Module 5 − Reorganized - eusddata

S D
C S
SAN DIEGO CITY SCHOOLS
Instructional Module to Enhance the Teaching of
H A R C O U R T
Math
California Edition
Grade 5
Module 5 − Reorganized
Multiply Whole Numbers and Decimals;
Percent
⎯ WORK IN PROGRESS⎯
Reorganized 9/04/04

Harcourt Math−Grade 5 MODULE 5
Grade Five Traditional Calendar – 2004-2005
Order of Units and Pacing Guide
Month Module Number of Days
Module 1: Data and Graphing
11 days
September
19 instructional days
Module 2:
Place Value and Addition and
Subtraction of Whole Numbers
and Decimals
8 days
October
21 instructional days
Module 2:
Place Value and Addition and
Subtraction of Whole Numbers
and Decimals
7 days
Module 3:
Algebra: Use Addition and
Multiplication; Integers
14 days
November
18 instructional days
Module 3:
Algebra: Use Addition and
Multiplication; Integers
8 days
Module 4:
Geometry
10 days
December
13 instructional days
Winter Break 12/20 – 12/31
January
20 instructional days
Module 4:
Module 5:
Module 5:
Geometry
Multiply Whole Numbers and
Decimals; Percent
Multiply Whole Numbers and
Decimals; Percent
2 days
11 days
3 days
Module 6:
Divide Whole Numbers and
Decimals
17 days
February
17 instructional days
Module 7:
Number Theory; Fraction
Concepts and Addition and
Subtraction of Fractions
17 days
March
18 instructional days
Spring Break 3/21 – 3/25
Module 7:
Number Theory; Fraction
Concepts and Addition and
Subtraction of Fractions
5 days
Module 8:
Geometry: Area, Perimeter, and
Volume
12 days
April
20 instructional days
Module 9:
Operations with Fractions:
Multiplication and Division
Module 10: Measurement, Probability and
Ratio
11 days
9 days
May Module 10: Measurement, Probability and 12 days
Reorganized 9/04/04 2

Harcourt Math−Grade 5 MODULE 5
21 instructional days
STAR 4/26 – 5/17
DMT 5/9 – 5/13
June
13 instructional days
Ratio
Review Grade 5 concepts
Preview Grade 6 Concepts
13 days
Grade Five – Year Round Calendar – 2004-2005
Order of Units and Pacing Guide
Month Module Number of Days
September Module 1: Data and Graphing
11 days
19 instructional days Module 2: Place Value and Addition and
Subtraction of Whole Numbers
and Decimals
8 days
October
21 instructional days
Module 2:
Module 3:
Place Value and Addition and
Subtraction of Whole Numbers
and Decimals
Algebra: Use Addition and
Multiplication; Integers
7 days
14 days
November
18 instructional days
Module 3:
Module 4:
Algebra: Use Addition and
Multiplication; Integers
Geometry
8 days
10 days
December
13 instructional days
Winter Break 12/22 – 1/17
Module 4:
Module 5:
Geometry
Multiply Whole Numbers and
Decimals; Percent
2 days
11 days
January
10 instructional days
Module 5:
Module 6:
Multiply Whole Numbers and
Decimals; Percent
Divide Whole Numbers and
Decimals
3 days
7days
February
17 instructional days
Module 6:
Module 7:
Divide Whole Numbers and
Decimals
Number Theory; Fraction
Concepts and Addition and
Subtraction of Fractions
10 days
7 days
March
11 instructional days
Spring Break 3/16 – 4/8
Module 7:
Number Theory; Fraction
Concepts and Addition and
Subtraction of Fractions
11 days
April
15 instructional days
Module 7:
Module 8:
Number Theory; Fraction
Concepts and Addition and
Subtraction of Fractions
Geometry: Area, Perimeter, and
Volume
4 days
11 days
Reorganized 9/04/04 3

Harcourt Math−Grade 5 MODULE 5
May
21 instructional days
Module 8:
Module 9:
Module 10:
Geometry: Area, Perimeter, and
Volume
Operations with Fractions:
Multiplication and Division
Measurement, Probability and
Ratio
1 days
11 days
9 days
June
22 instructional days
STAR 5/27 – 6/17
DMT 6/13 – 6/17
July
14 instructional days
Module 10:
Measurement, Probability and
Ratio
Review Grade 5 concepts
Preview Grade 6 Concepts
12 days
14 days
Reorganized 9/04/04 4

