1
SFUSD Mathematics Core Curriculum Development Project
2014–2015
Creating meaningful transformation in mathematics education
Developing learners who are independent, assertive constructors of their own understanding
SFUSD Mathematics Core Curriculum, Grade 5, Unit 5.4: Multiplying and Dividing Decimals by Whole Numbers, 2014–2015
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Grade 5
Unit 5.4: Multiplying and Dividing Decimals by Whole Numbers
Number
of Days
Lesson
Reproducibles
Number of
Copies
1
Entry Task
Breakfast Time and supplement (2 pages)
1 per student
4
Lesson Series 1
Engage NY 5.1 Place Value Patterns (8 pages)
Blank Engage NY Place Value Charts (2 pages front/back)
Multiplying by Powers of 10 Practice/Patterns (4 pages)
EM Journal p 212
EM Masters p 192-193 (2 pages)
Dividing by Powers of 10/Patterns (4 pages)
1 per student
1 per student
1 per student
EM Journal
1 per student
1 per student
1
Apprentice Task
Find Your Group
1 per student
5
Lesson Series 2
EM 4 Grade Lesson 9.8 (3 pages)
th
EM 4 Grade Lesson 9.9 (3 pages)
Engage NY 5.11 Student Worksheet (6 pages)
Engage NY 5.13 Student Worksheet (8 pages)
Decimal Grid Sheets (double-sided)
th
1 per student
1 per student
1 per student
1 per student
1 per student
Materials
White boards, personal place value
mats, disks, markers
Find Your Group cards, sets 1 and 2
Base 10 Blocks (enough for pairs)
Unit cubes
EM SRB p 5, 7
Whiteboards and dry erase markers (or
scratch paper)
Counters
Decimal Grid Sheets
Base 10 Blocks, Grid Paper
Duplicate your choice of games and
activities for the last lesson in this
series and the first 2 lessons of the next
series
1
Expert Task
Seymour’s Superstore task (2 pages)
Individual questions
1 per pair
1 per student
Butcher paper or poster paper (1 per
group)
3
Lesson Series 3
Flower Power Part 1
1 per student
Decimal Grid Sheets, Base 10 Blocks,
Grid Paper
1
Milestone Task
Flower Power Part 2
Exponents and Expressions
1 per student
1 per student
SFUSD Mathematics Core Curriculum, Grade 5, Unit 5.4: Multiplying and Dividing Decimals by Whole Numbers, 2014–2015
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Unit Overview
Big Idea
The same rules and patterns that apply to multiplying and dividing whole numbers apply to multiplying and dividing decimals because they are part of the baseten number system.
Focus Mathematical Understandings:
• Multiplying a whole number by a decimal less than 1 yields a product greater than the decimal and less than the whole number.
• Dividing a decimal by a whole number yields a quotient less than either number.
• Dividing a whole number by a whole number may yield a quotient that is not a whole number and can be represented by a decimal.
Unit Objectives
●
●
Students will be able to multiply and divide decimals to the hundredths by whole numbers:
○ Use concrete models or drawings.
○ Explain their thinking and strategies in numbers and words using understanding of place value and/or properties of operations.
○ Answer questions about their strategies, including, but not limited to:
■ How did you do it? What have you tried? What did you learn when that didn't work?
■ Why does that make sense to you?
■ Why do you think that's true? Is it always true? Under what conditions is it true?
Students will be able to apply properties of the base ten number system:
○ Compose and decompose decimals.
○ Place the decimal point when multiplying or dividing by a power of 10.
○ Express powers of 10 using exponents.
Unit Description
The entry task for this unit focuses on reviewing subtraction of decimals and problems that can be solved either with multiplication and division or addition and
subtraction (taught in the previous unit). Students are asked to find costs related to breakfast at a cafe.
The first lesson series begins with a review of the base-ten number system and teaching of powers of 10. Exponents will be a new piece of content for
students. Over the next two lessons, students will learn how to multiply and divide by powers of 10, focusing on patterns in the number system (practice
standard 7) to find shortcuts.
The apprentice task assesses the new skills of converting between standard notation and exponent notation with powers of 10 and multiplying and dividing by
powers of 10 using a game played during the first lesson series: Find Your Group.
The second lesson series helps students learn to multiply and divide decimals to the hundredths by whole numbers, building on the work of multiplying and
dividing by powers of 10.
