2nd Grade Unit: Addition and Subtraction · Web view*NOTE: See attached “Flipbook” .pdf for 2nd grade math (from Arizona Dept. of Ed) — read pages 1-3 to gain insight into the

2nd Grade Unit: Addition and Subtraction

Time for Unit: 15 days (9 days of lessons, 6 days flexible time for assessments, review, extensions)

Pre-Assessment:

Background Information: Counting to 100 Understanding the value of a number to 100 Place Value to 100 Vocabulary of word problems Equations and symbols Add to 10 Subtract to 10 Mental strategies

In first grade, students examined the mental strategies within 20. They solved word problems using three whole numbers that had a sum equal to or less than of 20 using objects, drawings, and equations with a symbol. Students counted to 120 starting at any number less than 120. Students examined two digit numbers to recognize they are composed of tens and ones.

Common Core Standards:2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

2. OA.2 Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.

2. NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations.

Concepts—What students need to know: Word problem Sum Addend Subtrahend Equals Digit fact family adding to, taking from putting together taking apart

Saluda County Schools Page 1


comparing (one more, two more doubles, doubles +1, doubles +2, make a ten, build up to ten, back down through ten)

Skills—What students need to be able to do: Unknown subtrahends and addends. Use drawing and equations to solve. Quickly recall all addition and subtraction facts to 20. EXPLAIN WHY and how regrouping strategies work.

*NOTE: See attached “Flipbook” .pdf for 2nd grade math (from Arizona Dept. of Ed) — read pages 1-3 to gain insight into the Standard of Mathematical Practices for the 2nd grade content standards. Read the summary of skills and sample questions to develop mathematical thinking and use this doc as a guide during instruction.

Big Ideas: Solve word problems and justify your answer using addition and subtraction. Fluently add and subtract within 20. When one quantity is joined or added on to another quantity, the result is greater

than or equal to the initial quantity. When one quantity is removed from another quantity, the result is less than or

equal to the initial quantity. When one quantity is compared to another quantity, the initial quantity is either

equal to, greater than, or less than the second quantity. Joining, removing, part-part-whole, and comparing problems can be modeled. The order of addends may be changed and the result will not change. However

this is not true for subtraction. The grouping of addends may be changed and the result will not change.

However this is not true for subtraction. Addends can be decomposed and regrouped differently to simplify adding. Addition and subtraction are inverse (opposite) operations. Solutions may be solved and checked by using the inverse relation between

addition and subtraction of numbers. Mental math strategies may be used to solve problems involving numbers. Problems involving numbers may be simplified by using the commutative,

associative, and identity properties. Problems can be solved in a variety of ways such as modeling, counting

strategies, or number facts. Problems and solutions can use various representations, including concrete

objects, pictures, number sentences, and words.

Materials/Manipulatives:


http://katm.org/wp/wp-content/uploads/2012/06/2FlipBookedited.pdf




Lesson 1: Addition Strategies

Common Core Standards:2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.2. OA.2 Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.2. NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations.

Standards for Mathematical Practice:1. Make sense of problems and persevere in solving them.3. Construct viable arguments and critique the reasoning of others.8. Look for and express regularity in repeated reasoning.

Day 1: Counting on

Table 1 gives examples of the various types of problems that have unknowns students need ample experience working on.

Common Addition and Subtraction Situations

Result Unknown Change Unknown Start UnknownAdd to

Two bunnies sat on the grass. Three more bunnies hopped there. How many bunnies are on the grass now?

2 + 3 = ?

Two bunnies were sittingon the grass. Some morebunnies hopped there. Then there were five bunnies. How many bunnies hopped over to the first two?

2 + ? = 5

Some bunnies were sitting on the grass. Three more bunnies hopped there. Then there were five bunnies. How many bunnies were on thegrass before?

? + 3 = 5

Take fromFive apples were on the table. I ate two apples. How many apples are on the table now?

5 – 2 = ?

Five apples were on thetable. I ate some apples.Then there were threeapples. How many apples did I eat?

5 – ? = 3

Some apples were on thetable. I ate two apples. Then there were three apples. How many apples were on the table before?

? – 2 = 3

Total Unknown Addend Unknown Both Addends Unknown



Put Together

Take Apart

Three red apples and two green apples are on the table. How many apples are on the table?

3 + 2 = ?Difference

Five apples are on the table. Three are red and the rest are green. How many apples are green?

3 + ? = 5, 5 – 3 = ?