San Diego City Schools
Instruction and Curriculum Division
MATHEMATICS CURRICULUM MAP – GRADE 5
MODULE 5 – Multiply Whole Numbers and Decimals; Percent
Modules represent individual units of study that lead to essential learnings
THREADS THROUGHOUT THE YEAR:
The threads represent ongoing learning opportunities in which students should be actively engaged throughout all units of inquiry during the entire
school year. These items should not be isolated to any one particular unit of inquiry.
Students will:
• Develop understanding of numbers and the number system and use their understanding to solve problems and recognize reasonable results.
• Develop understanding of and fluency in basic computation and procedural skills.
• Use mathematical reasoning to solve problems.
• Communicate their mathematical thinking by using words, numbers, symbols, graphs and charts and translate between different representations.
• Use equations and variables to express generalizations of patterns and relationships.
• Develop logical thinking to analyze evidence and build arguments to support or refute a hypothesis.
• Make connections among mathematical ideas and between other disciplines
• Develop and use strategies, skills, and concepts to solve problems.
• Use appropriate tools, including technology, as vehicles to learn mathematical concepts.
These are essential learnings that represent bigger ideas/concepts:
• Students apply their understanding of the operations and properties of multiplication using whole numbers to multiply decimals.
• Students use patterns of powers of ten and the area model to understand and compute with decimals.
• Students understand that multiplication with whole numbers and decimals results in the same digits, and they can place the decimal point using powers of ten and
estimation.
• Students use fractions and decimals to represent percents as a hundredth of a unit.
• Students find the percent of a number by multiplying by fractions or decimals.
• Students use models to represent, solve and explain solutions to percent problems.
These are essential questions that learners ask themselves in order to achieve the essential learnings:
• *How do I connect whole number concepts and strategies to solve decimal multiplication problems?
• How do I model, identify, and use multiplication properties with decimals?
• How do I use estimation strategies to evaluate decimal multiplication problems for reasonableness?
• How do I use an *area model to multiply a decimal by a decimal and translate the model to a numerical expression?
• How do I use patterns to multiply by hundredths and tenths?
• How do I explain and use strategies to place the decimal point in the product?
• How do I translate between percents, fractions*, decimals* and base-10 materials*?
• How do I use my understanding of multiplying and dividing by powers of ten and benchmark percents to find the percent of a number?
• How and why can I multiply by an equivalent decimal to find the percent of a number?
• How do I use models to understand finding percents and to explain the meaning of the procedure I use?
* Presented in previous grades
Resources: Van de Walle: Chapter17 (pp. 280-294); Mathematics Source Book: Decimals and Percents (pp. 77, 78, 95–98)
Reorganized 9/04/04

Harcourt Math−Grade 5 MODULE 5
MULTIPLY WHOLE NUMBERS AND DECIMALS
PERCENT
Key Mathematical Concepts:
• Connect whole number concepts and strategies to solve decimal
multiplication problems.
• Use estimation to evaluate multiplication problems for reasonableness.
• Use several strategies to place the decimal point in the product; estimation,
decimal model, patterns, and “moving” the decimal point using multiplication
and division by powers of ten.
• Model multiplication on a grid using repeated addition and an area model.
Translate the graphical representations to numerical expressions that are
equivalent.
• Interpret percent as part of a hundred.
• Know that percents represent a part-to-whole ratio/relationship.
• Understand how percents, fractions, and decimals can represent the same
value.
• Understand that percent can be expressed as a fraction or decimal to
compute a given percent of a whole number.
Reorganized 9/04/04 6

Harcourt Math−Grade 5 MODULE 5
MODULE 5 NOTES
Harcourt Mathematics
Grade 5
Chapter 18
Percent
• Lessons 4 and 5 in Chapter 18 are reversed so that mental strategies can
be emphasized prior to learning the algorithm.
• Lessons 18.6 and 18.7 are omitted because the lessons do not address
key fifth grade standards.
Day 1:
Chapter 9:
Multiply Whole
Numbers
Lesson 9.1
Estimation:
Patterns in
Multiples
Day 2:
Lesson 9.2
Multiply by a 1-
Digit Number
Day 3:
Lesson 9.3
Multiply by a 2-
Digit Number
Day 4:
Lesson 9.5
Evaluate
Answers for
Reasonableness
Day 5:
Chapter 10:
Multiply Decimals
Lesson 10.1
Multiply Decimals
and Whole
Numbers
Day 6:
Lesson 10.2
Algebra:
Patterns in
Decimal
Factors and
Products
Day7:
Lesson 10.3
Model Decimal
Multiplication
Day 8:
Lesson 10.4
Place the Decimal
Point
Day 9:
Lesson 10.5
Zeros in the
Product
Day 10:
Chapter 18:
Percent
Lesson 18.1
Hands On:
Understand
Percent
Day 11
Day 12:
Day 13:
Day 14:
Lesson 18.2
Relate
Decimals and
Percents
Lesson 18.3
Relate Fractions,
Decimals, and
Percents
Lesson 18.5
Mental Math:
Percent of a
Number
Lesson 18.4
Find a Percent
of a Number
Reorganized 9/04/04 7

Harcourt Math−Grade 5 MODULE 5
MATERIALS:
LESSON
FOCUS:
CALIFORNIA
STANDARDS:
Purpose of
Lesson:
LAUNCH:
Introduce
students to
concepts.
EXPLORE:
Work with the
concept. Focus
on students
“doing
mathematics.”
PRACTICE:
Focus on
Communication
and
Representation.
SUMMARIZE:
Connect purpose
to activities.
DAY 1
UNIT 3: Multiply Whole Numbers and Decimals
LESSON 9.1
Practice 9.2 one per student
Multiply by 1-Digit Numbers
Number Sense: 1.0
Students compute with very large and very small numbers, positive integers,
decimals, and fractions and understand the relationship between decimals,
fractions, and percents. They understand the relative magnitudes of numbers.
Mathematical Reasoning: 2.1
Use estimation to verify the reasonableness of calculated results.
Mathematical Reasoning 2.2
Apply strategies and results from simpler problems to more complex problems.
• Use estimation to determine reasonableness of a product & the number of
digits in the product.
• Multiply by a one-digit number using distributive property as one strategy.
Problem of the Day, T.E. p. 146A. Discuss solutions.
Learn, p. 146: Heavyweights. Write problem on board/overhead.
• Ask students to:
− Determine an estimate for the solution.
− Share their strategy with a partner.
− Calculate an exact answer.
− Compare their estimate with their exact answer.
− Share their solution strategies with the class.
• Record the different strategies.
Teach, p. 146, Modifying Instruction, discuss the reasoning behind this
strategy.
• Relate to Example of distributive property (a partial product strategy),
p. 146 bottom, as a way to get the actual product.
• Allow students to discuss and explain the process.
Check, p. 147 #1. Discuss. Then, #5 & 6.
• Student partners ESTIMATE FIRST, then try strategies use to solve.
• Share strategies.
Practice & Problem Solving, p. 147 #18-21 with a partner.
• Show distributive property solutions for # 18 & 19.
Practice 9.2 OR Practice & Problem Solving, p. 147 #15 – 17.
• Estimate first.
• Discuss strategies for solving.
T.E. ASSESS, p. 147: DISCUSS
T.E. ASSESS, p. 147: WRITE: In practice problem #2, how could you use
addition to check your multiplication?
• How did you use the distributive property when solving multiplication
problems?
HOMEWORK: Mixed Review, p. 147
Advanced Learners T.E. p. 142F (See Challenge 9.4 TE 151 for more
problems like this)
Reorganized 9/04/04 8

