Gr 4 Mod 6 - PBworks

Revised 1/23/04

SAN DIEGO CITY SCHOOLS

Grade 4

Module 6 − Revised

Unit 4: Multiply by 1- and 2-Digit Numbers

WORK IN PROGRESS

Instructional Module to Enhance the Teaching of

H A R C O U R T

Math California Edition

S

D

C

S

Harcourt Math−Grade 4 MODULE 6

Revised 1/23/04 2

Grade Four – Traditional Calendar – 2004-2005 Order of Units and Pacing Guide

Month Module Number of Days

September 19 instructional days

Module 1: Data, Graphing, and Time Module 2: Multiplication and Division Facts

10 days

9 days

October 21 instructional days

Module 2: Multiplication and Division Facts Module 3: Understand Numbers and Operations

4 days

17 days

November 18 instructional days

Module 3: Understand Numbers and Operations Module 4: Geometry

8 days

10 days

December 13 instructional days

Winter Break 12/20 – 12/31

Module 4: Geometry 13 days

January 20 instructional days

Module 4: Geometry Module 5: Fractions and Decimals

3 days

17 days

February 17 instructional days

Module 5: Fractions and Decimals Module 6: Multiply by 1 and 2-Digit Numbers

2 days

15 days

March 18 instructional days

Spring Break 3/21 – 3/25

Module 6: Multiply by 1 and 2-Digit Numbers Module 7: Divide by 1 and 2-Digit Divisors

3 days

15 days April

20 instructional days

Module 7: Divide by 1 and 2-Digit Divisors Module 8: Measurement, Algebra and Graphing

4 days

16 days May


STAR 4/26 – 5/17

Module 8: Measurement, Algebra and Graphing Module 9: Probability

5 days

8 days June


Module 10: Division with 2-Digit Divisors and Add and Subtract Fractions and Mixed Numbers

12 days


Revised 1/23/04 3

Grade Four – Year Round Calendar – 2004-2005 Order of Units and Pacing Guide

Month Module Number of Days

September 19 instructional days

Module 1: Data, Graphing, and Time Module 2: Multiplication and Division Facts

10 days

9 days

October 21 instructional days

Module 2: Multiplication and Division Facts Module 3: Understand Numbers and Operations

4 days

17 days

November 18 instructional days

Module 3: Understand Numbers and Operations Module 4: Geometry

8 days

10 days

December 13 instructional days

Winter Break 12/22 – 1/17

Module 4: Geometry 13 days

January 10 instructional days

Module 4: Geometry Module 5: Fractions and Decimals

3 days

7 days

February 17 instructional days

Module 5: Fractions and Decimals Module 6: Multiply by 1 and 2-Digit Numbers

12 days

5 days

March 11 instructional days Spring Break 3/16 – 4/8

Module 6 Multiply by 1 and 2-Digit Numbers

11 days

April 15 instructional days

Module 6: Multiply by 1 and 2-Digit Numbers Module 7: Divide by 1 and 2-Digit Divisors

2 days

13 days

May 21 instructional days

Module 7: Divide by 1 and 2-Digit Divisors Module 8: Measurement, Algebra and Graphing

6 days

15 days

June 22 instructional days

STAR 5/27 – 6/17

Module 8: Measurement, Algebra and Graphing Module 9: Probability

6 days

8 days

July 14 instructional days

Module 10: Division with 2-Digit Divisors and Add and Subtract Fractions and Mixed Numbers

12 days


Revised 1/23/04 4

UNIT 4: Multiply by 1- and 2-Digit Numbers MODULE 6 – 4 Weeks of Instruction

Key Mathematical Concepts:

• Use strategies/models such as multiplication patterns and partial products to visualize and understand the process of multiplying by 2-digit numbers.

• Know when a rounded solution is necessary/useful and explain why such a solution may be appropriate.

• Solve problems involving addition, subtraction, multiplication, and division of whole numbers using efficient and accurate strategies including the standard algorithms; understand and use the relationship between operations to solve computation problems.

• Understand how to use and interpret variables, math symbols, and properties to write and simplify expressions and sentences (equations).

• Know how to make decisions/select approaches to problems, such as analyze problems by identifying relationships or determine when/how to break a problem into simpler parts.

• Use strategies, skills, and concepts to find solutions; use estimation to verify reasonableness of results; apply strategies and results from simpler problems; use variety of methods to explain mathematical reasoning.

Chapter 10: Multiply by 1-Digit Numbers Lesson 1: Mental Math: Multiplication Patterns Lesson 2: Estimate Products Lesson 3: Hands On: Model Multiplication Lesson 4: Multiply 3-Digit Numbers Lesson 5: Multiply 4-Digit Numbers Lesson 6: Problem Solving Strategy: Write an Equation

Chapter 11: Understand Multiplication Lesson 1: Mental Math: Patterns with Multiples Lesson 2: Multiply by Multiples of 10 Lesson 3: Estimate Products Lesson 4: Hands On: Model Multiplication Lesson 5: Problem Solving Strategy: Solve a Simpler Problem

Chapter 12: Multiply by 2-Digit Numbers Lesson 1: Multiply by 2-Digit Numbers Lesson 2: More about Multiplying by 2-Digit Numbers Lesson 3: Multiply Greater Numbers Lesson 4: Practice Multiplication Lesson 5: Problem Solving Skill: Multi-step Problems


Revised 1/23/04 5

Harcourt Mathematics

Grade 4 Unit 4: Multiplying by 1- and 2-Digit Numbers

Chapters 10 - 12

MODULE 6 NOTES

Chapter 10 Recommendations: • Teach Lesson 10.3: Hands-on: Model Multiplication as the Day 1 lesson rather than on Day 3. • Teach Lesson 10.1 as Day 2 lesson – use strategies from Lesson 10.2: Estimate Products – and eliminate Lesson 10.2 as a formal lesson. Chapter 11 Recommendations: • Suggested re-ordering of lessons so students use the “hands-on” experiences to build understanding of

multiplication. Teach:

- Lesson 11.4: Hands-on: Model Multiplication on Day 7 - Lesson 11.1: Mental Math: Patterns With Multiplication on Day 8 - Lesson 11.5: Solve a Simpler Problem on Day 9 - Lesson 11.2: Multiply by Multiples of 10 on Day 10

The estimation concepts in Lessons 10.2 and 11.3 can be embedded in all lessons and these 2 lessons can be eliminated if additional instructional time is needed for other lessons. This module does not have lessons for: Day 18: California Connections and Unit Review Day 19: Unit Review and Assessment


Revised 1/23/04 6

MULTIPLY BY 1- AND 2-DIGIT NUMBERS

4 Weeks of Instruction – Unit 4

Day 1 CHAPTER 10.1: Multiply by 1-Digit Numbers Lesson 10.1 Mental Math: Multiplication Patterns

Day 2 *Lesson 10.2 Estimate Products

Day 3 Lesson 10.3 Hands-On Model Multiplication

Day 4 Lesson 10.4 Multiply 3-Digit Numbers

Day 5 Lesson 10.5 Multiply 4-Digit Numbers

Day 6 Lesson 10.6 Problem Solving Strategy: Write an Equation

Day 7 CHAPTER 11: Understand Multiplication” Lesson 11.1 Mental Math: Patterns with Multiples

Day 8 Lesson 11.2 Multiply by Multiples of 10

Day 9 *Lesson 11.3 Estimate Products

Day 10 Lesson 11.4 Hands On: Model Multiplication

Day 11 Lesson 11.5 Problem Solving Strategy: Solve a Simple Problem

Day 12 CHAPTER 12 Multiply by 2-Digit Numbers Lesson 12.1 Multiply by 2-Digit Numbers (Day 1 of a 2-Day Lesson)

Day 13 Lesson 12.1 Multiply by 2-Digit Numbers (Day 2 of a 2-Day Lesson)

Day 14 Lesson 12.2 More About Multiplying 2-Digit Numbers

Day 15 Lesson 12.3 Multiply Greater Numbers

Day 16 Lesson 12.4 Practice Multiplication

Day 17 Lesson 12.5 Problem Solving Skill: Multi-Step Problems

Day 18 California Connections Unit Review

Day 19 Unit Review and Assessment

Day 20 Begin Module 7

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Revised 1/23/04 7

DAY: 1

Unit 4: Multiply by 1-and 2-Digit Numbers Module 6: Chapter 10: Multiply by 1-Digit Numbers

LESSON 10.1, pp. 186-187 MATERIALS: Highlighters; crayons; markers; poster board LESSON FOCUS:

Mental Math: Multiplication Patterns

CALIFORNIA STANDARDS:

Mathematical Reasoning 2.3 1.1: Analyze problems by identifying relationships…observing patterns... Number Sense 3.1 3.0: Solve problems involving addition, subtraction, multiplication, and division of whole numbers using standard algorithms; understand and use the relationship among operations.

