module 4 - revised

REVISED 10/6/03 80

SAN DIEGO CITY SCHOOLS

Instructional Module to Enhance the Teaching of

H A R C O U R T

Math

California Edition

Grade 2

Module 4 - Revised

2-Digit Addition and Subtraction

– WORK IN PROGRESS –

Harcourt Math – Grade 2 MODULE 4

Revised 10/6/03 81

Harcourt Math – Grade 2

MODULE 4

2-Digit Addition 16 Days

Key Mathematical Concepts:

• Count on • Add tens • Add one and two digit numbers • Estimate sums • Use mental math • Solve a problem by using an appropriate strategy

Chapter 11 Explore Two-Digit Addition Lesson 11.1: Add Tens Lesson 11.2: Count on and Tens and Ones Lesson 11.3: Adding One to Two-Digit Numbers Lesson 11.4: Two-Digit Addition Lesson 11.5: Problem Solving: Make a Model

Chapter 12 Two-Digit Addition Lesson 12.1: Add Two-Digit Numbers Lesson 12.2: More Two-Digit Addition Lesson 12.3: Vertical and Horizontal Problems Lesson 12.4: Problem Solving: Estimate Sums

Chapter 13 Practice Two-Digit Addition Lesson 13.1: More Two-Digit Addition Lesson 13.2: Using Mental Math to Find Sums Lesson 13.3: Adding Two-Digit Numbers Lesson 13.4: Problem Solving: Make and Use a Graph Lesson 13.5: Problem Solving Lesson 13.6: Problem Solving

Chapter 13 Practice Two-Digit Addition Assessment

Day 1 Unit 11 Lesson 11.1















Day 16 Unit 13 Assessment


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Grade 2 Order of Units

2003-2004 School Year TRADITIONAL CALENDAR

September October

Module 1: Addition and Subtraction Strategies and Facts,

Place Value, and Graphing. Chapters 6, 1-4, 5

25 days

October

Module 2: Geometry Chapters 17 and 18

11 days

October

November

Module 3: Money and Time Chapters 7 and 9

12 days

November

Module 4: 2-Digit Addition Chapters 11-13

16 days

December

Module 5: Measurement Chapters 19 and 20

13 days

January February

Module 6: 2-Digit Subtraction Chapters 14 - 16

20 days

February

Module 7: Number Sense and Fractions Chapters 21 and 22

10 days

February March

Module 8: Multiplication and Division Chapters 28 - 30

15 days

March April

Module 9: 3-Digit Addition and Subtraction Chapters 25 and 26

16 days

April Module 10: Number Sense and Fractions Chapters 23 and 24

11 days

April May


11 days

May Module 12: 3-Digit Addition and Subtraction Chapter 27

10 days

Days to be used throughout the year (at teacher’s discretion) when more time is necessary to make meaning of a concept.

11 days


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GRADE 2 Order of Units

2003-2004 School Year YEAR ROUND CALENDAR

September October

Module 1: Addition and Subtraction Strategies and Facts,

Place Value, and Graphing. Chapters 6, 1-4, 5

25 days

October

Module 2: Geometry Chapters 17 and 18

11 days

October

November


12 days

November

Module 4: 2-Digit Addition and Subtraction Chapters 11-13

16 days

December

Module 5: Measurement Chapters 19 and 20

13 days

January February

Module 6: 2-Digit Addition and Subtraction Chapters 14 - 16

20 days

February March


10 days

March April

Module 8: Multiplication and Division Chapters 28 - 30

15 days

April May

Module 9: 3-Digit Addition and Subtraction Chapters 25 and 26

16 days

May June


11 days

May June


11 days

June July

Module 12: 3-Digit Addition and Subtraction Chapter 27

10 days

Days to be used throughout the year (at teacher’s discretion) when more time is necessary to make meaning of a concept.

11 days


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DAY 1: Chapter 11: Explore Two-Digit Addition

LESSON 11.1 TE P. 157A

LESSON FOCUS: Add Tens CALIFORNIA STANDARD:

Number Sense: 2.0 Students estimate, calculate, and solve problems involving addition and subtraction of two- and three-digit numbers.

Purpose of Lesson: Understand the relationship between adding groups of ones and adding the same groups of ten.

Routine Materials: • quart jar filled/half-filled with objects or other manipulatives

Suggestion: Making Estimates Continue using the quart jar Fill or half-fill with different materials. Continue procedure.

LAUNCH Materials: • One/Tens Relationships overhead

Introducing: Ones/Tens Relationships • Have a class discussion about the following pairs of

equations. • Let students use models/manipulatives (ten frames, base

ten materials, connecting cubes trains of tens, etc.) to confirm.

