California Edition Grade 1 - eusddata.pbworks.comeusddata.pbworks.com/f/1mod01.pdf · California Edition Grade 1 Module 1 - Revised Addition and Subtraction Concepts - WORK IN PROGRESS

Revised 7/3/03 1

SAN DIEGO CITY SCHOOLS

Instructional Module to Enhance the Teaching of

H A R C O U R T

Math

California Edition

Grade 1

Module 1 - Revised Addition and Subtraction

Concepts

- WORK IN PROGRESS -

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D

C

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Harcourt Math, Grade 1- Module 1

Revised 7/3/03 San Diego City Schools

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Module 1 Harcourt Math, Grade 1

Order of Units Days 1 – 26

Module 1 Unit 1

Addition and Subtraction Concepts 26 Days

Chapter 1: Addition Concepts • Lesson 1.1 Addition Stories • Lesson 1.2 More Addition Stories • Lesson 1.3 Add with Pictures • Lesson 1.4 Problem Solving: Write an Addition Sentence • Lesson 1.5 Add 0 Chapter 2: Using Addition • Lesson 2.1 Add in Any Order • Lesson 2.2 Ways to Make 7 and 8 • Lesson 2.3 Ways to Make 9 and 10 • Lesson 2.4 Vertical Addition • Lesson 2.5 Problem Solving: Make a Model Chapter 3: Subtraction Concepts • Lesson 3.1 Subtraction Stories • Lesson 3.2 Subtract with Pictures • Lesson 3.3 Write Subtraction Sentences • Lesson 3.4 Problem Solving: Make a Model • Lesson 3.5 Subtract All or None Chapter 4: • Lesson 4.1 Take Apart 7 and 8 • Lesson 4.2 Take Apart 9 and 10 • Lesson 4.3 Vertical Subtraction • Lesson 4.4 How Many More? • Lesson 4.5 Use Subtraction Assessment Problem Solving Workshop



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Module 1 Harcourt Math: Grade 1

Addition and Subtraction Concepts Days 1 – 26

26 Days

Day 1 Unit 1 Lesson 1.1




















Day 22 Assessment

Day 23 Problem Solving Workshop






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NOTES ABOUT TEACHING ADDITION AND SUBTRACTION PROBLEMS: PROBLEM TYPES Source: Carpenter, Thomas P., et. al., Children’s Mathematics, Cognitively Guided Instruction, Portsmouth, N.H.: Heinemann, 1999. Mathematicians would categorize the problems in this chapter and subsequent chapters as one particular problem type: result unknown (3 + 4 = ). Giving students experiences with a variety of problem types can encourage the development of different problem solving strategies that encourage the development of number sense (Carpenter, et. al., 1997). During routines, you may want to consider problem types that include: • Change unknown: I have 2 baseball cards. My friend gives me some more. Now I have 5 cards.

How many did my friend give me? (2 + = 5) • Start unknown: I have some baseball cards. My friend gave me 1 more. Now I have 5.

How many did I start with? ( + 1 = 5) This particular problem is challenging for many students, since most will only be

able to solve it through guess and check. • Result unknown: I have 2 baseball cards. My friend gave me 3 more.

Now how many baseball cards do I have? (2 + 3 = ). The majority of problems in Harcourt are of this variety. LANGUAGE Another consideration when teaching addition and subtraction through the use of story problems is the use of mathematical and natural language. In order to make meaning, it is necessary that students be exposed to both (K. Richardson, 1999). • Natural language: Mom put apples in the basket. Then she put one more apple. How many apples are in the basket now? • Mathematical language: Mom put three apples in the basket. She added one more apple to the basket. How many apples are there altogether?



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WHAT TO OBSERVE FOR From DEVELOPING NUMBER CONCEPTS BOOK TWO: ADDITION AND SUBTRACTION by Kathy Richardson © 1999 by Addison Wesley, publishing as Dale Seymour Publications, a imprint of Pearson Learning Group. Used by permission of Pearson Education, Inc. To interpret what children understand about addition and subtraction, careful observations are necessary. The following list of questions can be a guide to assist you in observing children as solve they addition and subtraction problems:

Interpreting Simple Story Problems:

• Can the children interpret simple addition and/or subtraction problems using physical models or drawings?

• Do they interpret the problem with ease or with difficulty? Do they need any prompts or hints?

• If they make a mistake, do they pay attention to their answer and self-correct if it doesn’t make sense, or do they just report whatever they came up with?

Interpreting Equations: • Can the children interpret addition and/or subtraction equations using models? • Can they read the equations? • Can they make up a story to go with the equation?

Reading and Writing Equations:

• Can the children write equations to describe story problems? Is this easy or

challenging for them? • After writing an equation, can they read it back? Do they know how the numbers

are connecting to the situation in the story? • If the children do not know how to use numbers and symbols to record in the

conventional way, can they represent the story symbolically in some other way?

Size of Numbers: • Does the size of the numbers used in the stories seem to make any difference to

the children’s understanding or confidence? • Can the children interpret simple addition and/or subtraction problems with ease? • What size numbers is the child most comfortable? 6 or less? 10 or less? Up to

20?

Level of Complexity: • Can the children interpret simple addition and/or subtraction problems with ease? • Can they act out complex problems that involve such concepts as missing parts

or comparative subtraction?



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GRADE 1 Order of Units

2003-2004 School Year TRADITIONAL CALENDAR

September October

Module 1: Addition and Subtraction Concepts Unit 1, Chapters 1 - 4

25 days

October

November

Module 2: Addition and Subtraction Facts to 10 Unit 2, Chapters 5 - 8

26 days

November December

Module 3: Numbers to 100 Unit 3, Chapters 9 - 11

19 days

December January

Module 4: Addition and Subtraction to 12 Unit 3, Chapter 12-14

15 days

January

Module 5: Data and Graphing Unit 4, Chapter 15

4 days

January February

Module 6: Money Unit 4, Chapter 16 – 17

11 days

February March

Module 7: Time Unit 4, Chapters 19 - 19

11 days

March

Module 8: Patterns Unit 5, Chapters 22

4 days

March April

Module 9: Addition and Subtraction to 20 Unit 6, Chapters 26 - 28

20 days

April Module 10: Measurement Unit 5, Chapters 23 – 24

10 days

April

Module 11: Fractions Unit 5, Chapter 25

5 days

April May

Module 12: Addition and Subtraction With 2-Digit Numbers Unit 6, Chapters 29 - 30