Grandma has five flowers. How many can she put in her red vase and how many in her blue vase?

5 = 0 + 5, 5 = 5 + 05 = 1 + 4, 5 = 4 + 15 = 2 + 3, 5 = 3 + 2

Difference Unknown Bigger Unknown Smaller UnknownCompare (“How many more?”

version): Lucy has two apples. Julie has five apples. How manymore apples does Julie have than Lucy?

(“How many fewer?” version): Lucy has two apples. Julie has five apples. How many fewer apples does Lucy have than Julie?

2 + ? = 5, 5 – 2 = ?

(Version with “more”):Julie has three more apples than Lucy. Lucy has two apples. How many applesdoes Julie have?

(Version with “fewer”):Lucy has 3 fewer apples than Julie. Lucy has two apples. How many apples does Julie have?

2 + 3 = ?, 3 + 2 = ?

(Version with “more”): Julie has three more apples than Lucy. Julie has five apples. How many apples does Lucy have?

(Version with “fewer”): Lucy has 3 fewer apples than Julie. Julie has five apples. How many apples does Lucyhave?

5 – 3 = ?, ? + 3 = 5

Instructional strategies:The teacher needs to make sure students understand that the unknown can be represented with a symbol, no matter where the unknown is located.

This standard mentions the word fluently when students are adding and subtracting numbers within 20. Fluency means accuracy (correct answer), efficiency (within 4-5 seconds), and flexibility (using strategies such as making 10 or breaking apart numbers (decomposing)). Research indicates that teachers’ can best support students’ memorization of sums and differences through varied experiences making 10, breaking numbers apart and working on mental strategies, rather than repetitive timed tests.

The teacher and students will complete the Every Day Counts calendar activities.

The teacher will pose the following task for student to work first by themselves and then discuss with a partner. Students will underline the important information (clues) needed to solve the task and circle the question. Students will place all the information on the chart in their Math Notebooks.



Chart format

Solution (Write your answer in a complete sentence)

TASKTwo bunnies sat on the grass. Three more bunnies hopped there. How many bunnies are on the grass now? Show how you solved either by writing or drawing your method.

As students are working on the task, the teacher is walking around questioning students and giving assistance as needed without giving the answer or telling how to solve the task. After a period of time, students will then discuss their solutions with a partner. Afterwards, the teacher and the students complete the chart and discuss why this is the add to, result unknown situation (see Table 1).

TASKTwo bunnies sat on the grass. Some more bunnies hopped there. Then there were five bunnies. How many bunnies hopped over to the first two? Show how you solved either by writing or drawing your method.As students are working on the problem, the teacher is walking around questioning students and giving assistance as needed without giving the answer or telling how to solve the problem. After a period of time, students will then discuss their solutions with a partner. Afterwards, the teacher and the students complete the chart and discuss why this is the add to, change unknown situation (see Table 1).

TASKSome bunnies were sitting on the grass. Three more bunnies hopped there. Then there were five bunnies. How bunnies were on the grass before? Show how you solved either by writing or drawing your method.


Clues Question

Strategy Explanation


As students are working on thetask, the teacher is walking around questioning students and giving assistance as needed without giving the answer or telling how to solve the task. After a period of time, students will then discuss their solutions with a partner. Afterwards, the teacher and the students complete the chart and discuss why this is the add to, start unknown situation (see Table 1).

Students will be given several word problems containing the three add to situations that are similar to the first three tasks. Students will write the equations and solve using unifix cubes. After they have solved the problem, students will work in pairs to discuss how they solved the problem. This will be done in their notebooks.

Formative Assessment:Students will write on their whiteboard the situation for the given word problems.

a. Add to-Result Unknownb. Add to-Change Unknownc. Add to-Start Unknown

1. Andy and Alex have some baseball cards. Alex gives three cards to Andy. Now there are seven baseball cards. How many cards did Andy have to begin with? (Add to-Start Unknown)

2. Andy and Alex are collecting baseball cards. Andy has four baseball cards. Alex has three baseball cards. If Andy and Alex put their cards together, how many would they have? (Add to-Result Unknown)

3. Andy and Alex are collecting baseball cards. Andy has four baseball cards. Alex gives him some of his baseball cards. Now, they have seven cards. How many cards did Alex give to Andy? (Add to-Change Unknown)

Day 2: Take From



TASK



Five apples were on the table. I ate two apples. How many apples are on the table now? Show how you solved either by writing or drawing your method.