• How does knowing… Help you to know… 4 + 3 4 tens + 3 tens 40 + 30 2 + 6 2 tens + 6 tens 20 + 60 4 + 5 4 tens + 5 tens 40 + 50 1 + 4 1 ten + 4 tens 10 + 40

EXPLORE Materials: • One/Tens Relationships worksheet

Ones/Tens Relationships • Have students build their own table, inserting their own

numbers. • Have them choose one or more equation pair about which

to write a convincing argument. Knowing… Helps me to know…


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PRACTICE As time allows: pages 157 and/or 158 SUMMARIZE Closure:

• Revisit purpose of the lesson with students. • See ASSESS, TE, P. 158: How does knowing 3 + 4 help

you solve 3 tens + 4 tens? HOMEWORK Materials: • 100 chart (P. TR 33) • index cards/slips of paper

Suggestion: See Alternative Teaching Strategy, TE, page 158A. Students make problems for themselves on index cards/slips of paper. They use the 100 chart to solve problems. Students write about how they used the chart. Students may: • Count out the first number by bones and count on the

second number by ones. • Start with a number and count on the second number by

ones or tens. • Start with the highest number and count on by ones or tens


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Ones/Tens Relationships

Knowing… Helps me to know…


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DAY 2: Chapter 11: Explore Two-Digit Addition


LESSON FOCUS: Count on Tens and Ones CALIFORNIA STANDARD:


Purpose of Lesson: Understand how to count on by tens and ones to a two-digit number.

Routine Materials: • base ten materials (a variety, including commercially available materials, bundles of sticks, beans and cups, and snap cubes)

Suggestion: Solving Problems • Give students a problem to solve:

Ms. Smith sent 17 students out to the playground. Mr. Brown sent 18 students out to the playground. How many students are out on the playground?

• To ensure that students understand what is happening in

the problem, ask volunteers to retell the story problem. • Discuss: what are ways that you could solve this problem?

Ask students to solve the problem using tools and strategies they understand. Make manipulatives available. Ask students to share their methods for solving the problem with the whole class.

• Chart students’ strategies. Discuss how to represent the problem in an equation. Record the equation horizontally.

When solving this join/result unknown problem, it is important that students use a method that makes sense to them. Some strategies students are likely to use include modeling the problem with materials (building the initial quantity, building the second quantity, joining them together and counting to find the final quantity) and counting (on from the initial or greater quantity). Students may also knowledge of number relationships (e.g., 18 + 10 = 28; 28 + 2 = 30; 30 + 5 = 35).


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LAUNCH Materials: • 100 charts, one per student (P. TR 33) • Traveling on the 100 Chart overhead

Introducing: Traveling on the 100 Chart • Students locate a start number on the 100 chart. They add

a given number. • Students locate the sum and a few report how they figured

out the ending number.

Start Add on 12 5 12 10 12 20 26 3 26 10 26 20 34 4 34 10 34 20 34 30 34 40

EXPLORE Materials: • Traveling on the 100 Chart worksheet

Traveling on the 100 Chart • Have students build their own table, inserting their own

numbers. • Have them give start and add on numbers to a partner;

partners share how they figured out the ending number. PRACTICE As time allows: pages 159 and/or 160: SUMMARIZE Closure:

• Revisit purpose of the lesson with students. • See Assess, TE, P. 160: How are 50 + 20 and 50 + 2

different? HOMEWORK Suggestion: See Advanced Learners, TE, Page 160A.

Students make up word problems that involve counting on by ones or tens (e.g., Marco gives me 23 jelly beans. Anita gives me 30 jelly beans. How many jelly beans do I have now?).


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Traveling on the 100 Chart

Start number Add On Stop number


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DAY 3 Chapter 11: Explore Two-Digit Addition


LESSON FOCUS: Adding One Digit to Two Digits CALIFORNIA STANDARD:


Purpose of Lesson: Generate ways of adding one-digit to two-digit numbers. Routine Materials: • coins • base ten materials (a variety, including commercially available materials, bundles of sticks, beans and cups, and snap cubes)

Suggestion: Number of the Day Encourage students to use money to represent the Number of the Day (e.g., 25¢ + 25¢ = 50¢, 10¢ + 10¢ + 10¢ + 10¢ + 10¢ = 50¢, 25¢ + 10¢ + 10¢ + 5¢ = 50¢). Have them prove their sum by recombining numbers. Suggestion: Solving Problems • Give students a problem to solve: 42 students were in the

cafeteria. 25 left to go on the playground. How many students are still in the cafeteria?

• To ensure that students understand what is happening in the problem, ask volunteers to retell the story problem.