15 days

May June

Module 13: Geometry Unit 5, Chapters 20 – 21

10 days



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GRADE 1 Order of Units

2003-2004 School Year YEAR ROUND CALENDAR

September October

Module 1: Addition and Subtraction Concepts Unit 1, Chapters 1 - 4

25 days

October

November

Module 2: Addition and Subtraction Facts to 10 Unit 2, Chapters 5 - 8

26 days

November December

Module 3: Numbers to 100 Unit 3, Chapters 9 - 11

19 days

December January February

Module 4: Addition and Subtraction to 12 Unit 3, Chapter 12-14

15 days

February

Module 5: Data and Graphing Unit 4, Chapter 15

4 days

February Module 6: Money Unit 4, Chapter 16 – 17

11 days

March Module 7: Time Unit 4, Chapters 19 - 19

11 days

March

Module 8: Patterns Unit 5, Chapters 22

4 days

April May

Module 9: Addition and Subtraction to 20 Unit 6, Chapters 26 - 28

20 days

May June

Module 10: Measurement Unit 5, Chapters 23 – 24

10 days

June

Module 11: Fractions Unit 5, Chapter 25

5 days

June Module 12: Addition and Subtraction With 2-Digit Numbers Unit 6, Chapters 29 - 30

15 days

July

Module 13: Geometry Unit 5, Chapters 20 – 21

10 days



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MODULE 1: ADDITION AND SUBTRACTION CONCEPTS Chapter 1: Addition Concepts

DAY 1: LESSON 1.1

TE pages 3A, 4, & IS90 LESSON FOCUS: Addition Stories CALIFORNIA STANDARD:

Number Sense: 2.5 Show the meaning of addition and subtraction.

Purpose of Lesson: To model and solve real-life addition problems. ROUTINE Suggestions - Mixed Review and Test Prep: TE, pg. 4

Use Calendar, Number Line, Hundred Chart, and Choral Counting (forward, backward, by twos, fives, and tens—whichever strategy is most appropriate for problems in the review and connects to the goals of the lesson). or Problem of the Day (P.O.D.): TE, pg. 3A Be sure the Number Line and Hundred Chart are visible to students to use as a tool for solving problems. As students respond to the problem, ask questions such as: How did you think about the problem to come up with that answer? Did anyone think about it another way? Do you agree or disagree with this response? What was your strategy? Explain how you got your answer.

LAUNCH Materials: • Hundreds chart • 2-color counters • Connecting cubes

Getting Started: Vocabulary Development: TE, pg.3A (Suggestion: Use connecting cubes because you will be using them throughout the lesson. Draw two hands on the overhead and place connecting cubes in each hand. Ask students to do the same in their own hands. Ask students to suggest other combinations and invite them to demonstrate on the overhead.)

EXPLORE Materials: For group – • 2-color connecting cubes • number cubes labeled 1-4 • number cubes labeled 1-2 • markers

Introduce Activity: Intervention Strategies Book; Skill 13 pg. IS90 only; “Alternative Teaching Strategy”: Students work in pairs or small groups on Skill 13. (Suggestion: If students have difficulty recording their number sentences, have them do the activity without writing. Have students share strategies they may have used to solve problems. Ask: “How did you figure out the number of cubes you had in all?” Did anyone do it another way? [Possible observations: Does the child need to recount the train after added 1 or 2 cubes? Do they know the amount without counting? Do they lose track what they have counted? Do they self correct?



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Some students will need to count out both groups and then recount all to find the total. Others might be able to keep one of the addends in their head and count on, while others “just know” (have derived facts). Observe which strategy each student uses.]

SUMMARIZE Materials: • Journals for each student

Discuss and Write: TE, pg. 4 You may want to construct a math journal for each student to use throughout the year. There are almost daily opportunities to write or draw about the math students are learning. However, because mathematics is the focus, many times discussion alone will be sufficient to summarize the lesson. Revisit the lesson’s objective, connecting discussion with the purpose of the lesson. Optional: Ask children to use crayons to illustrate the way they joined 2 sets of color cubes and write the number sentence. Students share and discuss illustrations. Connect their discussions with the purpose of the lesson.

Homework Suggestion: Practice 1.1 or Family Involvement Activities; pg. FA1-2 “Addition 3 in a Row.”



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DAY 2: LESSON 1.2 TE pages 5, 5A & IS94

LESSON FOCUS: More Addition Stories CALIFORNIA STANDARD:


Purpose of Lesson: To model addition stories. ROUTINE Materials: • For class - Hundred chart

Suggestions - Quick Review: TE, pg. 5. Use Calendar, Number Line, Hundred Chart, and Choral Counting. or P.O.D.: TE, pg. 5A Be sure the Number Line and Hundred Chart are visible to students to use as a tool for solving problems. How did you think about the problem to come up with that answer? Did anyone think about it another way?

LAUNCH Materials: • For each child – 2-color counters

Getting Started: Modeling Addition Stories: TE, pg.5A. Option: Extend situations to include: 1.) Subtraction -“If there are 4 children in all and one is called to the office, how many are left?” or 2.) Adding on/change unknown problems: I have 3 marbles. My friend gave me some more marbles. Now I have 5 marbles. How many marbles did my friend give me?

EXPLORE Materials: • For partners - 6 counters, small brown paper bag, paper, markers for each pair

Introduce Activity: Intervention Strategies Book; Skill 14 pg. IS94 only: “Alternative Teaching Strategy”: Students work in pairs on Skill 14. Note: While 6 color counters may be an appropriate number for most students, you may increase or decrease the number to better suit individual learning needs. Students may or may not (depending on instructional levels) record number sentences on blank paper. Optional: Teach and Practice: TE, pg.5-6, Workbook, pg. 5-6. Continue using counters for additional support.

SUMMARIZE Talk About It – Reasoning: TE, pg. 5 Revisit the lesson’s objective, connecting their discussion/sharing with the purpose of the lesson.

Homework Suggestion: Family Involvement Activities; pg. FA 3



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DAY 3: LESSON 1.3 TE pages 7-8, & 7A

LESSON FOCUS: Add with Pictures CALIFORNIA STANDARD:


Purpose of Lesson: To use pictures to describe addition situations and find sums. ROUTINE Materials: • For each student - 6 counters, cubes • For whole class - Hundred chart, number line

Suggestion - Quick Review: TE, pg. 7. Use Calendar, Number Line, Hundred Chart, and Choral Counting. P.O.D.: TE, pg. 7A Be sure the Number Line and Hundred Chart are visible to students to use as a tool for solving problems. Have connecting cubes available (not required) for each student to use as they solve the problem. How did you think about the problem to come up with that answer? Did anyone think about it another way? Explain how you got your answer.

LAUNCH Materials: • For partners – 6 12 connecting cubes, 6 each of 2 colors, number cube

Students work in pairs on Modeling Addition Sentences With Connecting Cubes, 7A. • Hold up a train showing 6 or fewer connecting cubes. • Ask children to tell you how many cubes. • Have them trace the numeral in the air and continue with

other numbers. • Distribute the number cubes and connecting cubes to

partners. The first child rolls the number cube and makes a train with that many connecting cubes using only one color.