Harcourt Math−Grade 5 MODULE 5
MATERIALS:
LESSON FOCUS:
CALIFORNIA
STANDARDS:
Purpose of
Lesson:
LAUNCH:
Introduce students
to concepts.
Number Line
Blackline pg. TR 6
DAY 2
UNIT 3: Multiply Whole Numbers and Decimals
LESSON 9.2
Number line blacklines, 3 per student, p. TR6
Estimation: Patterns in Multiples
Number Sense: 1.1
Estimate, round and manipulate very large and very small numbers.
Mathematical Reasoning: 1.1
Analyze problems by identifying relationships, distinguishing relevant from
irrelevant information, sequencing and prioritizing information, and observing
patterns.
• To round factors and determine an estimate.
• To use patterns in multiples as a tool for estimation.
Number of the Day, T.E. p. 144A
Alternative Teaching Strategy, T.E. p. 144B
• Label Number line #1 by 10s (0-100) #2 by 100s (100-1,000) and have
students make a third number line: #3 by 1,000s (1,000-10,000). Include
some numbers for students to place on line #3.
EXPLORE:
Work with the
concept.
Focus on students
“doing
mathematics.”
***Generally,
Student books are
closed during this
part of the lesson.
The teacher uses
the book as a
resource for
presenting
information to
students.
PRACTICE:
Focus on
Communication
and
Representation.
SUMMARIZE:
Connect purpose
to activities.
Assess
Individually.
Learn, p. 144: Orbiting Numbers
• Write problem on board/overhead.
• Highlight that the question begins “About…”
• Encourage students to use their number lines to help them calculate an
estimate.
Note: Accept any reasonable estimate; i.e., the correct place value.
• Remind students that an estimate is not computing the actual solution and
rounding off.
Teach, p. 144, Guided Instruction questions and Modifying Instruction to
guide discussion. Another Question to consider:
• What patterns do you notice when you multiply tens with tens, tens with
hundreds, hundreds with ones, etc.?
(One pattern is the total number of zeros in the factors is the same as the
number of zeros in the product.)
Practice & Problem Solving, p. 145 #26-30
• Discuss with partner groups to talk about any patterns they noticed.
Then share whole group.
T.E. ASSESS, p. 145: Write
Practice & Problem Solving, p. 145 #31
• Discuss.
HOMEWORK: Practice & Problem Solving, p. 145 #22 - 25
Mixed Review, p. 145
Reorganized 9/04/04 9

Harcourt Math−Grade 5 MODULE 5
DAY 3
UNIT 3: Multiply Whole Numbers and Decimals
LESSON 9.3
MATERIALS:
LESSON FOCUS:
CALIFORNIA
STANDARDS:
Purpose of Lesson:
LAUNCH:
Introduce students to
concepts.
Grid paper: TR32
700 + 0 + 4
20 14000 0 80
3 2100 0 12
EXPLORE:
Work with the concept.
Focus on students
“doing mathematics.”
PRACTICE:
Focus on
Communication and
Representation.
Dice/number cubes
Grid paper, p. TR32, as necessary
Multiply by 2-Digit Numbers
Number Sense: 1.0
Students compute with very large and very small numbers, positive
integers, decimals, and fractions and understand the relationship
between decimals, fractions, and percents. They understand the relative
magnitudes of numbers.
Mathematical Reasoning: 2.1
Use estimation to verify the reasonableness of calculated results.
Use understanding of the distributive property to use the strategy of
partial products to multiply two-digit numbers.
English Language Learners, T.E. p. 150B, to clarify “partial”
• Continue the discussion with a review of 3 different strategies for partial
products (distributive property; multiplication algorithm; area with
expanded notation).
• Practice partial products in different representations.
Distributive Property: see Example, bottom p. SE146
315 x 26 = (315 x 6) + (315 x 20) = 8,190
315 x 26 = (6 x 5) + (6 x 10) + (6 x 300) + (6 x 5) + (6 x 10) +
(6 x 300) = 8,190
*Traditional algorithm: grid for aligning partial products,
See Alternative Teaching Strategy, T.E. p. 150B
• Area Model: with expanded notation,
See Modifying Instruction, T.E. p. 151, margin
Learn, p. 148: Pedal Power
• Write problem on board/overhead.
• First, students estimate a possible answer.
• Accept all reasonable estimates.
• Ask students to work with a partner to develop a partial product with
each strategy to solve the problems.
• Share 3 representations and any other strategies, including any used
for estimation.
• Discuss and connect the different multiplication strategies.
• Ask what students notice as they examine the strategies. Chart
responses.
Practice & Problem Solving, p. 149 #15 – 16. Students show at least 2
different strategies for solutions.
Practice & Problem Solving, p. 149 #23 -28.
• Ask students to ESTIMATE FIRST. Ask students to use 2 of the
methods discussed to solve problems.
• Discuss. Share #28.
Reorganized 9/04/04 10