• Discuss: what are ways that you could solve this problem? • Ask students to solve the problem using tools and

strategies they understand. • Make manipulatives available. • Ask students to share their methods for solving the problem

with the whole class. • Chart students’ strategies. • Discuss how to represent the problem in an equation. • Record the equation horizontally. When solving this separate/result unknown problem, it is important that students use a method that makes sense to them. While this appears to be a subtraction problem, some students may solve it using an addition strategy. Some strategies students are likely to use include modeling the problem with materials (building the initial quantity, separating out the second quantity, and counting to find the final quantity) and counting (back from the initial or on from the separated to the initial quantity). Students may also use knowledge of number relationships (e. g., 42 - 20 = 32; 32 - 5 = 27).


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LAUNCH Materials: • base ten materials (flats, longs and units) • two dice per small group • Workmat 3 (P. TR 116; optional).

Introduce: Race for a Flat Students discuss what they notice about the materials. • After they discover the value of each different type, talk

about the various names of the pieces: units/ones, longs/tens, flats/hundred.

• Take turns (model teacher against the class or one other student). Roll two dice and take that many units.


• Discuss: What can you do if you have more than 10 units? What number do you have now? How many more units do you need to make a trade? Pass the dice and continue playing. Each time, players make necessary trades before passing the dice. The first player to trade ten longs for one flat is the winner.

• Players first play two against two, to check for understanding of the game directions and ensure they are reporting the answers to the following: What number do you have now? How many more units do you need to make a trade?

EXPLORE Materials: • base ten materials (flats, longs and units) • two dice per small group • Workmat 3 (P. TR 116; optional)

Race for a Flat Students play Race for a Flat. Players first play two against two, to check for understanding of the game directions and ensure they are reporting the answers to the following: What number do you have now? How many more units do you need to make a trade?

PRACTICE Materials: • base ten materials (flats, longs, and units) • Workmat 3 (P. TR 116; optional)

As time allows: • Students work in pairs to locate an equation on page 161 or

162. Partners build the problem. • Students connect with their experience playing Race for a

Flat. They consider and discuss with their partner: Imagine you are playing Race for a Flat. You have the first addend and add the second addend on the next roll. • Would you need to trade? • How many longs/tens would you have? • How many units/ones would you have?

SUMMARIZE Closure: Revisit purpose of the lesson with students. You are playing Race for a Flat. You have 19 and you roll 12. What would you have? How do you know? Do you trade? How many? Are there any leftovers? How many? What equation could you write?

HOMEWORK Suggestion: Students record equations that are equal to today’s Number of the Day. Students write about the following: Would you say the Number of the Day if you were counting by 2s? 5s? 10s? How do you know?


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LESSON FOCUS: Two-Digit Addition CALIFORNIA STANDARD:


Purpose of Lesson: Use models to understand regrouping in addition. Routine Materials: • base ten materials (a variety, including commercially available materials, bundles of sticks, beans and cups, and snap cubes)

Suggestion: Solving Problems • Give students a problem to solve: Ms. Johnson had 14

pencils. Mr. Gomez gave her 28 pencils. How many pencils does Ms. Johnson have now?


• Discuss: What are ways that you could solve this problem?

• Ask students to solve the problem using tools and strategies they understand. Make manipulatives available.

• Ask students to share their methods for solving the problem with the whole class.

• Chart students’ strategies. Discuss how to represent the problem in an equation.

• Record the equation horizontally. When solving this join/result unknown problem, it is important that students use a method that makes sense to them. Some strategies students are likely to use include modeling the problem with materials (building the initial quantity, building the second quantity, joining them together and counting to find the final quantity) and counting (on from the initial or greater quantity). Students may also knowledge of number relationships (e.g., 28 + 10 = 38; 38 + 2 = 40; 40 + 2 = 42). Suggestion: Homework Sharing Students share their Number of the Day work from Homework Lesson 11.3.

LAUNCH Materials: • base ten materials (a variety, including commercially available materials, bundles of sticks, beans and cups, and snap cubes)

Model: Regrouping/Trading • See Model Regrouping and Nonregrouping in TE, Page

163A. • Introduce to students that this is one way of solving the

problem above. You may want students to use connecting cubes in trains of tens/loose ones, cups of ten beans/loose ones, bundles of ten sticks/loose ones.


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EXPLORE Materials: • base ten materials (flats, longs, and units) • Workmat 3 (P. TR 116; optional)

Race for a Flat Students play Race for a Flat in small groups.

PRACTICE As time allows: • Students choose 2 – 4 problems from pages 163 and 164. • They write stories for some of the problems they have

chosen on another sheet of paper. • Students solve the problems using ways that they

understand and/or the method demonstrated in Launch, Model Regrouping/Trading.

SUMMARIZE Closure: • Revisit purpose of the lesson with students. • Students share a problem they wrote and solved. • Ask, Did you need to regroup? Why or why not? Who had

a similar strategy? HOMEWORK Suggestion: Students write stories for 39 + 34, 27 + 13, and

15 + 7.