• The second child rolls and does the same using the other color. Children tell a number story using amounts equivalent to the quantity in their trains. Students solve the problem.

• Ask some of the children to share their number stories with the class.

EXPLORE

Teach and Practice: TE, pg.7-8, Workbook, pg. 7-8. Pose some of the problems orally. Instead of saying, “four plus two equals,” use language that expresses action. For example, “There are five balls and I’m giving you one more.” Putting action into a problem gives access to more students. When possible, you pair natural language with mathematical terms. Write 5 = 3 + 2 on the board. Ask students if this tells the same story as 3 + 2 = 5.



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The concept is the meaning of the equal sign (many students believe that the meaning of = is “and the answer is.” This is obviously incorrect. What is on one side of the equal sign is the same quantity as that on the other side of the equal sign.) How do you know that 5 = 3 + 2 tells the same story as 3 + 2 = 5? Continue using counters for additional support. Possible observations: Does the child know how many more without counting? Does the child know the answer to one/two more without counting (can count on)? Do they know when they make a mistake? Math Background: • The pictures in this lesson show the part-part-whole connection. The parts are not the same. Example: I have 5 red marbles and 8 blue marbles. How many marbles do I have? • •Also, it is important that children understand that the equal symbol means, “is the same as.” This will help avoid misconceptions about the equal sign. Optional: Give students the choice to practice either Skill 13 or Skill 14 from Days 1 and 2, IS 90 & 94.

SUMMARIZE Discuss and Write: TE, pg. 8. Connect the purpose of the lesson with the students’ discussions.

Homework Suggestion: Practice Master 1.3



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DAY 4: LESSON 1.4

TE pages 8, 8A, 9, 9A, 10A

LESSON FOCUS: Problem Solving: Write an Addition Sentence CALIFORNIA STANDARD: Number Sense 1.1 Count, read, and write whole numbers to 100.

Purpose of Lesson: To solve problems by using an appropriate strategy such as write an

addition number sentence. ROUTINE Materials: • Number line/Hundred chart

Suggestion - Quick Review: TE, pg. 9. Use Calendar, Number Line, Hundred Chart, and Choral Counting or P.O.D.: TE, pg. 9A Be sure the Number Line and Hundred Chart are visible to students to use as a tool for solving problems. How did you think about the problem to come up with that answer? Did anyone think about it another way? How did you figure it out? Explain how you got your answer.

LAUNCH

Getting Started: Language Arts Connection: TE, pg 10A. Do as a whole class activity to demonstrate the parts of an addition sentence and their meanings. Ask students to make up a number story to go with 3 + 2 = 5; For example, John has 3 pieces of candy and Sue has 2 pieces. How many pieces of candy do they have all together? Make sure to pose some problems that are written with the equal sign at the beginning: 5 = 2+3 (“=” means “the same as,” not just “the answer is”).

EXPLORE Materials: • For partners – paper, crayons, masking tape

TE, pg.8A; “Advanced Learners.” Students work in pairs on Advanced Learners Activity. Ask: Which number shows how many you had in all? What part of your number sentence shows you added your pictures together?”

SUMMARIZE Select a few students to share their story problems with the class covering up the sum with their hand or a sticky note. They ask their classmates to figure out the answer and explain how they got their answer. Make sure to highlight possible strategies that students use: count all, count on, recalled fact, derived facts. Revisit the lesson’s objective connecting their sharing with the purpose.




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DAY 5: LESSON 1.5

TE pages 11A, 11-12, & 12A LESSON FOCUS: Add 0 CALIFORNIA STANDARD:


Purpose of Lesson: To solve addition stories adding zero. ROUTINE Materials: • Number line, hundred chart

Suggestion - Quick Review: TE, pg. 11 Use Calendar, Number Line, Hundred Chart, and Choral Counting.

LAUNCH • Materials; Two color counters

Daily Routine: TE, pg. 11A Ask: “What does zero mean?”

EXPLORE Materials: For partners – • Workmat 2 (p.TR 114) • ten 2-color counters • paper

Advance Learners, TE 12A • Students use the workmats and counters to pose problems to each other that involve adding 0 to a number. • Number sentences should be of two kinds: number + 0 = and 0 + number = • Model the activity and have children follow along. • Avoid providing arbitrary-sounding rules such as “Whenever you add zero, you get the same number back.” It is always better to have a good discussion through a story problem and models. Then have children pose problems to each other. Invite them to make up stories to go with their number sentences. Write on the board 5=0+5 Ask: Is this number sentence correct? Why or why not? (Children will need many opportunities to understand what equality means. Showing that the equal sign can come at the beginning of a number sentence is important in their development of this concept). Teach and Practice: TE, pg.11-12, pose problems orally instead of using worksheets. Make up word problems for students that match TE 11-12. Ask students to model and write number sentences that match word problems.

SUMMARIZE Summarize understanding of zero concept. Connect discussion with the purpose of the lesson

Homework Suggestion - Workbook, pg. 11-12



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MODULE 1: ADDITION AND SUBTRACTION CONCEPTS Chapter 2: Using Addition

DAY 6: LESSON 2.1 TE pages 18, 17A & IS90

LESSON FOCUS: Add in any Order CALIFORNIA STANDARD:


Purpose of Lesson: To discover and apply the Order Property ROUTINE Suggestions - Mixed Review and Test Prep: TE, pg. 18

Use Calendar, Number Line, Hundred Chart, and Choral Counting. Ask students to choose one of the number sentences and create a number story to go with it. or P.O.D.: TE, pg. 17A. Be sure the Number Line and Hundred Chart are visible to students to use as a tool for solving problems. How did you think about the problem to come up with that answer? Explain how you got your answer.

LAUNCH Materials: • counters

Getting Started: Show a set of counters on the overhead projector (dot cards could also be used). Ask children to say the addition name for the quantity shown. For example: Show:

“2 plus 4” Have children pay attention to the mat as you turn it completely around.

(Again request the addition name.) “ 4 plus 2” Discuss which is more, “2 plus 4” or “4 plus 2.“ Will this work for other numbers? Generate the order rule from the students’ experiences. Notice that the order rule is not arbitrary but comes from the students and the model.

EXPLORE Materials: • Connecting cubes in 2 colors, paper for recording answers, number cubes labeled 1-4 & number cubes labeled 1-2, crayons If number cubes are not available make

Introduce Activity: Intervention Strategies Book; Skill 13 pg. IS90 only: “Alternative Teaching Strategy” (from DAY 1). This time, use two number cubes labeled 1-4. Ask students to circle pairs of number sentences that demonstrate the order property. Students work in pairs or small groups on Skill 13. Ask: “Which number sentence(s) do not have pairs? Why?” (Doubles such as 2+2 and 3+3 will not have a pair. If you change the order, the number sentence stays the same.)



