Download 3rd Grade Mathematics

 3rd Grade Mathematics Modeling Multiplication and D ivision: Relationships and Properties Pacing: 48 Days Unit Overview
In this unit, students will: 1.) Begin to understand the concepts of multiplication and division and 2.) Learn the basic facts of multiplication and their related
division facts. Students develop an understanding of the meanings of multiplication and division of whole numbers through activities and problems involving
equal-sized groups, arrays, and area models; multiplication is finding an unknown product, and division is finding an unknown factor in these situations. For
equal-sized group situations, division can require finding the unknown number of groups or the unknown group size. Throughout the unit, students will have
extensive practice distinguishing between real life situations that require multiplication or division. In Grade 2 students have added groups of objects by skipcounting and using repeated addition (2.OA.4). In this unit students connect these concepts to multiplication and division by interpreting and representing products
and quotients. Students begin developing these concepts by working with numbers with which they are more familiar, such as 2s, 5s, and 10s, then develop
strategies to work with less familiar groupings. Since multiplication is a critical area for Grade 3, students will build on these concepts throughout the year,
working towards fluency by the end of the year. In this unit, students will use concrete objects or pictures to help conceptualize and solve problems (MP.1). As
the unit progresses, students will be required to implement multiple strategies to solve the same problem. They use arrays and other representations to model
multiplication and division (MP.4) and contextualize given expressions (MP.2).
Prerequisite Skills
1) Add groups of objects by skip counting and using repeated
addition
2) Fluently add and subtract number within 20.
3) Recognize that the multiplication symbol means “groups of”
4) Identify odd and even numbers
5) Skip count by two, threes, fives, and tens
6) Determine reasonableness of answers using estimation
7) Describe the inverse relationship of addition and subtraction
8) Construct a picture/visual representing repeated addition to find
the total number of objects represented
Vocabulary
Equal groups
Multiplication
Product
Partition
Division
Groups
Inverse operations
Commutative Property
Identity Property
Zero Property
Distributive Property
Factor
Repeated addition
Divisor
Dividend
Equal shares
Quotient
Associative Property
Mathematical Practices
MP.1: Make sense of problems and persevere in
solving them
MP.2: Reason abstractly and quantitatively
MP.3: Construct viable arguments and critique the
reasoning of others
MP.4: Model with mathematics
MP.5: Use appropriate tools strategically
MP.6: Attend to precision
MP.7: Look for and make use of structure
MP.8: Look for and express regularity in repeated
reasoning Common Core State Standards
Additional Standards (10%) 3.NBT.3:
Multiply by
Multiples of 10
3.MD.3: Scaled Picture
and Bar Graphs
Supporting Standards (20%) 3.OA.1: Interpret Products of
Whole Numbers
Major Standards (70%) 3.OA.2: Interpret Quotients of
Whole Numbers
3.OA.3: Multiplication and Division Fact
Word Problems
3.OA.4: Unknowns in Multiplication and Division Equations
3.OA.5: Apply Properties of Operations to Multiply and Divide
3.OA.6: Understand Division as an Unknown Factor Problem
3.OA.7: Fluently Multiply and Divide within 100
3.OA.8: Two-Step Word Problems
3.OA.9: Patterns in Addition and Multiplication
3.MD.2: Solve Word Problems with Mass and Volume and Estimate Mass and
Volume
According to the PARCC Model Content Framework, Standards 3.OA.3 and 3.OA.7 should serve as opportunities for in-depth focus: 3.OA.3—“Word problems involving equal groups, arrays, and measurement quantities can be used to build students’ understanding of and skill with
multiplication and division...” 3.OA.7—“Finding single-digit products and related quotients is a required fluency for grade 3. Reaching fluency will
take much of the year for many students.”
The key advance in multiplication and division concepts between third and fourth grade is:
“In grade 3, students studied multiplication in terms of equal groups, arrays and area. In grade 4, students extend their concept of multiplication to
make multiplicative comparisons (4.OA.1).”
2 | P a g e Progression of Skills
nd
2 Grade
3rd Grade
4th Grade
2.OA.4: Use addition to find the total number of
objects arranged in rectangular arrays with up to 5
rows and up to 5 columns
3.OA.1: Interpret products of whole numbers, e.g., interpret 5 × 7 as
the total number of objects in 5 groups of 7 objects each. For
example, describe a context in which a total number of objects can be
expressed as 5 × 7.