PURPOSE OF LESSON:

• Understand how to use basic multiplication facts and patterns to develop students' ability to multiply mentally.

• Use patterns such as the number of zeros, and using products of ten, to compute products when multiplying with large numbers without using paper and pencil.

LAUNCH: Introduce students to concepts.

Special Needs and Early Finishers (for all students) TE P. 186B. • Discuss the patterns and how they help students determine the next

product. • Continue strategy: Students create similar problems using basic facts and

multiplication patterns with partner.

EXPLORE: Work with the concept. Focus on students “doing mathematics.”

Learn, Pg. 186: Found Money. • Write problem on board/overhead. Students work with partner to solve

using: representations and numbers. • Discuss strategies and solution(s). Teach, Pg. 186: Guided Instruction questions to guide discussion. Examples A and B: Pg. 186: Create context for the number sentences (Ex: 7 plates with 20 cookies). • Highlight and discuss/record useful patterns students recognize. • Discuss Algebraic Thinking, margin TE p. 186.

PRACTICE: Focus on Communication and Representation.

Check, Pg. 186, #1: Discuss. • Then, make chart with students the multiples for #2 – 5. • Discuss patterns. Highlight basic facts and underline zeros as in Special

Needs, p. 186B. Practice & Problem Solving, Pg. 187, #22 – 27. • Discuss. Then, #28 – 32. Discuss strategies.

SUMMARIZE: Connect purpose to activities.

• Show a sequence of products: Ex: 240; 2,400; 24,000, etc. Students identify the factors for each: (240: 4, 6, and 10; 2,400: 4, 6 and 100; 24,000: 4, 6 and 1,000).

ASSESS, TE Pg. 187: WRITE. Share responses.

HOMEWORK: Practice & Problem Solving, p. 187: # 18-21; Mixed Review and Test Prep: #s: 33 -37.


Revised 1/23/04 8

ROUTINES:

Find the Factors Write the following one at a time. Students give all possible factors for each, omitting 1 and the number itself, e.g., 12: 2, 3, 4, 6 18 15 30 42 24 36 45 27 14 Students write numbers having three or more factors (omitting 1 and the number itself), and list the factors, e.g., 20: 2, 4, 5, 10. Encourage students to include larger numbers, e.g., 48, 72, 128… Discussion Question: How can you be sure you have found all the factors for a number? Discuss. Give an example of factors beginning with 2, then 3, combined with pairing the factors as a means of checking. Example: 20 is divisible by 2: 20 ÷ 2 = 10, so 2 and 10 are factors of 20. 20 is not divisible by 3. 20 is divisible by 4: 20 ÷ 4 = 5; so 4 and 5 are factors. 20 is not divisible by 6, 7, 8, 9, etc. Ask if there are any other factors of 20 besides 1 and 20. Discuss other strategies students use to determine the all the factors as numbers such as arrays and "facts".


Revised 1/23/04 9

DAY: 2

HM Unit 4: Multiply by 1- and 2-Digit Numbers Module 6: Chapter 10: Multiply by 1-Digit Numbers

LESSON 10.2, pp. 188-189

MATERIALS: Special Needs: index cards LESSON FOCUS:

Estimate Products


Number Sense 1.4: Decide when a rounded solution is called for and explain why such a solution may be appropriate. 3.0: Solve problems involving addition, subtraction, multiplication, and division of whole numbers using standard algorithms; understand and use the relationship among operations. Mathematical Reasoning: 2.5

PURPOSE OF LESSON:

• Understand how to estimate products by rounding to the greatest place value.

• Learn how estimation helps determine the reasonableness of the answer. LAUNCH: Introduce students to concepts

Special Needs (for all students), TE Pg. 188 B. • Students discuss strategies for solving. Ask students to place their

cards on a number line. • Continue strategy by having students create and share similar problems

with partners.

EXPLORE: Work with the concept. Focus on students “doing mathematics.” Students have books closed.

Learn, Pg. 188: Flour Power. Write problem on board/overhead. • Teach, p. 188: Guided Instruction questions to guide discussion of Steps

and Examples A & B. • Record and discuss strategies for solving. Check, Pg. 188: Do #s: 1 - 3 with students. • Create context/situations for Problems 2-3. • Discuss rounding strategies. Practice & Problem Solving, Pg. Pg. 189: #26 - 29: • Put problems and factors on board/overhead. Students work with partners

to solve. Discuss solutions and strategies. PRACTICE: Focus on Communication and Representation.

Practice & Problem Solving, Pg. 189: #30 – 34; 6-9 • For problems 30 -33: Students show/explain/justify answers with pictures

and number sentences. • Students work with partners/individually. Confer as students' work.

Discuss and share solutions and strategies for solving. • Ask students to round and estimate the product of 3 x 27. Share

estimates when rounding 9 to 10 (10 x 27 = 270) and 27 to 30 (9 x 30 = 270).

• Repeat procedure for 87 x 6: (90 x 6 = 540) (87 x 10 = 870) • Emphasize both are reasonable estimates. • Discuss which rounded answer is closer to actual product and why.


ASSESS, TE Pg. 189: DISCUSS. ASSESS, TE Pg. 189: WRITE. • Students make up their own similar problems to round and multiply and

share.


Revised 1/23/04 10

HOMEWORK: Practice & Problem Solving, Pg. 189: #s: 18 - 20 and Mixed Review and Test Prep: # 35 -39.

ROUTINES: Mental Math: Round and Round Begin going around class, saying 2-digit numbers. Students round to nearest ten. Continue, saying 3-digit numbers. Students round to nearest 100. Continue with 4-digit numbers, rounding to nearest thousand. Practice rounding and multiplying mentally by writing and saying the following. Students round only the first number; e.g., 28 x 6 becomes 30 x 6 or 180. Go around class, alternating by having one student give rounded form (30 x 6) and next student gives product (180). 39 x 5 72 x 3 63 x 4 58 x 2 43 x 9 15 x 6 83 x 7 24 x 9 9 x 20 91 x 3 Continue as needed.

Reteach/reinforce any skills and concepts identified in homework check as needing attention.


Revised 1/23/04 11

DAY: 3

HM Unit 4: Multiply by 1- and 2-Digit Numbers Module 6: Chapter 10: Multiply by 1-Digit Numbers

LESSON 10.3, pp. 190-191

MATERIALS: Base-ten blocks; Routines: 1-cm grid paper for each student (TR60); ten 10-cm 1-inch wide strips (5 each of 2 colors); masking tape for each student/group.