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spinners found in Teacher Resource Book

Optional: Teach and Practice: TE, pg.17-18; Workbook 17-18

SUMMARIZE Discuss: How can the Order Property help us to remember our addition facts?” (If you know 2+3=5, you automatically know 3+2=5).

Homework Suggestion - Family Involvement Activities; pg. FA 5-6 Ask students to bring ten pennies from home in a baggie. You will start using the pennies on Day 8.



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DAY 7: LESSON 2.2 TE pages 19A & 20A

LESSON FOCUS: Ways to Make 7 and 8 CALIFORNIA STANDARD:


Purpose of Lesson: To identify combinations for the sums of 7 and 8 ROUTINE Suggestions: Quick Review - Ask students to solve 2+3, 3+2,

1+3, 3+1, 6+0, 0+6 Ask: How are these problems alike, different? Ask students what they remember about the order property. Ask them to explain how it can help them with these problems. or Number of the Day: The number of the day is 7. Ask: What are ways to show for 7? Include number sentences such as 7+0, 3+4, 7-0 (Be sure to write them both horizontally and vertically so that students get used to seeing both ways). Also encourage thinking beyond number sentences such as 7 tally marks, 7 cents, 7 cookies, 7 o’clock, my sister’s age, etc. Each day, while doing Routines, continue to ask students to use Calendar, Number Line, Hundred Chart, and Choral Counting. or P.O.D.: TE, pg. 19A Each day while doing Problem of the Day, continue to keep the Number Line, Hundred Chart visible and connecting cubes available to students to use as a tool for solving problems. Continue questioning each day: How did you think about the problem to come up with that answer? Did anyone think about it another way? Explain how you got your answer.

LAUNCH Materials: • Paper and pencil

Alternative Teaching Strategy, TE 20A Help 7 children arrange themselves in 2 groups. Record the addition sentence that describes the arrangement. Ask the children to rearrange themselves in other groups to make as many different combinations of 7 as they can. Record the addition sentences and talk about the different combinations of 7 for each arrangement.

EXPLORE Materials: • For each small group 7 red and 7 blue connecting cubes, 2 sheets of 3/4-inch Grid Paper

Addition Combinations - TE, pg. 19A • Use connecting cubes to model combinations for 7. • Challenge children to work in pairs to find as many different combinations as they can using 7 cubes. • Ask them to build a new cube train for each new combination. • Have them color a sheet of grid paper to show each combination they find. • Next, have children add an eighth cube to their piles.



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(p.TR101) red and blue crayons

• Ask them to use the combinations for 7 as the basis for counting to 8. • After they have found the combinations, invite them to work together to order the combinations on a second sheet of grid paper so that the graph looks like a staircase. Refer to picture on pg. 19A.

SUMMARIZE ASK: How do you know when you have found all of the combinations? If you know the combinations for 7, can that help you find combinations for 8?

Homework Suggestion: Problem Solving Master 2.2



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MODULE 1: ADDITION AND SUBTRACTION CONCEPTS

Chapter 2: Using Addition DAY 8: LESSON 2.3

NOTE: This lesson introduces ten-frames. When using ten frames, students will need to know that they always fill the top row first, starting on the left, the same way as you read. When the top row is full, counters can be placed on the bottom row, also from the left. Ten-frames can be surprisingly problematic for students because students must reflect on the two rows of five, the spaces remaining, and how a particular number of dots is more or less than five. It is suggested that you incorporate ten-frames into routines to provide additional practice. Suggestions for routines are given at the end of the lesson. LESSON FOCUS: Ways to Make 9 and 10 CALIFORNIA STANDARD:

Number Sense: 1.3 Represent equivalent forms of the same number through the use of physical models, diagrams, and number expressions (to 20).

Purpose of Lesson: To identify combinations for sums through 10 ROUTINE Suggestions: Mixed Review and Test Prep: TE, pg. 22

or Number of the Day: 8 Ask: What are other ways to show 8?

LAUNCH Materials: • For each student- Workmat 7 (p.TR119) 10 two color counters

Do the “Problem-Solving” TE, pg.22. In the space to the right, ask students to draw a picture to show their thinking. Ask students to share their drawings. Then introduce Workmat 7 (Ten frame) as one more way to show thinking. Ask: What do you notice about this frame? Each child has a 10 frame. Call out numbers between 5 and 10. The children respond by saying how many more are needed to make 10. This ten-frame activity can also be used as a daily routine. For students who are having difficulty with this task, begin with a five-frame, call out numbers between 1 and 5, and ask students how many more are needed to make 5 (a five frame model follows this lesson in the module). Do Teach and Practice TE 22-23. Students use workmats and counters to find combinations for 9 and 10.

EXPLORE Materials: • For partners – cup. 10 pennies

Introduce Activity: “Hide the Pennies” • Directions: Partners play this game with a cup and 10

pennies. You may increase or decrease the amount of pennies depending on the instructional level of the students.

• Players take turns. Player 1 turns the cup upside down, hides some of the pennies under the cup, and places the rest of the pennies on top of the cup. Player 2 counts the pennies on top and states how many are hidden



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underneath. If the amount is correct, Player 2 gets a point. Players then trade roles.

• Players keep a tally of their points. The player who has the most points after 5 rounds wins the game.

• If students are having difficulty, give them a copy of the ten frames from Teacher’s Resource Book, pg. TE63. They can put the pennies from the top of the cup into the frames and count the remaining squares.

Students work in pairs on Hide the Pennies. Note: Keep pennies in class to use as counters in lessons throughout the year.

SUMMARIZE Discuss and Write: Tell me everything you know about ten. Homework Suggestion: Teach someone at home to play Hide the Pennies *The following routines using ten frames build key number concepts: spatial relationships, part-part whole relationships, anchors of 5 and 10.

1. Showing 10. Students will need to have a ten frame and counters for this activity. Begin by calling out a number between 0 and 10. Children make the number you call out and respond with the amount needed to make a total of ten. This is most effective with numbers between 5 and 10.

2. Five-and. Students will need to have ten frames and counters. Begin by calling

out a number between 5 and 10. Students respond “five and_____ using the appropriate number. For example, if you say,” Seven”, students respond “five and two”.

3. 10 Frame-Flash: You will need to prepare in advance ten frames that show

different quantities. Begin by flashing the ten frames to the class and see how fast the students can tell how many dots are shown. This routine can be varied by: 1) asking the students to say the number of empty spaces rather than the number of dots; 2) Asking students to say one more/ two more than the number of dots.