Harcourt Math−Grade 5 MODULE 5
SUMMARIZE:
Connect purpose to
activities.
T.E. ASSESS, p. 149: DISCUSS:
• Students use different strategies and explain.
• Chart strategies used so students can refer back to.
• Be sure distributive property is represented.
T.E. ASSESS, p. 149: WRITE:
• Describe how to multiply 45 x 61. Use words & diagrams & numbers.
HOMEWORK: Practice & Problem Solving, p. 149 #18 - 22
Mixed Review, p. 149
Reorganized 9/04/04 11

Harcourt Math−Grade 5 MODULE 5
DAY 4
UNIT 3: Multiply Whole Numbers and Decimals
LESSON 9.5
LESSON FOCUS:
CALIFORNIA
STANDARDS:
Purpose of Lesson:
LAUNCH:
Introduce students to
concepts.
EXPLORE:
Work with the concept.
Focus on students
“doing mathematics.”
PRACTICE:
Focus on
Communication and
Representation.
SUMMARIZE:
Connect purpose to
activities.
Problem Solving Skill: Evaluate Answers for Reasonableness
Mathematical Reasoning: 2.1
Use estimation to verify the reasonableness of calculated results.
Mathematical Reasoning: 3.1
Evaluate the reasonableness of the solution in the context of the original
situation.
To learn to use estimation as a tool to check for reasonableness before
solving problems.
Science Connection, T.E. p. 152B
Prompt: Why is it a good idea to determine if an answer is reasonable?
Students suggest a real life situation when estimation would be helpful.
Present the problem, p. 152
• Paper Products. Write on board/overhead.
• Include Teach, p. 152, Guided Instruction questions and Talk About It
(bottom p. 152) to guide discussion.
Note: Whenever students give estimates, accept any reasonable
estimate, that is, an estimate with the correct number of digits.
Problem Solving Practice, p. 153 Discuss #2 Reasoning: “What If.”
Discuss: T.E. ASSESS, p. 153: WRITE
Problem Solving Practice, p. 153 #1, 3, 4. Discuss. Share thinking.
Mixed Application, p. 153.
• Students work with partners.
• Discuss solutions & strategies.
T.E. ASSESS, p. 153: DISCUSS
HOMEWORK: Review/Test #1-2, 20 - 25
Reorganized 9/04/04 12

Harcourt Math−Grade 5 MODULE 5
DAY 5
UNIT 3: Multiply Whole Numbers and Decimals
LESSON 10.1
MATERIALS:
LESSON FOCUS:
CALIFORNIA
STANDARDS:
PURPOSE OF
LESSON:
LAUNCH:
Introduce students
to concepts.
TR9-10: Hundreds
Grid
EXPLORE:
Work with the
concept. Focus on
students “doing
mathematics.”
TR 9-10: hundreds
grids
PRACTICE:
Focus on
Communication and
Representation.
Decimal modules (100 grids) p. TR9-10
Multiply Decimals and Whole Numbers
Number Sense: 2.1
Add, subtract, multiply, and divide with decimals; add with negative
numbers; subtract positive integers from negative integers; and verify the
reasonableness of the results.
• Connect multiplying of whole numbers and decimals to models.
• Understand that the product of a whole number and a decimal less than 1
will always be less than the whole number.
• Understand the relationship of the number of decimal places in the factors
and in the product.
Problem of the Day, T.E. p. 158A.
• Share strategies. Highlight decimal placement. Also, connect repeated
addition to check decimal placement (0.20 + 0.20 + 0.02 = 0.60).
Quick Review, p 158.
• Discuss representation (labels) as with #1 (450¢ OR $4.50 but not 4.50¢)
Write Explore problem, p. 158 on the board/overhead and read with
students.
• Provide students decimal models T.R. pg. 9-10 (hundreds grids) to
represent the problem. (You may need to remind students that they can
represent multiplication as repeated addition. Example: 2 x 0.53 = 0.53 +
0.53).
Teach, T.E. p. 158, Guided Instruction questions to guide discussion.
Try It, p. 158 and Connect, p. 159 provide further explanations and checks
for understanding.
Practice, p. 159 #1, 5, 7
• Students work with partners.
• Discuss.
• Share decimal representations.
Practice, p. 159 #9 – 14
• Students work with partners or independently.
• Students do a written explanation for #14.
• Students share solutions & strategies with the class.
SUMMARIZE:
Connect purpose to
activities.
T.E. ASSESS, p. 159: DISCUSS
T.E. Assess, p. 159: WRITE:
• Explain how to use a model to find the product 5 x 0.37.
• Provide students decimal models to use to verify products.
HOMEWORK: Mixed Review, p. 159
Reorganized 9/04/04 13