LESSON FOCUS:

Hands-On: Model Multiplication


Number Sense: 3.0: Solve problems involving addition, subtraction, multiplication, and division of whole numbers using standard algorithms, understand and use the relationship among the operations. Mathematical Reasoning: 2.3

PURPOSE OF LESSON:

• Understand that multiplication involves combining equal groups. • Use manipulative models to facilitate visualizing the multiplication process. • Understand how using Base-10 blocks connects to the process of

regrouping in the multiplication algorithms. LAUNCH: Introduce students to concepts Base-10 blocks

• Quick Review, p. 190. Review orally with students. Discuss strategies. • Ask students estimate the product of 12 x 5: • Explain/discuss strategies for multiplying 12 x 5. • Ask students to rewrite problem separating the tens and ones. (10 + 2) • Remind students the problem asks for 5 groups of 12. This can be written

5(10 +2) or 5(10) + 5(2) (this is an example of the distributive property – see lesson 10.4, top p. 193).

Write: 12 x 5 • Use Base 10 blocks to model: • Ask students to show the product of 5 times

2 ones. Model with blocks. Ask for the product of 5 times 1 ten:

• Model with blocks. • Explain: This shows two partial products and the sum of both = complete

product. So, show adding 50 + 10 = 60. • Discuss/model each step again with Base-10 blocks – connect blocks to

numbers in equation. • Discuss product of 60 – is it close to the estimate of 50? • Students do 2 – 3 problems with blocks, such as 4 x 14; 3 x 17; 3 x 13 with

students.

(10 + 2) x 5 (10 + 2) x 5 10 + 50

60


Revised 1/23/04 12

• Present this problem: 345 • Ask students to estimate the product. x 2 • Follow the same procedure of renaming 10

345 to hundreds, tens, ones. 80 (300 + 40 + 5) Model with blocks. Remind + 600 students the problem asks for 2 groups of 690 345.

• Remind students to add to find the sum of the “partial products.” Discuss process with students: What numbers are being multiplied for each partial product?

• Repeat with other examples. • Continue as needed. See Try It, Pg. 190. Students may check problems with repeated addition. (345 + 345)


Connect, top SE Pg. 191: Students do with partner. Discuss and record partial products and find sum. Verify the partial product by using repeated addition: Ex: 138 + 138 + 138 = _____ Pg. 191, #5 – 8. See Modifying Instruction, margin TE p. 190. Students work with partners/individually - solve using blocks, record partial products, and add to find product.


ASSESS, TE Pg. 191: WRITE.

HOMEWORK: Mixed Review and Test Prep, Pg. 191 • Write and solve a word problem in which you multiply a 2- or 3-digit number

by a 1-digit number. Ex: There are 125 stamps on a page. How many stamps are on 3 pages? Show 125 x 3 on 1 – 3 pages or 125 + 125 + 125 = _____

} Partial Products


Revised 1/23/04 13

ROUTINES:

How Many of These? How Many of Those? (Equivalent Measurements) Use measuring tools to review equivalent measurements, e.g., Examples: 100 cm = 1 m 1,000 m = 1 km 1,000 mm = 1 m Show students how to make their own measuring tapes using masking tape and ten 10-cm strips (five of one color and five of another color), which they place on masking tape, alternating the colors, to make 1 meter. Record 10 cm marks on meter tape. Ask how many 10-cm strips are needed to show 1 meter (10). Ask how many millimeters are in 1 cm (10). In 100 cm (1,000). If desired, students can mark millimeters. Give a measurement: Ex: 100 cm. Ask students for equivalent measurements, i.e., 1 m or 1,000 mm. Continue with 5 m, 10 cm, etc. Students use measuring tapes to find objects which are of given lengths. Ex: 5 cm, 10 cm, 20 cm, 25 cm, 50 cm, 100 cm, 150 cm, 1 m, 2m, etc. Reteach/reinforce any skills and concepts identified in homework check as needing attention.


Revised 1/23/04 14

DAY: 4 Unit 4: Multiply by 1-and 2-Digit Numbers

Module 6: Chapter 10: Multiply by 1-Digit Numbers LESSON 10.4, pp. 192-195

MATERIALS: Pp. 131-132, Skill 28: Intervention Strategies and Activities:

*Transparencies or worksheets for students; Base-10 blocks for small group work.

LESSON FOCUS:

Multiply 3-Digit Numbers


Number Sense 3.0: Solve problems involving addition, subtraction, multiplication, and division of whole numbers using standard algorithms; understand and use the relationship among operations. Mathematical Reasoning: 2.1, 2.3

PURPOSE OF LESSON:

• Understand how using Base-10 blocks connects to the process of regrouping in the multiplication algorithms.

• Connect and generalize the process of multiplying 2-digit numbers to the process of multiplying 3-digit numbers.

• Understand how estimating can help determine the reasonableness of the product.

LAUNCH: Introduce students to concepts Bse-10 Blocks *Transparencies

Quick Review, Pg. 192. Model with blocks. Discuss. P IS 129-132: Alternative Teaching Strategy in Intervention Strategies and Activities, Skill 28: • This strategy combines using base-ten blocks and partial products,

which are recorded on place-value tables. Activity sheets are provided on pp. 131-132.

• Students use Base-10 blocks to model process. EXPLORE: Work with the concept. Focus on students “doing mathematics.” Student’s books are closed.

Learn, Pg. 192: Mix It Up: Write problem on board/overhead. Do with students. Teach, Pg. 192; Guided Instruction questions to discuss. • Place Value & Multiplication, p. 193: Another Way. • See bullets in margin TE p. 193 to guide discussion. • Discuss Reasoning & Algebraic Thinking bullet with students. Highlight/connect the relationship between the Base-10 blocks, place-value chart, and expanded form to develop understanding of the process for multiplying 3-digit numbers by a 1-digit number. • Continue emphasis and practice using the partial products strategy

(similar to place value/expanded form).


Revised 1/23/04 15


Practice & Problem Solving, Pg. 194: # 42, 47 – 49, 50 – 53, 56 - 58. • Students work individually/with partners to solve. Discuss solutions and

strategies.


On board/overhead: 243 x 4 = ____. Students round to estimate the product. • Students choose two different ways to do problem and use them to solve

it. • Discuss strategies they use. Examples:

1) partial products and add 2) expanded form 3) round a factor

• Students share work and procedures. Emphasize: each procedure must be clearly explained. Discuss if the product is reasonable based on the estimate.

HOMEWORK: Mixed Review and Test Prep, Pg. 195: # 59-62. Thinkers’ Corner, p. 195

ROUTINES:

Problem Solving: How Much? How Many? Divide class into groups. Take turns asking each group a problem dealing with measurements similar to the following. Students must answer problem correctly and give equation that could be used to solve it. Ask a variety of problems dealing with measurements; e.g., This year the tickets to the game cost $40. This is $4 more than last year. What was their cost last year? (40 – 4 = 36; or 40 = x + 4 = 36, etc.) Tabby slept for 8 1/2 hours last night. That is 1 1/2 hours less than she slept the night before. How many hours did she sleep the night before? Duc went on the yearly nature hike. He hiked 22 km. Last year he hiked twice as far. How far did he hike last year. This month school lunches cost $1.50. This is 25¢ more than last month. What did they cost last month? The new bus is 40 feet long. This is 5 feet shorter than the old bus. How long was the old bus? Jessica finished her work 6 minutes sooner than her sister. Jessica finished in 26 minutes. When did her sister finish? Have students make up similar problems. Go around the groups asking each group to share a problem for the class to answer and give the equation used to solve it. Reteach/reinforce any skills and concepts identified in homework check as needing attention.