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


Purpose of Lesson: Model story problems using regroup/trading and nonregrouping.


Suggestion: Solving Problems • Give students a problem to solve: Mr. Peters has 32

students. Mrs. Gordon has 19 students. How many more students does Mr. Peters have than Mrs. Gordon?


• Discuss: What are ways that you could solve this problem? • Ask students to solve the problem using tools and

strategies they understand. Make manipulatives available. • Ask students to share their methods for solving the problem

with the whole class. Chart students’ strategies. Discuss how to represent the problem in an equation. Record the equation horizontally.

While there is a tendency to teach this compare/difference unknown problem as a subtraction situation, it is important that students use a method that makes sense to them. Some strategies students are likely to use include modeling the problem with materials (building each quantity and counting the difference between the two) and counting (on from the lesser quantity or back from the greater quantity). Students may also knowledge of number relationships (e.g., 32 – 10 = 22; 22 – 9 = 13).


Model: Regrouping/Trading • Individual students share homework stories from Lesson

11.4. • Discuss what is happening in the problem. Ask students to

retell the story in their own words. Students suggest how they might begin solving the problem. Ask students to solve the problem in way that makes sense to them. Make manipulatives available. Ask students to share their methods for solving the problem with the whole class.

• Record what they did on a class chart. Discuss how to represent the problem in an equation. Record the equation horizontally (see Model Story Problems and Reading Support in TE, page 165A for additional support).


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EXPLORE Materials: • base ten materials (a variety, including commercially available materials, bundles of sticks, beans and cups, and snap cubes)

Solving Homework Stories Students work in pairs. • One student reads a homework story to the partner. • The partner retells the story in his or her own words, solves

the problem and explains the method used. • Students take turns.

PRACTICE As time allows: • Students choose 2 – 4 problems from Pages. 165 and 166

(you may want to pick a problem for all students to solve). • Students read the problem, explain it to a partner, solve it

and record a horizontal equation to match the method used. Students solve the problems using ways that they understand and/or the method demonstrated in Launch, Model Regrouping/Trading, Day 52.

SUMMARIZE Closure: • Revisit purpose of the lesson with students. • Students share a problem they wrote and solved. This

problem could be the one all students were assigned. HOMEWORK Suggestion:

• Students record equations that are equal to today’s Number of the Day.

• Students write about the following: Would you say the Number of the Day if you were counting by 2s? 5s? 10s? How do you know?


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DAY 6 Chapter 12: Two-Digit Addition


LESSON FOCUS: Add Two-Digit Numbers CALIFORNIA STANDARD:

Number Sense: 2.2 Find the sum or difference of two whole numbers up to three digits long.

Purpose of Lesson: Understand when and how to regroup with 2-digit numbers in addition.


Suggestion: Solving Problems • Give students a problem to solve: Jason had 24 peanuts.

Carrie gave him some. Now he has 41 peanuts. How many peanuts did Carrie give him?

• To ensure that students understand what is happening in the problem, ask volunteers to retell the story problem. Discuss: What are ways that you could solve this problem?

• Ask students to solve the problem using tools and strategies they understand. Make manipulatives available.

• Ask students to share their methods for solving the problem with the whole class. Chart students’ strategies.

• Discuss how to represent the problem in an equation. • Record the equation horizontally. While there is a tendency to teach this join/change unknown problem as a subtraction situation, it is important that students use a method that makes sense to them. Some strategies students are likely to use include modeling the problem with materials (building the initial quantity and joining to make the final quantity) and counting (on from the initial quantity or back from the final quantity). Students may also have knowledge of number relationships (e.g., 24 + 10 = 34; 34 + 6 = 40; 40 + 1 = 41; 10 + 6 + 1 = 17). Suggestion: Homework Sharing Students share homework from Lesson 11.5. Ask students to prove sums by recombining addends.


Model: Two-Digit Addition • Take a student example that uses an addition method from

above. • Demonstrate using the method suggested in Model and

Draw Two-Digit Addition in TE, 1A. [Model building a 2-digit number with base-ten materials. Build the 2nd number. Show how to add together, using regrouping if necessary.] Discuss that this is one method for solving the problem. Vary materials used.

EXPLORE Materials:

Adding Ten Advanced Learners, TE, Page 172A. • Students shuffle the numeral cards and place them face


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• one set of numeral cards, 0-9 (pages. TR 38 and 39), per small group

down. • Each student writes ‘10’ on his/her paper. One student

chooses a card, writes the numeral chosen under 10, finds the sum of these two numbers, and writes down the sum.

• Each player takes a turn, drawing a card, adding the chosen numeral to 10, finding and recording the sum.

• On additional rounds, students add the number chosen to the previous sum.

• The student who reaches the sum of 50 scores a point and the game is over.