Harcourt Math−Grade 5 MODULE 5
DAY 6
UNIT 3: Multiply Whole Numbers and Decimals
LESSON 10.2
MATERIALS:
LESSON FOCUS:
CALIFORNIA
STANDARDS:
Purpose of
Lesson:
LAUNCH:
Introduce students
to concepts.
Hundreds grids
EXPLORE:
Work with the
concept. Focus on
students “doing
mathematics.”
Hundreds grids.
Algebra: Patterns in Decimal Factors and Products
Mathematical Reasoning: 1.1
Analyze problems by identifying relationships, distinguishing relevant from
irrelevant information, sequencing and prioritizing information, and observing
patterns.
Number Sense: 1.0
Students compute with very large and very small numbers, positive integers,
decimals, and fractions and understand the relationship between decimals,
fractions, and percents. They understand the relative magnitudes of numbers.
To use a decimal model, mental math and patterns to find decimal products.
Books Closed:
Quick Review, p. 160. Discuss patterns
Alternative Teaching Strategy, T.E. p. 160B:
• Use the decimal model to have students investigate patterns numerically
and also verify with the grids: (0.04x1, 0.04 x 10, 0.04 x 100).
• Continue with other examples.
• For example: Ask students to predict/investigate patterns.
(0.98 x1), (0.98 x 10), (0.98 x100), and (0.98 x 1,000)
(0.24 x 1), (x10), (x100) and (x1000)
Learn, p. 160. Review examples.
Teach, T.E. p. 160, Guided Instruction questions to guide discussion.
Check, p. 161 #1. Discuss patterns. Apply discussion to #5, 6, 7. Discuss.
PRACTICE:
Focus on
Communication and
Representation.
SUMMARIZE:
Connect purpose to
activities.
Assess Individually.
Practice & Problem Solving, p. 161 #16 – 23. Discuss. Highlight decimal
patterns by charting responses.
Practice & Problem Solving, p. 161: Discuss #24.
• Ask students to generalize a rule about what they observe about the
movement of the decimal.
• Where does it move, which direction, how many places does it move, and
WHY? What if there was no decimal in the factors of the problem – is there
still a decimal “moving”? (yes)
• Connect back to money as in #22.
HOMEWORK: Practice & Problem Solving, p. 161 #13 - 15
Mixed Review, p. 161
Reorganized 9/04/04 14

Harcourt Math−Grade 5 MODULE 5
DAY 7
UNIT 3: Multiply Whole Numbers and Decimals
LESSON 10.3
MATERIALS: Hundreds decimal model (grid), p. TR 10
LESSON FOCUS: Model Decimal Multiplication
CALIFORNIA Number Sense: 2.1
STANDARDS: Add, subtract, multiply, and divide with decimals; add with negative integers;
subtract positive integers from negative integers; and verify the
reasonableness of the results.
Mathematical Reasoning: 2.3
Use a variety of methods, such as words, symbols, charts, graphs, tables,
diagrams, and models, to explain mathematical reasoning.
PURPOSE OF Use an area model to multiply a decimal by a decimal; translate the model to
LESSON:
LAUNCH:
Introduce students
to concepts
Hundreds grids
EXPLORE:
Work with the
concept. Focus on
students “doing
mathematics.”
TR10: hundreds
grids
PRACTICE:
Focus on
Communication
and
Representation.
SUMMARIZE:
Connect purpose to
activities.
a numerical representation.
Early Finishers, T.E. p. 162B.
• Students work with partners.
• Whole class discussion.
Alternative Teaching Strategy, T.E. p. 162B.
• Highlight finding a decimal (fractional) part of a decimal (fractional) amount.
• Discuss student strategies and models using the board/overhead.
• Record the numerical expression and product.
Learn, p. 162.
• Present Fast Food problem on board/overhead.
• Ask students to create a model to solve the problem.
Teach, p. 162, Guided Instruction questions to guide discussion of p. 162,
especially Reasoning, middle of SE p. 162.
• Help students translate the equation into words to help find the value of the
variable. E.g., n x 0.2 = 0.14 translated into words is: “What number times
two tenths is equal to fourteen one-hundredths?”
Check, p. 162 #1 – 5.
• Groups discuss how the colored model in the book is equivalent to the
numerical expression and how it is used to find the product.
Practice & Problem Solving, p. 162, #29 -33.
• Use decimal models to find products, where appropriate, particularly #30.
• Ask students to look for patterns with the decimal point.
For Early Finishers write a Challenge Problem on the board (T.E. pg. 163).
T.E. ASSESS, p. 163: WRITE
THEN, T.E. ASSESS, p. 163: DISCUSS:
• Discuss the error in p. 163 #32: How does using a decimal model help you
find the product?
• Discussion points: “What do you notice about the size of the product
compared to the size of the factors?” “What patterns did you notice with the
decimal point?”
HOMEWORK: Pg. 163, #12, 13
Mixed Review, p. 163
Reorganized 9/04/04 15

