, making ten

I gave students 35 seconds (10 facts on each sheet x 3 seconds = 30 seconds per assessment + an extra five seconds to get them started) from the time I said “go” to complete each assessment. When I called “time” it was understood that all pencils needed to go down on their desks. I only required students to work through level “8” because it was obvious that students were slowing down and not finishing the levels. I was prepared to give the multiplication/division pre-assessments if the class seemed as though they needed to move to that level. I thought perhaps some students would be ready to move onto multiplication and division since they were exposed to these operations in 2nd grade. I must admit, prior to entering the classroom, I was dreading giving the



September 9,

2008 (continued)

students the packet of assessments. I was thinking that they were going to be really annoyed to have to work on this many facts and would kindly request that I never come back to their classroom again. However, the students really surprised me. They were enthusiastic and excited to “show me what they knew” about their basic facts. No one cried or begged not to continue. It really turned out to be a positive experience.

Wednesday September 10,

2008

I graded all of the assessment packets and determined a level for each student. I allowed 1 mistake or 1 fact that was not completed to achieve mastery of a particular level. My first “time to think” moment occurred when students mastered a higher level of strategy and missed a lower level. For example, a student mastered doubles but not +1, + 2. Because the strategies run as part of a hierarchy this caused me to take pause and think about how to handle this. I decided that I would record the mastery for doubles on my assessment grid but have the student start with the lowest level. Then, when they mastered that level they would move past the doubles and onto the next level that they didn’t master. I recorded the results on the grid in the appendix. Teachers may have a better way to organize this data but for me this has worked well (so far). (See Appendix)

Thursday

September 11, 2008

Using the data grid, I determined a strategy level for each student. Because this classroom already had fact practice as part of their daily homework, I decided to make up take-home center bags for each student for the strategy that they are working on. I included a parent letter (see appendix), list of facts for that particular level (see appendix), a few games, and strategy flash cards for each bag (all items came from the fact packet).

Tuesday September 16,

2008 (1 hour class session)

I returned to the classroom today with fact bags in hand excited to share the activities with students. Before I handed out the bags I wanted to review the strategies. I went back through the hierarchy, provided a brief explanation and asked students to help me come up with facts that fit into each strategy. Then I passed out one flashcard (two sided commercial cards) to each student. I hung strategy cards around the room (151-157) and asked the students to scatter to their corner. When they arrived there they were supposed to solve the fact and describe how they did it. Then, I asked them to move, if they could to another strategy card that helped them to solve their fact in a different way. Students who couldn’t move flipped their card to the other side to move to a different card. After we had plenty of time to reacquaint with the strategies I paired students up with a student focusing on the same strategy and passed out the bags and asked them to play a game from the bag. Students did a great job of reading the directions and playing their game with their partners. They were thrilled to be able to take the bags home to play with their parents. I told them to bring them back every day so that we would have them at school if we had some extra time to practice the facts.

Friday September 19,

Prior to arriving in the classroom I prepared a fact assessment for each child for the level they were working on throughout the week. I went ahead and made 50 copies of the original packet that I used originally to



2008 (10 minutes)

assess the students. I organized the assessments into levels and put them into a file box so that I could easily access the assessments each week. Gave the assessments for 35 seconds. Collected assessments and the strategy bags.

Sunday September 21,

2008 (15 minutes)

First thing I did was grade each assessment and recorded it on the grid. Then, I pulled all the parent letters out of each bag. I recorded “mastery” or “currently working on” on the parent letter. Then, I placed the letter into the appropriate strategy bag for that particular student. The student will work on this bag throughout the week.

Friday September 26,

2008 (15 minutes)

I will go back into the classroom every Friday to assess the students and rearrange the bags.



Name

One

More

Than

Tw

o M

ore Than

Doubles

Doubles +

1

Inside Doubles

Making T

en

Thinking A

ddition O

ne More T

han Tw

o More

Than

Thinking A

ddition D

oubles

Thinking A

ddition D

oubles + 1

Thinking A

ddition Inside D

oubles

Thinking A

ddition M

ake Ten





One More Than Two More Than

Facts



One-More-Than and Two-More-Than Facts This strategy is used for facts that have a 1 or a 2 as one of it’s addends (example: 8 + 2). Out of the 100 addition facts students will learn, 36 fall under the one-more-than and two-more-than facts. In these situations, students simply count up 1 or 2 from the greatest addend. This should be the only situation where students “count” to find their answer.

+ 0 1 2 3 4 5 6 7 8 9

0 1 2

1 1 2 3 4 5 6 7 8 9 10

2 2 3 4 5 6 7 8 9 10 11

3 4 5

4 5 6

5 6 7

6 7 8

7 8 9

8 9 10

9 10 11



One-More-Than and Two-More-Than Facts Beginning Exploration

Ten Black Dots Written by: Donald Crews

TSW solve a variety of addition facts with an addend of 1 or 2. TSW will identify similarities among the word problems and determine a rule to help solve these problems. C.C. 6.C.1.a (1st Grade) Materials:

Ten Black Dots, written by Donald Crews (1st Grade Marilyn Burns Library) Nine transparent containers for each pair of students 45 counters for each pair of students

Procedures: 1. Collect nine transparent containers. Clear cups labeled 0-9 would be an appropriate choice for this activity. With the help of the students, begin to line the cups up in order from 0-9. Ask the students questions such as How many bottles do I have now? How do you know? Because I counted 3. What cup should be placed next? The four. How do you know? Because 4 comes after 3. Continue this process until all the cups are lined up in the appropriate sequence. 2. Start this activity by reading a counting book to the students. Choose a book that focuses on the sequence 0-10. This lesson uses the book Ten Black Dots by Donald Crews. However, any counting book can be used. If you choose a different book, you will need to alter the story problems for the students to explore. As you read, ask volunteers to drop the number of counters into each cup as you read about that particular number. 3. At the end of the story, share some simple addition stories with the students. (See examples on the attached page.) Students may build their own sets of cups to have available to them as they solve the problems. 4. Students will choose 3 or 4 stories from the attached sheet to solve. They will write a number sentence to represent the story. Then, they will describe how they would solve the problem. Finally, they will look for similarities among the number sentences



5. Bring the students together and discuss what they discovered throughout the activity. Chart the variety of strategies they discussed. If the opportunity warrants it, name the strategy A/E Teacher Observation, Evaluation of Classwork and Exit Slip



Ten Black Dots Name ____________________________________ Directions: Choose three number stories. Use your numbered cups to solve the story problem. Answer the questions.

2 dots can make the eyes of keys that open locks. If we added 2 more dots how many dots would there be?

3 dots can make a snowman’s face. If we added 2 more dots to the face how many dots would there be? 4 dots can make seeds from which flowers grow. If we added 1 dot, how many seeds would there be?

5 dots can make buttons on a coat. If we added 1 dot, how many buttons would there be?

6 dots can make marbles that you hold. If we added 2 marbles, how many buttons would there be?

7 dots can make the spots on a snake. If we added 1 dot, how many dots would there be?



Draw a picture of your story problem here.

How would you solve this sentence?

What is the same about all of these number trains?







Ten Black Dots Exit Ticket Name______________________ Write a different expression that could be solved in the same way that you solved the other three number expressions. Use words, numbers, or symbols to explain your thinking.

Ten Black Dots Exit Ticket Name______________________ Write a different expression that could be solved in the same way that you solved the other three number expressions. Use words, numbers, or symbols to explain your thinking.



One-More-Than and Two-More-Than Facts Flip Cards-Pictorial Copy the attached pages onto cardstock. Cut out the set of cards. Select a card. Fold back the flap that shows one dot so that students cannot see the dot. Ask the students to tell you how many dots they see. Counting should not be encouraged. Then fold the flap forward and ask the students to tell you how many dots there are in all. Always start with the larger number on the right so that students realize the importance of always starting with the largest addend. One-More-Than and Two-More-Than Facts Flip Cards-Abstract Once the students have mastered the pictorial version of the flip cards, move onto the flip cards with the numeric digit.



































One-/Two More-Than Dice Play with 2 dice:

1 dice should be marked +1, +2, +1, +2, +1, +2, 1 dice should be marked with 1, 2, 3, 4, 5, 6 or 4, 5, 6, 7, 8, 9

Roll each dice. After each roll, record the addition fact in the space below. Make sure that you say the fact aloud as you solve.

+ =

+ =

+ =

+ =

+ =

+ =



One-/Two More-Than Spinner Spin the spinner. Then roll the dice. After each roll, record the addition fact in the space below. Make sure that you say the fact aloud as you solve.

+ =

+ =

+ =

+ =

+ =



2 more

1 more



One More Two More Memory Match Cut apart the cards. Place them face down on the desk. Draw two cards, if they match you get the cards. Make sure you say the fact along with the sum before you pick up the cards.

1 more than 3

3 + 1

1 more than 4

4 + 1

1 more than 5

1 + 5

1 more than 6

1 + 6



1 more than 7

7 + 1

1 more than 8

8 + 1

1 more than 9

1 + 9

2 more than 3

2 + 3

2 more than 4

2 + 4



2 more than 5

5 + 2

2 more than 6

6 + 2

2 more than 7

2 + 7

2 more than 8

2 + 8

2 more than 9

9 + 2



Four in a Row Directions: You will need

3 number cubes labeled in the following way: 1, 2, 3, 4, 5, 6 4, 5, 6, 7, 8, 9 +1, +2, +1, + 2, +1, +2

approximately 12 different colored markers for each player In this game, students will work to cover the game board. Roll all three number cubes. Choose one of the digits and one of the (+1, +2) choices. Students should mark the sum on the board. If there is no sum available, the student loses a turn. The first player to get 4 in a row wins the game.

2 3 4 5 6 7 8 9 10 11 2 3 4 5 6 7 8 9 10 11



Roll My Sum! Directions: You will need

2 number cubes labeled in the following way:

4, 5, 6, 7, 8, 9 1, 2, 1, 2, 1, 2

pencil game board

In this game, students will work to fill in all the squares on the game board. Roll both number cubes. Choose one of the digits and one of the (+1, +2) choices. Students fill in one of the squares on the game board to accurately complete the number sentence. If there is square available, the student loses a turn. The first player to complete the game board wins the game.

Player 1 Player 2

+ = 5 + = 5 + = 6 + = 6 + = 7 + = 7 + = 8 + = 8 + = 9 + = 9 + = 10 + = 10 + = 11 + = 11



Find My Expression Directions: You will need

2 number cubes labeled in the following way: 2, 3, 4, 5, 6, lose a turn 7, 8, 9, 10, 11, free choice

game board approximately 12 different colored markers for each player

In this game, students roll both dice and choose a sum. If an expression is on the board that matches the sum, students should cover it with their marker. The first player to have 4 in a rose horizontally, vertically, or diagonally wins the game.

1 + 5 2 + 2 9 + 1 8 + 2 7 + 2

1 + 2 2 + 1 3 + 2 3 + 1 2 + 8

8 + 1 9 + 2 6 + 1 2 + 6 4 + 2

1 + 4 2 + 5 1 + 9 1 + 1 7 + 1



Honey Bee Journey Directions: Roll the dice (1‐6). The first player finds a cell where the tossed number correctly completes an addition fact. The player covers the cell with a marker. The other player follows the same rule. Continue to take turns until one pair forms a continuous pathway across the game board.