* From John A. Van DeWalle, Elementary and Middle School Mathematics: Teaching Developmentally, 4/e. Published by Allyn and Bacon, Boston, MA. © 2001 by Pearson Education. Reprinted by permission of the publisher.



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Five Frames



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Chapter 2: Using Addition

DAY 9: LESSON 2.4 TE pages 23A, 23 – 24

LESSON FOCUS: Vertical Addition CALIFORNIA STANDARD:


Purpose of Lesson: To write vertical addition sentences and to understand the similarities/differences between vertical and horizontal addition sentences.

ROUTINE Suggestion: P.O.D.-TE, pg. 23A Change Questions to: “Who has more marbles? How do you know? How many more does Jody have? Explain your thinking.”

LAUNCH Materials • For partners – 9 red and 9 blue connecting cubes

Do Getting Started: Model addition sentences, TE 23A • Have children make a cube train that models an addition

sentence such as 6+3=9. • Point out that the cubes are horizontal from left to right. • Then have children make a tower and say the number

sentence holding the tower first horizontally and then vertically.

• Then ask children to make a cube train that helps them solve 4+5=9.

• Have children write the problem horizontally. • Then have them turn the train vertically and write the

problem vertically. Ask: How are these number sentences alike? Different? Does the answer change if you write the problem one way or the other? You might also point out that the problems could be written 9 = 4+5 to help them better understand the role of the equal sign as meaning “ the same as.”

EXPLORE Materials: • For each child 3 to 5 index cards, markers

Alternative Teaching Strategy, TE 24A Write an addition sentence vertically on each card. Ask children to draw circles to show each addend and count the circles to find the sums. Is this the same number as the answer in the addition sentence? If it is, ask the children to read the addition sentences to each other.

SUMMARIZE Discuss and Write: TE, pg. 24 Homework Problem Solving Master 2.4



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DAY 10: LESSON 2.5 TE pages 25A, 25 -26

LESSON FOCUS: Problem Solving: Make a Model CALIFORNIA STANDARD:

Mathematical Reasoning 1.2: Use tools, such as manipulatives or sketches to model problems.

Purpose of Lesson: To use the strategy make a model to solve story problems about money to 10 cents.

ROUTINE Suggestions: Quick Review - TE, pg. 25 Number of the Day: 0 Ask: What are some other ways to make 0? or P.O.D.: TE, pg. 25A

LAUNCH Materials • For partners- a variety of classroom objects, such as pencils, markers, block, 10 pennies • For the teacher- self-stick notes

Getting Started: Modeling Problem Solving: TE pg. 25A • Have partners gather a variety of small classroom objects,

masking tape, blocks. • Use self-stick notes to attach price tags from 1¢ to 8¢ to

each item. • Give partners 10 pennies and tell them they need to buy 2

objects with their money. • Help them see that the total cost of the 2 items must add up

to 10¢ or less. • Have them select the 2 items they think they can buy and

draw pennies to show the price of each item. • Discuss how they could check their answers.

EXPLORE Teach and Practice: TE, pg. 25-26; Workbook, pg. 25-26. Encourage students to work with real pennies when completing workbook pages as well as drawing pictures. Students work in pairs on Hide the Pennies from Day 8. Increase or decrease the number of pennies students worked with on Day 9 depending on levels of understanding.

SUMMARIZE Suggestion: Discuss and Write - TE pg. 26 Connect discussions with the purpose of the lesson.




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MODULE 1: ADDITION AND SUBTRACTION CONCEPTS Chapter 3: Subtraction Concepts

DAY 11: LESSON 3.1 NOTE: This is the first lesson on subtraction. “For subtraction facts, the concept think addition is the most important idea. What goes with this part to make the total? When children see 5-3, you want them to think spontaneously, “three and what makes five?” When done in the think-addition manner, the child uses known addition facts to produce the unknown quantity or part.” (from Van De Walle, Elementary and Middle School Mathematics, Teaching Developmently. Allyn and Bacon. Boston, MA. © 2001 by Pearson Education.) LESSON FOCUS: Subtraction Stories CALIFORNIA STANDARD:

Number Sense 2.5: Show the meaning of addition and subtraction.

Purpose of Lesson: To model subtraction ROUTINE Suggestion: Mixed Review and Test Prep: TE, pg. 32

or Problem of the Day: 1 P.O.D.: TE, pg. 31A Make pennies available as a tool for problem solving.

LAUNCH Materials: • For each child – six 2 color counters

Getting Started: How Many Are Left?: TE pg.31A After the first two bullets, make a connection to addition. For example: “Two lions are left. The two that went away come back. Now how many in all?” Write both number sentences on the board: 4 – 2 = 2 2 + 2 = 4 What is the same about these number sentences? What is different? Change the third bullet to a question: How can you find out how many are left? Some may respond, “I counted.” Others may respond, “I saw three were left.” Or “ I pictured how many were left in my head.” Or something else altogether. Ask the class to practice the strategies the students offer with more problems.

EXPLORE Materials: • Small paper bag, 5 to 6 cubes/ manipulatives Pencil, paper

Introduce Activity: Intervention Strategies and Activities, Skill 27, pg. IS152 only: Alternative Teaching Strategy Students work in pairs on Skill 27. You may increase or decrease the amount of counters based on instructional levels of students. Optional: Teach and Practice: TE, pg. 31-32; Workbook, pg. 31-32.

SUMMARIZE Discuss and Write: When you were working on subtraction today, how did you figure out how many were left? Did anyone do it another way?

Homework Suggestion: Family Involvement Activities pg. FA 9-10



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DAY 12: LESSON 3.2

TE pages 33A, 33 & 34 LESSON FOCUS: Subtract With Pictures CALIFORNIA STANDARD:


Purpose of Lesson: To identify how many are left when subtracting ROUTINE Suggestion: Quick Review: 2+4=, 4+2=, 6-4=, 6-2= or

Number of the Day: 2 or P.O.D.: TE, pg. 33A

LAUNCH Getting Started: Literature Connection TE pg. 34 from Read Aloud Anthology AN6

EXPLORE Materials: • For each student – 6 connecting cubes

Intervention Strategies and Activities, Skill 27, pg. IS152 only: Alternative Teaching Strategy Students work in pairs on Skill 27. You may increase or decrease the amount of counters based on instructional levels of students. Teach and Practice: TE, pg.33-34; Workbook, pg. 33-34 • Introduce these problems orally first. Putting action into the problems is a way to give more students access. For example, “ I have 4 soccer balls and I gave two of them to my friend. How many do I have now?” • You might also introduce different problem types to encourage strategy development. “I have 4 soccer balls. I lost some of them. Now I only have 2. How many did I lose?” or “Children were playing soccer. 6 were boys and the rest were girls. How many girls were playing soccer?”