4.OA.1: Interpret a multiplication equation as a comparison,
e.g., interpret 35 = 5 7 as a statement that 35 is 5 times as many
as 7 and 7 times as many as 5.
N/A
3.OA.2: Interpret whole-number quotients of whole numbers, e.g.,
interpret 56 ÷ 8 as the number of objects in each share when 56 objects
are partitioned equally into 8 shares, or as a number of shares when 56
objects are partitioned into equal shares of 8 objects each. For example,
describe a context in which a number of shares or a number of groups
can be expressed as 56 ÷ 8.
3.OA.3: Use multiplication and division within 100 to solve word
problems in situations involving equal groups, arrays, and measurement
quantities, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.
N/A
N/A
3.OA.4: Determine the unknown whole number in a multiplication or
division equation relating three whole numbers.
N/A
3.OA.6: Understand division as an unknown-factor problem. For
example, find 32 ÷ 8 by finding the number that makes 32 when
multiplied by 8.
4.OA.2: Multiply or divide to solve word problems involving
multiplicative comparison, e.g., by using drawings and equations
with a symbol for the unknown number to represent the problem,
distinguishing multiplicative comparison from additive
comparison.
4.OA.4: Find all factor pairs for a whole number in the range 1–
100. Recognize that a whole number is a multiple of each of its
factors. Determine whether a given whole number in the range 1–
100 is a multiple of a given one-digit number. Determine whether a
given whole number in the range 1–100 is prime or composite.
N/A
3.OA.7: Fluently multiply and divide within 100, using strategies such
as the relationship between multiplication and division (e.g., knowing
that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By
the end of Grade 3, know from memory all products of two one-digit
numbers.
4.NBT.5: Multiply a whole number of up to four digits by a onedigit whole number, and multiply two two-digit numbers, using
strategies based on place value and the properties of operations.
3.OA.9: Identify arithmetic patterns (including patterns in the addition
table or multiplication table), and explain them using properties of
operations. For example, observe that 4 times a number is always even,
and explain why 4 times a number can be decomposed into two equal
addends.
4.OA.5: Generate a number or shape pattern that follows a given
rule. Identify apparent features of the pattern that were not explicit
in the rule itself. For example, given the rule “Add 3” and the
starting number 1, generate terms in the resulting sequence and
observe that the terms appear to alternate between odd and even
numbers. Explain why the numbers will continue to alternate
N/A
2.OA.3: Determine whether a group of objects (up
to 20) has an odd or even number of members, e.g.,
by pairing objects or counting them by 2s; write an
equation to express an even number as a sum of two
equal addends.
3 | P a g e 4.OA.3: Solve multistep word problems posed with whole
numbers and having whole-number answers using the four
operations, including problems in which remainders must be
interpreted
4.NBT.6: Find whole-number quotients and remainders with up to
four-digit dividends and one-digit divisors, using strategies based
on place value, the properties of operations, and/or the relationship
between multiplication and division
Big Ideas
• What is multiplication/division? In what
real world contexts do we use
multiplication and division?
• What is the relationship between
multiplication and division? ( e.g. both
represent the manipulation of equal-sized
groups; they are inverse operations, etc.)
• How does understanding the relationship
between multiplication and division, as
well as their properties, help me multiply
and divide efficiently?
• What do the numbers in multiplication
and division problems represent? How
does understanding these numbers
help us interpret, represent and solve
mathematical equations?
• How can we solve for unknown whole
numbers in multiplication and division
problems? Why is learning this
process important to us as
mathematical thinkers?
• What strategies can I use to become
fluent with multiplication and division
facts?
•
How can I use equations to represent oneand two-step word problems?
4 | P a g e Students Will…
Know/Understand
Be Able To…
• Multiplication represents repeated addition of groups.
• A rectangular array can represent a multiplication
problem.
• The product of a multiplication problem may represent
the combination of a number of groups with multiple
objects in each group.
• Division is the splitting of a number into equal groups.
• Division represents repeated subtraction.
• The quotient resulting from a division problem represents
the number of times one group of objects is split equally
among another group.
• A symbol can represent an unknown number in a math
problem.
• To identify whether an operation in a word problem is
multiplication or division you must consider key words
and relationships defined in the problem.
• The inverse relationship of multiplication and division
• A division problem is a multiplication problem with an
unknown factor.
• A symbol can represent an unknown whole number in a
math problem relating three whole numbers.
• The concepts behind the commutative property of
multiplication, the associative property of multiplication,
and the distributive property
• An equation may represent information from a two-step
word problem.