The expert task asks students to multiply and divide decimals in a creative context: planning a party and buying inventory for a store. This provides an
opportunity to review, reinforce, and extend the learning that happens during the second lesson series. Students will work in groups to answer questions about
buying items that come singly and in groups, each of which costs a decimal value (multiplying decimals by whole numbers). They will also need to find the
individual costs of the items that come in groups (dividing decimals by whole numbers). As part of this task there will be an individual section that students will
be assessed on. Students that are struggling during group work can be pulled into small groups for reinforcing lessons on the material.
SFUSD Mathematics Core Curriculum, Grade 5, Unit 5.4: Multiplying and Dividing Decimals by Whole Numbers, 2014–2015
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The third lesson series is an opportunity to review and extend all material learned in the unit. Part of this will be preparation for the milestone assessment task:
designing and finding the cost of a flower made of pattern blocks (multiplying and adding decimals).
The milestone assessment asks students to multiply and divide decimals by whole numbers, multiply by powers of 10, express powers of 10 in both standard
and exponent notation, and form equivalent expressions using patterns of the base-10 number system.
CCSS-M Content Standards
Numbers and Operations in Base Ten
Understand the place value system.
5.NBT.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the
decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
Perform operations with multi-digit whole numbers and with decimals to hundredths.
5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of
operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
SFUSD Mathematics Core Curriculum, Grade 5, Unit 5.4: Multiplying and Dividing Decimals by Whole Numbers, 2014–2015
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Progression of Mathematical Ideas
Prior Supporting Mathematics
Current Essential Mathematics
Fourth grade students will recognize the base-ten
number system and the relationship between places.
They will be able to multiply 4 digits by 1 digit and 2
digits by 2 digits, and will be able to illustrate and
explain their work using words, equations, arrays,
and/or area models. They will also be able to find
whole number quotients and remainders using up to
4 digit dividends and 1-digit divisors, and will be able
to illustrate and explain their work using words,
equations, arrays, and/or area models.
In this unit, students will multiply and divide whole
numbers by decimals to the hundredths, using
concrete models, drawings, and/or strategies
based on place-value and properties of operations.
They will also write and explain thinking in numbers
and words.
In fifth grade, students will be able to fluently multiply
whole numbers using the standard algorithm, and will
be able to divide whole numbers by whole numbers
to get a whole number quotient. They will be able to
explain their thinking in words, numbers, concrete
models, and drawings, using their understanding of
place value and properties of operations.
Students will also use their previous knowledge of
number system patterns to explain the
relationships between places to the thousandths.
They will use those patterns to explain where a
decimal point will be placed when dividing or
multiplying by a power of 10. They will also use
whole-number exponents to express powers of 10.
Future Mathematics
In fifth grade, students will learn to multiply and
divide decimals by decimals using words and
numbers and visual representations, using their
knowledge of place value and properties of
operations.
In sixth grade, students will fluently use all
operations of multi-digit numbers and decimals
using the standard algorithm. They will also write
and evaluate expressions using whole-number
exponents.
Fifth graders will also know place value to the
thousandths, be able to read, write, and compare
these decimals, be able to add and subtract decimals
and show these calculations in words, numbers, and
visual representations, and be able to round decimals
to the thousandths place. Students will also
recognize patterns in the base-10 system (how much
the place is increasing or decreasing as you move to
the right or left of a digit). This knowledge is
developed in Unit 5.2.
SFUSD Mathematics Core Curriculum, Grade 5, Unit 5.4: Multiplying and Dividing Decimals by Whole Numbers, 2014–2015
Lesson Series 2
Milestone
Task
Expert
Task
Unit Design
Apprentice
Task
Entry Task
Lesson Series 1
Lesson Series 3
6
All SFUSD Mathematics Core Curriculum Units are developed with a combination of rich tasks and lessons series. The tasks are both
formative and summative assessments of student learning. The tasks are designed to address four central questions:
Entry Task:
Apprentice Task:
Expert Task:
Milestone Task:
1 day
What do you already know?
What sense are you making of what you are learning?
How can you apply what you have learned so far to a new situation?
Did you learn what was expected of you from this unit?
4 days
1 day
5 days
2 days
2 days
1 day
Total Days: 16
SFUSD Mathematics Core Curriculum, Grade 5, Unit 5.4: Multiplying and Dividing Decimals by Whole Numbers, 2014–2015
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Entry Task
Apprentice Task
Expert Task
Milestone Task
Breakfast Time MARS Task and Entry
Task Supplement
Find Your Group
Seymour’s Superstore
Flower Power Part 2 and Exponents
and Expressions
CCSS-M
Standards
5.NBT.7
5.NBT.2
5.NBT.7
5.NBT.2, 5.NBT.7
Brief
Description
of Task
Students work individually to solve
three problems in the context of people
eating at a cafe. They need to calculate
change (subtracting decimals), find the
total cost for a number of people
(adding or multiplying decimals), and
find the number of individuals paying a
given amount (dividing, adding, or
subtracting).