SUMMARIZE Discuss and Write: TE pg. 34 Ask: What strategies can you use to solve 5 – 2 = ? You may want to emphasize the think-addition strategy if students don’t bring it up.

Homework Suggestion: Family Involvement Activities pg. FA11.



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DAY 13: LESSON 3.3 TE pages 35A & 35-36

LESSON FOCUS: Write Subtraction Sentences CALIFORNIA STANDARD:

Algebra and Functions 1.0: Students use number sentences with operational symbols and expressions to solve problems.

Purpose of Lesson: To find differences by writing subtraction stories. ROUTINE Suggestion: Mixed Review and Test Prep - TE, pg. 36 or

Number of the Day: 3 LAUNCH P.O.D.: TE, pg. 35A

Note: This problem does not have to be solved using subtraction. It is possible that the student could use the strategy of counting on to solve (thinking addition). Both approaches should be accepted. Make the connection to the symbolic representation for both: 5 – 2 = 3

EXPLORE Do Problem Solving/Visual Thinking (pg. 36) and Problem Solving 3.3. • Pose the problems orally first. • Encourage the think addition strategy for subtraction. • You may want to reframe some of the questions to include

different problem types that would encourage students to develop strategies. For example: “Pete has 5 balloons. He loses some of them and they fly away. Now he has only 2. How many flew away?” “Mia has 4 balloons. 3 of them are red and the rest are yellow. How many yellow balloons does she have?”

Optional: Reteach Master 3.3. SUMMARIZE Discuss and Write: “Explain using words, pictures or numbers

how subtraction sentences are alike and how they are different.” Homework Suggestion: Teach and Practice

TE, pg. 35-36; Workbook, pg. 35-36. or Family Involvement Activities pg. FA12



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DAY 14: LESSON 3.4 TE, pg. 37A, 37 & 38A

LESSON FOCUS: Problem Solving: Make a Model CALIFORNIA STANDARD:

Mathematical Reasoning 1.2: Use tools, such as manipulatives or sketches, to model problems.

Purpose of Lesson: To solve subtraction problems by using the strategy make a model.

ROUTINE Suggestion: Quick Review - TE, pg. 37 or Number of the Day: 4 or P.O.D.: TE, pg. 37A Note: This problem does not have to be solved using subtraction. It is possible that the student could use the strategy of counting on to solve (think addition). Both approaches should be accepted.

LAUNCH Introduce Activity: Early Finishers: Students act out subtraction stories; TE, pg. 38A • Have the children work in groups of 3 to 5. • Each group takes a subtraction sentence card and the

children make up a story that illustrates the subtraction sentence.

• Each group acts out the illustrated story. • Other groups decide what the subtraction sentence should

be. The group acting out the story holds up the subtraction sentence card they started with.

EXPLORE Introduce Activity: Advanced Learners: • Students make up subtraction stories; TE pg. 38A • Have children listen to problems such as the following and

draw pictures to solve problems : “Seven apples are on a tree. Three fell off the tree. How many are left on the tree?”

• Have children write the subtraction sentence for each picture.

SUMMARIZE Discuss and Share: Students share their stories with the class asking classmates to solve the subtraction problem. Ask: What did you learn today about subtraction? Connect discussions with the purpose of the lesson.




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DAY 15: LESSON 3.5 TE pages 39A & 40

LESSON FOCUS: Subtract All or None CALIFORNIA STANDARD:

Number Sense 2.5 Show the meaning of addition and subtraction.

Purpose of Lesson: To identify how many are left when subtracting all or none. ROUTINE Mixed Review and Test Prep: TE, pg. 40

Number of the Day: 5 LAUNCH P.O.D.: TE, pg. 39A

Getting Started: Model Subtracting All or None: TE pg.39A. EXPLORE Materials: • For partners – 10 section Spinner labeled 1-10 (p. TR106) ten 2-color counters

Game Centers: Set up student-choice stations for • Skill 13: IS90 • Skill 14: IS94 • Skill 27: IS152 • Hide the Pennies: Day 8 • Read class book of subtraction stories. • Other math games/activities your students enjoy.

All of the centers listed above are activities students have previously experienced. Review the stations, then establish your guidelines for station time. For example: • No more than 4 students per station. • Use inside voices. • How to handle disagreements, etc. While students are at stations, call small group back for Facts Practice 40A Have one partner spin the pointer. Optional: Teach and Practice: TE, pg. 39-40; Workbook, pg. 39-40.

SUMMARIZE Use ELL/SDAIE Strategy TE40. Ask children to role-play with a small group to act out what is happening when all or none are subtracted from a number. Encourage students to use math vocabulary while acting out the scene. ASK: What do you know about subtracting with zero? Connect discussions with the purpose of the lesson.




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Chapter 4: Using Subtraction

DAY 16: LESSON 4.1 TE pages 45, 45A

LESSON FOCUS: Take Apart 7 and 8 CALIFORNIA STANDARD:


Purpose of Lesson: To model subtraction combinations for 7 and 8 and to complete the subtraction sentences.

ROUTINE Quick Review: TE, pg. 45 or Number of the Day: 6 or P.O.D.: TE, pg. 45A Encourage students to act out the number sentences.

LAUNCH Materials • For each child – connecting cubes in 5 colors

Combining Cubes – • Direct children to build the following stacks of cubes:

a red stack of 2; a yellow stack of 1; a blue stack of 3; a green stack of 4; an orange stack of 2.

• Ask students to pick up 5 cubes. They may pick up any combination of cubes to make five, but they may not take stacks apart or stack cubes on top of one another. For example, tell the students to pick up 6. The students might respond, “ I picked up the red 2 and the green 4.” Ask if anyone did it a different way? (Activity adapted from Kathy Richardson, Developing Number Concepts, 1999, pp. 112-113).

EXPLORE Materials: • Collections of 7 & 8 objects in bags or other containers, Paper, pencil for each

Introduce Activity: Intervention Strategies and Activities, Skill 29, pg. IS160 only: Alternative Teaching Strategy Direct students see how many ways they can take apart 7. You may adjust the amount of counters based on instructional levels of students. Instruct them to record their work on scratch paper either with pictures or subtraction sentences or both. Students work individually on Skill 29. Share strategies you observe. Ask: “How many ways did you find to take apart 7? 8? Do you think there are any more? Why or why not?”

SUMMARIZE Discuss and Write: What strategy did you use to take apart 7? 8? Did anyone use a different strategy? Is there another strategy that would work?