Adapted from Nimble With Numbers (Factors Pathway) Grades 3 & 4

6 + ___=8

4 + ___=5

2 + ___=3

__ + 2 = 6

__ + 2 = 7

2 + ___=3

__ + 7 = 9

2 + ___=5

3 + 1 = __

__ + 2 = 7

2 + ___=8

__ + 2 = 3

2 + __= 4

__ + 0 = 3

3 + 1 = __

__ + 2 = 7

5 + 1 =__

1 + ___=7

2 + __= 4

5 + 1 =__

__ + 7 = 9

3 + 1 = __

0 + __ = 1

2 + ___=5

0 + __ = 1

__ + 2 = 6

__ + 2 = 7

__ + 2 = 7



Finish

Move back

1 space

Move forward 2 spaces

Go Back to Start

Move back

4 spaces

Lose a Turn

Start


Up and Down and All Around You will need:

1 pawn for each player

1 set of game cards (facts)

Directions Draw a card from the deck.

Solve the fact. Move that number of spaces on the

game board.

The first player to “finish” wins the game.



Up and Down and All Around/Hop On Over Game Cards

2 + 2 2 + 3 4 + 2 2 + 5

6 + 2 2 + 7 8 + 2 2 + 9

1 + 2 3 + 1 1 + 4 5 + 1

1 + 6 7 + 1 1 + 8 1 + 9



Connect Four

6 7 2 3 4 5 8 9 10 11 2 3 4 5 6 7 8 9 10 11 2 3 4 5 8 9 10 11 6 2 5 6 7 8 9 10 7 2 3 4 5 6

Directions: The first player will spin the spinner and then decide whether to add “1” of “2” to the number spun. The player will find the sum on the game board with their color marker. The second player will follow the same procedure. The winner is the student who lines up four markers in a row (vertically, horizontally, or diagonally.

9

1 2

3

4

5

8

76



Three For All

2 3 4 1 5 2 2 1 4 7 2 3 6 9 1 8

7 1 5 6 9

3 4 11 6 2

6 10 8 5 4

7 3 8 9 12 2 1 2 1 1 1 2 2 1 2 1 2 2 1 1

Directions:

1. Players take turns using any two numbers in the box to make a Count On addition fact. Cross out used numbers.

2. If the answer is in a circle on the game board the player places a counter on the circle.

3. The first player to get three counters in a row wins.



Directions: Each player should begin on the start position. Choose a game card. Use the key to determine how many spaces to move. Players may take any route to the lily pad. The first player to reach the lily pad wins the game. Hop On

Over!

If your sum is ____ then: 3: 1 space forward 7: Lose a Turn 4: 2 spaces forward 8: Go back to Start 5: 3 spaces forward 9: Move back 1 space 6: 4 spaces forward 10: Move back 2 spaces 11: 2 spaces forward

Start



7 3 6 9 10 4 8 129 10 5 4 12 10 4 92 6 7 3 8 3 2 58 5 3 2 10 6 5 79 6 4 6 3 8 11 97 2 11 7 9 3 7 63 5 9 4 5 7 5 2

Five in a Row Materials: Cards 1-9, 2 different color counters Directions: Players take turns drawing cards.

Players add either 1 or 2 to the card. Choose a space on the game board that has that sum on it and place a counter on that number. The first player to line up five counters in a row wins!

One-More Than Two-More Than





Drill of Efficient Methods and Strategy Selection It is appropriate to make a distinction between drill and practice. Practice refers to problem-based activities in which students are encouraged to develop (invent, consider, try—but not master) flexible and useful strategies that are meaningful. The types of introductory lessons included in this packet can be thought of as practice lessons. Whether from story problems or from consideration of a collection of similar facts, students are wrestling with the development of strategies that they can use themselves. Drill refers to repetitive non-problem-based activity. Drill activity is appropriate for children who have a strategy that they understand, like, and know how to use but have not yet become facile with it. Drill with an in-place strategy focuses students’ attention on that strategy and helps to make it more automatic. Drill plays a significant role in fact mastery, and the use of old-fashioned methods such as flash cards and fact games can be effective if used wisely. It is critical that you do not introduce drill too soon. Suppose that a child does not know the 9 + 5 fact and has no way to deal with it other than to count fingers or use counters. These are inefficient methods. Premature drill introduces no new information and encourages no new connections. It is both a waste of time and a frustration to the child. Drill should only be used when an efficient strategy is in place.

Teaching Student Centered Mathematics John A. Van De Walle

Pages 96-97



Flash Cards Flash cards are among the most useful approaches to fact strategy practice. For each strategy, make several sets of flash cards using all of the facts that fit that strategy. These flash cards have been included in this packet for each strategy. On the cards, you can label the strategy or use drawings or cues to remind the children of the strategy.


Pages 98



1 + 0

One More/Two More

1 + 1 One More/Two More


1 + 3

One More/Two More

1 + 4

One More/Two More



1 + 7

One More/Two More

1 + 8

One More/Two More



2 + 1

One More/Two More



2 + 0

One More/Two More



2 + 3

One More/Two More

2 + 4

One More/Two More



2 + 7

One More/Two More

2 + 8

One More/Two More




Turn Around Facts Commutative

Property



Turn Around Facts Turn around facts are a very important property for students to explore early on in their addition fact acquisition. Students must understand that despite the order of the addends the sum always remains the same. Beginning Exploration Create a laminated shirt hanger for each pair of students.

1. Laminate a 8 ½ x 11 piece of cardstock. 2. Fold the piece of cardstock in half so that the 11 inch portion of the paper is

folded in half.

3. Position the hanger inside of the folded paper. Staple around the top of the hanger just above where the paper covers the hanger.

4. Trim the excess paper off the top of the hanger.

5. Record an anchor number on each side of the laminated cardstock. Start with numbers 5 or 10.

6. The target number will designate how many clothespins should be added to the bottom wire of the hanger.

7. Attach 3 clothespins on one side and 7 clothespins on the other side and show it to the students.

8. Ask the students what fact they see. (3 and 7 equals 10) 9. Turn the hanger to show the other side. Ask the students what fact they see.

(7 and 3 equals 10.) 10. Tell the students that they will spend the class time exploring a very special

“trick” that happens in addition. See attached lesson plan for details.

10



Turn Around Fact Exploration

TSW create a variety of addition facts to equal 10. TSW use the “turn-around” strategy to solve addition facts. C.C. 6.C.1.c Materials:

Hangers 10 clothespins (per hanger) “Turn Around Facts” Student Response Sheet “Turn Around Exit Slip”

Procedures:

1. Bring the students together on the carpet. Explain to the students that today they will focus on finding different combinations to equal the number 10. Then, explain to the students that they are going to be investigating a very special “trick” that happens when you add two numbers together.

2. Use the student response sheet to model the process of this activity. 3. Place the students into pairs. 4. Allow time for students to work within their groups. The teacher will circulate

to monitor and observe the progress of students. 5. Bring students back together to share the number combinations and addition

sentences that they created during their partner work. Record a variety of number sentences on the board.

6. Ask the students if they notice anything special between the two numbers sentences they created for each hanger.

7. Develop a conclusion with students about the inverse operation for addition. Fast Finishers: Record the number 12 on hangers of those students who finish early. A/E Teacher Observation, Evaluation of Classwork and Exit Slip



Name ____________________

“Turn Around Facts”

1. 1 + 9 = 10 9 + 1 = 10

2.

3.

4.

10

10

10

10



5.

6.

7.

8.

10

10

12

12



Turn Around Facts-Exit Ticket Name ____________________

6 + 2 = 8

6 + 5 = 11

Turn Around Facts-Exit Ticket Name ____________________

6 + 2 = 8

6 + 5 = 11

8

11

8

11



Name ____________________

“Turn Around Facts”

1.

2.

3.

4.



Beginning Exploration of Subtraction as Think Addition Using think-addition strategy, the child uses known addition facts to produce the unknown quantity or part. If this important relationship between parts and wholes—between addition and subtraction—can be made, subtraction facts will be much easier. When children see 9-4, you want them to think spontaneously, “Four and what makes nine?” By contrast, observe a third-grade child who struggles with this fact. The idea of thinking addition never occurs. Instead, the child will begin to count either back from 9 or up from 4. The value of think-addition cannot be overstated. Word problems that promote think-addition are those that sound like addition but have a missing addend: join, initial part unknown; join, change unknown; and part-part-whole, part unknown. Consider this problem: Janice had 5 fish in her aquarium. Grandma gave her some more fish. Then she had 12 fish. How many fish did Grandma give Janice? Notice that the action is join and thus, suggests addition. There is a high probability that students will think 5 and how many more makes 12. In the discussion in which you use problems such as this, your task is to connect this thought process with the subtraction fact, 12 – 5.

Teaching Student Centered Mathematics K-3 John Van De Walle

Pages 106-107



Name ____________________

Fact Families

1. 1 + 9 = 10 9 + 1 = 10 10 – 1 = 9 10 – 9 =1

2.

10

10



3.

4.

5.

10

10

10



Facts with Zero



Facts with Zero 19 facts have zero as one of the addends. Although these facts seem to be the simplest of all, some students will overgeneralize the idea that answers to addition are bigger. Putting these facts into real life situations oftentimes help the students to reinforce the zero rule.

+ 0 1 2 3 4 5 6 7 8 9

0 0 1 2 3 4 5 6 7 8 9

1 1 2 3 4 5 6 7 8 9 10

2 2 3 4 5 6 7 8 9 10 11

3 3 4 5

4 4 5 6

5 5 6 7

6 6 7 8

7 7 8 9

8 8 9 10

9 9 10 11



Dad bought 8 fish for the fish bowl. There were no fish in the fish bowl when he added the fish. How many fish are now in the fish bowl?

Record the addition fact on a post-it note and say the fact aloud.



5 pinecones fell of the tree in the front yard. No other pinecones fell off the tree. How many pinecones fell off the tree in all? Record the addition fact on a post-it note and say the fact aloud.



There were 4 dishes on the table. Marcie washed all the dishes on the table and put them away. How many dishes did Marcie wash? Record the addition fact on a post-it note and say the fact aloud.



Mom put 7 brussel sprouts on Timmy’s plate. He did not eat any of the sprouts. How many sprouts are still on the plate? Record the addition fact on a post-it note and say the fact aloud.



Billy and Cole put 9 buttons on the snowman. All of the buttons were still on the snowman when they woke up the next morning. How many buttons were on the snowman in all? Record the addition fact on a post-it note and say the fact aloud.



1 + 0

Facts with Zero

2 + 0 Facts with Zero


4 + 0

Facts with Zero

5 + 0

Facts with Zero



8 + 0

Facts with Zero

9 + 0

Facts with Zero



0 + 3

Facts with Zero



0 + 4

Facts with Zero



0 + 7

Facts with Zero

0 + 8

Facts with Zero




Doubles



Doubles There are only 10 doubles facts. These facts are relatively easy to learn and become a powerful way to learn many other facts. Examples of double facts include: 5 + 5, 3 + 3, 6 + 6. Dice from board games are good visuals to use to help students remember their double facts.

+ 0 1 2 3 4 5 6 7 8 9

0 0 1 2 3 4 5 6 7 8 9

1 1 2 3 4 5 6 7 8 9 10

2 2 3 4 5 6 7 8 9 10 11

3 3 4 5 6

4 4 5 6 8

5 5 6 7 10

6 6 7 8 12

7 7 8 9 14

8 8 9 10 16

9 9 10 11 18



Number Cube Trains Name______________________ Date ________________________ Directions: Choose three number stories. Build a number train based on the story. On the next page, draw a picture of your number trains. Answer the questions.

Alex has 4 pencils. His mom gave him 4 more. How many pencils does he have now?