Entry Task Supplement: Students work
individually to identify equivalent
expressions. These expressions ask
students to reason using place value
and multiplication by multiples and
powers of ten.
Students work individually and use the
context of the game, Find Your Group,
played in previous lessons, to show
their knowledge of equivalent
expressions using place value. They
need to identify expressions that are
equivalent, for example, 3.4 x 100 and
0.34 x 1000. Then they need to justify
their decisions both for expressions
they think are equivalent and for an
expression they think is not equivalent.
In groups, students will use a list of
products with wholesale prices and
selling prices to plan inventory for a
store. They need to find the prices of
individual items (dividing decimals by
whole numbers), the total cost of items
purchased (multiplying decimals by
whole numbers), the total cost (adding
decimals), and the total profit for each
product and for the store (multiplying
decimals by whole numbers). In
addition, groups are trying to maximize
profit based on the wholesale and
selling prices of items.
Students are also asked to do an
individual assessment based on the
context of the store.
Students find products and quotients of
decimals and whole numbers in the
context of prices of flowers that the
students have designed previously
(Flower Power Part 1). Students find
the prices of multiple flowers, find the
price of one flower based on the price
of multiple flowers, and design a new
flower with a specified price.
Exponents and Expressions:
Students are asked to find exponent
equivalents for standard notation and
vice versa. Students are also asked to
create their own equivalent expressions
using place value rationale.
Source
Mathematics Assessment Resource
Service (MARS)
SFUSD teacher created
SFUSD teacher created
Teachers Pay Teachers: Flower Power
SFUSD teacher created
SFUSD Mathematics Core Curriculum, Grade 5, Unit 5.4: Multiplying and Dividing Decimals by Whole Numbers, 2014–2015
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Lesson Series 1
Lesson Series 2
Lesson Series 3
CCSS-M
Standards
5.NBT.2
5.NBT.7
5.NBT.2
5.NBT.7
5.NBT.2
5.NBT.7
Brief
Description
of Lessons
The first lesson series begins with a review of the
base-ten number system, focusing on the
relationship between adjacent places by playing the
game “Find Your Group”. Over the next two lessons,
students will learn how to multiply and divide by
powers of 10, focusing on patterns in the number
system (practice standard 7) to find shortcuts. They
will also learn exponential notation, which will be new
content for students. The lesson series ends with a
second round of Find Your Group to prepare for the
Apprentice Task.
The second lesson series focuses on the main
content of the unit, multiplying and dividing decimals
by whole numbers. The first two days look at using
estimation to ascertain where the decimal should be
placed in a product or quotient. The next two days
involve building the concept of what
multiplying/dividing decimals by whole numbers is, as
well as giving them some problem solving and
computational practice. The last day has a menu of
items for you to choose from, giving students extra
practice with using their computational skills to
problem solve.
This series provides an opportunity for students to
review all that they learned during this unit and to
prepare for the milestone assessment.
Sources
Engage NY Lesson 5.1
Bridges in Mathematics
Everyday Math Grade 5 Lesson 7.2
SFUSD Teacher Created
Everyday Math
Engage NY
North Carolina Department of Public Instruction 5th
Grade
Number SENSE Grades 4-6
Mathematics Assessment Resource Service (MARS)
Investigations in Number, Data, and Space - Grade
5, Investigation 2
Illustrative Mathematics
30 Wild and Wonderful Math Stories
North Carolina Department of Public Instruction 5th
Grade
Number SENSE Grades 4-6
Mathematics Assessment Resource Service (MARS)
Investigations in Number, Data, and Space - Grade
5, Investigation 2
Illustrative Mathematics
30 Wild and Wonderful Math Stories
Teachers Pay Teachers: Flower Power
SFUSD Teacher Created
SFUSD Mathematics Core Curriculum, Grade 5, Unit 5.4: Multiplying and Dividing Decimals by Whole Numbers, 2014–2015
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Entry Task
Breakfast Time and Supplement
What will students do?
Mathematics Objectives and Standards
Math Objectives:
● Students will be able to subtract, multiply, and divide decimals to the
hundredths by whole numbers:
○ Use concrete models or drawings.
○ Explain their thinking and strategies in numbers and words
using understanding of place value and/or properties of
operations.
● Students will be able to apply properties of the base-10 number
system:
○ Find equivalent expressions using manipulations of place
value.
CCSS-M Standards Addressed:
5.NBT.2,
5.NBT.7
Potential Misconceptions
● There is only one way to solve each problem.