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DAY: 5


LESSON 10.5, pp. 196-199

MATERIALS: Base-10 blocks, including thousands cubes. Reteach 10.5 LESSON FOCUS:

Multiply 4-Digit Numbers


Number Sense 3.0: Solve problems involving addition, subtraction, multiplication, and division of whole numbers using standard algorithms; understand and use the relationship among operations. Mathematical Reasoning: 2.1, 2.3

PURPOSE OF LESSON:

• Understand how using Base-10 blocks, and expanded notation, and partial products connect to the process of multiplication.

• Connect and generalize the process of multiplying 2- and 3-digit numbers to the process of multiplying 4-digit numbers. Understand how estimating can help determine the reasonableness of the answer.

LAUNCH: Introduce students to concepts Base-10 Blocks

Students estimate the product of 1,432 and 3. (3000) Ask how they multiply these numbers. Use partial products. Students use Base-10 blocks to model each partial product and the sum with teacher and/or expanded notation: 3(1000) + 3(400) + 3(30) + 3(2). Write equations to match each partial product represented by the blocks. Discuss product: Is it reasonable based on the estimate? Continue with similar problems that require regrouping in various places. Students explain/discuss procedures used.


Learn, Pg. 197: Pen Pals. Write problem on board/overhead. Discuss. • Students using Base-10 blocks to model process. Teach, Pg. 197; Guided Instruction questions to guide discussion. • Use Reteach 10.5 to represent finding partial products when

multiplying 4-digit numbers by 1 digit. (partial products & expanded notation) Show horizontal representation. 4(2000) + 4(200) + 4(80) + 4(1)

Multiply Money, Pg. 197. See bullets top margin TE p. 197 to guide discussion. • Students discuss/explain process for determining where to place

decimal point when multiplying amounts of money.

1,432 x 3

6 (6 x 1) 90 (3 x 30)

1,200 (3 x 400) 3,000 (3 x 1,000) 4,296


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PRACTICE:

Focus on Communication and Representation.

Practice and Problem Solving, Pg. 198: #30-31. • Do with students. Students check process by using repeated addition

with each problem. • Then, #32 – 33. Discuss. • Students work with partners or individually to solve. Verify solution by

using a different strategy. • Discuss partial products process and verify using repeated addition. • Then, #34 – 36 and p. 199, #37 – 38. Discuss as above.


Assess, TE Pg. 199: DISCUSS: • Discuss and compare process of multiplying 4-digit number by a 1-

digit number, with multiplying by a 3-digit number by a 1-digit number. Assess, TE Pg. 199: WRITE.

HOMEWORK: Practice & Problem Solving, Pg. 198: # 24-26. Link Up to Reading – Discuss using bullet top margin, p. 199.

ROUTINES:

Problem Solving: Analyzing Information P. 199, TE: Students work in partners to do Linkup to Reading and K-W-L Reading Strategy: What I know, What I Want to Know, What I Learned.

Predict what the Linkup is about. Make a K-W-L chart using the above three

categories. Complete the first two columns. Read the paragraphs in Link Up and fill in the third

column as they read. Partners share solutions for both problems with class. Reteach/reinforce any skills and concepts identified in homework check as needing attention.


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MATERIALS: *Transparency: Practice 10.6 or Challenge 10.6 LESSON FOCUS:

Problem Solving Strategy: Write an Equation


Algebra and Functions: 1.1 1.0: Use and interpret variables, mathematical symbols, and properties to write and simplify expressions and sentences. Number Sense 3.0: Solve problems involving addition, subtraction, multiplication, and division of whole numbers using standard algorithms; understand and use the relationship among the operations. Mathematical Reasoning: 1.0, 1.1, 2.1

PURPOSE OF LESSON:

• Understand that an equation has an equal sign and shows that two values are equal.

• Recognize that a variable represents an unknown number. • Understand that an equation can be written to show how the facts in

a problem are related. • Know that multiplication can be used when combining equal-size

groups. LAUNCH: Introduce students to concepts

HW: Partner check and discuss solutions to Link Up to Reading. Problem, Pg. 200: Ray Uses His Computer…write on board/overhead. • Read & discuss with students. See Alternative Teaching Strategy, TE Pg. 200B and Teach, Pg. 200, • Guided Instruction questions to guide discussion. • Write equations to use to solve this problem. • Students write and share equations. • Students estimate the product before using the equation to solve.


• Compare their estimate with the solution. Discuss reasonableness of estimate.

Question: What if the problem was changed to: It costs $66.06 for internet service for 6 months or $24.00 for 2 months. What is the cost per month? • Discuss: What equation solves this problem? • Students share a division or missing factor equation to solve the

problem. • Record different representations of the same information.

(66.06 ÷ 6 = c OR 6 x c = 66.06)


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PRACTICE: Focus on Communication and Representation. *Transparency: Practice 10.6 or Challenge 10.6

Problem Solving Practice, Pg. 201: # 1-3: Do with students. Problem Solving Practice, P. 201: # 4 and 5: Students work with partners or individually. Use Practice 10.6 #s 1-5 or Challenge 10.6 #s 1-10. • Put on board/overhead. Students choose 3-4 problems to solve. • Solutions include representation or equation to justify the answer. • Discuss and share solutions and strategies.


ASSESS, TE Pg. 201: DISCUSS. Share ASSESS, TE Pg. 201: WRITE. Share and discuss.

HOMEWORK: Mixed Strategy Practice, Pg. 201: #6-9 • Make up 1 word problem that uses multiplication and 1 that uses

division to solve it. • Encourage estimation first for checking reasonableness of the

solution. ROUTINES:

Pg. 202: Chapter Review/Test Students to look over the problems on p. 202. Do #s 1-3 and 24-25 with students. Pg. 198: Problems 32 and 33: Discuss and do with students. Reteach/reinforce any skills and concepts identified in homework check as needing attention.


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Module 6: Chapter 11: Understand Multiplication LESSON 11.1, pp. 206-207

MATERIALS: LESSON FOCUS:

Mental Math: Patterns with Multiples


Number Sense 3.2: Demonstrate an understanding of, and ability to use, standard algorithms for multiplying a multi-digit number by a two-digit number and for dividing a multi-digit number by a one-digit number; use relationships between them to simplify computations and to check results. 3.3: Solve problems involving multiplication of multi-digit numbers by two-digit numbers. Algebra and Functions: 1.0 Mathematical Reasoning: 1.0, 2.0, 2.3, 3.0, 3.3

PURPOSE OF LESSON:

• Understand how to use basic facts to figure an estimate for multiplication problems and develop strategies to solve problems mentally.

• Use patterns to determine the relationship between the number of zeros in the factors and the product.

LAUNCH: Introduce students to concepts

• Skip Counting: Practice and record patterns for skip counting by 2s, 20s, and 200s; 5s, 50s, and 500s.

Science Connection, TE Pg. 206B • Ask students to discuss the product of 4 x 4. • Highlight what each digit of the product represents (1 ten, 6 ones). • Using that model, discuss 4 x 40. (1 hundred, 6 tens, 0 ones) • Then discuss 4 x 400. Connect the products, 16, 160, 1600, by

highlighting the pattern of zeros and that the products are 10 times greater just as 4, 40, 400.

What happens to a number when multiplying by 10? Discuss the multiplication patterns and connect patterns to

generalizations – how many ones, tens, hundreds, etc., in the product and how do patterns/place value help students know the number of places in the product.


Learn, Pg. 206: Cross-Country. • Write problem on board/overhead: Discuss and do with students. Teach, Pg. 206; Guided Instruction questions to guide discussion. Check, p. 206, #1, do with students. Check, Pg. 207: #4-5: Do with students and discuss patterns. • Discuss products: Ex. 270 – What are the factors? (Use multiples of

10; 9 and 30) • Share Common Error Alert with students, top margin TE p. 207.