Kathy paid $8 for lunch on Monday and $8 for lunch on Tuesday. How much did she spend in all for lunch? Tommy spent 9 minutes emptying the trash. David spent 9 minutes putting away the laundry. How much time did the boys spend altogether on chores?

Grandma gave Billy $5 for his birthday and $5 for Valentine’s Day. How much money did Grandma give Billy in all?

Amanda and Sally put the shoes they were wearing by the door when they arrived home. How many shoes were by the door?



Draw a picture of your number train here.

How would you solve this expression?








Number Cube Trains Exit Ticket Name______________________ Write a different expression that could be solved in the same way that you solved the other three number expressions. Use words, numbers, or symbols to explain your thinking.




Doubles Beginning Exploration There are a variety of activities that can be used to develop the pictorial version of doubles. Double Paint Give each student a sheet of paper (suggested 11 x 14). Tell the students to fold their paper in half so that the edge that measures 14 inches is divided into 2 separate parts. Give each student a small sponge. The sponge can be pre-cut so that it resembles a shape. Tell students to use the sponge to create shapes on one side of the paper. Students should fold the paper in half again so that the sponge paint transfers to the other side. Then, the students should write a number sentence to represent the fact. Doubles in the Real World Give the students a collection of old catalogs or magazines. Ask students to find representations of doubles in the real world. Students may also draw pictures of doubles that they see in the real world. Some examples of doubles are: 2 sets of hands (5 + 5), 1 spider (4 legs + 4 legs = 8 legs), 1 dozen eggs (6 eggs + 6 eggs = 12 eggs), etc. Double Domino Sort Give students a set of double six or double nine dominoes. Tell the students to pull out the doubles and draw the domino on a sheet of paper that is divided into equal parts. Then, the students should create a number sentence to accompany the picture. Double Flip Book The following pages can be copied onto cardstock and bound with a plastic spiral binding. The teacher may use the dot representation to help students recognize double sums.





















Doubles, Doubles Directions: Two players may play this game. Each player will need 4 counters (a different color for each student). To play the game, the players will need a cube marked with the numbers 1, 2, 3, 4, 5, 6. The first player rolls the cube. The player doubles the number and then covers the number on the grid that matches the sum. The other player takes a turn. If the space has already been covered with a counter then the player loses a turn. The first player to place all of their counters wins the game.

2 4 2 10 8 12 6 10 6 12 4 8



Doubles, Doubles Directions: Two players may play this game. Each player will need 4 counters (a different color for each student). To play the game, the players will need a cube marked with the numbers 4, 5, 6, 7, 8, 9. The first player rolls the cube. The player doubles the number and then covers the number on the grid that matches the sum. The other player takes a turn. If the space has already been covered with a counter then the player loses a turn. The first player to place all of their counters wins the game.

14 16 18 10 8 12 16 10 18 12 14 8



Order, Order!!! Directions: To play this game, you will need two dice. One should be labeled 1, 2, 3, 4, 5, 6 and the other should be labeled 4, 5, 6, 7, 8, 9.

1. The player with the shortest last name goes first. 2. The player rolls both dice and chooses one of the numbers to double. 3. The player then chooses a box in which to put their sum. Once a number is written

in a box, it can’t be moved. 4. If a player can’t place a sum, he/she loses a turn. 5. Players take turns rolling the dice. 6. The first player to fill in all of their boxes from least to greatest wins.

Player 1 Name:

Player 2 Name:



Doubles Bingo Directions: To play this game, you will need two dice. One should be labeled 0, 2, 4, 6, 8, 10 and the other should be labeled 8, 10, 12, 14, 16, 18. Each player will need 15 counters (1 color for each player).

1. The player with the shortest first name goes first. 2. The player rolls both dice and chooses one of the numbers. 3. The player then looks for the math fact on the game board that would produce

that sum. 4. If a player can’t place a counter, he/she loses a turn. 5. Players take turns rolling the dice. 6. The first player to use their counters to make a vertical, horizontal, diagonal, or

four corner pattern wins the game.

2 +2 6 + 6 2 + 2 5 + 5 8 + 8

4 + 4 1 + 1 9 + 9 7 + 7 3 + 3

0 + 0 8 + 8 0 + 0 6 + 6 9 + 9

7 + 7 6 + 6 7 + 7 4 + 4 5 + 5

5 + 5 9 + 9 1 + 1 8 + 8 3 + 3



Domino Sort You will need a set of double nine dominoes. Sort all of your dominoes. Pull out all of the double facts. Record the picture of the domino and the fact.

1 + 1 = 2



Cover the Board Directions: Draw a game card from the pile. Use a crayon (a different color for each player) to create a double of the card drawn. The player must create a rectangular array. Players alternate turns. The game ends when no more doubles can be added to the game board. The player with the most squares filled wins the game.



Cover the Board-Game Cards



Finish

Move back

1 space


Go Back to Start

Move back

4 spaces

Lose a

Turn

Start


Up and Down and All Around You will need:

1 pawn for each player

1 set of game cards (facts)

Directions Draw a card from the deck.

Solve the fact. Move that number of spaces on the

game board. The first player to “finish” wins the game.



Up and Down and All Around Game Cards

1 + 1= 2 + 2= 3 + 3= 4 + 4=

5 + 5= 6 + 6= 7 + 7 = 8 + 8=

9 + 9 = 1 + 1 = 2 + 2 = 3 + 3=

4 + 4 = 5 + 5 = 6 + 6 = 7 + 7 =



DOUBLES FACTS Matching Game Directions: Cut out each set of cards. Players place all cards face down in front of them. Players will take turns uncovering two cards at a time to find a match. Follow the rules of concentration.

1 + 1 =



2 + 2 =

3 + 3 =



4 + 4 =

5 + 5 =



6 + 6 =

7 + 7 = 2 weeks



8 + 8 =

9 + 9 =



Double-Up

10

2 18

8

20

12

4 14

6 8

12 4

18 2

14 10

16 6

Double-Up Materials:

Spinner and Wipe off Markers (optional)

Directions:

1. Spin the spinner. 2. Double the number. 3. Cross off that sum on your side of the board. 4. Players take turns. 5. The first player to fill cross off all of their sums wins.





Doubles Dominos



0 + 0

Doubles

1 + 1 Doubles

2 + 2 Doubles

3 + 3

Doubles

4 + 4

Doubles

5 + 5 Doubles

6 + 6 Doubles

7 + 7

Doubles

8 + 8

Doubles

9 + 9 Doubles



Doubles + 1



Doubles + 1 Near doubles are also called the “doubles-plus-one” facts and include all combinations where one addend is one more than the other. There are 18 of these facts. When students realize that these are facts that have addends with a difference of 1 (1 + 2), (3+ 4), (5 + 6) etc. they simply double the smaller addend and add 1.

+ 0 1 2 3 4 5 6 7 8 9

0 0 1 2 3 4 5 6 7 8 9

1 1 2 3 4 5 6 7 8 9 10

2 2 3 4 5 6 7 8 9 10 11

3 3 4 5 6 7

4 4 5 6 7 8 9

5 5 6 7 9 10 11

6 6 7 8 11 12 13

7 7 8 9 13 14 15

8 8 9 10 15 16 17

9 9 10 11 17 18



Number Cube Trains Name______________________ Date ________________________ Directions: Choose three number stories. Build a number train based on the story. On the next page, draw a picture of your number trains. Answer the questions.

Danny had 8 pennies. Susan gave him 9 more. How many pennies does Danny have altogether?

Danny has 5 pennies and 6 nickels. How many coins does he have?

Danny has 4 pennies and Susan has 5 pennies. They put their pennies into a piggy bank. How many pennies did they put into the bank?

Susan has 3 pennies. Her mom gave her 4 more for helping to brush the dog. How many pennies does Susan have now?

Danny’s dad gave him 7 pennies on Monday, 8 pennies on Tuesday, and a big hug on Wednesday. How many pennies does Danny have?
















Doubles Song If You’re Happy & You Know It)

You’ve got to get the doubles in your brain. You’ve got to get the doubles in your brain.

Oh, in math you’ll have no troubles If you only learn the doubles.

You’ve got to get the doubles in your brain.

1 + 1 is 2 You knew! 2 + 2 is 4 Some more? 3 + 3 is 6 Wiggle all your sticks.


4 + 4 is 8 You’re great! 5 + 5 is 10 Amen! 6 + 6 is 12 Who can we tell?


7 + 7 is 14 (Cheer!) 8 + 8 is 16 (Cheer!) 9 + 9 is 18 10 + 10 is 20

You’ve got to get the doubles in your brain!



Extra Credit, If You Please Doubles + 1 Directions: Two players may play this game. Each player will need a collection of counters (a different color for each student). To play the game, the players will need two number cubes marked with the numbers 2, 3, 4, 5, 6, 7 and 9, 8, 7, 6, 5, 4. The first player rolls both cubes. To be able to place a counter on the board the student must be roll two numbers that equal a sum on the game board. If the student rolls a doubles + 1 fact to produce the sum, the student should stack 2 counters on the sum. When the game board is filled, the student with the most counters wins the game.

5 11 15 5 13 7 9 7 15 17 9 13 13 5 17 11



Fill the Board To play this game you will need to wooden cubes labeled: 1, 2, 3, 4, 5, 6 and 9, 8, 7, 6, 5, 4. Each player will roll both cubes. If the fact rolled is one of the identified strategies, the student should solve the fact and record it beside that strategy. Example: Doubles + 1 (6 + 5 = 11 total points= 10). If the student rolls a fact that has already been completed, they may place the fact in the “reject” row and receive no points. Once all the “reject” boxes are filled, the player will begin to “x” out remaining strategies. The player with the most points at the end of the game wins.

Player #1 Player #2

Strategy Record your fact here.

Total points

Strategy

Record your fact here.

Total points

Doubles

+ 1 (10 points)

Doubles + 1

(10 points)

Doubles

(5 points)

Doubles

(5 points)

+ 2 Facts (2 points)




Reject Reject Reject Reject Reject Reject

Total Points Total Points



Domino Sort You will need a set of double nine dominoes. Sort all of your dominoes. Pull out all of the double +1 facts. Record the picture of the domino and the fact.

2 + 1



Double Points for Doubles + 1 Directions: To play this game you will need 2 sets of digit cards (0-9) and a collection of markers (a different color for each player). The first player, draws four digit cards and displays them in the four large squares. The player then chooses 2 numbers to create a sum listed on their game board. Then, they will cover the sum with their marker. If they create a doubles + 1 they should place 2 markers on the sum. The game ends when all the spaces have been filled. The player with the most markers placed wins the game.

Game Board 2 3 4 5 6

7 8 9 10 11 12

13 14 15 16 17 18



Digit Cards

1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9



Find Me, Find Me, If You Can! To play this game you will need 4 sets of (0-9) digit cards. Arrange the cards face down on a flat surface. Students will take turns turning over two cards. If the two cards form a doubles + 1 fact the students states the sum and keeps the cards. The player records the fact on their record sheet. The first player to complete their board wins the game.

Player #1 Record your

doubles + 1 fact.

Player # 2 Record your

doubles + 1 fact.



1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9



Name _______________________ Create a Doubles fact. Build the doubles fact using cubes. Add one more to one of the trains. Write down the Doubles fact and the Doubles +1 fact you created. 1.

3 + 3 = 6 3 + 4 = 7

2.

+ =

+ =

3.

+ =

+ =

4.

+ =

+ =

5.

+ =

+ =



Name _______________________

Create a doubles fact. Build the doubles fact using cubes. Add two more cubes to one train. Write down the doubles fact and the Inside Doubles fact you created. 1.

4 + 4 = 8 3 + 5 = 8

2.