● When dividing, you always divide the “longer” number by the shorter
number.
Framing Student Experience
Teacher Note:
This is a two-part assessment: part 1 is the Breakfast Time MARS Task; part 2
is the Entry Task Part 2. Both are important to gauge where students are before
starting the unit. Resources are included with both tasks to assess where the
class is as a whole: rubrics, class score sheets, etc.
Launch:
Explain that as we begin this unit, we are going to do a couple of short tasks to
find out what you know about the new topics. What happens when you go to a
restaurant to eat? If you feel your class or some subset needs support, read the
problems aloud to the whole class or a small group (eg., ELs, SPED students,
etc.) and discuss.
During:
Students work independently on the Breakfast Time MARS Task and the
supplement. Encourage students to solve each problem of Breakfast Time a
second way if they finish solving it one way.
Closure/Extension:
Either in class or as homework during Lesson Series 2 or 3, students can revisit
their work and correct it to see (and show) what they have learned during the
unit.
Find Your Group:
There should be time in a 55-minute class period to play a first round of the Find
Your Group game as a class. Find the directions for this game in Lesson Series
1, Day 1. You will need to make the first set of cards ahead of time.
SFUSD Mathematics Core Curriculum, Grade 5, Unit 5.4: Multiplying and Dividing Decimals by Whole Numbers, 2014–2015
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Breakfast Time and Supplement
How will students do this?
Focus Standards for Mathematical Practice:
2. Reason abstractly and quantitatively.
7. Look for and make use of structure.
Structures for Student Learning:
Academic Language Support:
Vocabulary: context dependent vocabulary: cafe, continental breakfast
Sentence frames:
Differentiation Strategies:
● Read the task for students as necessary.
● Make manipulatives available to students.
● There are games in 5.2 that could be played as review for students who finish early.
Participation Structures (group, partners, individual, other):
● Individual
SFUSD Mathematics Core Curriculum, Grade 5, Unit 5.4: Multiplying and Dividing Decimals by Whole Numbers, 2014–2015
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Lesson Series #1
Lesson Series Overview:
The first lesson series begins with a review of the base-ten number system, focusing on the relationship between adjacent places, and a round of the game “Find
Your Group”. The purpose of the first day's lesson is to reinforce and re-establish place value with decimals, and their relative value to whole numbers and each
other. Over the following two lessons, students will learn how to multiply and divide by powers of 10, focusing on patterns in the number system (practice
standard 7) to find shortcuts. They will also learn exponential notation, which will be new content for students. The lesson series ends with a second round of
Find Your Group to prepare for the Apprentice Task.
CCSS-M Standards Addressed: 5.NBT.2, 5.NBT.7
Time: 4 days
Lesson Overview – Day 1
Description of Lesson:
This lesson has two parts: base-10 place value review and a first round of Find Your Group game.
The lesson portion of this day is Engage NY Lesson 5.1, which is also found in Unit 5.2. If you feel your class has
mastered the concepts in this lesson, then feel free to skip it. They should be able to use place value charts and
explain what happens when digits move between place values (e.g., when a 6 moves from the ones place to the
10s place, it is 10 times bigger). This fundamental understanding of place value is necessary for this unit. If your
class needs some review, repeat the lesson, focusing on the conceptual understanding rather than the
procedure. If you do not repeat the lesson, do a quick refresher moment on the place value and relative
value of decimals, emphasizing verbal and written explanations of how place values relate. This will be
assessed and repeated throughout the unit.
Resources
Decimals Song by Mr. Heath,
http://www.youtube.com/watch?v=0JB3bNfLq
EM
Part 1:
Engage NY Lesson 5.1
Blank Engage NY Place Value Charts
Part 2:
Find Your Group Game Directions
If you do plan on repeating this lesson, you can make up your own problems to use with the Blank
Engage NY Place Value Charts for further practice in class or for homework.
This lesson reviews the base-10 place value system and guides students to see the relationship between
adjacent places (multiplied by 10, divided by 10). It also guides students to look for patterns when multiplying or
dividing by powers of 10 (10, 100, 1000, etc.).
After the student work and debrief sections of the lesson, the class will play the game Find Your Group for the
first time. In this game, students sort themselves based on equivalent expressions written on index cards. The
expressions use multiplication of decimals and whole numbers by powers of 10. In this round, the powers of 10
are written in standard notation only. Even if you skip Engage NY Lesson 5.1, do play a round of Find Your
SFUSD Mathematics Core Curriculum, Grade 5, Unit 5.4: Multiplying and Dividing Decimals by Whole Numbers, 2014–2015
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Group. This may be done on the same day as the Entry Task. In order to play the game, you will need to
make a copy of the first set of cards. Take time to review the multiplication/place value rules that underlie
the equivalence: when you multiply one factor and divide the other factor by the same number (in this
case a multiple of 10), you get the same product.