Homework Suggestion: Workbook, pg. 45-46



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MODULE 1: ADDITION AND SUBTRACTION CONCEPTS Chapter 4: Using Subtraction

DAY 17: LESSON 4.2 TE pages 47A-47 & 48

LESSON FOCUS: Take Apart 9 and 10 CALIFORNIA STANDARD:


Purpose of Lesson: To model subtraction combinations for 9 and 10 and to complete the subtraction sentences

ROUTINE Suggestions: Quick Review: TE, pg. 47 Number of the Day: 7 P.O.D.: TE, pg. 47A Use the Number Line to explore this pattern as it continues into negative numbers 7.

LAUNCH Materials: • For each child – 10 connecting cubes

Alternative Teaching Strategy, 48A • Tell children a subtraction story problem that uses the

numbers 9 or 10. • Ask children to model the problem with connecting cubes.

For example, a story problem for 9 may be this: “I had 9 pennies and gave my brother 2 of them. How many do I have left?”

• Ask children to model the problem using connecting cubes. EXPLORE • For the teacher_ Subtraction Fact Cards (pp. TR 49 – 62) • For each student – 10 two color counters, 3 Ten Frames sheets (p. TR63)

Variation of Model Subtraction Combinations: TE pg.47A. • Students work in small groups. • Have each group fill a ten frame with counters. One of the

ten frames will be used to record answers; the others are for modeling the problems.

• Shuffle fact cards, draw a card and read the problem. • Students take turns modeling the problem with counters on

their ten frames to find the difference and then coloring in the answer on the second ten frame.

• Choose a new card, read it and have children again take turns solving the problem removing counters from their ten frames, and coloring in the answer square.

• Continue until all groups have 5 squares colored. • Make sure to connect the subtraction fact using the think-

addition strategy. • Repeat for subtraction facts with 9.

SUMMARIZE Discuss and Write: TE pg 48 ASK: How did you solve the subtraction problems? Note: The problems presented in this lesson do not have to be solved through the take-away method. Some students might think, “What do I have to add to 9 to make 10 (10-9=?)” Both approaches are to be accepted.

Homework Suggestion: Workbook, pg. 47-48. pg. 47-48.



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DAY 18: LESSON 4.3

TE pages 49A, 49-50 & 50A LESSON FOCUS: Vertical Subtraction CALIFORNIA STANDARD:


Purpose of Lesson: To write and subtraction sentences vertically and horizontally. ROUTINE Quick Review: TE, pg. 49

or Number of the Day: 8 or P.O.D.: TE, pg. 49A

LAUNCH • Bingo Grid (master on next page) 10 counters For Teacher – Subtraction Fact Cards (pp. TR49-62)

Introduce Activity: Advanced Learners TE pg. 50A Modifications: • Have students create their own subtraction game mats by

using the black-line “Bingo Grid” master on the next page of the module.

• Display Subtraction Fact Cards. • Tell students to copy any 9 problems they want onto the

bingo grid. • Teacher draws a fact card without showing students. • Teacher makes up a number story to illustrate subtraction

sentence. • Students look for corresponding number sentence on game

board and place a marker if they have it.

EXPLORE Play Subtraction Bingo as a whole class activity. This may become a station activity for a small group with a student leader taking on the teacher’s role. Optional: Teach and Practice: TE, pg.49-50; Workbook, pg. 49-50.

SUMMARIZE Ask students to summarize the difference between vertical and horizontal subtraction problems. ASK: Does it matter which way we write the subtraction problem? Why or why not?

Homework Suggestion: Problem Solving 4.3



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DAY 29: LESSON 4.4 TE pages 51A, 52

Note: This lesson introduces subtraction through using the comparison model, rather than through take-away or separate from model. In Children’s Mathematics: Cognitively Guided Instruction (Carpenter, Fennema, Franke, Levi, Empson, 1999) researchers identified 3 types of comparison problems: • John has 10 marbles. Ray has 6 marbles. How many more marbles does Ray have? • John has 10 marbles. Ray has 4 more marbles. How many marbles does Ray have? • Ray has 10 marbles. He has 4 more marbles than John. How many marbles does John

have? These types of problems are inherently more challenging to students. In their early understandings of number concepts, young children often make meaning of comparison problems through the use of a matching strategy. They may line up each set and match one-to-one until one set is used up. The answer is the number of unmatched objects remaining in the larger set. Other children might solve it by counting on, or through counting down to. What is important to note is that young children must be able to make sense of the problems they are working with and therefore we must acknowledge that answers can be derived in a variety of ways. Some variations of the Problems of the Day have been included in the next few lessons to provide more opportunities for students to work on these problem types.

LESSON FOCUS: How Many More? CALIFORNIA STANDARD:


Purpose of Lesson: To model and record comparison subtraction situations. ROUTINE Mixed Review and Test Prep: TE, pg. 52 or

Number of the Day: 9 LAUNCH Materials: For each child -Connecting cubes

P.O.D.: TE, pg. 51A Note: not all students will solve this problem through take away. It is possible to solve this problem with the strategy of adding on to two until the total of 8 is reached. Both strategies are mathematically appropriate. Students share how they thought about and solved the problem.

EXPLORE Materials: • For Partners – paper bag, nine 2 color tiles, 1-inch Grid Paper (p.TR100)

Introduce Activity: Model Subtracting to Compare: TE pg. 51A Students work in pairs. Have students share how they approached and solved the problems. Ask: “How could you tell which color had more tiles? How did you figure out how many more? Did anyone do it a different way?” Optional: Partner Activity - Advanced Learners: TE pg. 52A

SUMMARIZE ASK: How did you solve this problem? Make sure to highlight the strategies that students used to solve this problem.

Homework Suggestions: Workbook, pg. 51-52 or Problem Solving Master 4.4.



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DAY 20: LESSON 4.5 TE pages 54, 53A & 53

LESSON FOCUS: Use Subtraction CALIFORNIA STANDARD:

Number Sense 2.1: Know the addition facts (sums to 20) and the corresponding subtraction facts and commit them to memory. [Number Sense 2.2: Use the inverse relationship between addition and subtraction to solve problems.]

Purpose of Lesson: To find differences and sums through ten and to show how subtraction and addition are related to each other in fact families.

ROUTINE Suggestions: Mixed Review and Test Prep: TE, pg. 54 On #5 Ask: What is the addition sentence? If they use Ali’s apples to make a pie, how many apples are left? What is the subtraction sentence? How are these two number sentences the same? How are they different? or Number of the Day: 10 Compare today’s strategies with the strategies students chose on day 10. Ask: “What does this tell us about what we are learning about numbers?” or P.O.D.: “Arjay has 4 books. Ivan has 10 books. How many more books does Ivan have?”

LAUNCH Getting Started: Vocabulary Development: TE pg. 53A Questions: • How can we use this group of 3 and this group of 4 to write

an addition sentence? • What is the sum? • What if we switch the order of the cubes to 4 first, then 3?