+ =

+ =

3.

+ =

+ =

4.

+ =

+ =

5.

+ =

+ =



Double-Up Again!

17

15

13

11

9 7

5 3

Free

Sp

ace

3 5

7 9

11 13 15 17 Free

Space

Double-Up Again! Materials:

Cards (Use Cards from Hop On Over)

Directions:

1. Choose a card. 2. Double the number. 3. Choose a box in which to put the sum. Once the

number is written in the box, it can’t be moved. 4. If a number cannot be placed in a box, the player

loses their turn. 5. Players take turns. 6. The first player to fill in all the boxes from least

to greatest wins.



Directions: Each player should begin on the start position. Choose a game card. Use the key to determine how many spaces to move. Players may take any route to the lily pad. The first player to reach the lily pad wins the game. Hop On

Over!

If your sum is ____ then: 3: 1 space forward 11: Lose a Turn 5: 2 spaces forward 13: Go back to Start 7: 3 spaces forward 15: Move back 1 space 9: 4 spaces forward 17: Move back 2 spaces

Start



Hop on Over Game Cards

1 + 2 2 + 3 3 + 4 4 + 5

5 + 6 6 + 7 7 + 8 8 + 9

2 + 1 3 + 2 4 + 3 5 + 4

6 + 5 7 + 6 8 + 7 9 + 8



1 + 0

Doubles + 1

2 + 1 Doubles + 1

3 + 2 Doubles + 1

4 + 3

Doubles + 1

5 + 4

Doubles + 1

6 + 5 Doubles + 1

7 + 6 Doubles + 1

8 + 7

Doubles +1

9 + 8

Doubles + 1

0 + 1 Doubles +1

1 + 2

Doubles + 1

2 + 3 Doubles +1



3 + 4

Doubles + 1

4 + 5 Doubles + 1

5 + 6 Doubles + 1

6 + 7

Doubles + 1

7 + 8

Doubles + 1

8 + 9 Doubles + 1



Inside Doubles



Inside Doubles Inside doubles or “doubles plus two” facts focus on facts that have 2 addends that are separated by 2 numbers. Some examples are: (5 + 7), (4 + 6), (7+ 9). Once the students are able to recognize these facts, they are able to look at the number that falls between the 2 addends and double it to find the answer. For example: 5 + 7, the number that comes between the 2 numbers is 6. The student doubles the number to find the answer (6 + 6 = 12).

+ 0 1 2 3 4 5 6 7 8 9

0 0 1 2 3 4 5 6 7 8 9

1 1 2 3 4 5 6 7 8 9 10

2 2 3 4 5 6 7 8 9 10 11

3 3 4 5 6 7 8

4 4 5 6 7 8 9 10

5 5 6 7 8 9 10 11 12

6 6 7 8 10 11 12 13 14

7 7 8 9 12 13 14 15 16

8 8 9 10 14 15 16 17

9 9 10 11 16 17 18



Inside Doubles Cut out the cards. Lay the cards face down on the table in front of you. Each partner should take a turn matching the inside double (doubles + 2) to the double fact that help. Then, say the fact aloud.

3 + 3

3 + 5

2 + 2

2 + 4

4 + 4

4 + 6

5 + 5

5 + 7



6 + 6

6 + 8

7 + 7

7 + 9

8 + 8

8 + 10



Extra Credit, If You Please Directions: Two players may play this game. Each player will need a collection of counters (a different color for each student). To play the game, the players will need two number cubes marked with the numbers 1, 2, 3, 4, 5, 6, and 9, 8, 7, 6, 5, 4. The first player rolls both cubes. To be able to place a counter on the board the student must be roll two numbers that equal a sum on the game board. If the student rolls an inside double fact to produce the sum, the student should stack 2 counters on the sum. When the game board is filled, the student with the most counters wins the game.

4 10 16 6 12 6 14 6 8 12 8 14 14 4 12 10



Fill the Board To play this game you will need to wooden cubes labeled: 1, 2, 3, 4, 5, 6 and 9, 8, 7, 6, 5, 4. Each player will roll both cubes. If the fact rolled is one of the identified strategies, the student should solve the fact and record it beside that strategy. Example: 7 + 5 = 12 (total points= 10). If the student rolls a fact that has already been completed, they may place the fact in the “reject” row and receive no points. Once all the “reject” boxes are filled, the player will begin to “x” out remaining strategies. The player with the most points at the end of the game wins.

Player #1 Player #2

Strategy Record your fact here.

Total points

Strategy

Record your fact here.

Total points

Inside Doubles 10 points

Inside Doubles 10 points

Doubles

+ 1 5 points

Doubles

+ 1 5 points

Doubles 2 points

Doubles 2 points

+ 1, + 2 Facts

2 points

+ 1, + 2 Facts

2 points

Reject Reject Reject Reject Reject Reject

Total Points Total Points



Domino Sort You will need a set of double nine dominoes. Sort all of your dominoes. Pull out all of the inside doubles facts. Record the picture of the domino and the fact.

2 + 4



Double Points for Inside Doubles Directions: To play this game you will need 2 sets of digit cards (0-9) and a collection of markers (a different color for each player). The first player, draws four digit cards and displays them in the four large squares. The player then chooses 2 numbers to create a sum listed on their game board. Then, they will cover the sum with their marker. If they create an inside double they should place 2 markers on the sum. The game ends when all the spaces have been filled. The player with the most markers placed wins the game.

Game Board 2 3 4 5 6

7 8 9 10 11 12

13 14 15 16 17 18



Digit Cards

1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9



Find Me, Find Me, If You Can! To play this game you will need 4 sets of (0-9) digit cards. Arrange the cards face down on a flat surface. Students will take turns turning over two cards. If the two cards form an inside double fact the students states the sum and keeps the cards. The player records the fact on their record sheet. The first player to complete their board wins the game.

Player #1 Record your

doubles + 1 fact.

Player # 2 Record your

doubles + 1 fact.



1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9



Inside Doubles Game Variations

Included in this packet you will find inside doubles cards that can be used for Concentration/Memory, Old Maid, or Go Fish games. Here are some of the variations that can be made from the included cards:

Match doubles fact with snap cube picture with inside double fact with snap cube pictures

Match inside doubles fact with snap cube pictures and the sum

Match doubles fact with inside double fact with snap cube pictures

Match doubles fact and inside doubles fact without snap cube pictures

Match all three – doubles fact, inside doubles fact, and sum or



Old Maid Game Put students into groups of 3 or 4. Instruct students to deal out the cards. It is okay if some players have 1 more card than the

others. The players put all of the cards into their hand.

The dealer begins. The dealer draws one card from the person on the right. If they have a

pair of cards in their hand that match they announce the match and place the matched pair on the table.

The next player draws a card from the person on his/her right. If they have a pair of cards in

their hand that matches they announce the match and place the matched pair on the table. If a player draws a card and does not have a match in their hand they do not lay any cards

down and the next player continues. The match does not have to be made from the card they pulled from the other player.

The loser is the person left with the “old maid” card. The winner is the person with the most

matches.

Fish

Put students into groups of 2, 3 or 4. Instruct students to deal out seven cards to each player.

Place the remaining cards in the center face down.

The dealer begins. The dealer asks another player if they have a card to match a card in their

hand. If the player does have the card he/she surrenders it to the requester. The requester makes the match and lays the two cards to the side. If the player does not have the card, he/she says “go fish” and the requester draws a card from the center of the table.

The next player follows the same procedure.

The winner is the person with the most matches at the end of the game.



Concentration

Lay all cards face down on the table. Students will take turns choosing two cards at a time. If they make a match they pick up the

two cards and place them to the side. The next player takes a turn and follows the same procedure.

The game ends when all the matches have been made.



3 + 3

9 + 9

4 + 4

5 + 5



6 + 6

7 + 7

8 + 8



3 + 5

2 + 4

4 + 6

5 + 7



6 + 8

7 + 9

8 + 10



6

8

10

12



14 16

18



Old Maid

Old Maid

Old Maid

Old Maid

Old Maid

Old Maid

Old Maid

Old Maid



3 + 3

9 + 9

4 + 4

5 + 5



6 + 6

7 + 7

8 + 8



3 + 5

2 + 4

4 + 6

5 + 7



6 + 8

7 + 9

8 + 10



2 + 0

Inside Doubles

3 + 1 Inside Doubles


5 + 3

Inside Doubles

6 + 4

Inside Doubles



9 + 7

Inside Doubles

0 + 2

Inside Doubles


2 + 4

Inside Doubles




4 + 6

Inside Doubles



7 + 9

Inside Doubles



Make Ten Facts



Make-Ten Facts These facts all have at least one addend of 8 or 9. One strategy for these facts it to build onto the 8 or 9 and up to 10 and then add on the rest. For 6 + 8, start with 8, then 2 more makes 10, and that leaves 4 more for 14.

+ 0 1 2 3 4 5 6 7 8 9

0 0 1 2 3 4 5 6 7 8 9

1 1 2 3 4 5 6 7 8 9 10

2 2 3 4 5 6 7 8 9 10 11

3 3 4 5 6 7 8 11 12

4 4 5 6 7 8 9 10 12 13

5 5 6 7 8 9 10 11 12 13 14

6 6 7 8 10 11 12 13 14 15

7 7 8 9 12 13 14 15 16

8 8 9 10 11 12 13 14 15 16 17

9 9 10 11 12 13 14 15 16 17 18



Make Ten Facts-Beginning Exploration For students to effectively use the make ten strategy, they must have a strong sense of making tens. For students who are not ready to use the make ten strategy for basic addition facts, activities such as the one listed below should be used to build a stronger sense of 10. Number Sandwiches (Page 53, Activity 2.25 Teaching Student Centered Mathematics) Copy the attached ten frame cards onto the designated paper. This activity can be used as a whole group warm-up, small group, or center activity. Lay all of the cards face up on the carpet so that all students can view the frames. Tell students that they are going to match the cards together to form the number 10. Two ten frames (1 card stock and 1 transparency) should be joined to show the total of 10. Students can elaborate by providing the number sentence that the 2 parts represent.



Copy this set of ten frames onto colored cardstock. Cut out into individual ten frames.









Copy this set of ten frames onto overhead transparencies. Cut out into individual ten frames.









Making Ten Flash Cards Make 10 on the Ten-Frame (Page 103, Activity 4.8 Teaching Student Centered Mathematics) Give students a mat with two ten-frames. Flash cards are placed next to the ten-frames, or a fact can be given orally. The students should first model each number in the two ten-frames and then decide on the easiest way to show (without counting) what the total is. The obvious (but no the only) choice is to move counters into the frame showing either 8 or 9. Get students to explain what they did. Focus especially on the idea that 1 (or 2) can be taken from the other number and put with the 9 (or 8) to make 10. Then you have 10 and whatever is left. After students feel comfortable with the concrete version of this activity, teachers should use a bingo blotter to represent the numbers. This requires students to begin to move the dots visually.



9

+ 2



9

+ 3

9

+ 4



9

+ 5

9

+ 6



9

+ 7



8

+ 2

8

+ 3



8

+ 4



8

+ 5

8

+ 6



8

+ 7

8

+ 9



Fill Me Up with 9’s! Directions: To play this game, you will need one game board, approximately 30 counters (15 of each color for each player) the attached ten frame 8 counters for the ten frame a wooden cube marked 3, 4, 5, 6, 7, and 8.