Harcourt Math−Grade 5 MODULE 5
DAY 8
UNIT 3: Multiply Whole Numbers and Decimals
LESSON 10.4
LESSON FOCUS:
CALIFORNIA
STANDARDS:
PURPOSE OF
LESSON:
LAUNCH:
Introduce students
to concepts
Thousand grids
EXPLORE:
Work with the
concept. Focus on
students “doing
mathematics.”
PRACTICE:
Focus on
Communication
Place the Decimal Point
Number Sense: 2.1
Add, subtract, multiply, and divide with decimals; add with negative integers;
subtract positive integers from negative integers; and verify the
reasonableness of the results.
Number Sense: 1.1
Estimate, round, and manipulate very large and very small numbers.
• To use estimation and patterns to place the decimal point.
• To understand that to estimate, you round each decimal to the greatest
place value, and multiply as with whole numbers.
• Explore two strategies for estimating decimal products:
Alternative Teaching Strategy, T.E. p. 164B (algorithm)
Alternative Teaching Strategy, T.E. p. 166 (number line)
• Connect the two strategies. Highlight the pattern of total number of
decimal places in the factors is equal to the number of decimal places in
the product.
• Suggestion: Use the context below to practice strategies:
“Sam used a calculator to do multiplication problems, but he forgot
to put in the decimal point. His teacher says he needs to place the
decimal point correctly in the problems.”
How would you explain your strategy for correctly placing the decimal
points?
3.1 x 6.1 = 1891 3.2 x 4.5 = 1440 2.7 x 5.6 = 1512
31 x 6,1 = 1891 32 x 4.5 = 1440 2.7 x 56 = 1512
• Discuss the reasoning students used to place the decimal point. If
estimation does not come up, ask how it could be used.
• Ask the students to estimate and then find the exact product for 31 x 61.
(Prompt students to notice that multiplying whole numbers results in the
same digits in the product as multiplying with decimals.)
• If students come up with the rule for counting decimal places, record it, and
ask them to continue to test it out to see if they can eventually figure out a
way to explain why it works.
Books closed: Learn, p. 164. Put “Tip to Tip” on the board/overhead.
Read with students.
• Allow students to solve the problem and determine the placement of the
decimal point. (connect to estimation strategy)
• Remind students to estimate the product and place the decimal point
where it makes sense.
Practice & Problem Solving, p. 166 #50 – 55. Discuss.
and Representation
SUMMARIZE: T.E. ASSESS, p. 167: DISCUSS
Connect purpose to T.E. ASSESS, p. 167: WRITE
activities
Assess Individually
HOMEWORK: Mixed Review, p. 167
Link Up to Reading, p. 167
Reorganized 9/04/04 16

Harcourt Math−Grade 5 MODULE 5
DAY 9
UNIT 3: Multiply Whole Numbers and Decimals
LESSON 10.5
LESSON FOCUS:
CALIFORNIA
STANDARDS:
PURPOSE OF
LESSON:
LAUNCH:
Introduce students
to concepts.
Place value chart,
1000 Grid
transparency and
copy for students
EXPLORE:
Work with the
concepts. Focus
on students “doing
mathematics.”
Zeros in the Product
Number Sense: 2.1
Add, subtract, multiply, and divide with decimals; add with negative integers;
subtract positive integers from negative integers; and verify the
reasonableness of the results.
Number Sense: 1.0
Students compute with very large and very small numbers, positive integers,
decimals, and fractions and understand the relationship between decimals,
fractions, and percents. They understand the relative magnitudes of numbers.
• To use a model, estimation and patterns to multiply by tenths, hundredths
and thousandths with problems that result in zeros before the product.
• Sometimes zeroes are inserted at the left in the product to keep the same
number of decimal places in the product as in the factors.
• Special Needs, T.E. p. 168B. Emphasize the products where extra zeros
have been added such as 6 x 0.002 as different from 6 x 0.02 or 7 x 0.0002
as different from 7 x 0.02. Can extend to other factors such as 5; 0.5; 0.05;
0.005; 0.0005 times 6 or 4 or 7.
Optional:
• Establish one of the grids with 1000 pieces as the whole unit. Have
students determine the value of one strip (1/10= 0.1); one small square
(1/100=0.01) and the small strip (1/1000=0.001)
• Record the value of each piece as a fraction. Write the equivalent decimal
representation on the place value chart while students record it on their
charts. (“1/1000 equals 0 ones, 0 tenths, 0 hundredths and 1
thousandth”) Make sure students recognize the pieces on their grids.
• Have students use the grid to find 2 x 0.1 (1/10), 2x 0.01 (1/100) and 2x
0.001 (1/1000). (Make the connection between the graphical and
decimal representations of the product by filling in the place value
chart with the number of ones, tenths, hundredths and thousandths.)
Practice & Problem Solving, p. 169 #, 3, 4, 5 Discuss.
Partner work:
One set of partners in a group computes Problems 6, 8, and 12. The other
set of partners computes problems 7, 9, 11. Students check each others
papers using a calculator.
Calculators for
partners
PRACTICE: Practice & Problem Solving, p. 169 #22 - 27
Focus on
Communication
and
Representation.
SUMMARIZE: T.E. ASSESS, p. 169: DISCUSS
Connect purpose
to activities. Check, p. 169 #1. Discuss. Chart responses.
HOMEWORK: Practice & Problem Solving, p. 169 # 28
Mixed Review, p. 169
Reorganized 9/04/04 17