• Students repeat the game. PRACTICE Materials: • base ten materials (a variety, including commercially available materials, bundles of sticks, beans and cups, and snap cubes)

As time allows: • Students choose 2 – 4 problems from pages 171 and 172

(you may want to pick a problem for all students to solve). • Students may need to rewrite the problems on another

sheet of paper if the problem format is confusing to them. • Students solve the problems using the demonstrated on

these pages, as well as another way. • Remind students that the method described on these

pages is one method to add two-digit numbers. SUMMARIZE Closure:

• Revisit purpose of the lesson with students. • Students share a problem they solved. This problem could

be the one all students were assigned. HOMEWORK Suggestion: Students choose a two-digit number and write

clues about the number; e.g., 51. I am greater than 50. Both of my digits are odd numbers. The sum of the digits is 6.


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LESSON FOCUS: More Two-Digit Addition CALIFORNIA STANDARD:


Purpose of Lesson: Add two-digit numbers, with and without regrouping. ROUTINE Materials: • quart jar filled/half-filled with objects or other manipulatives

Suggestion: Making Estimates Continue using the quart jar. Fill or half-fill with different materials. Continue procedure. Suggestion: Solving Problems • Give students a problem to solve: Kimberly had 32

stickers. She gave some to Kyle. Now she has 16 stickers. How many stickers did Kimberly give to Kyle?


• Discuss: What are ways that you could solve this problem? • Ask students to solve the problem using tools and

strategies they understand. Make manipulatives available. • Ask students to share their methods for solving the problem

with the whole class. Chart students’ strategies. • Discuss how to represent the problem in an equation. • Record the equation horizontally.

When solving this separate/change unknown problem, it is important that students use a method that makes sense to them. Some strategies students are likely to use include modeling the problem with materials (building the initial quantity, separating out to the final quantity, and counting the separated quantity) and counting (back from the initial or on from the final quantity). Students may also have knowledge of number relationships (e.g., 32 - 2 = 30; 30 - 10 = 20; 20 – 4 = 16).


Number Clues Students share homework from Lesson 12.1. Model: Adding Two-Digit Addition • Take a student example that uses an addition method from

above. • Demonstrate using the method suggested in Model and • Draw Two-Digit Addition in TE, page 171A. [Model building

a 2-digit number with base-ten materials. • Build the 2nd number. Show how to add together, using

regrouping if necessary.] Explain how this is one method for solving the problem. Vary materials used.

EXPLORE Materials:

Rolling and Solving Problems • See Alternative Teaching Strategy, TE, Page 174A.

Students designate one die as the tens die and one as the


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• base ten materials (a variety, including commercially available materials, bundles of sticks, beans and cups, and snap cubes) • two dice per pair of students

ones die. • One student rolls both cubes and writes the number as a

two-digit addend; the partner does the same. • Partners write the addition problem. • One child solves with materials and the other solves

without. • Partners explain their method for solving the problem. • Partners switch roles.

PRACTICE Materials: • base ten materials (a variety, including commercially available materials, bundles of sticks, beans and cups, and snap cubes)



sheet of paper if the problem format is confusing. • Students solve the problems using the method

demonstrated, as well as another way (see Launch). • Remind students that the method described on pages 173

and 174 is one method. SUMMARIZE Closure:

• Revisit purpose of the lesson with students. • Students share a problem they solved. This could be the

problem all students were assigned. HOMEWORK Suggestion: Students record equations that are equal to

today’s Number of the Day. Students write about the following: Would you say the Number of the Day if you were counting by 2s? 5s? 10s? How do you know?


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LESSON FOCUS: Rewrite Two-Digit Addition CALIFORNIA STANDARD:


Purpose of Lesson: Understand that vertical and horizontal formats represent the same mathematical idea.

Routine Materials: • 100 chart

Suggestion: Arrow Math Display the 100 chart. Give students situations like the following. Give them time to figure out “code,” without telling them what the arrow notation means. Have them explain their reasoning. 25�26 25�26 25�36 37��39 37��48 37��57

LAUNCH Number of the Day Students share homework from Lesson 12.2. Model: Adding Two-Digit Addition • See Model Rewriting 2-Digit Addition, TE, Page 175A. • Write a horizontal equation and ask a volunteer to rewrite it

as a vertical equation. • Write a vertical equation and ask a volunteer to rewrite it as

a horizontal equation. • Discuss the two formats: How are they similar and how are

they different? (It is not recommended to have students rewrite horizontal equations in a vertical format.)

Note: Students tend to reason more about the quantities involved in a problem when it is written horizontally, rather than focusing on the procedure only.

EXPLORE Writing Arrow Math Problems Have students write Arrow Math Problems for a partner to solve. Save student work to be shared in Launch lessons on subsequent days.