The first player will roll the wooden cube. The player will take that number of counters and place them on the bottom ten frame. Then, the player will adjust to make ten using the top ten frame to create a new equation. For example, if the player rolls a 5 they will place 5 counters in the bottom ten frame. Then, they will move one counter to fill in the top ten frame creating the new equation 10+ 4 = 14. The player will then place a marker under the 14. When the board is filled, the player with the most markers wins the game.

17 16 15 14 13 12

+ 9



Ten Frame



Fill Me Up with 8’s! Directions: To play this game, you will need one game board, approximately 30 counters (15 of each color for each player) the attached ten frame 8 counters for the ten frame a wooden cube marked 3, 4, 5, 6, 7, and 8.

The first player will roll the wooden cube. The player will take that number of counters and place them on the bottom ten frame. Then, the player will adjust to make ten using the top ten frame to create a new equation. For example, if the player rolls a 5 they will place 5 counters in the bottom ten frame. Then, they will move two counters to fill in the top ten frame creating the new equation 10 + 3 = 13. The player will then place a marker under the 13. When the board is filled, the player with the most markers wins the game.

16 15 14 13 12 11

+ 8



Ten Frame



Clear a Path of 9’s! Directions: To play this game, you will need one game board, approximately 30 counters (15 of each

color for each player) a wooden cube marked 12, 13, 14, 15, 16, and 17.

The first player will roll the wooden cube. The player will look for a cell with an expression that matches the sum on the cube. The player will place the marker on the cell. The first player to form a continuous pathway from one side of the game board to the other wins the game.

9 + 3 9 + 8 9 + 4 9 + 8 9 + 6 9 + 7

9 + 7 9 + 5 9 + 7 9 + 8 9 + 8 9 + 4

9 + 8 9 + 6 9 + 3 9 + 7 9 + 3 9 + 6

9 + 4 9 + 3 9 + 5 9 + 4 9 + 5 9 + 8

9 + 6 9 + 4 9 + 6 9 + 5 9 + 3 9 + 5

9 + 3 9 + 7 9 +8 9 + 6 9 + 7 9 + 4



Clear a Path of 8’s! Directions: To play this game, you will need one game board, approximately 30 counters (15 of each

color for each player) a wooden cube marked 11, 12, 13, 14, 15, and 17.

The first player will roll the wooden cube. The player will look for a cell with an expression that matches the sum on the cube. The player will place the marker on the cell. The first player to form a continuous pathway from one side of the game board to the other wins the game.

8 + 3 8 + 3 8 + 4 8 + 3 8 + 6 8 + 7

8 + 7 8 + 5 8 + 7 8 + 3 8 + 3 8 + 4

8 + 3 8 + 6 8 + 3 8 + 7 8 + 3 8 + 6

8 + 4 8 + 3 8 + 5 8 + 4 8 + 5 8 + 3

8 + 6 8 + 4 8 + 6 8 + 5 8 + 3 8 + 5

8 + 3 8 + 7 8 + 3 8 + 6 8 + 7 8 + 4



Making Ten Match Game Cut out the cards. Lay the cards face down on the table in front of you. Each partner should take a turn matching the +8 or +9 fact to the 10 fact that can help them solve the fact.

8 + 3

10 + 1

8 + 4

10 + 2

8 + 5

10 + 3

8 + 6

10 + 4



8 + 7

10 + 5

8 + 9

10 + 7

9 + 3

10 + 2

9 + 4 10 + 3



9 + 5 10 + 4

9 + 6 10 + 5

9 + 7 10 + 6

9 + 8 10 + 7



0 + 8

Making Ten

1 + 8 Making Ten

2 + 8 Making Ten

3 + 8

Making Ten

4 + 8

Making Ten

5 + 8 Making Ten

6 + 8 Making Ten

7 + 8

Making Ten

8 + 8

Making Ten

9 + 8 Making Ten

8 + 0

Making Ten

8 + 1 Making Ten



8 + 2

Making Ten

8 + 3 Making Ten

8 + 4 Making Ten

8 + 5

Making Ten

8 + 6

Making Ten

8 + 7 Making Ten

8 + 9 Making Ten

1 + 9

Making Ten

2 + 9

Making Ten

3 + 9 Making Ten

4 + 9

Making Ten

5 + 9 Making Ten



6 + 9

Making Ten

7 + 9 Making Ten

8 + 9 Making Ten

9 + 9

Making Ten

9 + 0

Making Ten

9 + 1 Making Ten

9 + 2 Making Ten

9 + 3

Making Ten

9 + 4

Making Ten

9 + 5 Making Ten

9 + 6

Making Ten

9 + 7 Making Ten



9 + 8

Making Ten



Additional Resources for Making Ten



Resource Activity Page Number Fundamentals, Grades K-1, Origo

Towers of Ten 32Pick a Pair Solitaire 52

Fundamentals, Grades 1-2, Origo

Triple Combo 8-11First to Forty 52-55

Nimble with Numbers, Grades 1 & 2

Roll Ten 46



Strategy Selection Strategy Retrieval



Strategy Selection/Strategy Retrieval “Strategy selection or strategy retrieval is the process of deciding what strategy is appropriate for a particular fact. If you don’t think to use a strategy, you probably won’t. Many teachers who have tried teaching fact strategies report that the method works well while the children are focused on whatever strategy they are working on. They acknowledge that children can learn and use strategies. But, they continue, when the facts are all mixed up or the child is not in the “fact practice” mode, old counting habits return.”

Teaching Student Centered Mathematics John Van De Walle

Page 97 Strategy Scatter Post the attached strategy cards in different areas of the room. Pass out 1 addition fact card to each child. It works well if you can find addition fact cards that have a different fact on each side of the card. Ask the students to choose an addition fact and think about which strategy they would use to solve the fact. Then, have the students “scatter” to the appropriate posted strategy chart. When they arrive under the strategy, they should discuss how they would solve the fact. Then, tell the students to look at the same fact and determine if there is a different strategy that they could use to solve the fact. If so, they should “scatter” to the new strategy. All others should stay where they are and welcome the newcomers into the group. Then, the students can flip their card and follow the same process for the other fact on their flashcard. Fact Folder Sort File folders are used as a sort mat for students to distinguish between the strategies. To create these folders you will need:

file folder

8 library pockets (If these are not available, simply label the inside of the folder with the various strategies.)

Marker

A variety of flashcards that can fit inside of the library pockets.

One More Than

TwoMore Than

Facts with Zero

Doubles

Doubles + 1

Inside Doubles

Doubles + 1 ?



Give students a variety of flashcards. The students should sort the flashcards based on the strategy they would use to solve the fact. As they sort, they should solve the fact. Strategy Stand Pass out one flashcard to each child. Call out the different strategies. Students should stand when they hear the strategy that they would use to solve the fact. Addition Roll and Sort To play this game, students will need two dice labeled in the following ways: 0, 1, 2, 3, 4, 5 and 9, 8, 7, 6, 5, 4. Each player should take turns rolling both dice to create an addition fact. Then, the students should record the addition fact under the strategy that they would use to solve the fact. The “Addition Roll and Sort” is attached for students to use. Domino Sort To play this game, students will need a sorting mat and a set of double nine dominoes. Place all the dominoes face down on a flat surface. Students will take turns choosing a domino and placing it under an appropriate strategy. Students should solve the fact before placing the domino.



One More Than



Two More Than



Facts with Zero



Doubles



Doubles + 1



Inside Doubles



Making Ten



I can think of a different way to solve

this fact.



Addition Roll and Sort Directions: To play this game, you will need two dice labeled in the following ways: 0, 1, 2, 3, 4, 5 and 9, 8, 7, 6, 5, 4. Take turns rolling both dice to create an addition fact. Then, record the addition fact under the strategy that you would use to solve the fact.

One More Than Two More Than

Facts with Zero Doubles

Doubles + 1 Inside Doubles

Making Ten



Domino Sort + 1, + 2 Zero Facts

Doubles Doubles + 1

Inside Doubles Making 10



Julie’s Game

This game is used to reinforce math skills. We will use addition strategies for this focus.

However, many contents can be covered by using this game.

Strategy Review Each student will record an addition fact on the paper provided. The students will place their card on the floor somewhere around the room. The teacher will play the music. When the music stops each student should step onto one of the facts. The teacher will call out a fact strategy: doubles, doubles + 1, make tens, etc. If the student is standing on a fact that matches the strategy, the student will follow the direction of the teacher: wiggle, jump, etc. The music plays again.



Subtraction Facts



Strategies for Subtraction Facts Subtraction facts prove to be more difficult than addition. This is especially true when children have been taught subtraction through a “count-count-count” approach; for 13 – 5, count 13, count off 5, count what’s left. There is little evidence that anyone who has mastered subtraction facts has found this approach helpful. Unfortunately, many sixth, seventh, and eighth graders are still counting.

Beginning Exploration of Subtraction as Think Addition Using think-addition strategy, the child uses known addition facts to produce the unknown quantity or part. If this important relationship between parts and wholes—between addition and subtraction—can be made, subtraction facts will be much easier. When children see 9-4, you want them to think spontaneously, “Four and what makes nine?” By contrast, observe a third-grade child who struggles with this fact. The idea of thinking addition never occurs. Instead, the child will begin to count either back from 9 or up from 4. The value of think-addition cannot be overstated. Word problems that promote think-addition are those that sound like addition but have a missing addend: join, initial part unknown; join, change unknown; and part-part-whole, part unknown. Consider this problem: Janice had 5 fish in her aquarium. Grandma gave her some more fish. Then she had 12 fish. How many fish did Grandma give Janice? Notice that the action is join and, thus, suggests addition. There is a high probability that students will think 5 and how many more makes 12. In the discussion in which you use

Think Addition:

6 and 4 is 10.



problems such as this, your task is to connect this thought process with the subtraction fact, 12 – 5. Subtraction Facts with Sums to 10 Think-addition is most immediately applicable to subtraction facts with sums of 10 or less. These are generally introduced with a goal of mastery in the first grade. Sixty-four of the 100 subtraction facts fall into this category. If think-addition is to be used effectively, it is essential that addition facts be mastered first. Evidence suggests that children learn very few, if any, subtraction facts without first mastering the corresponding addition facts. In other words, mastery of 3 + 5 can be thought of as prerequisite knowledge for learning the facts 8 – 3 and 8 – 5. Facts involving 0, 1, and 2 may be solved by different children in many different ways including think-addition. These facts are closely related to important basic number relationships. If children experience difficulties with facts such as 8 – 0 or 7 – 2, it would be a good idea to investigate their number concepts. A child who says that 7 – 0 is 6 may have overgeneralized that subtraction makes the number smaller.

Assessment Note: Before working on mastery of subtraction facts, it is a good idea to check on students’ mastery of addition and subtraction. Prepare a drill by writing about 20 facts on a transparency that you will show to students one fact at a time. The 20 facts should be made of 10 pairs—a subtraction fact and the corresponding addition fact. For example, if you have 9 – 4 in the list, include 4 + 5 elsewhere in the list. Have students write the answers as you go. They may not go back to facts they missed. Keep the pace quick so that students will not have a chance to count on their fingers. In an activity such as this, it is essential to explain that you are simply trying to find out what they know so that you can help them. This is not a test or quiz. They should do their best to write what they think the answers are without counting.