Harcourt Math−Grade 5 MODULE 5
DAY 10
UNIT 5: Percent
LESSON 18.1
MATERIALS: For each pair, 2 double-side copies of TR 10;
Homework: Problem Solving 18.1 – 1 copy for each student.
Newspapers, advertisements, catalogs
LESSON FOCUS:
CALIFORNIA
STANDARDS:
PURPOSE OF
LESSON:
Hands On: Understand Percent
Number Sense
1.2: Interpret percents as a part of a hundred; find decimal and percent
equivalents for common fractions and explain why they represent the same
value; compute a given percent of a whole number.
• To understand that percent represents a part of a hundred.
• To model percent on a grid helps understand percent.
• To understand percents are part to whole ratios.
• To understand percent is a comparison of a quantity to 100.
LAUNCH:
Introduce students
to concepts.
• Ask students what they know about percent. Chart responses.
• Possible questions: What does 50% mean?
What percents do you know?
• Discuss the meaning of the word percent.
Early Finishers, T.E. p. 316B.
• Students work with partners. Posters can be of any size.
EXPLORE:
Work with the
concepts. Focus
on students “doing
mathematics.”
PRACTICE: Focus
on Communication
and
Representation.
SUMMARIZE:
Connect purpose to
activities.
Explore, p. 316. Write problem on board/overhead. Read with students.
Teach, p. 316, Guided Instruction questions to guide discussion.
• Ask students to model the Try It problems on grid paper.
• Highlight that these models are area models of percents.
Connect, p. 317. Discuss.
• Expand with Common Error Alert, T.E. p. 317 top margin.
Talk About It, p. 317.
• Students work in pairs and use grid paper. Include Reasoning discussion.
Practice, p. 317, #1 – 4. Discuss.
Then, #5, 8 – 11. Share & discuss.
T.E. ASSESS, p. 317: DISCUSS
T.E. ASSESS, p. 317: WRITE
HOMEWORK: Problem Solving, p. 316: 18.1
ROUTINES:
Keep a class chart of equivalent fractions, decimals, and percents. List common fractions down
the left side, and write the equivalent fractions, decimals, and percents as you work with them,
and have representations/models for each.
Reorganized 9/04/04 18

Harcourt Math−Grade 5 MODULE 5
DAY 11
UNIT 5: Percent
LESSON 18.2
MATERIALS: For each student, six blank 100 grids and four crayons (different colors), 6-
100 grid transparencies (3 X TR 10)
LESSON FOCUS: Relate Decimals and Percents
CALIFORNIA Number Sense
STANDARDS: 1.0: Students compute with very large and very small numbers, positive
integers, decimals, and fractions and understand the relationship between
decimals, fractions, and percents. They understand the relative magnitudes of
numbers.
1.2: Interpret percents as a part of a hundred; find decimal and percent
equivalents for common fractions and explain why they represent the same
value; compute a given percent of a whole number.
PURPOSE OF To write a percent as a decimal and a decimal as a percent.
LESSON:
LAUNCH:
Introduce students
to concepts.
Blank 100 Grids
EXPLORE:
Work with the
concept. Focus
on students “doing
mathematics.”
PRACTICE:
Focus on
Communication
and
Representation.
SUMMARIZE:
Connect purpose
to activities.
Problem of the Day, T.E. p. 318A
Alternative Teaching Strategy, T.E. p. 318B
• Connect to prior knowledge by asking students to show what a quarter
would look like on a hundred grid if the grid represents one dollar (one
whole). (25 squares colored)
• Discuss, compare, and share students’ grids.
• Explain how the decimal and percent were figured.
Learn, p. 318: Money, Money, Money.
• Model different representations of the same quantity under Math Idea.
Reminder: This is an area model of percent/fractions.
• Model examples A, B, and C, writing each as a decimal and percent.
• Emphasize that each grid represents one whole, but the shaded portion
represents the percent named.
Check, p. 318 #2 – 4. Share & discuss.
Practice & Problem Solving, p. 319 #5 – 7.
Practice & Problem Solving, p. 319 #15, 16, 24 – 26, 27 – 29. Discuss
thinking.
T.E. ASSESS, p. 319: DISCUSS
T.E. ASSESS, p. 319: WRITE
HOMEWORK: Mixed Review, p. 319
ROUTINES:
Provide students with blank hundred grids (TR10). Ask them to find different ways to shade
common fractions. These can be posted to reinforce the quantity of each. (See p. 317: Challenge
18.1 for an example.)
Reorganized 9/04/04 19

Harcourt Math−Grade 5 MODULE 5
DAY 12
UNIT 5: Percent
LESSON 18.3
MATERIALS:
LESSON FOCUS:
CALIFORNIA
STANDARDS:
PURPOSE OF
LESSON:
LAUNCH:
Introduce students
to concepts
100 Grids available, p. TR 10; Overhead transparencies of hundred
grids.
Relate Fractions, Decimals, and Percents
Number Sense
1.0: Students compute with very large and very small numbers, positive
integers, decimals, and fractions and understand the relationship
between decimals, fractions, and percents. They understand the relative
magnitudes of numbers.
1.2: Interpret percents as a part of a hundred; find decimal and percent
equivalents for common fractions and explain why they represent the
same value; compute a given percent of a whole number.
• To write percents as fractions and decimals, and to write fractions and
decimals as percents.
• To understand ratios can be expressed as decimals or percents.
• Ask students to shade 1/4 of a blank 100 grid.
Possible Prompts:
• How many squares did you shade? (25 squares)
• Can we write another fraction that describes the portion of the grid that
is shaded? (25/100)
• What percent of the grid is shaded? (25 percent)
Discuss: The numbers 1/4, 25/100, and 25% all represent the same
amount; that is they are equivalent, they represent the same value.
EXPLORE:
Work with the
concepts. Focus on
students “doing
mathematics.”
• What if I shaded 50%, how many squares would be shaded?
(shade 50 squares)
What fraction would be shaded? (50/100 or 1/2)
What simplified fraction is equivalent to the fraction 50/100? (1/2)
How can I represent this number as a decimal? (0.50 or 0.5)
How would I represent 0.75 on the grid? (Color 75 squares.)
What percent of the grid would be shaded? (75%)
What fraction of the grid have I shaded? (75/100 or 3/4)
What simplified fraction is equivalent to the fraction 75/100? (3/4)
Alternative Teaching Strategy, T.E. p. 320B
• Construct the chart, filling in the fraction, decimal, and percent
equivalencies from the launch (25/100; 75/100).
• Include pictorial representations/sketches for each.
• Students explore the following numbers, extending the chart:
• Find equivalents for: 1/5; 30/100; 0.80; 100%; 1.5; 40%; 1/10.
10 x 10 grid paper,
p. TR10
PRACTICE: Focus
on Communication
and Representation.
SUMMARIZE:
HOMEWORK: Mixed Review, p. 323
Link Up to Reading, p. 323
Practice & Problem Solving, p. 322: #36 – 39. Discuss. Then, #40 –
46 Students work with a partner. Share solutions & thinking.
T. E. ASSESS, p. 323: WRITE: Explain strategies used.
Reorganized 9/04/04 20