Revised 1/23/04 21


Practice & Problem Solving, Pg. P. 207: • Discuss and do #s 18-21 with students. • Emphasize approaches/strategies for solving. • Ask students to write solutions on board/overhead and share

thinking. Practice and Problem Solving, Pg. 207: # 22-23: Do with students. Practice & Problem Solving, p. Pg.207: #11-13: Students work with partners or individually.


Practice & Problem Solving, pg. 207: Problem #24: Discuss with students. ASSESS, TE Pg. 207: WRITE. Explain how to find the product. Write student responses; accept all that are mathematically accurate.

HOMEWORK: Practice & Problem Solving, Pg. 207: #14-15 Mixed Review and Test Prep: #s 25-28 *Write and solve a word problem involving multiplying by a multiple of

10 and another multiplying by a multiple of 100. ROUTINES:

P. 202: Chapter Review/Test Review the work completed the previous day. Focus on items students don’t understand and give students additional practice on concepts involved.


Revised 1/23/04 22



MATERIALS: Base-10 blocks for small group work; Routines: Performance

Assessment 4.4A: “Fish Story” – 1 copy per student. LESSON FOCUS:

Multiply by Multiples of 10


Number Sense 3.2: Demonstrate an understanding of, and ability to use, standard algorithms for multiplying a multi-digit number by a two-digit number and for dividing a multi-digit number by a one-digit number; use relationships between them to simplify computations and to check results. 3.3: Solve problems involving multiplication of multi-digit numbers by two-digit numbers. Algebra and Functions: 1.1 Mathematical Reasoning: 1.0, 2.0. 3.0

PURPOSE OF LESSON:

• Understand how to use patterns to find the product when multiplying by multiples of 10.

• Understand the Zero Property of Multiplication – any number multiplied by zero equals zero.

LAUNCH: Introduce students to concepts Base-10 blocks for each group.

• Review/emphasize partial products and have students identify them

as you discuss. Explain that finding partial products and adding them to get the complete product (answer) is a strategy for multiplying multi-digit numbers.

• Students estimate the product of 48 and 3 and explain/show how they multiplied 48 x 3.

• Do the following with students: Ask questions and explain each step with Base-10 blocks.

• Show product of 3 times 8 ones as 24 ones or 2 tens and 4 ones.

Model with blocks. Discuss where to record 24. • What is the product of 3 times 4 tens? Model using Base-10 blocks

and show as: 12 tens or it can be thought of as 120 ones. • Discuss where to record. • Find the sum of 48 and 120. • Model with blocks and record. • Ask if the product is reasonable based on the estimate. • Repeat using 48 x 30. Emphasize multiplying 30 x 8 ones and 30 x

40 to find the partial products, because there are zero ones in this number.

Alternative Teaching Strategy, TE Pg. 208B; To reinforce and extend warm-up.


Revised 1/23/04 23


Learn, Pg. 208: Roundup. Write problem on board/overhead. • Ask students to solve using the partial products strategy. Use arrays

(area models or base 10 blocks) to represent partial products for 2 x 30 and 50 x 30.

Teach, Pg. 208; Guided Instruction questions to guide discussion.


Check, Pg. 208, #1. Discuss. Check, Pg. 208, # 2-4. Do with students. • Students use partial products. Practice and Problem Solving Pg. 209, #37 – 42. Discuss. Then students do #43 – 48. • Discuss solutions/strategies with students.


• Students make up, write, and solve a problem involving multiplying a 2-digit number by another 2-digit number that is a multiple of ten.

• Share problems and procedures used. Students explain strategies/procedures to the class.

ASSESS, TE p. 209: WRITE. HOMEWORK: Practice & Problem Solving, Pg. 209, #32 – 34.

Mixed Review and Test Prep, Pg. 209 #s 49-50 and 52-53. ROUTINES:

Pg. PA28-30: Performance Assessment 4.4A: Fish Story #s 32-34: Performance Assessment booklet. Read problem with students. Answer any questions. Be encouraging…motivate, guide… Be clear. Reword any words or phrases; insert others as needed. Be supportive. Assist students who need help. Be fair. Allow students adequate time to do their best work. Be flexible. All students will not do the task in the same order/way. Involve students in the evaluating process. The suggested completed performance task is on p. PA32. Rubrics (3-point) are provided on pp. PA33-34. These should be used for the next day’s Routine when the Performance Assessment is reviewed. Reteach/reinforce any skills and concepts identified in homework check as needing attention.


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DAY: 9

Unit 4: Multiply by 1-and 2-Digit Numbers Module 6: Chapter 11: Understand Multiplication

LESSON 11.3, pp. 210-211 MATERIALS: Routines: Transparencies of student work from Performance

Assessment: Fish Story 4.4A; Alternative teaching Strategy: 2 index cards for each student.

LESSON FOCUS:

Estimate Products


Number Sense 3.2: Demonstrate an understanding of, and ability to use, standard algorithms for multiplying a multi-digit number by a two-digit number and for dividing a multi-digit number by a one-digit number; use relationships between them to simplify computations and to check results. Mathematical Reasoning: 1.0, 2.0

PURPOSE OF LESSON:

• Understand how to round factors to estimate the product and use rounding strategies effectively.

• Recognize the number of zeros in the factors determines the number of zeros in the product unless the “basic fact” includes a zero, then the number of zeros will be one more than the number of zeros in the factors.

LAUNCH: Introduce students to concepts Index cards

Warm-up: Use Rounding Rules: • Go around class, saying 2- and 3-digit numbers for students to round

(2-digit to nearest ten; 3-digit to nearest 100).

Alternative Teaching Strategy, TE P. 210B


Learn, Pg. 210: Juice Break: Write problem on board/overhead. • Discuss strategies for estimating product. • Students explain approaches. Include using a number line as a

strategy if it is not suggested. Teach, Pg. 210; Guided Instruction questions to guide discussion.


Practice & Problem Solving, Pg. 211, #38 – 40. • Students work with partner or individually. • Discuss solutions and strategies for rounding and estimating products.

Practice & Problem Solving, Pg. 211: #s 35-37: • Students work with partners to develop situation/context for problem. • Discuss/show solutions and strategies.

Practice & Problem Solving, Pg. 211, #41. • Share thinking.


ASSESS, TE Pg. 211: WRITE. Share responses. Writing in Mathematics, TE Pg. 210B


Revised 1/23/04 25

HOMEWORK: Practice & Problem Solving, Pg. 211: # 32-34

Mixed Review and Test Prep, Pg. 211: # 42-46 ROUTINES:

Review p. PA28-30: Performance Assessment 4.4A: Fish Story, and PA 33-34 in Performance Assessment booklet. Involve students in the evaluation of the Performance Assessment, Fish Story, completed on the previous day. Explain that papers are scored using rubrics. Share sample rubrics on pp PA33-34, beginning with the Level 3 rubric. Ask why students think the paper scored 3 is better than the others. Ask them to give its best points while you record them. Ask if anything important has been left out. Continue with similar questions. Share the other two rubrics, one at a time, asking appropriate questions. Ask how each paper could be improved. Return papers to students. Ask for ways they might improve their work. Help them to edit and/or rewrite, if desired. Ask students what they learned from the experience. Discuss. Reteach/reinforce any skills and concepts identified in homework check as needing attention.


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MATERIALS: Transparency 11.3; Base-10 blocks for partners; two sheets of cm grid

paper for each student; *Transparencies of cm. grid paper. LESSON FOCUS:

Hands-On: Model Multiplication


Mathematical Reasoning: 1.0, 2.0, 3.0 1.2: Determine when and how to break a problem into simpler parts. Number Sense: 3.3 3.2: Demonstrate an understanding of, and ability to use, standard algorithms for multiplying a multi-digit number by a two-digit number and for dividing a multi-digit number by a one-digit number; use relationships between them to simplify computations and to check results.