PRACTICE As time allows: • Students choose 2 – 4 problems from pages 175 and 176



demonstrated on these pages, as well as another way. • Remind students that the method described on these

pages is one method. SUMMARIZE Closure:

• Revisit purpose of the lesson with students. • Students share a problem they solved. This could be the

problem all students were assigned.


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HOMEWORK Suggestion: Students record equations that are equal to

today’s Number of the Day. Students write about the following: Would you say the Number of the Day if you were counting by 2s? 5s? 10s? How do you know?


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LESSON FOCUS: Problem Solving: Estimate Sums CALIFORNIA STANDARD:

Number Sense: 6.0 Students use estimation strategies in computation and problem solving that involve numbers that use the ones, tens, hundreds, and thousands places.

Purpose of Lesson: Understand how to estimate sums of two-digit numbers.

Routine Suggestion: Introduce: Mental Math with Friendly Numbers • Give students the following problem to solve mentally:

28 + 10 • Ask a few students to explain how they solved the problem. • Give students this problem to solve mentally:

28 + 11 • Ask a few students to explain how they solved the problem.

Discuss which problem was easier to solve and why. Discuss the relationship between the two problems. Discuss “friendly” numbers and how it can be easier to adjust one number to be a friendly number.

• Give students this next problem to solve mentally: 28 + 9

• Ask a few students to explain how the solved the problem. Discuss the relationship between this problem and the previous one.

LAUNCH Materials: • Number lines (P. TR 37)

Model: Rounding to the Nearest Ten See Model Rounding to the Nearest Ten, TE, Page 177A. • Ask students how this process is related to doing mental

math with friendly numbers.

EXPLORE Writing and Illustrating Problems Advanced Learners, TE, Page 178A: • Students write and illustrate short stories that include a 2-

digit addition problem (i.e., Adam saw 23 red flowers. Then he saw 18 yellow flowers. About how many flowers did he see?). On the back of the paper, they write the estimated sum.

• Students exchange stories. They check each other’s estimates by solving the problem to find the actual sum.


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PRACTICE Materials: • tic-tac-toe grids (P. TR 123) • 100 charts (P. TR 33) • game pieces

As time allows: Nearest Ten Tic-Tac-Toe • Students play Nearest Ten Tic-Tac-Toe, using tic-tac-toe

grids, 100 charts, or a classroom number line. • Students choose a grid. • Partners take turns, choosing a number on their grid.

Before a partner can “claim” a number, they must name the number that is the “closest ten” to the chosen number and explain their reasoning; students may use a 100 chart or classroom number line. If their partner agrees, they may place a game piece on the number chosen.

SUMMARIZE Closure: • Revisit purpose of the lesson with students. • See Assess, TE, Page. 178. This may be difficult for

students. Possible questions: Is 23 closer to 20 or 30? How do you know? What about 45? Is it closer to 40 or 50? How do you know? What’s the rule for numbers in the middle?

HOMEWORK Materials: • tic-tac-toe grids (P. TR 123) • 100 charts (P. TR 33) • game pieces

Suggestion: • Have students teach Nearest Ten Tic-Tac-Toe to someone

at home.


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DAY 10 Chapter 13: Practice Two-Digit Addition


LESSON FOCUS: More Two-Digit Addition CALIFORNIA STANDARD:


Purpose of Lesson: To practice adding two-digit numbers. Routine Suggestion: Mental Math with Friendly Numbers

• Give students the following problem to solve mentally: 20 + 10

• Ask a few students to explain how they solved the problem. • Give students this problem to solve mentally:

19 + 11 • Ask a few students to explain how they solved the problem. • Discuss which problem was easier to solve and why.

Discuss the relationship between the two problems. Discuss “friendly” numbers and how it can be easier to adjust one number to be a friendly number.



LAUNCH Materials: • base ten materials (a variety, including commercially available materials, bundles of sticks, beans and cups, and snap cubes) • 2 sets of numeral cards per pair of students (P. TR 38, 39; optional)

Model: Two-Digit Addition with and without Regrouping • See Model 2-Digit Addition with and without Regrouping in

TE, Page 183A. • Display problems horizontally and vertically. It may or may

not be helpful to divide the tens and ones columns. • Have students solve each problem in the way that makes

sense to them. • Ask students to explain the method they used. • Demonstrate the method described on this page. • Remind students that this is one of many ways of solving

this problem.

EXPLORE Regrouping or Not? • Have students make up two-digit addition problems so that

some involve regrouping and some do not. • Ask them to choose one problem from each category and

explain how they know it belongs in that group; explanations can be verbal and/or written.


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PRACTICE Materials: • base ten materials (a variety, including commercially available materials, bundles of sticks, beans and cups, and snap cubes)



sheet of paper if the problem format is confusing. Students solve the problems using the method demonstrated, as well as another way. Remind students that the method described on these pages is one method.