Harcourt Math−Grade 5 MODULE 5
DAY 13
UNIT 5: Percent
LESSON 18.5
MATERIALS:
LESSON FOCUS:
CALIFORNIA
STANDARDS:
Purpose of
Lesson:
LAUNCH:
Introduce students
to concepts.
EXPLORE:
Work with the
concepts. Focus on
students “doing
mathematics.”
For Alternative Teaching Strategy, T.E. p. 324B – prepare 2 envelopes
for each student, green & white paper to be cut into strips
Mental Math: Percent of a Number
Number Sense
1.0: Students compute with very large and very small numbers, positive
integers, decimals, and fractions and understand the relationship
between decimals, fractions, and percents. They understand the relative
magnitudes of numbers.
1.2: Interpret percents as a part of a hundred; find decimal and percent
equivalents for common fractions and explain why they represent the
same value; compute a given percent of a whole number.
Develop strategies to use mental math to find the percent of a number.
Use benchmark percents, such as 10%, to determine other percents.
Alternative Teaching Strategy, T.E. p. 324B
• Discuss/explain strategies. What if you had 30 strips and 10% were
green, how many strips would be green?
• Discuss students’ thinking/reasoning. (One possible response: To find
one tenth, divide the whole into ten parts and take one of the parts.)
• Discuss how “friendly numbers/benchmark numbers” can be used to
find percents.
(examples: 50%, 25% and 10% can be used to compute other percents
mentally.)
Alternative Teaching Strategy, T.E. p. 328B.
• Extend discussion of benchmark percents to do mental math.
• Students work with partners to find 10%, 25% and 50% of 40; 200;
1000; 25
• Possible prompts: How can knowing 10% of 40 help you know 20% of
40? 5% of 40? 15% of 40?
• Students record sketches/models of each.
Learn, p. 328
• Discuss examples using Teach, p. 328 Guided Instruction questions.
Social Studies Connection, T.E. p. 328B.
• Students work with partners.
• Present solutions.
PRACTICE:
Focus on
Communication and
representation.
SUMMARIZE:
Connect purpose to
Practice & Problem Solving, p. 329 #30 – 34. Discuss; share thinking.
T.E. ASSESS, p. 329: DISCUSS
T.E. ASSESS, p. 329: WRITE
activities.
HOMEWORK: Practice & Problem Solving, p. 329 #26 – 29
Mixed Review, p. 329
Reorganized 9/04/04 21

Harcourt Math−Grade 5 MODULE 5
DAY 14
UNIT 5: Percents
LESSON 18.4
MATERIALS:
LESSON FOCUS:
CALIFORNIA
STANDARDS:
PURPOSE OF
LESSON:
LAUNCH:
Introduce students
to concepts.
EXPLORE:
Work with the
concept. Focus on
students “doing
mathematics.”
Index cards.
Find a Percent of a Number
Number Sense
1.0: Students compute with very large and very small numbers, positive
integers, decimals, and fractions and understand the relationship
between decimals, fractions, and percents. They understand the relative
magnitudes of numbers.
1.2: Interpret percents as a part of a hundred; find decimal and percent
equivalents for common fractions and explain why they represent the
same value; compute a given percent of a whole number.
• Understand how to compute the percent of a number by multiplying by a
decimal equivalent.
• Use models to extend understanding of finding percents of a number.
Learn, p. 324.
• Write “ZZZZZ” problem on the board/overhead.
• Discuss with students using Teach, p. 324, Guided Instruction
questions.
• Students work in pairs to discuss/solve problem.
Change the Percent and Multiply, p. 325
• Use bullets top margin T.E. p. 325 to guide discussion.
• Apply strategies to Practice & Problem Solving, p. 326 #22 – 25.
• Discuss. Then, #26 – 28.
• Use estimation to check.
PRACTICE:
Focus on
Communication and
Representation.
SUMMARIZE:
Connect purpose to
activities.
Practice & Problem Solving, p. 326 - 327 # 34 – 42.
• Students work with partners.
• Discuss solution strategies.
T.E. ASSESS, p. 327: WRITE:
• Discuss with students.
HOMEWORK: Mixed Review, p. 327
Reorganized 9/04/04 22