Assessment Note continued: If students know the addition facts but not the subtraction facts, more effort should be placed on developing the addition-subtraction facts, more effort should be placed on developing the addition-subtraction facts, more effort should be placed on developing the addition-subtraction connection. Use missing-part activities and join-type story problems in which the change amount is unknown. Discuss the way that both an addition sentence and a subtraction sentence can be written for these situations. Be very overt in your own modeling of think-addition. For 9 – 4 you might say, “I know that 4 and 5 make 9, so 9 minus 4 is 5.” Draw a part-while picture to go with this explanation. This simple diagnostic exercise can be repeated at various times to see how well students are connecting addition and subtraction. This same approach can be used in a diagnostic interview format. After students have completed the problems, have them go back over those that they hesitated on, especially the subtraction facts. Ask them to think aloud about how they would get the answer. If they have answered an addition fact but not the corresponding subtraction fact, ask if they can think of any way that the addition fact could help with the subtraction fact. Remember, interview time is a time to gather information—not to teach.



Subtraction Facts with Sums to 10

- 1 2 3 4 5 6 7 8 9 10 0 1-0=

1 2-0= 2

3-0= 3

4-0= 4

5-0= 5

6-0= 6

7-0= 7

8-0= 8

9-0= 9

10-0= 10

1 1-1= 0

2-1= 1

3-1= 2

4-1= 3

5-1= 4

6-1= 5

7-1= 6

8-1= 7

9-1= 8

10-1= 9

2 2-2= 0

3-2= 1

4-2= 2

5-2= 3

6-2= 4

7-2= 5

8-2= 6

9-2= 7

10-2= 8

3 3-3= 0

4-3= 1

5-3= 2

6-3= 3

7-3= 4

8-3= 5

9-3= 6

10-3= 7

4 4-4= 0

5-4= 1

6-4= 2

7-4= 3

8-4= 4

9-4= 5

10-4= 6

5 5-5= 0

6-5= 1

7-5= 2

8-5= 3

9-5= 4

10-5= 5

6 6-6= 0

7-6= 1

8-6= 2

9-6= 3

10-6= 4

7 7-7= 0

8-7= 1

9-7= 2

10-7= 3

8 8-8= 0

9-8= 1

10-8= 2

9 9-9= 0

10-9= 1

10 10-10= 0



The 36 “Hard” Subtraction Facts: Sums Greater Than 10

Many people will use a different strategy for each of these facts. For 14 – 9, it is easy to start with 9 and work up through 10: 9 and 1 more is 10, and 4 more makes 5. For the 12 – 6 fact, it is quite common to hear “double 6, “ a think-addition approach. For the last fact 15 – 6, 10 is used again but probably by working backward from 15—a take-away process: Take away 5 to get 10, and 1 more leaves 9. We could call these three approaches, respectively, build up through 10, think-addition, and back down through 10. Each of the remaining facts with sums of 11 or more can be learned using one or more of these strategies. Keep in mind these are not required strategies. Some children may use a think-addition method for all. Others may have a completely different strategy for some or all of these. The three approaches suggested here are based on ideas already developed: the relationship between addition and subtraction and the power of 10 as a reference point.

Before reading further, look at the three subtraction facts shown here and try to reflect on what thought process you use to get the answers. Even if you “just know them,” think about what a likely process might be.

14 - 9 12 - 6 15 - 6



Build Up Through 10 This group includes all facts where the part or subtracted number is either 8 or 9. Examples are 13 - 9 and 15 - 8.

Activity 4.12 (Page 109) Teaching Student-Centered Mathematics John Van De Walle

Build Up Through the Ten-Frame On the board or overhead, draw a ten-frame with 9 dots. Discuss how you can build numbers between 11 and 18, starting with 9 in the ten-frame. Stress the idea of one more to get to 10 and then the rest of the number. Repeat for a ten-frame showing 8. Next, with either the 8 or 9 ten-frame in view, call out numbers from 11 to 18, and have students explain how they can figure out the difference between that number and the one on the ten-frame. Later, use the same approach but show fact cards to connect this idea with the symbolic subtraction fact.



Back Down Through 10 Here is one strategy that is really take-away and not think-addition. It is useful for facts where the ones digit of the whole is close to the

number being subtracted. For example, with 15 – 6, you start with the total of 15 and take off 5. That gets you down to 10. Then take off 1 more to get to 9. For 14 – 6, just take off 4 and then take off 2 more to get 8. Here we are working backward with 10 as a “bridge.”

1. Begin with ten-frames that show 14.

14 - 6

2. Think about the difference between 4 and 6. The difference is +2. 3. Go back 2 on the ten-frame. That equals 8.


Back Down Through the Ten-Frame Start with two ten-frames on the overhead, one filled completely and the other partially filled. For 13, for example, discuss what is the easiest way to think about taking off 4 counters or 5 counters. Repeat with other numbers between 11 and 18. Have students write or say the corresponding fact. See example below:

14 – 6

1. Begin with ten-frames that show 14. 2. Take off the 4. That leaves 10.



Expanded Lesson

Build Up Through the Ten-Frame Based on: Activity 4.12, page 109

Grade Level: Second grade or early third grade Mathematics Goal: To continue development of ten-structured thinking: When finding the difference

between a number less than 1- and one in the teens, it is useful to think of that distance in two parts—from the smaller number up to the 10 and from 10 to the larger number.

To utilize 10 in some way as a strategy for subtraction facts in which the whole is greater than 10 and the subtrahend is either 8 or 9.

Thinking About the Students: Students should have mastered all of the addition facts for sums to 10. They should be exploring the relationship between addition and subtraction through story problems—especially join problems with change unknown. They should have discussed and been familiar with the idea that a number in the teens is 10 and some more; for example, 15 is 10 and 5. Materials and Preparation No materials other than a chalk board are required. Students will write in their journals or on plain paper. Before Brainstorm On the board or overhead, draw a ten-frame with 9 dots. Ask: How many dots? How many more dots do I need to draw to have 14 ? (Write

14 on the board.) Have one or more students explain their reasoning. Repeat the question with 17, 12, and 15 dots.

If students’ explanations involve first filling in one dot on the ten-frame and then adding the rest to make the required number, have them come to the board to explain again by drawing the required dots.

Change the ten-frame to 8 dots. Ask: How many more dots do I need to have 13? (Write 13 on the board.) Repeat with other numbers in the teens. Again, look for and focus on explanations that involve the use of 10.



The Task Draw two prominent ten-frames side by side on the board, one with 8 dots and one

with 9 dots. Beneath write the following five facts: 13 – 9, 17 – 9, 11 – 8, 15 – 9, 13 – 8

The task is for students to describe a good way to think about subtracting 14-8 that makes getting the answer easy—no counting, something they can do in their heads.

Students should use the same idea to answer each of the five subtraction problems.

During Students may have difficulty articulating an idea. Look for students who are not

writing anything and ask them what the answer to 14 – 9 is. Ask: How do you know? What did you think about to get the answer? Help students use what they say to write down an idea. Do not push students to use an add-up through-ten strategy or even any approach that involves 10. Allow students to use their own ideas.

Some students may be helped by simply focusing their attention on the two ten-frames and reminding them of the discussion in the first part of the lesson.

Identify students who you will have share their ideas. After Ask several students to share their ideas. Include several different ideas. Be

sure to find at least one or two students who worked up through 10 that you identified in the during stage.

After a student shares how he or she worked up through 10, ask all students to try the strategy on 15 – 8. Also, have students try other strategies that are suggested when the strategy seems to be efficient (does not involve counting). Some students may work down through 10 and others may use a known fact as a helper.

Assessment Notes Look for students who count on or back and do not use 10 at all. These students

will need further help with their understanding of the teen numbers. Some students may use 10 but not efficiently. They may have to count by ones for

one or both of the two parts. These students need help with the other part of 10 and also understanding the teens as 10 and some more.

For students having difficulty, check to see if they know the corresponding addition facts (14 – 9 and 9 + 5).



Next Steps Students not effectively using 10 may benefit from building a teen number on a

pair of ten-frames using counters. Present the numbers in random order. Discuss easy ways to put the counters on the two ten-frames without having to count.

These same students may benefit from ten-frame flash cards and also from telling the total dots on two ten-frames when on of them is an 8 or 9. (See Activity 4.8, p. 103)

Make flash cards for facts involving -8 or -9 with a single ten-frame showing 8 or 9 dots accordingly. Have students practice using these flash cards plain flash cards for the same facts. Be sure that students using the flash cards have an efficient strategy and are not counting to get answers.



Extend Think-Addition Think-addition remains one of the most powerful ways to think about subtraction facts. When the think-addition concept o f subtraction is well developed, many children will use that approach for all subtraction facts. (Notice that for division virtually everyone uses a think-multiplication approach. Why?) What may be most important is to listen o children’s thinking as they attempt to answer subtraction facts that they have not yet mastered. If they are not using on e of the three ideas suggested here, it is a good bet that they are counting—an inefficient method. The activities that follow are all the think-addition variety. There s, of course, no reason why these activities could not be used for all of the subtraction facts. They need not be limited to the “hard facts.”


Missing-Number Cards Show children, without explanation, families of numbers with the sum circled as in Figure A. Ask why they think the numbers go together and why one number is circled. Ask why they think the numbers go together and why one number is circled. When this number family idea is fairly well understood, show some families with one number replaced by a question mark (Figure B), and ask what number is missing. When students understand this activity, explain that you have made some missing-number cards based on this idea. Each card has two of three numbers that go together in the same way. Sometimes the circled number is missing (the sum), and sometimes one of the other numbers is missing (a part). The cards can be made both vertically and horizontally with the sum appearing in different positions. The object is to name the missing number. This same activity can be used with the triangular relationship cards.



Figure A Figure B

John A. Van De Walle Teaching Student- Centered Mathematics

Pages 106-110

8 5 13

? 4 10

5 9 14

3 6 ?


Find a Plus Fact to Help Select a group of subtraction facts that you wish to practice. Divide a sheet of paper into small cards, about 10 or 12 to a sheet. For each subtraction fact, write he corresponding addition fact on one of the cards. Two subtraction facts can be related to each addition fact. Duplicate the sheet and have students cut the cards apart. Now write one of the subtraction facts on the board. Rather than call out answers, students find the addition fact that helps with the subtraction fact. On your signal, each student holds up the appropriate fact. For 12 – 4 or 12 – 8, the students would select 4 + 8. The same activity can be made into a matching card game.



Triangular Relationship Cards Triangular relationship cards are a great way to support subtraction as think addition. The cards can be ordered directly from the Washington County Public Schools Printing Department. The printing number for addition/subtraction cards is M-125. A parent letter has been included to support the explanation of these cards.



Dear Parents, One of the tools we will be using in our classroom this year to support addition and subtraction facts is triangular relationship cards. These cards bridge the relationship between addition and subtraction facts and encourage students to make connections between the fact families.

For example, the card above shows 2 addition facts: 7 + 6 = 13 and 6 + 7 = 13. It also shows 2 subtraction facts that belong to the same family: 13 – 7 = 6 and 13- 6 = 7.

When using these cards for addition, always cover the largest number with a finger so the child can not see that number. Then ask, what is 7 + 6? When they successfully answer 13, cover the 6 and say, “7 + ___ = 13”. Using this method, students are encouraged to link what they already know about addition to subtraction. These cards can be especially effective for subtraction fact mastery. If this important relationship between addition and subtraction can be made, subtraction facts will be much easier. (Van De Walle, 2006, p. 106)

If you have any questions about the triangular relationship cards, feel free to contact me. Sincerely,

13

7 6 +



One More Than Two More

Think Addition Subtraction Facts



One More Than Two More Than (Think Addition) Subtraction Facts

The main strategy that will be used with subtraction facts is subtraction as “think addition”. When done in this think-addition manner, the child uses known addition facts to find the answer. When your child sees 9 – 4, you want them to think spontaneously, “Four and what makes nine?”

The facts listed below include all of the think addition one-more than two-more than facts.