Notes:
The Engage NY lesson is slightly modified from the original with a couple of parts of the lesson removed to make
time for Find Your Group.
Lesson Overview – Days 2-3
Description of Lesson:
This lesson has two parts: multiplication by powers of 10 and exponential notation for powers of 10.
The first section focuses on multiplying by powers of 10. Students use base-10 blocks to find and identify
patterns when multiplying by powers of 10 and connect that to the base-10 number system, extending on the
material from Day 1 of this lesson series.
The second section focuses on how to write powers of 10 using exponential notation (positive exponents only).
This uses Everyday Mathematics Lesson 7.2. Begin with the section called “Introducing Exponential Notation for
Powers of 10” using Student Reference Book, p. 5. Students should do the top of Math Journal 2, p. 212, and
Math Masters, p. 192. The other pages can be skipped. An optional extension into negative exponents is Student
Reference Book, p. 7, and Math Masters, p. 193. Take this opportunity to review the vocabulary word
“standard notation” for regular numbers. This will return in the Milestone Task.
Resources
Part 1:
Multiplying by Powers of Ten Teacher
(Teacher Notes)
Multiplying by Powers of Ten Practice &
Patterns in Multiplying by Powers of 10
(Student Handouts)
Part 2:
Everyday Mathematics Grade 5 Lesson 7.2
Part 3:
Find Your Group directions
2
nd
set of cards
If the class finishes both of these activities before the end of Day 3, you can play Find Your Group for a second
time with the exponent cards. Take time to review the multiplication/place value rules that underlie the
equivalence: when you multiply one factor and divide the other factor by the same number (in this case a multiple
of 10), you get the same product.
Notes:
In Everyday Mathematics Lesson 7.2, use only the sections called “Introducing Exponential Notation for Powers
of 10,” part of “Using Guides for Powers of 10,” and “Finding Patterns in a Place-Value Chart” (see above for
explanation).
If your class is solid on computation, some of this material may be used for homework instead of classwork. If
your class needs more help with the conceptual work, you can take the time to make other practice problems on
the model of Engage NY Lesson 5.1 (Lesson Series 1, Day 1). A blank sheet may be found in your materials list.
SFUSD Mathematics Core Curriculum, Grade 5, Unit 5.4: Multiplying and Dividing Decimals by Whole Numbers, 2014–2015
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Lesson Overview – Day 4
Description of Lesson:
This lesson has two parts: division by powers of 10 and a second round of Find Your Group game.
The first section focuses on dividing by powers of 10. Students use base-10 blocks to find and identify patterns
when dividing by powers of 10 and connect that to the base-10 number system, extending on the material from
the previous two days.
The second part of the day will be used to play the Find Your Group game for a second time. This time students
find equivalent expressions that include multiplication and division by powers of 10 written in standard and
exponential notation.
Resources
Dividing by Powers of Ten Teacher
Dividing by Powers of Ten Practice & Patterns
in Dividing by Powers of 10
Find Your Group directions
Notes:
The two rounds of Find Your Group (today and during Lesson 1) set students up to do the Apprentice Task.
Today you should use the numbers that use the exponential notation so that students are getting practice with
this skill.
If your class is solid on computation, some of this material may be used for homework instead of classwork. If
your class needs more help with the conceptual work, you can take the time to make other practice problems on
the model of Engage NY Lesson 5.1 (Lesson Series 1, Day 1). A blank sheet may be found in your materials list.
SFUSD Mathematics Core Curriculum, Grade 5, Unit 5.4: Multiplying and Dividing Decimals by Whole Numbers, 2014–2015
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Apprentice Task
Find Your Group
What will students do?
Mathematics Objectives and Standards
Math Objectives:
● Students will be able to identify equivalent expressions using
properties of place value and the number system.
○ Justify their decisions using words, equations, and visual
representations.
● Students will be able to identify expressions that are not equivalent
using properties of place value and the number system.
○ Justify their decisions using words, equations, and visual
representations.
Framing Student Experience
Teacher Note:
This activity takes about half a class period. The rest of the time can be used for
review or moving on to the next topic.
Launch:
Remind students about the game they played yesterday, Find Your Group.
Discuss what patterns or strategies they used to find equivalent expressions
yesterday.
During:
Students work independently solving problems using the Find Your Group
context and justifying their thinking. Circulate and direct students as necessary.