SUMMARIZE Closure: • Revisit purpose of the lesson with students. • Students share a problem they solved. Possible question:

Which way of solving this problem is easier for you? This could be the problem all students were assigned. See Assess, TE, Page 184.

HOMEWORK Suggestion: Tell how these problems are related and then solve each one: 28 + 10 27 + 11 26 + 12


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LESSON FOCUS: Use Mental Math to Find Sums CALIFORNIA STANDARD:

Number Sense: 2.3 Use mental arithmetic to find the sum or difference of two two-digit numbers.

Purpose of Lesson: Use place value (decomposing numbers) to find sums. Routine Suggestion: Mental Math with Friendly Numbers





• Give students this next problem to solve mentally: 28 + 22.


LAUNCH Model: Splitting Tens and Ones • Display the equation in Model Mental Addition, TE, Page

185A (21 + 36) horizontally and vertically. • Show students the following way of solving the problem:

20 + 30 = 50 1 + 6 = 7

• Ask students if they understand this method of solving the problem. Ask a few students to explain why this method makes sense.

EXPLORE Different Equations/Same Sum Students think of two equations that result in the same sum. They write about the thinking they did to come up with the equations. Students prove that they have the same sum. Partners solve each to check.

PRACTICE As time allows: pages. 185 and 186. SUMMARIZE Closure:

• Revisit purpose of the lesson with students. • Assess, TE, Page. 184 (You may want to use “splitting tens

and ones”, instead of “mental math”). HOMEWORK Suggestion: Tell how these problems are related and then

solve each one: 27 + 12 26 + 13 28 + 11


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LESSON FOCUS: Adding Two-Digit Numbers CALIFORNIA STANDARD:

Number Sense: 2.0 Students estimate, calculate, and solve problems involving addition, and subtraction of two- and three-digit numbers.

Purpose of Lesson: To use mental math to find sums. Routine Suggestion: Mental Math with Friendly Numbers







LAUNCH Friendly Numbers • Give students this problem:

25 + 28 • Ask students how the equations in Routine helped to solve

this problem. EXPLORE • Ask students to use words, numbers and/or pictures to

explain how they figured out the solution to 25 + 28. • Ask if they can solve it in another way.

PRACTICE • base ten materials (a variety, including commercially available materials, bundles of sticks, beans and cups, and snap cubes)




demonstrated, as well as another way. Remind students that the method described on these pages is one method.

SUMMARIZE Closure: • Revisit purpose of the lesson with students. • Students share a problem they solved. This could be the

problem all students were assigned. HOMEWORK Suggestion: Tell how these problems are related and then

solve each one: 15 + 15 14 + 16 15 + 14 15 + 17


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LESSON FOCUS: Problem Solving: Make and Use a Graph CALIFORNIA STANDARD:

Algebra and Functions: 1.3 Solve addition and subtraction problems by using data from simple charts, picture graphs, and number sentences.

Purpose of Lesson: Make and use a graph to solve problems. Routine Materials: • quart jar filled/half-filled with objects or other manipulatives

Suggestion: Making Estimates Continue using the quart jar. Fill or half-fill with different materials. Continue procedure.

LAUNCH Model: Using a Graph See TE, Page 189A. • Students work together to make a bar graph. • They decide how to collect, record, and display data. • Groups count different items. • They make a chart and a related bar graph. • Children use the bar graph to make and solve two-digit

addition problems EXPLORE Writing Graph Questions

• Ask students to write questions about the class graph from Launch.

• Model how to ask questions that will require use of the graph in order to solve addition problems.

• Students write down their questions for display. They will be used in Practice.

PRACTICE As time allows: Answering Graph Questions Students answer some of their classmate’s questions from Explore.

SUMMARIZE Closure: • Revisit purpose of the lesson with students. • Students share a problem they solved from

Explore/Practice. HOMEWORK Suggestion: Pages 189 and/or 190.


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DAY 14

Chapter 13: Practice Two-Digit Addition LESSON 13.5 TE P. 183A-189A

(additional practice)

LESSON FOCUS: Problem Solving CALIFORNIA STANDARD:

Number Sense: 2.2 Find the sum or difference of two whole numbers up to three digits long

Purpose of Lesson: To solve problems using a variety of strategies. Routine Suggestion: Mental Math with Friendly Numbers







LAUNCH Solving Problems Give students a problem to solve: 38 students went out to recess. More came. Then there were 85 students on the playground. How many students joined the students on the playground?