2 - 1 3 - 1 3 - 2 4 - 2 4 - 3 4 - 1 5 - 3 5 - 2 5 - 4 5 - 1 6 - 4 6 - 2 6 - 5 6 – 1 7 - 5 7 - 2 7 - 6 7 - 1 8 - 6 8 - 2 8 - 7 8 - 1 9 - 7 9 - 2 9 - 8 9 - 1 10 - 8 10 - 2 10 - 9 10 - 1 11 - 9 11 - 2 1 - 0 1 - 1 2 - 0



Directions: All players begin in the start position. Draw a card. Find the difference. Move to the next spot on the game board with that number. The first player to reach the winner’s circle wins the game.



Rocket Blaster Game Cards

2 - 1

3 - 2 4 – 3 5 – 4 6 – 5 7 – 6 8 – 7 9 – 8 10 – 9



1 – 0 4 – 1 5 – 1 6 – 1 7 – 1 1 – 1 3 – 1 4 – 2 5 – 3 6 – 4



7 – 5 8 – 6 9 – 7 10 – 8 11 – 9 5 – 2 6 – 2 7 – 2 8 – 2

Go Back to Start



Doubles Think Addition

Subtraction Facts



Doubles (Think Addition) Subtraction Facts


The facts listed below include all of the think addition double facts.

2 - 1 4 - 2 6 - 3 8 - 4 10 - 5 12 - 6 14 - 7 16 - 8 18 - 9



Directions: Draw a card. Find the difference. Move to the next spot on the game board with that number. The first player to reach the winner’s circle wins the game.



18 - 9 2 – 1 4 – 2 6 – 3 8 – 4 10 – 5 12 – 6 14 – 7 16 – 8

Double Trouble

Game Cards



2 – 1 4 – 2 6 – 3 8 – 4 10 – 5 12 – 6 14 – 7 16 – 8



If you spin: then:

2 or 9 Move 2 spaces

3 or 8 Move 3 spaces

4 Move back 1 space

5 or 6 Move 1 space

7 Move 1 space then spin again

Directions: Spin the spinner and answer the subtraction fact. Look at the box below to see how many places you should move on the game board. The first player to reach the end wins the game.





Doubles + 1 Think Addition

Subtraction Facts



Doubles + 1 (Think Addition) Subtraction Facts

The main strategy that will be used with subtraction facts is

subtraction as “think addition”. When done in this think-addition manner, the child uses known addition facts to find the answer. When your child sees 9 – 4, you want them to think spontaneously, “Four and what makes nine?”

The facts listed below include all of the think addition doubles + 1 facts.

1 - 1 1 - 0 3 - 2 3 - 1 5 - 3 5 - 2 7 - 4 7 - 3 9 - 5 9 - 4 11 - 6 11 - 5 13 - 7 13 - 6 15 - 8 15 - 7 17 - 9 17 - 8







7 - 4

7 – 3 9 – 5 9 – 4 11 - 6 11 - 5 13 - 7 13 – 6 15 - 8



15 – 7 17 - 9 17 - 8 7 – 3 11 - 6 9 – 4 13 - 7 11 - 5 15 - 8 13 – 6



Inside Doubles Think Addition

Subtraction Facts



Inside Doubles (Think Addition) Subtraction Facts



The facts listed below include all of the think addition inside doubles facts.

2 - 2 2 - 0 4 - 3 4 - 1 6 - 4 6 - 2 8 - 5 8 - 3 10 - 6 10 - 4 11 - 7 12 - 5 14 - 8 14 - 6 16 - 9 16 - 7









16 - 7

4 -1 6 – 4 6 – 2 8 – 5 8 – 3 10 -6 10 - 4 11 - 7



12 – 5 14 – 8 14 – 6 16 - 9 16 - 7 16 - 7

8 – 3 6 – 4 10 - 4 8 – 5



Make Ten Think Addition

Subtraction Facts



Make Ten (Think Addition) Subtraction Facts

The main strategy that will be used with subtraction facts is subtraction as “think addition”. When done in this think-addition manner, the child uses known addition facts to find the answer. When your child sees 9 – 4, you want them to think spontaneously, “Four and what makes nine?”The facts listed below include all of the think addition Make Ten facts.

10 - 2 10 - 8 10 - 1 10 - 9 11 - 3 11 - 8 11 - 2 11 - 9 12 - 4 12 - 8 12 - 3 12 - 9 12 - 5 13 - 8 13 - 4 13 - 9 14 - 6 14 - 8 14 - 5 14 - 9 15 - 7 15 - 8 15 - 6 15 - 9 16 - 8 10 - 1 16 - 7 16 - 9 17 - 9 10 – 2 17 - 8 10 – 5 10 - 4 10 - 3 18 - 9 10 – 6 10 – 7 10 – 8 10 – 9



Taking from 10! Adapted from Nimble with Numbers Grades 1 and 2 Directions: To play this game, you will need one game board, approximately 30 counters (15 of each color for each player) a wooden cube marked 1, 2, 3, 4, 5, choose

The first player will roll the wooden cube. If choose is rolled, the pair may select any number one through five. When a number is rolled, the player subtracts the number from 10. The player places a marker in the appropriate difference column. The game continues until all cells are filled. The player with the most markers on the board after the boards has been filled wins the game.

5 6 7 8 9



Addition and Subtraction Match Copy the addition facts onto one color of cardstock. Copy the subtraction facts onto a different color. Cut the cards out and lay them face down on a flat surface. Players will attempt to match the subtraction fact with the addition fact that helps to solve the fact.

5 + 5 = 10 3 + 5 = 8

7 + 2 = 9 4 + 5 = 9

2 + 8 = 10 3 + 2 = 5

5 + 2 = 7 3 + 4 = 7

4 + 2 = 6 6 + 3 = 9



10 – 5 = 5 9 – 5 = 4

9 – 2 = 7 5 – 2 = 3

7 – 2 = 5 7 – 4 = 3

6 – 2 = 4 9 – 3 = 6

8 – 5 = 3 10 – 8 = 2



Choose and Subtract-A! Adapted from Nimble with Numbers Grades 1 and 2 Directions: To play this game, you will need one game board approximately 30 counters (15 of each color for each player) 3 wooden cubes marked 1, 2, 3, 4, 5, 6

The first player rolls the three Number Cubes. The player selects two of the three number cubes to subtract, states the subtraction equation, and places a counter on the resulting difference. Example: If 2, 3, and 5 are rolled, the player could cover 1 (3 -2), 2 (5 – 3), or 3 (5 -2). The first player to cover three counters in a row horizontally, vertically, or diagonally wins.

2 1 3 2 0 0 3 2 4 1 1 0 3 1 3 5 2 0 2 1 1 4 2 1 0



Choose and Subtract-B! Adapted from Nimble with Numbers Grades 1 and 2 Directions: To play this game, you will need one game board approximately 30 counters (15 of each color for each player) 2 wooden cubes marked 5, 6, 7, 8, 9, 10 and 1 wooden cube marked 1, 2, 3, 4, 5, 6

The first player rolls the three Number Cubes. The player selects two of the three number cubes to subtract, states the subtraction equation, and places a counter on the resulting difference. Example: If 2, 3, and 5 are rolled, the player could cover 1 (3 -2), 2 (5 – 3), or 3 (5 -2). The first player to cover three counters in a row horizontally, vertically, or diagonally wins.

0 3 4 6 1 2 5 1 2 9 1 3 4 1 0 7 0 6 0 2 3 8 2 5 4



How Many More to Make 8? Adapted from Nimble with Numbers Grades 1 and 2 Directions: To play this game, you will need one game board approximately 30 counters (15 of each color for each player) 1 number cube marked 1 – 6 Paper for recording equations

The first player rolls the number cube to determine how many more are needed to make 8. The player places a counter on a cell that represents the missing amount. Example: If a 2 is rolled, 6 is needed to make 8. Thus, the pair selects and covers one of the number 6’s on the board. Players are required to say aloud the related subtraction fact for each turn. The first player to place three of their counters in a row horizontally, vertically, or diagonally wins.

4 2 5 3 7 3 6 2 3 5 7 4 6 4 2 5



How Many More to Make 10? Adapted from Nimble with Numbers Grades 1 and 2 Directions: To play this game, you will need one game board approximately 30 counters (15 of each color for each player) 1 number cube marked 1 – 6 Paper for recording equations

The first player rolls the number cube to determine how many more are needed to make 10. The player places a counter on a cell that represents the missing amount. Example: If a 2 is rolled, 8 is needed to make 10. Thus, the pair selects and covers one of the number 8’s on the board. Players are required to say aloud the related subtraction fact for each turn. The first player to place three of their counters in a row horizontally, vertically, or diagonally wins.

5 9 4 7 8 6 5 9 4 7 8 6 9 5 7 4



Additional

Strategies for Subtraction Facts



The 36 “Hard” Subtraction Facts: Sums Greater Than 10 Build Up Through 10

This group of facts includes all facts where the part or subtracted number is either 8 or 9. Examples are 13 – 9 and 15 – 8.

- 11 12 13 14 15 16 17 18 2 11-2=

9

3 11-3= 9

12-3= 9

4 11-4= 7

12-4= 8

13-4= 9

5 11-5= 6

12-5= 7

13-5= 8

14-5= 9

6 11-6= 5

12-6= 6

13-6= 7

14-6= 8

15-6= 9

7 11-7= 4

12-7= 5

13-7= 6

14-7= 7

15-7= 8

16-7= 9

8 11-8= 3

12-8= 4

13-8= 5

14-8= 6

15-8= 7

16-8= 8

17-8= 9

9 11-9= 2

12-9= 3

13-9= 4

14-9= 5

15-9= 6

16-9= 7

17-9= 8

18-9= 9



The 36 “Hard” Subtraction Facts: Sums Greater Than 10 Back Down Through 10

Here is one strategy that is really take-away and not think-addition. It is useful for facts where the ones digit of the whole is close to the number being subtracted. For example, with 15 – 6, you start with the total of 15 and take off 5. That gets you down to 10. Then take off 1 more to get 9. For 14-6, just take off 4 and then take off 4 and then take off 2 more to get 8. Here we are working backward with 10 as a “bridge.”


Page 109

- 11 12 13 14 15 16 17 18 2 11-2=

9

3 11-3= 9

12-3= 9

4 11-4= 7

12-4= 8

13-4= 9

5 11-5= 6

12-5= 7

13-5= 8

14-5= 9

6 11-6= 5

12-6= 6

13-6= 7

14-6= 8

15-6= 9

7 11-7= 4

12-7= 5

13-7= 6

14-7= 7

15-7= 8

16-7= 9

8 11-8= 3

12-8= 4

13-8= 5

14-8= 6

15-8= 7

16-8= 8

17-8= 9

9 11-9= 2

12-9= 3

13-9= 4

14-9= 5

15-9= 6

16-9= 7

17-9= 8

18-9= 9



Back Down Through the Ten-Frame (Page 109, Activity 4.13 Teaching Student Centered Mathematics) Start with two ten-frames on the overhead, one filled completely and the other partially filled. For 13, for example, discuss what is the easiest way to think about taking off 4 counters or 5 counters. Repeat with other numbers between 11 and 18. Have students write or say the corresponding fact. The attached lesson comes from Teaching Student Centered Mathematics, John A. Van De Walle, Pages 120-121.



The 36 “Hard” Subtraction Facts: Sums Greater Than 10 Extend Think-Addition

Think-addition remains one of the most powerful ways to think about subtraction facts. When the think-addition concept of subtraction is well developed, many children will use that approach for all subtraction facts. (Notice that for division virtually everyone uses a think-multiplication approach. Why?) What may be most important is to listen to children’s thinking as they attempt to answer subtraction facts that they have not yet mastered. If they are not using one of the three ideas suggested here, it is a good bet that they are counting—an efficient method.