As students are working on the task, the teacher is walking around questioning students and giving assistance as needed without giving the answer or telling how to solve the task. After a period of time, students will then discuss their solutions with a partner. Afterwards, the teacher and the students complete the chart and discuss why this is the take from, result unknown situation (see Table 1).

TASKFive apples were on the table. I ate some apples. Then there were three apples. How many apples did I eat? Show how you solved either by writing or drawing your method.

As students are working on the task, the teacher is walking around questioning students and giving assistance as needed without giving the answer or telling how to solve the task. After a period of time, students will then discuss their solutions with a partner. Afterwards, the teacher and the students complete the chart and discuss why this is the take from, change unknown situation (see Table 1).

TASKSome apples were on the table. I ate two apples. Then there were three apples. How many apples were on the table before? Show how you solved either by writing or drawing your method.

As students are working on the task, the teacher is walking around questioning students and giving assistance as needed without giving the answer or telling how to solve the task. After a period of time, students will then discuss their solutions with a partner. Afterwards, the teacher and the students complete the chart and discuss why this is the take from, start unknown situation (see Table 1).

Students will be given several word problems containing the three take from situations that are similar to the first three tasks. Students will write the equations and solve using unifix cubes. After they have solved all the problems, the students will work in pairs to discuss how they solved the problems. This will be done in their notebooks.

Formative Assessment:

Students will write on their whiteboard the situation for the given word problems.

a. Take from-Result Unknownb. Take from-Change Unknown c. Take from-Start Unknown



1. Mrs. Jones had nine dogs in a pen. Some of the dogs jumped out of the pen. Then there were six dogs. How many dogs jumped out of the pen? (Take from-Change Unknown)

2. Some dogs were in a pen in Mrs. Jones’ backyard. Three of the dogs jumped out. Then there were six dogs. How many dogs were in the pen before? (Take from-Start Unknown)

3. Mrs. Jones had nine dogs in a pen. Three of the dogs jumped out of the pen. How many dogs are still in the pen? (Take From-Result Unknown)

Day 3: Put together/Take Apart



TASKThree red apples and two green apples are on the table. How many apples are on the table? Show how you solved either by writing or drawing your method.

As students are working on the task, the teacher is walking around questioning students and giving assistance as needed without giving the answer or telling how to solve the task. After a period of time, students will then discuss their solutions with a partner. Afterwards, the teacher and the students complete the chart and discuss why this is the put together/take apart, total unknown situation (see Table 1).

TASKFive apples are on the table. Three are red and the rest are green. How many apples are green? Show how you solved either by writing or drawing your method.

As students are working on the task, the teacher is walking around questioning students and giving assistance as needed without giving the answer or telling how to solve the task. After a period of time, students will then discuss their solutions with a partner. Afterwards, the teacher and the students complete the chart and discuss why this is the put together/take apart, addend unknown situation (see Table 1).

TASK



Grandma has five flowers. How many can she put in her red vase and how many in her blue vase? Show how you solved either by writing or drawing your method.

As students are working on the task, the teacher is walking around questioning students and giving assistance as needed without giving the answer or telling how to solve the task. After a period of time, students will then discuss their solutions with a partner. Afterwards, the teacher and the students complete the chart and discuss why this is the put together/take apart, both addends unknown unknown situation (see Table 1).

Students will be given several word problems containing the three put together/take apart situations that are similar to the first three tasks. Students will write the equations and solve using unifix cubes. After they have solved all the problems, the students will work in pairs to discuss how they solved the problems. This will be done in their notebooks.


a. Put Together/Take Apart- Total Unknownb. Put Together/Take Apart- Addend Unknownc. Put Together/Take Apart- Both Addends Unknown

1. Nine bicycles are in the carport. Six bicycles are blue and the rest are yellow. How many bicycles are yellow? (Put Together/Take Apart- Addend Unknown)

2. John has six cookies. How many cookies can be chocolate chip and how many cookies can be oatmeal? (Put Together/Take Apart- Both Addends Unknown)

3. There are six blue bicycles and three yellow bicycles in the carport. How many bicycles are in the carport? (Put Together/Take Apart- Total Unknown)Day 4: Compare



TASK(“How many more?” version): Lucy has two apples. Julie has five apples. How manymore apples does Julie have than Lucy?(“How many fewer?” version): Lucy has two apples. Julie has five apples. How many fewer apples does Lucy have than Julie?



As students are working on the task, the teacher is walking around questioning students and giving assistance as needed without giving the answer or telling how to solve the task. After a period of time, students will then discuss their solutions with a partner. Afterwards, the teacher and the students complete the chart and discuss why this is the compare, difference unknown situation (see Table 1).