PURPOSE OF LESSON:

• Understand that area of a rectangle represents a model of multiplication.

• When multiplying multi-digit numbers, each digit in each factor must be multiplied by every digit in the other factor.

LAUNCH: Introduce students to concepts Base-10 blocks

Lesson Quiz, Pg. 211: Transparency 11.3: • Students choose 2-3 problems, estimate the product, and

share/explain solutions and strategies for estimating to partner/class. Alternative Teaching Strategy, TE Pg. 212B: • Use Base-10 blocks with partner to multiply 12 x 13. First, students

estimate the product of 12 x 13. Highlight representing 12 as (10 + 2) and 13 as (10 + 3).

• Discuss and record student explanations. • Discuss: Is product is reasonable based on your estimate? • Discuss the area model and continue with other problems as needed.

10 + 3

10 + 2

• Discuss and model if necessary (with blocks and on grid paper). • Label each part of the array, e.g., 10 x 10; 3 x 10; 2 x 10; 2 x 3. • Students write/match multiplication equations for each part of the

array to the four partial products: 2 x 3 = 6; 3 x 10 = 30; 2 x 10 = 20; and 10 x 10 = 100.

• Students add four partial products to find product.

100

30

20 6


Revised 1/23/04 27

EXPLORE: Work with the concept. Focus on students “doing mathematics.” Base-10 blocks & grid paper. Students have books closed.

Explore, Pg. 212: Write question on board/overhead. Teach, Pg. 212; Guided Instruction questions to guide discussion as you model problem on grid paper. • Students show 18 x 24 array on grid paper and with

blocks. • Connect (20 x 10) + (4 x 10) + (20 x 8) + (8 x 4) to model

on cm. grid paper. • Connect, Pg. 213: Show 16 x 23 array (area model). • Model and do with students. • Explain/show the 4 partial products in the area model.

Record the equation for each. Add partial products to find final product.


Practice, Pg. 213: #s 1-3: Students use blocks and grid paper to model and solve.


ASSESS, TE Pg. 213: Discuss: “What are some models…” ASSESS, TE Pg. 213: Write: • Explain how to use partial products to multiply 23 x 15. • Chart and record student responses. • Include model of area model and note partial products.

HOMEWORK: Mixed Review and Test Prep, Pg. 213

ROUTINES:

What’s My Number? (2-step Mental Computation) Process: Show partial products. Working with partners. Write a word problem for 1 of the problems. Discuss and share solutions and strategies with class. Go around the class or divide class into groups. Give a problem like the following: I am 4 more than 2 x 8. What’s my number? Continue with such problems as: I am 8 less than 6 x 8. What’s my number? I am 2 more than 4 x 7. What’s my number? I am 7 more than 3 x 10. What’s my number? I am 10 less than 9 x 10. What’s my number? I am the sum of 7, 3, and 6. What’s my number? I am 25 less than 25 x 2. What’s my number? Each student makes up and writes a similar problem. Go around class as each student gives a problem for the class to solve. Discuss and record strategies for solving problems. Reteach/reinforce any skills and concepts identified in homework check as needing attention.


Revised 1/23/04 28



MATERIALS: Routines - four decks of 1-10 numeral cards for partners.

Base 10 blocks for each student LESSON FOCUS:

Solve a Simpler Problem


Mathematical Reasoning: 1.0, 2.0, 3.0 1.2: Determine when and how to break a problem into simpler parts. Number Sense 3.3 3.2: Demonstrate an understanding of, and ability to use, standard algorithms for multiplying a multi-digit number by a two-digit number and for dividing a multi-digit number by a one-digit number; use relationships between them to simplify computations and to check results. Algebra and Functions: 1.0

PURPOSE OF LESSON:

• Understand that a 3-digit factor can be multiplied by the number in each place value to make the problem simpler.

• The Distributive Property of multiplication defines the process for multiplying numbers by their place value.

LAUNCH: Introduce students to concepts Base 10 blocks

HW: Collect and check Mixed Review: • Discuss models and partial products and strategies for multiplying. Alternative Teaching Strategy, TE Pg. 214B


Problem, gP. 214: Ms. Alexander Buying Art Supplies. • Write problem on board/overhead. • Discuss problem solving strategies. • Use: Understand, Plan, Solve and Check questions. Do problem with

students.

PRACTICE: Focus on Communication and Representation. Transparency 11.5

Practice & Problem Solving, Pg. 215: # 1 – 2: Do with students. • Encourage students to draw models. • Discuss and share solutions. • Students explain/use representations or equations to justify answers. Practice & Problem Solving, Pg. 215: #s 3-4. Discuss. • Transparency 11.5: Lesson Quiz Problems 1-3. • Students work individually/with partners. • Confer with students. Discuss solutions and strategies.

OR P. 216: #s 23-25 SUMMARIZE: Connect purpose to activities.

ASSESS, Pg. 215: Discuss: “How can you change a multiplication problem…”

ASSESS, Pg. 215: Write: “Greg bought… ” • Record student strategies for making problem “simpler.”

HOMEWORK: Mixed Strategy Practice, Pg. 215, #5-9 • Use partial products method for solving the multi-digit multiplication

problem.


Revised 1/23/04 29

ROUTINES:

Top My Product! Give two decks of 1-10 numeral cards to each student. (Note: If making cards from tag board, etc., use two different colors so partners have two decks each of contrasting colors.) Students play with partners. Students shuffle cards. Each player turns over two cards at same time and says the product. Player with greater product “keeps” all four cards used in that turn. Players continue, reshuffle as needed, until one player has all the cards or any given greater number, as time permits. After game is over, players sort cards according to color and keep their original two sets. Discuss strategies for solving problems. Variation: Make 1 deck with numerals 1-10 and second deck with numerals 10, 20, 30, 40, 50, 60, 70, 80, 90, and 100. Reteach/reinforce any skills and concepts identified in homework check as needing attention.


Revised 1/23/04 30


Module 6: Chapter 12: Multiply by 2-Digit Numbers LESSON 12.1, pp. 220-223 Day 1 of a 2-Day Lesson

MATERIALS: Base-ten blocks for each small group; *Transparency 12.1. LESSON FOCUS: Multiply by 2-Digit Numbers CALIFORNIA STANDARDS:

Mathematical Reasoning: 2.1, 2.3, 2.4, 3.1, 3.3 1.2: Determine when and how to break a problem into simpler parts. Number Sense 3.0 3.2: Demonstrate an understanding of, and ability to use, standard algorithms for multiplying a multi-digit number by a two-digit number and for dividing a multi-digit number by a one-digit number; use relationships between them to simplify computations and to check results. 3.3: Solve problems involving multiplication of multi-digit numbers by two-digit numbers. Algebra and Functions: 1.0

PURPOSE OF LESSON:

• Understand how to multiply 2-digit numbers using basic multiplication facts and strategies for multiplying 1-digit numbers.

• Use partial products to record the process of multiplying by the digit in each place-value position.

LAUNCH: Introduce students to concepts Student’s books are closed.

• If students need more help in 2-digit multiplication, use TE Pg. 220B, Alternative Teaching Strategy where students model repeated addition of equal addends.

Learn, Pg. 220: Totally Tomatoes. • Write question on board/overhead. Teach, Pg. 220; Guided Instruction questions to guide discussion of p. 220. Find Products, Pg. 221: Review and discuss. • See bullets top margin TE Pg. 221 to guide discussion.

Possible Observations: Colleen’s process: Analyze the 2 partial products.

• Discuss and compare where the equivalent partial products in Brad’s model. Record similarities and differences.

Note: Emphasize Pg. 221: Math Idea –With the partial product algorithm students work with numbers according to the value of each digit and can be more accurate when multiplying.