Identify students who need more reinforcement of the content.
CCSS-M Standards Addressed:
5.NBT.2
Potential Misconceptions
● There is only one right answer.
Closure/Extension:
Students share their justifications for various cards being equivalent. Take time
to review the multiplication/place value rules that underly the equivalence: when
you multiply one factor and divide the other factor by the same number (in this
case a multiple of 10), you get the same product. Keep reviewing this concept
throughout the unit as it comes up.
SFUSD Mathematics Core Curriculum, Grade 5, Unit 5.4: Multiplying and Dividing Decimals by Whole Numbers, 2014–2015
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Find Your Group
How will students do this?
Focus Standards for Mathematical Practice:
3. Construct viable arguments and critique the reasoning of others.
7. Look for and make use of structure.
Structures for Student Learning:
Academic Language Support:
Vocabulary: expression, power of 10, exponent
Sentence frames:
These two cards match because...
These expressions are equal because...
I know this is true because...
Differentiation Strategies:
● Encourage students to write the powers of 10 all in standard notation if exponential notation is challenging.
● Remind students of the work that they have done on the previous days, especially cuing them to think about strategies and patterns that they and other
students used to find their pairs and groups.
Participation Structures (group, partners, individual, other):
● Students work individually, but the work is based on group work from previous days.
SFUSD Mathematics Core Curriculum, Grade 5, Unit 5.4: Multiplying and Dividing Decimals by Whole Numbers, 2014–2015
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Lesson Series #2
Lesson Series Overview: The second lesson series focuses on the main content of the unit, multiplying and dividing decimals by whole numbers. The first two
days look at using estimation to ascertain where the decimal should be placed in a product or quotient. The next two days involve building the concept of what
multiplying/dividing decimals by whole numbers is, as well as giving them some problem solving and computational practice. The fifth day is a flex day: if your
class has finished the activities from the first four lessons, use this day for extra review and extension. There is a menu of items provided for you to choose from,
giving students extra practice with using their computational skills to problem solve. These extra items may be used for homework throughout the lesson series.
If, however, the class needs an extra day on any of the previous lessons, use the fifth day for that. Before students do the Expert Task, they need to have a solid
grounding in multiplying and dividing decimals.
CCSS-M Standards Addressed: 5.NBT.2, 5.NBT.7
Time: 5 days
Lesson Overview – Day 1
Description of Lesson:
Everyday Mathematics Grade 4 Lesson 9.8, Magnitude Estimates for multiplying decimals by a
whole number guides students to make an estimate of what their product will be before they do
their computation. They then proceed to do their calculations without the decimal and are able to
correctly place their decimal in their product based on their estimate.
Once students have had sufficient practice with Lesson 9.8, you should move on to 9.9.
Resources
Everyday Mathematics Grade 4 Lesson 9.8
Everyday Mathematics Grade 4 Lesson 9.9
Student explanation of multiplying decimals,
http://www.youtube.com/watch?v=unsDhvtuhqQ
Notes:
You are focusing on the math message and Part 1 of this lesson, and will not need to do the mental
math.
Be careful not to use the phrase “ignore the decimal.” Instead, remind students of powers of 10
they have been practicing. If they are trying to find 4.5 x 50, remind them that they can rewrite this
as 45 x 5 or (45 x 50)/10. This is why they can multiply without the decimal and then replace it in
their product or quotient.
Lesson Overview – Day 2
Description of Lesson:
Magnitude Estimates for multiplying and dividing decimals dividing decimals by a whole number
guides students to make an estimate of what their quotient will be before they do the computation.
Resources
Everyday Mathematics Grade 4 Lesson 9.9
SFUSD Mathematics Core Curriculum, Grade 5, Unit 5.4: Multiplying and Dividing Decimals by Whole Numbers, 2014–2015
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They then proceed to do their calculations without the decimal and are able to correctly place their
decimal in their product based on their estimate.
Notes:
You should have begun Lesson 9.9 yesterday, so this should be review and practice, and will only
take you part of the lesson time.
See notes from yesterday.
Lesson Overview – Day 3
Description of Lesson:
In this lesson, students learn to multiply decimals by whole numbers using concrete and pictorial
representations. They should focus on using place value reasoning, building on all of the work that
has come previously.
Resources
Engage NY Lesson 5.11
Notes:
The lesson directions use the word “discs” to describe the dots that students draw.
Some of the parts of the lesson have been removed in its move into this unit. If there is extra time,
students can continue one of the games or activities begun on previous days.