TASK(Version with “more”):Julie has three more apples than Lucy. Lucy has two apples. How many applesdoes Julie have?

(Version with “fewer”):Lucy has 3 fewer apples than Julie. Lucy has two apples. How many apples does Julie have?

As students are working on the task, the teacher is walking around questioning students and giving assistance as needed without giving the answer or telling how to solve the task. After a period of time, students will then discuss their solutions with a partner. Afterwards, the teacher and the students complete the chart and discuss why this is the compare, bigger unknown situation (see Table 1).

TASK(Version with “more”): Julie has three more apples than Lucy. Julie has five apples. How many apples does Lucy have?

(Version with “fewer”): Lucy has 3 fewer apples than Julie. Julie has five apples. How many apples does Lucy have?

As students are working on the task, the teacher is walking around questioning students and giving assistance as needed without giving the answer or telling how to solve the task. After a period of time, students will then discuss their solutions with a partner. Afterwards, the teacher and the students complete the chart and discuss why this is the put together/take apart, addend unknown situation (see Table 1).

Students will be given several word problems containing the three compare situations that are similar to the first three tasks. Students will write the equations and solve using unifix cubes. After they have solved all the problems, the students will work in pairs to discuss how they solved the problems. This will be done in their notebooks.




a. Put Compare-Difference Unknownb. Compare-Bigger Unknownc. Compare-Smaller Unknown

1. Erica has five pencils. Juan has three pencils. How many more pencils does Erica have than Juan? (Compare-Difference Unknown)

2. Erica has two more pencils than Juan. Erica has five pencils. How many pencils does Juan have? (Compare-Smaller Unknown)

3. Juan has 3 fewer pencils than Erica. Erica has five pencils. How many pencils does Juan have? (Compare-Bigger Unknown)

Lesson 2: Two-step word problems

Day 5:The teacher and students will complete the Every Day Counts calendar activities.

The teacher will pose the following task for student to work first by themselves and then discuss with a partner. Afterwards, the teacher will pick several students to explain how they solved the task.

TASKThere were 15 jellybeans in a bowl on the table. Lynn took 8 jellybeans and Ann took three. How many jellybeans are in the bowl now? Show how you solved either by writing or drawing your method.

As students are working on the task, the teacher is walking around questioning students and giving assistance as needed without giving the answer or telling how to solve the task. After a period of time, students will then discuss their solutions with a partner.

TASKThere are six duck on a pond. Three flew over to join them. Some of the ducks swam away and now there are only five. How many ducks swam away? Show how you solved either by writing or drawing your method.

As students are working on the task, the teacher is walking around questioning students and giving assistance as needed without giving the answer or telling how to solve the task. After a period of time, students will then discuss their solutions with a partner.



The teacher will create additional two-step problems for the students to gain proficiency.

Formative Assessment:Students will write their own two-step word problem. They will exchange problems with a partner, solve the problem and discuss the steps used to solve the new problem.

Day 6: Mental Strategies for Adding


The teacher will pose the following task for student to work first by themselves and then discuss with a partner. Afterwards, the teacher will pick several students to explain how they solved the task.

TASK

9 + 5 = ___ Explain how you would find the sum to a partner.

The teacher will model two strategies thinking aloud.

Strategy 1: Counting on“I started at 9 and then counted 5 more. I landed at 14.”The teacher will give students the problem 9 + 2=___ to practice counting on with a partner.

Strategy 2: Decomposing a Number Leading to a Ten“I know that 9 and 1 is 10, so I broke 5 into 1 and 4. 9 plus 1 is 10. Then I have to add 4 more, which gets me to 14.”

The teacher will give students the problem 9 + 2=___ to practice decomposing a number leading to a ten with a partner.

Activity:Working with a partner, students will use a deck of cards with the face cards pulled out. Students will draw two cards and find the sum by practicing the two strategies above. They will write the equation in their Math Notebooks with the sum and explain the strategy used.

The teacher will walk around listening to students as they explain, to their partner, how they solved the equation, making notes of who will need remediation.



Formative Assessment:Students will solve the following problem on an exit ticket by explaining which strategy they used and how they used it.

7 + 9 =_______

Day 7: Mental Strategies for SubtractingThe teacher and students will complete the Every Day Counts calendar activities.

The teacher will pose the following task for student to work first by themselves and then discuss with a partner.