See Reteach 12.1 if a recording model for partial products is needed. Alternative Teaching Strategy, Pg. 222: provides another model that may help students understand multi-digit multiplication.


Revised 1/23/04 31


Practice & Problem Solving, Pg. 222: #43-44: • Do with students. Do problems using regrouping algorithm and one

other model with students. Check: Pg. 221, #2 & 4: Do with students. • Show regrouping and partial product methods for each problem.

Discuss connections.


Practice & Problem Solving, Pg. 222, # 36 – 38. • Discuss solution strategies.


Assess, TE Pg. 223: DISCUSS. • Discuss and compare the methods for multiplication, i.e., partial

products, the algorithm, and any other method students use. • List/chart the similarities and differences. • Students multiply 23 by 34, estimate the product, solve, and explain

the steps used. HOMEWORK: Mixed Review and Test Prep, Pg. 223: #s 51-53, 55-56.

ROUTINES: P. 234: Math Detective: Deductive Reasoning with Multiplication and Estimation Introduce and do problem with students. Discuss steps in “estimating” for each one. Do Think It Over! After students solve the first question, have them work with partner to find the missing digits yielding products close to 1,000, 10,000, and 1,000,000. Review. *P. 234: Stretch Your Thinking Reteach/reinforce any skills and concepts identified in homework check as needing attention.


Revised 1/23/04 32

DAY: 13


LESSON 12.1, pp. 220-223 Day 2 of a 2-Day Lesson

MATERIALS: Base-ten blocks for each small group; *Transparency of Challenge

12.1 LESSON FOCUS:

Multiply by 2-Digit Numbers


Mathematical Reasoning: 2.1, 2.3, 2.4, 3.1, 3.3 1.2: Determine when and how to break a problem into simpler parts. Number Sense 3.0 3.2: Demonstrate an understanding of, and ability to use, standard algorithms for multiplying a multi-digit number by a two-digit number and for dividing a multi-digit number by a one-digit number; use relationships between them to simplify computations and to check results. 3.3: Solve problems involving multiplication of multi-digit numbers by two-digit numbers. Algebra and Functions: 1.0g

PURPOSE OF LESSON:

• Understand how to multiply 2-digit numbers using basic multiplication facts and strategies for multiplying by 1-digit numbers.


LAUNCH: Introduce students to concepts Base-10 Blocks

HW: Partner check and discuss Practice & Problem Solving, Pg. 222 #47. • Ask students to estimate the product of 24 x 35.

Students estimate product using a variety of strategies and explain/justify. Record estimates.

• Students solve using 2 different strategies to solve. • Compare answer with estimate to determine if estimate is/is not

reasonable. EXPLORE: Work with the concept. Focus on students “doing mathematics.” Base-10 Blocks

Practice & Problem Solving, Pg. 222: #s 45-46: Do with students. • Discuss strategies for solving. Emphasize strategies/approaches to

correct Emilia’s error.

Practice & Problem Solving, Pg. 222: #s 39-42: Do with students. • Students explain/show strategies for solving.

Discussion: How will this strategy be useful when solving problems?


Practice & Problem Solving, Pg. 223, #48 - 50: Students work with partners or individually. • Show process and sketch the array for at least one problem.

Discuss and share solutions and strategies.

*Early Finishers: Challenge 12.1 on overhead.


Revised 1/23/04 33


ASSESS TE Pg. 223: DISCUSS. • Discuss and chart more than one model for multiplying by 2-digit

number, and generalizations of the process.

• Example: 37 x 23: the 4 partial products are the result of multiplying: (7 x 3) + (7 x 20) + (30 x 20) + (30 x 3), or students can multiply: 3 x 37 and 20 x 37, and add those partial products.

HOMEWORK: Practice & Problem Solving, P. 222: #s 27-30. • Use a variety of strategies to solve. (partial products; regrouping;

algorithm; base 10 blocks; area model) ROUTINES:

Pg. 223: Pathfinder: Multiplication Practice (Thinker’s corner). Read the directions for Path Finder in the Thinker’s Corner. After students finish, review their answers. Discuss the reasoning they used to reach their conclusions. Reteach/reinforce any skills and concepts identified in homework check as needing attention.


Revised 1/23/04 34



MATERIALS: Transparency 12.2; Routines: Performance Assessment 4.4B: Speed

Writing - 1 copy for each student. LESSON FOCUS:

More About Multiplying by 2-Digit Numbers


Mathematical Reasoning: 2.1, 2.3, 2.4 1.2: Determine when and how to break a problem into simpler parts. Number Sense: 3.0 3.2: Demonstrate an understanding of, and ability to use, standard algorithms for multiplying a multi-digit number by a two-digit number and for dividing a multi-digit number by a one-digit number; use relationships between them to simplify computations and to check results. 3.3: Solve problems involving multiplication of multi-digit numbers by two-digit numbers.

PURPOSE OF LESSON:

• Understand how to multiply 2-digit numbers using basic multiplication facts and strategies for multiplying by 1-digit numbers.


• Alignment of digits is critical to maintain correct place values. LAUNCH: Introduce students to concepts Transparency 12.2

Problem of the Day, Pg. 224A. Discuss Wayne’s method and ask students to explain. Record explanations.

Alternative Teaching Strategy, Pg. 224B: Do several examples together or with partners.


Learn, Pg. 224: Fields of Fruit. • Write problem on board/overhead. • Discuss strategies for solving. • Emphasize estimation first. Teach, Pg. 224; Guided Instruction questions to guide discussion. • Connect the 3 steps for multiplying to partial products and to the area

(array) model.

Check, Pg. 225: #s 2-4: Do with students. • Use partial product strategy, or area model, and with traditional

algorithm to verify solutions.


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Practice & Problem Solving, Pg 225: #22 - 27: • Students work with partners or individually. • Discuss solutions and strategies for solving problems. Then, Practice & Problem Solving, Pg. 225: #28 - 31: • Discuss problems with students. • Students explain/justify strategies. • Encourage a variety of strategies.


• Discuss and chart how multiplying 3-digit numbers by 2-digit numbers is similar/different from multiplying 2-digit numbers by 2-digit numbers.

• Students write, estimate the product, and solve a word problem using multiplication of a 3-digit number by a 2-digit number.

• Discuss students’ problems and solutions. HOMEWORK: Practice & Problem Solving, Pg. 225: #s 12-14

Mixed Review and Test Prep, Pg. 225: #s 32-36 ROUTINES:

Pg. PA28-29, PA31-32, and PA35-36: Performance Assessment 4.4B: Speed Writing in Performance Assessment booklet. Read problem with students. Answer any questions. Be encouraging…motivate, guide… Be clear. Reword any words or phrases; insert others as needed. Be supportive. Assist students who need help. Be fair. Allow students adequate time to do their best work. Be flexible. All students will not do the task in the same order/way. Involve students in the evaluating process. The suggested completed performance task is on p. PA32. Rubrics (3-point) are provided on pp. PA35-36. These should be used for the next day’s Routine when the Performance Assessment is reviewed. Reteach/reinforce any skills and concepts identified in homework check as needing attention.


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MATERIALS: Cm-grid paper for each student; *Routines: Performance Assessment:

Speed Writing: Transparencies of student work. LESSON FOCUS:

Multiply Greater Numbers


Mathematical Reasoning: 2.1, 2.2, 2.3, 3.1, 3.3 1.2: Determine when and how to break a problem into simpler parts. Number Sense: 3.0 3.2: Demonstrate an understanding of, and ability to use, standard algorithms for multiplying a multi-digit number by a two-digit number and for dividing a multi-digit number by a one-digit number; use relationships between them to simplify computations and to check results. 3.3: Solve problems involving multiplication of multi-digit numbers by two-digit numbers.