• Arithmetic patterns exist and can be identified using a
variety of strategies.
• Categories on a scaled picture or scaled bar graph can be
compared to each other to determine how many more or
less of that category.
• What operation(s) are required from "how many more"
and "how many less" word problems.
• The relationship between place value and multiplication.
• The relationship between the associative property of
multiplication and decomposing large numbers to solve
multiplication problems.
• Interpret the product of whole numbers using rectangular
arrays and pictures.
• Draw equal groups of objects to represent a multiplication
expression.
• Find the quotient of a division problem by identifying
how many equal groups can be made out of a certain
number of objects.
• Interpret the quotient of a division problem by describing
what it means in the context of a problem.
• Use repeated subtraction to understand a quotient by
finding the number of equal groups within a number.
• Use arrays, manipulatives, and drawings to represent and
solve multiplication and division problems.
• Create multiplication and division equations to represent
the information in word problems.
• Solve for an unknown whole number in a multiplication
or division equation with the unknown number in any
position.
• Apply properties of operations to multiply and divide
• Find an unknown factor in a division problem using
multiplication.
• Multiply and divide within 100 quickly, accurately, and
efficiently using multiple strategies.
• Create equations to represent and solve a two-step word
problem.
• Solve equations to find an unknown number
• Assess the reasonableness of answers when solving twostep equations by using mental math and estimation
• Identify, extend, and explain arithmetic patterns.
• Solve one-step addition, subtraction, multiplication, and
division word problems involving masses or volumes
• Interpret, translate, and represent data as a scaled picture
graph and scaled bar graph to represent a data set
• Determine a scale for a scaled picture or scaled bar graph
in order to convert data correctly.
• Use information from scaled picture or bar graphs to
solve "how many more" and "how many less" problems.
• Multiply one-digit factors by multiples of 10 up to 90.
Unit Sequence 1
Student Friendly
Objective
SWBAT…
Use visual models to
demonstrate
understanding of
multiplication as equal
groups.
Key Points/
Teaching Tips
•
Students should practice interpreting,
creating, and evaluating visual
models of multiplication and writing
corresponding multiplication
equations.
Exit Ticket
1. There are 4 pretzels in each bag. How many
pretzels are in 6 bags?
Instructional
Resources
My Math
Chapter 4, Lesson 1
“Engage NY
Lesson1.1”
(Appendix C)
a. 4 x 6 = _____
b. There are _____ pretzels altogether.
2. Kevin has 3 bags of candy. There are 4
candies in each bag.
a. Draw a picture to represent the
situation.
b. Write a multiplication sentence to
represent the situation.
3. The picture below shows 2 groups of
pencils. Does the picture below show 2 x 3?
Explain why or why not.
5 | P a g e 2
Use visual models to
represent and identify
factors as the size of
the group or the
number of groups.
•
•
Students should learn the definitions
of “factors” and “product” and begin
to develop an understanding of
“multiplication” that includes equal
groups.
Students should begin to distinguish
between real world situations that
require multiplication versus
addition and justify their reasoning
based on equal groups.
1. There are 3 stars in each group. How many
stars are in 4 groups?
a.
b.
c.
d.
Number of groups: _____
Size of each group: _____
Multiplication equation: __________
There are _____ stars altogether.
“Engage NY
Lesson1.3”
(Appendix C)
“What’s My Product?” (Appendix C) 2. Kevin has 5 bags of oranges. There are 6
oranges in each bag.
a. Draw a picture to represent the
situation.
b. How many groups are there?
c. What is the size of each group?
d. Write a multiplication sentence to
represent the situation.
3. Which statement can be represented by the
expression 4 x 8?
a. A teacher put 8 chairs at each of 4
tables.
b. Tom buys 4 red markers and 8 black
markers.
4. There are 8 ducks in the pond, then 4 more
ducks join them.
6 | P a g e 3
Model multiplication
using repeated addition
on a number line and
write related addition
and multiplication
number sentences.
•
Students’ understanding of
“multiplication” should expand
to include repeated addition of
equal groups.
•
Each arrow “bump” on the
number line should represent one
equal group and expand the
range of the size of one group.
Students may benefit from
drawing smaller “bumps” to
count the size of the groups with
precision.
1. Write an addition sentence and a
multiplication sentence to represent the
picture above:
My Math
Chapter 4
Lesson 2
*Modify resource to
include representing
repeated addition
on a number line
_____ + _____ + _____ = _____
_____ x _____ = _____
2. Use the number line below to model the total
number of smiley faces using repeated
addition:
4. Explain the relationship between
multiplication and addition in complete
sentences.