EXPLORE Brainstorming Strategies To ensure that students understand what is happening in the problem: • Ask volunteers to retell the story problem. • Discuss: What are ways that you could solve this problem? While there is a tendency to teach this join/change unknown problem as a subtraction situation, it is important that students use a method that makes sense to them. Some strategies students are likely to use include modeling the problem with materials (building the initial quantity and joining to make the final quantity) and counting (on from the initial quantity or back from the final quantity). Students may also knowledge of number relationships (e.g.,


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38 + 40 = 78; 78 + 7 = 85; 40 + 7 = 47). PRACTICE • base ten materials (a variety, including commercially available materials, bundles of sticks, beans and cups, and snap cubes)

As time allows: Using Strategies • Ask students to solve the problem using tools and

strategies they understand. • Make manipulatives available. • Students record their method using words, numbers, an

equation and/or pictures.

SUMMARIZE Closure: • Revisit purpose of the lesson with students. • Ask students to share their methods for solving the problem

with the whole class. • Chart students’ strategies. • Ask questions to compare and contrast the strategies used. • Discuss how to represent the problem in an equation. • Record the equation horizontally.

HOMEWORK Suggestion: • Give students the equations from Launch: 15 + 10,

15 + 9, 15 + 19 • Ask students to recall how these equations used “friendly

numbers.” • Have students explain how they would use their knowledge

of friendly numbers and the equations above to solve these equations: 28 + 19, 28 + 32, 39 + 21

• Students solve these equations and use words, numbers and/or pictures to explain how they were solved and how they connect to the other equations.


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DAY 15

Chapter 13: Practice Two-Digit Addition LESSON 13.6 TE P. 183A-189A

(additional practice)

LESSON FOCUS: Problem Solving CALIFORNIA STANDARD:


Purpose of Lesson: Use multiple strategies to solve problems. Routine Suggestion: Mental Math with Friendly Numbers

• Give students the following problem to solve mentally (This group of equations is supposed to help students develop a "swapping" strategy where students take some off of one number and tack it onto the other number): 34 + 19


39 + 14 • Ask a few students to explain how they solved the problem. • Discuss which problem was easier to solve and why. • Discuss the relationship between the two problems. • Discuss “friendly” numbers and how it can be easier to

adjust one number to be a friendly number. LAUNCH Solving Problems

Give students a problem to solve: • 43 students were on the playground. Some went back to

their classrooms. Then there were 26 students on the playground. How many students went back to their classrooms?

EXPLORE Brainstorming Strategies To ensure that students understand what is happening in the problem: • Ask volunteers to retell the story problem. • Discuss: What are ways that you could solve this problem? When solving this separate/change unknown problem, it is important that students use a method that makes sense to them. Some strategies students are likely to use include modeling the problem with materials (building the initial quantity, separating out to the final quantity, and counting the separated quantity) and counting (back from the initial or on from the final quantity). Students may also knowledge of number relationships (e.g., 43 - 20 = 23; 23 - 6 = 17).


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PRACTICE Materials • base ten materials (a variety, including commercially available materials, bundles of sticks, beans and cups, and snap cubes)

As time allows: Using Strategies • Ask students to solve the problem using tools and

strategies they understand. • Make manipulatives available. • Students record their method using words, numbers, an

equation and/or pictures.

SUMMARIZE Closure: • Revisit purpose of the lesson with students. • Ask students to share their methods for solving the problem

with the whole class. • Chart students’ strategies. • Ask questions that help make connections between their

solution strategies. • Discuss how to represent the problem in an equation. • Record the equation horizontally.

HOMEWORK Suggestion: • Give students the equations from Launch:

34 + 19 39 + 14 • Ask students to recall how these equations used “friendly

numbers.” • Have students explain how they would use their knowledge

of friendly numbers and the equations above to solve these equations: 71 + 26 76 + 21

Students solve these equations and use words, numbers and/or pictures to explain how they were solved and how they connect to the other equations.


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Assessment TE P. 167, 168; 179, 180; 191, 192

LESSON FOCUS: Assessment CALIFORNIA STANDARD:


Purpose of Lesson: Assess understanding of two-digit addition concepts. Routine Materials: • snap cubes • base ten materials • money • other manipulatives

Suggestion: Number of the Day Students represent today’s number with snap cubes, base ten materials, money and other manipulatives. Students share their representations with the rest of the class. Students assist in recording equations to represent models.


Review • Revisit the models and activities used during this module.

Refer to vocabulary generated. Sample Problems • Give students sample problems similar to those on pages

167, 168; 179, 180; 191, 192. • Let students use familiar materials to model solutions to the

problems. • Provide students opportunities to share solution strategies

with their classmates. Questions to think about: Are students using efficient strategies? Will their strategies work every time? Are they able to communicate effectively about their solutions? Are they able to apply a strategy to a different type of problem? Are their solutions accurate? As time allows: pages. 167, 168; 179, 180; 191, 192.

HOMEWORK Suggestion: • Students choose a two-digit number and write clues about

a number; e.g., 28 I am less than 50. Both of my digits are even numbers. The sum of the digits is 10.

module 4 - revised

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