PURPOSE OF LESSON:

• Compare estimated products to actual products to determine the reasonableness of the answer.

• Understand how to multiply by a multiple of 10 and 100 and know why zeros are in the ones and tens place.

LAUNCH: Introduce students to concepts Note: If students are having trouble aligning numbers when multiplying, use grid paper, TR60.

*HW: Practice & Problem Solving, Pg. 225: #12 - 14: • Students share solutions and discuss strategies for solving.

Writing in Mathematics, Pg. 226B. • If students need prompting, remind them about situations such as

buying multiple copies of an item, finding the number of objects in rows and columns such as plants or small boxes, etc.

• Share their problems to highlight estimating products first and the variety of solution strategies. (partial products; regrouping; algorithm; base 10 blocks; area model)


Learn, Pg. 226: Foreign Exchange. • Write problem on board/overhead. • Do with students. Remind students to estimate the product first. • Discuss approaches/strategies for solving. Teach, Pg. 226; Guided Instruction questions to guide discussion. • Check, Pg. 226-227, # 1-3: Do with students. • Compare estimates to answers.


Practice & Problem Solving, Pg. 227, #17 – 20. Discuss with students. • Then, pp. 227 #21 – 24. Students work with partners/individually. • Discuss strategies with students.


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ASSESS, TE Pg. 227: Discuss: • Compare the process for multiplying 4-digit numbers by 2-digit

numbers and multiplying 3-digit numbers by 2-digit numbers. • Emphasize: The process of multiplying multi-digit numbers is the

same for 2-digit by 2-digit, 3-digit by 2-digit, etc.

HOMEWORK: Practice & Problem Solving, Pg. 227: #15-16 Mixed Review and Test Prep, Pg. 227: #s 25-29.

ROUTINES:

P. PA28-29, PA31-32, and PA35-36: Review of Performance Assessment 4.4B: Speed Writing in Performance Assessment booklet. Read problem with students. Answer any questions. Be encouraging…motivate, guide… Be clear. Reword any words or phrases; insert others as needed. Be supportive. Assist students who need help. Be fair. Allow students adequate time to do their best work. Be flexible. All students will not do the task in the same order/way. Involve students in the evaluating process. The suggested completed performance task is on p. PA32. Rubrics (3-point) are provided on pp. PA35-36. These should be used for the next day’s Routine when the Performance Assessment is reviewed. Reteach/reinforce any skills and concepts identified in homework check as needing attention.


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MATERIALS: *Transparency 12.4

Play Money for each group, pp. TR 31 -34 LESSON FOCUS:

Practice Multiplication


Number Sense: 3.0 3.2: Demonstrate an understanding of, and ability to use, standard algorithms for multiplying a multi-digit number by a two-digit number and for dividing a multi-digit number by a one-digit number; use relationships between them to simplify computations and to check results. 3.3: Solve problems involving multiplication of multi-digit numbers by two-digit numbers. Mathematical Reasoning: 2.1, 2.3, 3.2

PURPOSE OF LESSON:

• Understand that multiplying dollar amounts is similar to multiplying whole numbers.

• Know where to place the decimal point when multiplying dollar amounts.

• Understand that a dollar amount can be multiplied by a whole number but cannot be multiplied by another dollar amount.

LAUNCH: Introduce students to concepts Transparency 12.4 Play money

Alternative Teaching Strategy, Pg. 228B.

• Discuss the importance of estimating to find about what the answer is. Put the following on board/overhead. Ask only for estimates of products: $18.35 x 43 $67.13 x 9 $186 x 31

• Discuss each emphasizing the placement of the decimal.


Learn, Pg. 228: Bike Bonanza. • Write problem on board/overhead. Do with students. • Estimate product and complete multiplication of the problems. Teach, Pg. 228; Guided Instruction questions to guide discussion. Check, Pg. 228 #1 Discuss with students. Check, p. 228 #3 – 4. Students may be more accurate if they continue using partial products.


Practice & Problem Solving, Pg. 229, #22 – 28. Do with students. • Discuss strategies. • Then students do #29 – 31. Estimate first. Compare estimates with

answers.


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• Summarize importance of estimating before solving problem. Identify situations in which students (and adults) should estimate first.

ASSESS, TE Pg. 229: DISCUSS. • Students write a word problem requiring multiplication by 2-digit

number, estimate product, solve, and compare product with estimate. HOMEWORK: Practice & Problem Solving, Pg. 229 #20 – 21 and

Mixed Review and Test Prep: #s 33-37

ROUTINES:

Time to Check Your Calendar! Review the months of the year. Ask: What is the first month? What is the last month? What is the ninth month? Which months are in the first half of a year? Students take turns asking class similar questions. Discuss notation for recording dates: 11/12/02. Ask: What does the 11 represent? What does the 12 represent? What does the 02 represent? How should you record January 1, 2003? How should you record July 5, 2010?

Review concept of decade and century. Ask: How many decades are in a century? If a census is taken and recorded once a decade on the same date, and the last census happened to be dated 1/10/01, when would the next census be dated? February normally has 28 days. In a leap year, it has 29. How long is it from February 28 to March 2 in a regular year? In a leap year? Review: How many decades are in 200 years? How many centuries are in 200 years? Three years = how many months? 21 days = how many weeks? 24 months = how many years? Continue as needed.


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DAY: 17


LESSON 12.5, pp. 230-231

MATERIALS: *Transparency 12.5; Cm-grid paper for each student. Play Money and small plates or placemats for each group.

LESSON FOCUS:

Problem Solving Skill: Multi-step Problems


Mathematical Reasoning: 1.0, 1.1, 1.2, 2.0, 2.3, 3.3 1.2: Determine when and how to break a problem into simpler parts. Number Sense: 3.0 3.2: Solve problems involving addition, subtraction, multiplication, and division of whole numbers and understand the relationships among the operations. 3.3: Solve problems involving multiplication of multi-digit numbers by two-digit numbers. Algebra and Functions: 1.0

PURPOSE OF LESSON:

• Understand how drawing and labeling diagrams can help to identify the steps needed to solve a problem.

• Understand how to identify the steps for solving problems that require more than one operation or step.

LAUNCH: Introduce students to concepts. Transparency 12.5

HW: Practice & Problem Solving, p. 229 #32: review student problems.

Alternative Teaching Strategy, p. 230B

• Emphasize the importance of going back after work is done and

checking that each step has been done. EXPLORE: Work with the concept. Focus on students “doing mathematics.” Students have books closed.

Problem, Pg. 230: Reach Your Goal. • Write problem on board/overhead. • Do with students. Record process for solving. Teach, Pg. 230; Guided Instruction questions to guide discussion.

Talk About It, Pg. 230: Do with students.


Problem Solving Practice, Pg. 231, # 1 and 2: Do with students. • Discuss solutions and strategies for solving. • Then, students do #3 – 4 and discuss. Note: See Pg. 230B: Special Needs Strategy if students need additional support with this concept. Mixed Application, Pg. 231: # 5-7: • Students work with partners and use representations/models, with

diagrams/sketches and equations. • Discuss strategies for solving.


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ASSESS, TE Pg. 231: DISCUSS. • Discuss and explain how to work through a multi-step problem. • Record students’ strategies. ASSESS, TE Pg. 231: WRITE. • Share procedures.

HOMEWORK: Mixed Applications, Pg. 231, #s 9-10 • Students use menu on p. 231. • Write two problems that can be solved using the data in your menu.

ROUTINES:

Pg. 232: Chapter Review Test Look over Review/Test with students. Answer any questions. Students do #s 1-3, 8-15, 24, and 25. Reteach/reinforce any skills and concepts identified in homework check as needing attention.

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Gr 4 Mod 6 - PBworks