Did the sum change? If you know one fact then you know three more facts automatically because 3, 4, and 7 are part of the same fact family.

• Can we use the same numbers to write subtraction problems?

Note: • Make sure to model the action of each subtraction problem. • It is not uncommon for students to write “turn around” facts

for subtraction: if 7 – 4 = 3 they think 4 - 7 = 3. • Instead of giving students arbitrary rules such as “You can’t

subtract a bigger number from smaller number,” directly model the action of the problem so that the reasoning becomes apparent as to why 4 - 7 in not possible using the set of natural numbers.

• Take 2 cubes and 1 cube. How can we write four facts



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using these cubes? What are the 3 numbers in this fact family. Give several more examples.

EXPLORE Materials: • For each student - blank paper

Teach and Practice: TE, pg. 53 Modification: • Direct students to fold a piece of blank paper into 6 parts. • Instruct students to number each part 1 through 6. • Ask them to write the addition sentences that correspond

with the subtraction sentences on page 53. • (Make sure to stress the Think Addition strategy when

posing these problems.)

SUMMARIZE Discuss and Write: How are the numbers 8, 2, and 6 related to each other? Draw pictures to show your thinking.

Homework Study Guide and Review: TE, pg. 59-60, Workbook pg. 59-60



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DAY 21: Module 1 Assessment LAUNCH Review center games and guidelines. EXPLORE Game Stations: Choose from the activities below to create

stations where your students can practice skills independently while you observe and take anecdotal records.

• Skill 13: IS90 • Skill 14: IS94 • Skill 15: IS98 • Skill 27: IS152 • Hide the Pennies: Day 8 • Skill 29: IS160 • Subtraction Bingo: Day 19 • Other math games/activities your students enjoy

ASSESS Refer to: • What to Observe

for questions at beginning of module

• Performance Assessment Guide

• Assessment Guide

While students are practicing skills at game stations, take this opportunity to assess individuals or small groups by the means you deem most appropriate. You may want to use the questions that were listed at the beginning of the module to guide observations and anecdotal notes.

SUMMARIZE Discuss: What was your favorite activity today? Explain why and what you learned.



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DAY 22: Module 1 Problem Solving Workshop

LAUNCH Suggestion: Performance Assessment: Task A pg. PA3 Problem Solving Workshop Model for Instruction (Making Sense: Teaching and Learning Mathematics with Understanding/James Hiebert…[et al.]; 1997 by the University of Wisconsin Foundation):

• Teacher provides problem. • Students work with a group, with a partner or individually

to solve the problem. • Students present methods to peers and teacher.

Methods are discussed. • Teacher provides suggestions for notation and

terminology when necessary, but does not demonstrate solution method.

• Students use mathematical reasoning to determine correctness of peers’ methods and solutions.

NOTE: This problem utilizes the format of “start unknown” ( + 3 = ? ). These problems are inherently more difficult for children. Typically, children will only be able to solve it with the strategy of guess and check. You may want to restate the problem so that it is either a result unknown (Larry placed 3 bears on the shelf. Jasmine placed 3 more bears on the shelf. How many bears are on the shelf now?) or change unknown ( Larry placed 3 bears on the shelf. Jasmine placed some more bears on the shelf. Now there are 6 bears on the shelf. How many bears did Jasmine place on the self? ) You can use the black-line master on the next page of the module as an alternative.

EXPLORE Students work on solving the problem independently. Provide students with a variety of manipulatives they are accustomed to working with: two colors of connecting cubes, counting bears, 2-colored counters, etc. Observe and take anecdotal records. Refer to What to Observe For at beginning of Module 1 (see pg. 5). As students complete problem, they continue work at the Game Centers as you observe and take anecdotal records.

ASSESS Continue with assessment options.

SUMMARIZE Discuss: Why is it important that we learn to use addition? When do we need to use addition?



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Name_____________________________________________

Larry and his sister Jasmine were playing with bears from their toy box. • Larry placed 3 bears on the shelf. • Jasmine placed 3 more bears on the shelf. • How many bears are on the shelf now? Write an addition number sentence from this math story. Draw pictures to help you. Show your work



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DAY 23: Module 1 Problem Solving Workshop LAUNCH Discuss the problem from Day 22 using transparencies of

student work. Have students discuss their strategies. EXPLORE Game Centers:

Observe and take anecdotal records. ASSESS Continue with assessment options. SUMMARIZE Discuss and Write:

Why is it important that we learn to subtract? When do we need to use subtraction?

Homework Workbook: pg.57.



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DAY 24: Module 1 Problem Solving Workshop

LAUNCH Materials: • For group -Two-color counters or cube

Introduce Activity: Performance Assessment: Task B pg. PA4 Problem Solving Workshop Model for Instruction (Making Sense: Teaching and Learning Mathematics with Understanding/James Hiebert…[et al.]; 1997 by the University of Wisconsin Foundation):

• Teacher provides problem. • Students work with a group, with a partner or individually

to solve the problem. • Students present methods to peers and teacher.

Methods are discussed. • Teacher provides suggestions for notation and

terminology when necessary, but does not demonstrate solution method.

• Students use mathematical reasoning to determine correctness of peers’ methods and solutions.

NOTE: This problem utilizes the format of “start unknown” ( - 2 = ? ). These problems are inherently more difficult for children. Typically, children will only be able to solve it with the strategy of guess and check. You may want to restate the problem so that it is either a result unknown (Jenny placed 5 jacks in a circle. Ann picked up 2 jacks from the circle. How many jacks are left in the circle?) or change unknown/missing addend (Jenny placed 5 jacks in the circle. Ann picked some of the jacks up. Now there are only 3 jacks left in the circle. How many jacks did Ann pick up?)

EXPLORE Students work on solving the problem independently. Provide students with a variety of manipulatives they are accustomed to working with: two colors of connecting cubes, counting bears, 2-colored counters, etc. Observe and take anecdotal records. As students complete problem, they continue work at the Game Stations as you observe and take anecdotal records.

ASSESS Continue with assessment options. SUMMARIZE Discuss:

“How does knowing 4 + 2 = 6 help you know that 6 – 2 = 4?

Homework Suggestion: Workbook: pg.58



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DAY 25: Module 1 Problem Solving Workshop LAUNCH Discuss the problem from Day 24 using transparencies of

student work. EXPLORE Game Centers:

Observe and take anecdotal records. ASSESS Continue with assessment options. SUMMARIZE Discuss and Write: What have you learned about math this

year that you didn’t know in Kindergarten? Homework Suggestion: Workbook: pg.A-J

Documents

California Edition Grade 1 - eusddata.pbworks.comeusddata.pbworks.com/f/1mod01.pdf · California Edition Grade 1 Module 1 - Revised Addition and Subtraction Concepts - WORK IN PROGRESS