Materials:
Whiteboards and dry erase markers (or scratch paper)
Lesson Overview – Day 4
Description of Lesson:
In this lesson, students learn to divide decimals by whole numbers using concrete and pictorial
representations. They should focus on using place value reasoning, building on all of the work that
has come previously.
Resources
Engage NY Lesson 5.13
Notes:
Some of the parts of the lesson have been removed in its move into Google Docs. If there is extra
time, students can continue one of the games or activities begun on previous days.
SFUSD Mathematics Core Curriculum, Grade 5, Unit 5.4: Multiplying and Dividing Decimals by Whole Numbers, 2014–2015
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Lesson Overview – Day 5
Resources
Description of Lesson:
Depending on how the class is doing, there are many options for this day. In the resources box,
find a number of options that are more or less structured.
Menu of Options:
Lesson: Multiplying Whole Numbers by Decimals (NC
Department of Public Instruction)
Notes:
Teachers should choose a lesson, task, game, or combination fitting the needs of their students.
These lessons, games, and tasks, can also be used for homework, additional practice, or any other
way that the teacher may want to use them.
Tasks:
●
●
●
●
●
Any of these may also be used for the first two days of Lesson Series 3, depending on the results
of the Expert Task.
The Value of Education
Window Time, NC 5th Grade, pp. 25–27
Pepe’s Party MARS Task
Sports Blab with Buzz Busby
What Planet Am I From?
Games:
● Everyday Mathematics Grade 5: Multiplication
Top-It: modify by adding a decimal point to make
either of the factors into a decimal.
● Everyday Mathematics Grade 5: Division Top-It:
modify by adding a decimal point to make the
dividend into a decimal.
● Everyday Mathematics Grade 5: Scientific
Notation Toss
● Everyday Mathematics Grade 5: Exponent Ball:
use as an extension.
Possible Homework/Reteaching/Extensions:
● Name a Decimal, Activities 1, 2, and 3
● Will You Do It in Your Head?
● Relating Multiplication and Division Situations
● Lessons for Learning
SFUSD Mathematics Core Curriculum, Grade 5, Unit 5.4: Multiplying and Dividing Decimals by Whole Numbers, 2014–2015
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Expert Task
Seymour’s Superstore
What will students do?
Mathematics Objectives and Standards
Math Objectives:
● Students will use a real life problem to practice their skills of
multiplying and dividing decimals by whole numbers.
● Students will be asked to make sense of a real world problem and to
conduct an investigation into finding out which products will yield the
most profit.
● Students will be asked to organize their thinking and calculations into
a visual representation (table, list, or chart).
CCSS-M Standards Addressed:
5.NBT.7
Potential Misconceptions
● Students may believe that profit is the selling price, rather than the
difference between the selling price and the wholesale price.
Framing Student Experience
Launch:
Go over the task with the students. Particular vocabulary to go over: product,
item, profit.
Put students into groups of three or four.
You may need to go over an example (not from the task) of how to find a profit.
During:
Circulate during this task, observing how students are making sense of the
problem and checking for conceptual and computational misunderstandings.
This can also be a time to pull a student or small group of students to do some
review or reteaching if needed.
Students may need to be reminded that tables are a visual representation. This
is probably the best choice for most students in this task.
Closure/Extension:
Have students share some of their strategies for maximizing profits.
The group rubric is available if you choose to use it.
The individual rubric should be done to assess each student's understanding.
SFUSD Mathematics Core Curriculum, Grade 5, Unit 5.4: Multiplying and Dividing Decimals by Whole Numbers, 2014–2015
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Seymour’s Superstore
How will students do this?
Focus Standards for Mathematical Practice:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
Structures for Student Learning:
Academic Language Support:
Vocabulary: item, product, profit, per
Sentence frames:
Differentiation Strategies:
● Students should be put into heterogeneous groups so that there will be peer assistance available.
● Vocabulary should be taught to all students, but should be reinforced for the EL students.
● The task itself is set up to allow for a wide variety of knowledge and ability. High-functioning students can stretch beyond the expectations set, while the
teacher can circulate to address individual misconceptions among students.
Participation Structures (group, partners, individual, other):
Group task followed by an individual written assessment connected to their group work.
SFUSD Mathematics Core Curriculum, Grade 5, Unit 5.4: Multiplying and Dividing Decimals by Whole Numbers, 2014–2015
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Lesson Series #3
Lesson Series Overview: This series provides an opportunity for students to review all that they learned during this unit and to prepare for the milestone
assessment.
CCSS-M Standards Addressed: 5.NBT.2, 5.NBT.7
Time: 2 days
Lesson Overview – Day 1 & 2
Description of Lesson:
Depending on the results of the formative assessment during the Expert Task, choose
another item or items off of the menu from the last day of Lesson Series 2.