TASK13 – 9 = _____ Explain how you would find the difference to a partner.

Afterwards, the teacher will pick several students to explain how they solved the task.

The teacher will model three strategies thinking aloud.

Strategy 1: Using the Relationship between Addition and Subtraction“I know that 9 plus 4 equals 13. So 13 minus 9 equals 4.”

The teacher will give students the problem 15 - 9=___ to practice Using the Relationship between Addition and Subtraction with a partner.

Strategy 2: Creating an Easier Problem“I added 1 to each of the numbers to make the problem 14 minus 10. I know the answer is 4. So 13 minus 9 is also 4.”

The teacher will give students the problem 15 - 9=___ to practice creating an easier problem with a partner.

Strategy 3: Using the benchmark of 10.“I know that 13 minus 3 equals 10, so I take 3 away from the 9 and 3 away from the 13. 10 minus 6 equals 4.”

The teacher will give students the problem 15 - 9=___ to practice using the benchmark of 10 with a partner.

Several of these strategies may need modeling more than one and/or practiced more than once.



The teacher will walk around listening to students as they explain, to their partner, how they solved the equation, making notes of who will need remediation.

The teacher will need to create additional problems for practicing the strategies for addition and subtraction with 9 as an addend/subtrahend.

Formative Assessment:To show proficiency in at least one of the subtraction strategies, the students will have to write an explanation of how they would solve 16 – 9 = ____

Day 8: Doubles, Doubles +1 and Doubles +2The teacher and students will complete the Every Day Counts calendar activities.


TASKDad put 7 pennies in my piggy bank on Monday. On Thursday, he put 7 more pennies in my piggy bank. How much money is in my piggy bank? Students will illustrate their way of thinking in their Math Notebooks. Afterwards, a discussion will be held about the problem.





Have students illustrate the equations and objects in their notebooks. Look for a pattern. How will knowing these help solve other equations?

After students have explored doubles, give each group a set of word problems similar to the set below that have doubles and their corresponding doubles +1 equation. Have the students pair them together and look for the patterns when adding doubles +1 (odd, one more than the doubles equation). Glue them into their notebook in a chart.

Double Double +1 Double +2

Finally, give students another set of problems that extend to doubles +2. Have them sort these onto their existing chart. Look for the patterns when adding doubles +2 (even, two more-same as the next double).

Sample Questions:

“Spiders have four legs on each side. How many do they have in all?”

“Mira and Miguel both have eight lollipops. Mira gets one more for making an ‘A’ on her test. How many total lollipops do Mira and Miguel have?”

“The blue bird has six eggs in her nest. The red bird has eight eggs in her nest. How many eggs are in the two nests?”

Formative Assessment:Provide the students with a set of 5 word problems. Have the students color code the problems by circling them as to the strategy they used. Solve the problems.

Day 9: Place Value Strategies



TASKStudents will have the opportunity to use math manipulatives from their “toolboxes” to solve the problem.67 + 25 =________

As students are working on the task, the teacher is walking around questioning students and giving assistance as needed without giving the answer or telling how to solve the task. After a period of time, students will then discuss their solutions with a partner. Afterwards, the teacher will pick several students to explain how they solved the task.



The teacher will model the place value strategy using place value blocks: a flat = tens, units= ones. The teacher will repeat this strategy several times using different addition sentences. Afterwards, the teacher will write examples on the Smartboard for students to practice with a partner.

TASKStudents will have the opportunity to use math manipulatives from their “toolboxes” to solve the problem.63 -32 =_____

If students are permitted to follow their natural instincts and begin with the big pieces (from the left instead of the right), recording schemes similar to that shown below are possible. The trades are made from the pieces remaining after the subtraction in the column to the left has been done. (John Van De Wall. Teaching Student-Centered Mathematics Grades K-3. 2006. pg. 171)

13 14 Ex. 7 3 4 - 2 7 5 5 0 0 4 6 0 5 9 4 5 9

The teacher will model the place value strategy using place value blocks: a flat = tens, units= ones. The teacher will repeat this strategy several times using different addition sentences. Afterwards, the teacher will write examples on the Smartboard for students to practice with a partner.

Formative Assessment:

Students will demonstrate the strategy used to solve: 74 + 17 =______ and 96 – 54 =____


Documents

2nd Grade Unit: Addition and Subtraction · Web view*NOTE: See attached “Flipbook” .pdf for 2nd grade math (from Arizona Dept. of Ed) — read pages 1-3 to gain insight into the