Page 109

- 11 12 13 14 15 16 17 18 2 11-2=

9

3 11-3= 9

12-3= 9

4 11-4= 7

12-4= 8

13-4= 9

5 11-5= 6

12-5= 7

13-5= 8

14-5= 9

6 11-6= 5

12-6= 6

13-6= 7

14-6= 8

15-6= 9

7 11-7= 4

12-7= 5

13-7= 6

14-7= 7

15-7= 8

16-7= 9

8 11-8= 3

12-8= 4

13-8= 5

14-8= 6

15-8= 7

16-8= 8

17-8= 9

9 11-9= 2

12-9= 3

13-9= 4

14-9= 5

15-9= 6

16-9= 7

17-9= 8

18-9= 9



Center Bag Support

The following cards were created as a resource for students and parents to identify all the facts that fall under a particular strategy. These cards can be placed in the front of center bags so that students and parents are

aware of the specific facts that they are practicing.



One More Than/Two More Than Addition Facts

This strategy is used for facts that have 1 or 2 as one of it’s addends. Out of the 100 addition facts students will learn, 36 fall under the one-more than and two-more than facts. In these situations, students simply count up 1 or 2 from the greatest added. This should be the only situation where students “count” to find their answer.

The facts listed below include all of the one-more than two-more than facts.

1 + 1 2 + 1 1 + 2 2 + 2 1 + 3 3 + 1 2 + 3 3 + 2 1 + 4 4 + 1 2 + 4 4 + 2 1 + 5 5 + 1 2 + 5 5 + 2 1 + 6 6 + 1 2 + 6 6 + 2 1 + 7 7 + 1 2 + 7 7 + 2 1 + 8 8 + 1 2 + 8 8 + 2 1 + 9 9 + 1 2 + 9 9 + 2 1 + 0 0 + 1 2 + 0 0 + 2



One More Than Two More Than (Think Addition) Subtraction Facts


The facts listed below include all of the think addition one-more than two-more than facts.

2 - 1 3 - 1 3 - 2 4 - 2 4 - 3 4 - 1 5 - 3 5 - 2 5 - 4 5 - 1 6 - 4 6 - 2 6 - 5 6 – 1 7 - 5 7 - 2 7 - 6 7 - 1 8 - 6 8 - 2 8 - 7 8 - 1 9 - 7 9 - 2 9 - 8 9 - 1 10 - 8 10 - 2 10 - 9 10 - 1 11 - 9 11 - 2 1 - 0 1 - 1 2 - 0



Facts with Zero Addition Facts

19 facts have zero as one of the addends. Although these facts seem

to be the simplest of all, some students will overgeneralize the idea that answers to addition are bigger. Putting these facts into real life situations oftentimes help the students to reinforce the zero rule.

The facts listed below include all of the zero facts.

1 + 0 2 + 0 3 + 0 4 + 0 5 + 0 6 + 0 7 + 0 8 + 0 9 + 0



Doubles Addition Facts

There are only 10 double facts. These facts are relatively easy to

learn and become a powerful way to learn many other facts. Examples of double facts include: 5 + 5, 3 + 3, 6 + 6. Dice from board games are good visuals to use to help students remember their double facts.

The facts listed below include all the double facts.

0 + 0 1 + 1 2 + 2 3 + 3 4 + 4 5 + 5 6 + 6 7 + 7 8 + 8 9 + 9



Doubles (Think Addition) Subtraction Facts



The facts listed below include all of the think addition double facts.

2 - 1 4 - 2 6 - 3 8 - 4 10 - 5 12 - 6 14 - 7 16 - 8 18 - 9



Doubles + 1 Addition Facts

Doubles + 1 facts include all combinations where one addend is one

more than the other. There are 18 of these facts. When students realize that these are facts that have addends with a difference of 2 (1 + 2), (3 + 4), etc. they simply double the smaller addend and add 1.

The facts listed below include all of the doubles + 1 facts.

0 + 1 1 + 0 1 + 2 2 + 1 2 + 3 3 + 2 3 + 4 4 + 3 4 + 5 5 + 4 5 + 6 6 + 5 6 + 7 7 + 6 7 + 8 8 + 7 8 + 9 9 + 8



Doubles + 1

(Think Addition) Subtraction Facts The main strategy that will be used with subtraction facts is


The facts listed below include all of the think addition doubles + 1 facts.

1 - 1 1 - 0 3 - 2 3 - 1 5 - 3 5 - 2 7 - 4 7 - 3 9 - 5 9 - 4 11 - 6 11 - 5 13 - 7 13 - 6 15 - 8 15 - 7 17 - 9 17 - 8



Inside Doubles Addition Facts

Inside doubles facts focus on facts that have 2 addends that are

separated by 2 numbers. Some examples are: (5 + 7), (4 + 6), (7 + 9). Once the students are able to recognize these facts they are able to look at the number that falls between the 2 addends and double it to find the answer. For example: 5 + 7, the number that comes between the 2 numbers is 6. The student doubles the number to find the answer ( 6 + 6 = 12)

The facts listed below include all of the inside double facts.

0 + 2 2 + 0 1 + 3 3 + 1 2 + 4 4 + 2 3 + 5 5 + 3 4 + 6 6 + 4 5 + 7 7 + 5 6 + 8 8 + 6 7 + 9 9 + 7



Inside Doubles

(Think Addition) Subtraction Facts The main strategy that will be used with subtraction facts is


The facts listed below include all of the think addition inside doubles facts.

2 - 2 2 - 0 4 - 3 4 - 1 6 - 4 6 - 2 8 - 5 8 - 3 10 - 6 10 - 4 11 - 7 12 - 5 14 - 8 14 - 6 16 - 9 16 - 7



Make Ten Addition Facts

These facts all have at least one addend of 8 or 9. Once strategy for these facts is to build onto the 8 or 9 and up to 10 and then add on the rest. For 6 + 8, start with 8, then 2 more makes 10 and that leaves 4 more for 14.

The facts listed below include all of the make ten facts.

8 + 2 2 + 8 9 + 1 1 + 9 8 + 3 3 + 8 9 + 2 2 + 9 8 + 4 4 + 8 9 + 3 3 + 9 8 + 5 5 + 8 9 + 4 4 + 9 8 + 6 6 + 8 9 + 5 5 + 9 8 + 7 7 + 8 9 + 6 6 + 9 8 + 8 9 + 7 7 + 9 8 + 9 9 + 8

9 + 9



Make Ten (Think Addition) Subtraction Facts

The main strategy that will be used with subtraction facts is subtraction as “think addition”. When done in this think-addition manner, the child uses known addition facts to find the answer. When your child sees 9 – 4, you want them to think spontaneously, “Four and what makes nine?”The facts listed below include all of the think addition Make Ten facts.

10 - 2 10 - 8 10 - 1 10 - 9 11 - 3 11 - 8 11 - 2 11 - 9 12 - 4 12 - 8 12 - 3 12 - 9 12 - 5 13 - 8 13 - 4 13 - 9 14 - 6 14 - 8 14 - 5 14 - 9 15 - 7 15 - 8 15 - 6 15 - 9 16 - 8 10 - 1 16 - 7 16 - 9 17 - 9 10 – 2 17 - 8 10 – 5 10 - 4 10 - 3 18 - 9 10 – 6 10 – 7 10 – 8 10 – 9



Fact Assessment

Forms



WCPS Fact Assessment Philosophy

• Mastery of basic facts means that a child can give a quick response (in about 3 seconds) without resorting to non-efficient means, such as counting. Consequently, to assess the fact fluency of a student, fact assessments must be timed. Without the timing element in place, teachers are unable to determine if the student is fluent or is simply able to add or subtract.

• According to Van De Walle, if there is any defensible purpose for a

timed test of basic facts it may be diagnosis to determine which combinations are mastered and which remain to be learned.

• The students will no longer bubble their responses on a scantron.

Instead, they will simply record their answer. At the end of the assessment, the teacher will score the student’s work and calculate the percentage of accurate answers. Ninety percent and above will be considered “mastery”. Eighty percent and below will be considered “non-mastery”.

• Teachers will be provided with one or two scantrons (addition/

subtraction and/or multiplication/division) depending on the levels of their students. The columns on the scantrons will be labeled with the 5 different levels of the addition and subtraction levels. The teacher will locate the level of assessment that the student took and record a “0” for non-mastery and a “1” for mastery. If the student mastered the assessment they will move onto the next level during the next assessment window. If the student did not master the assessment they will be reassessed on the same level during the next assessment window.

• All assessments will be timed for 2 minutes giving the students

approximately 6 seconds per fact.



• The table below designates the fact assessment with the strategies assessed in those particular areas. The assessments follow the hierarchy of strategies introduced throughout the addition and subtraction fact program.

•

Level Operation Fact Strategies 1 Addition 1 More Than

2 More Than Facts with Zero

2 Addition Doubles Doubles + 1 Inside Doubles

3 Addition Making Ten 4 Subtraction Sums to 10

5 Subtraction Sums Greater Than 10



Name:

Date:

5 + 0= 1 + 3=

1 + 8= 0 + 9=

3 + 2= 1 + 7=

2 + 2= 6 + 2=

2 + 9 = 1 + 0=

3 + 0= 4 + 2=

2 + 5 = 9 + 1=

4 + 1= 0 + 4=

8 + 2= 7 + 2=

8 + 0= 2 + 1=

Level 1 Percentage Correct:

Mastery 90% - 100%

Non-Mastery 80% or lower

Time Limit: 2 minutes Next Month’s Assessment Level:



Name:

Date:

2 + 2= 5 + 7 =

3 + 5 = 3 + 3 =

9 + 9 = 4 + 5 =

5 + 6 = 8 + 8 =

7 + 5= 7 + 8 =

9 + 8 = 4 + 6=

7 + 9 = 7 + 7=

1 + 1= 8 + 6 =

6 + 6 = 6 + 7 =

6 + 8 = 4 + 4 =


Mastery 90% - 100%





Name:

Date:

8 + 2 = 8 + 8 =

1 + 9 = 9 + 6 =

9 + 3 = 9 + 0 =

8 + 9 = 8 + 5 =

4 + 8 = 4 + 9 =

9 + 9 = 7 + 8 =

5 + 9 = 3 + 8 =

7 + 9 = 2 + 9 +

8 + 0 = 9 + 4 =

6 + 8 = 9 + 8 =


Mastery 90% - 100%





Name:

Date:

10 – 2 = 7 – 2 =

6 – 5 = 4 – 3 =

4 – 1 = 9 – 4 =

9 – 1 = 8 – 1 =

8 – 5 = 10 – 9 =

3 – 3 = 5 – 2 =

9 – 2 = 3 – 0 =

10 – 3 = 7 – 6 =

6 – 6 = 9 – 7 =

5 – 4 = 10 – 6 =


Mastery 90% - 100%





Name:

Date:

11 – 9 = 15 – 7 =

15 – 6 = 12 – 6 =

12 – 3 = 14 – 8 =

16 – 9 = 12 – 4 =

12 – 5 = 11 – 5 =

13 – 5 = 14 – 6 =

11 – 3 = 17 – 9 =

18 – 9 = 11 – 2 =

14 – 5 = 13 – 4 =

12 – 8 = 16 – 7 =


Mastery 90% - 100%



Documents

Addition and Subtraction Basic Math Packet 2009-2010