Notes:
Choose a lesson, task, game, or combination fitting the needs of your students.
These lessons, games, and tasks can also be used for homework, additional practice, or
any other way you may want to use them.
Resources
Menu of options:
Lesson:
Multiplying Whole Numbers by Decimals (NC Department of Public
Instruction)
Tasks:
●
●
●
●
●
The Value of Education
Window Time, NC 5th Grade, pp. 25–27
Pepe’s Party MARS Task
Sports Blab with Buzz Busby
What Planet Am I From?
Games:
● EM Grade 5: Multiplication Top-It: modify by adding a
decimal point to make either of the factors into a decimal.
● EM Grade 5: Division Top-It: modify by adding a decimal
point to make the dividend into a decimal.
● RM Grade 5: Scientific Notation Toss
● EM Grade 5: Exponent Ball: use as an extension.
Possible Homework/Reteaching/Extensions:
● Name a Decimal, Activities 1, 2, and 3
● Will You Do It in Your Head?
● Relating Multiplication and Division Situations
SFUSD Mathematics Core Curriculum, Grade 5, Unit 5.4: Multiplying and Dividing Decimals by Whole Numbers, 2014–2015
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Lesson Overview – Day 3
Description of Lesson:
In order to prepare for the milestone task, students need to do Flower Power Part 1 on
this day. This task asks students to create a flower out of pattern blocks and find the
price of that flower given a price for each pattern block. They will be using this price to
calculate the price of groups of flowers on the milestone task.
If students finish work on Flower Power Part 1, they can continue a task or game from a
previous day or begin a new one from the menu of options.
Resources
Flower Power Part 1
Menu of Options: See Lesson Series 3 Day 1
Notes:
Choose a lesson, task, game, or combination fitting the needs of your students.
These lessons, games, and tasks, can also be used for homework, additional practice,
or any other way you want to use them.
SFUSD Mathematics Core Curriculum, Grade 5, Unit 5.4: Multiplying and Dividing Decimals by Whole Numbers, 2014–2015
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Milestone Task
Flower Power Part 2 and Exponents and Expressions
What will students do?
Mathematics Objectives and Standards
Math Objectives:
● Students will be able to multiply and divide decimals to the hundredths
by whole numbers:
○ Use concrete models or drawings.
○ Explain their thinking and strategies in numbers and words
using understanding of place value and/or properties of
operations.
● Students will be able to apply properties of the base-10 number
system:
○ Place the decimal point when multiplying or dividing by a
power of 10.
○ Express powers of 10 using exponents.
CCSS-M Standards Addressed:
5.NBT.2
○ 5.NBT.7
Potential Misconceptions:
● Exponents refer to the number of times you multiply a value by itself
rather than the number you multiply the value by.
Framing Student Experience
Materials:
Each student's Flower Power Part 1, completed the day before
Flower Power Part 2 – 1 per student
Exponents and Expressions – 1 per student
Rubrics for both parts 1 and 2
Launch:
On the previous day, do Flower Power Part 1, designing a flower and finding the
cost of that flower, from Lesson Series 3. On the day of the assessment remind
students to check their work to make sure they have the correct cost for the
flower. Let them know that they will also be answering a few separate questions
about exponents and expressions, which they learned about during the lessons
early in the unit and the game Find Your Group.
During:
Students work individually to answer the questions based on the cost they found
of their flower. Circulate to observe student work. Because this is a milestone
assessment, do not direct students to correct work during this time. Part 2 will
be assessed using whatever cost the student found for Part 1, whether this is
accurate or not.
Closure/Extension:
Students may be provided the opportunity to share the flowers they designed
and how much those flowers cost.
SFUSD Mathematics Core Curriculum, Grade 5, Unit 5.4: Multiplying and Dividing Decimals by Whole Numbers, 2014–2015
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Flower Power Part 2
How will students do this?
Focus Standards for Mathematical Practice: (no more than 2)
2. Reason abstractly and quantitatively
7. Look for and make use of structure
Structures for Student Learning:
Academic Language Support:
Vocabulary: dozen, expression, related expression
Sentence frames:
None needed.
Differentiation Strategies:
● Students are designing their own flowers; students who have more comfort with the content can make flowers that have more complicated costs.
● Provide guidance for students who need it.
Participation Structures (group, partners, individual, other):
● Students work individually on all parts of this task.
SFUSD Mathematics Core Curriculum, Grade 5, Unit 5.4: Multiplying and Dividing Decimals by Whole Numbers, 2014–2015