7 | P a g e 4
Construct rectangular
arrays to represent a
multiplication problem
and to model the
Commutative Property
of Multiplication.
•
•
•
•
•
•
•
8 | P a g e On 4 square Do Now, assess
students’ ability to construct a simple
(5 by 2) array in the “I’m ready to
tackle today’s objective” box
Inquiry Based Lesson:
Start with the task “Seating
Arrangements” and give students 24
tiles or counters to model their
solutions (within a mixed group,
with a partner or independently).
Provide time for students to share
their different solutions
Use this task to lead into a minilesson, modeling the different
combinations of factors that were
possible to create an array of 24
Use this model to introduce the
Commutative Property of
multiplication (i.e. an array of 8 x 3
and 3 x 8 both equal 24) – when
modeling the combinations it would
be helpful to write these pairs side by
side in a table so students can see
how each set of factors can be
written in two different ways
Explicitly teach how to distinguish
between rows and columns.
Students should be able to physically
rotate their arrays (either
manipulatives or pictures) to model
the Commutative Property of
Multiplication.
1. Write an addition sentence and a
multiplication sentence to represent the
picture below:
____ + ____ + ____ + ____ = ____
____ x ____ = ____
2. Write another addition sentence and
multiplication sentence to represent the
picture.
__ + __ + __ + __ + __ + __ + __ + __ = __
____ x ____ = ____
“Seating
Arrangement”
(Appendix C)
*Inquiry-based
hook
My Math Chapter 4
Lesson 4
*Note: For students
who require
remediation, use
lesson 3 to review
arrays (a concept
that was taught in
2nd grade)
EngageNY
Lesson 1.2
(Appendix C)
3. In the multiplication table below, shade four
factors and two products that demonstrate
the Commutative Property of Multiplication.
Explain your reasoning in complete
sentences.
5
6
Use manipulatives and
visual models to
demonstrate
understanding of
division as partitioning
a number into equal
groups.
Interpret the unknown
in division as the
number of groups or
the size of the group.
•
Students should become comfortable
with the word “partition,” as it will
appear again in the unit on fractions.
•
Students must be able to identify
whether a problem gives them the
number of groups or the size of the
groups.
•
Students should learn division
vocabulary: “dividend,” “divisor,”
and “quotient” and recognize that
only the divisor or the quotient can
refer to the number or size of groups.
•
Students should be required to label
their answers when possible (i.e. the
best response for exit ticket question
#2 is “7 stacks,” as opposed to “7” or
“7 erasers”).
Partition 15 counters into 3 equal groups.
1. How many counters are in each group?
2. Write a division sentence to model the
situation: ____ ÷ ____ = ____
3. Ali drew a picture to model 20 ÷ 4 = 5.
4. Is her picture accurate? Give at least 2
reasons to explain why or why not.
1. Use the picture below to answer parts a and
b:
My Math
Chapter 5
Lessons 1 - 2
EngageNY
Lessons 1.4-1.5
“Appendix C)
a. Write a division sentence in which
the solution tells the size of the
group.
b. Write a division sentence in which
the solution tells the number of
groups.
2. Alyssa has 14 erasers. She puts them in
stacks of 2. How many stacks does she
have? Draw a picture and write a division
sentence to support your answer.
Write a division problem in which the number of
equal groups is given.
9 | P a g e 7
Model division using
repeated subtraction on
a number line and
write related
subtraction and
division number
sentences.
•
Each arrow “bump” on the number
line should represent one equal
group and span the size of one group.
Students may benefit from drawing
smaller “bumps” to count the size of
the groups with precision.
My Math
Chapter 5 Lesson 3
1. Fill in the blanks to represent the picture
above:
_____ ÷ _____ = _____
2. Use the number line below to model the total
number of smiley faces using repeated
addition:
2. Explain the relationship between division
and subtraction in complete sentences.
8
Use arrays to model
related multiplication
and division facts.
Describe the
relationship between
multiplication and
division.
10 | P a g e •
•
Students should continue to use
manipualtives (i.e. tiles, counters,
etc) to model multiplication
sentences in the form of arrays
Given the definition of division as an
unknown factor problem, build the
lesson around relating an array that
represents a multiplication sentence
to an unknown factor or division
problem
Create an array to show 6 x 4:
Write a related division sentence that matches this
array:
Explain multiplication and division are related to
each other:
My Math
Chapter 5 Lesson 4
“Engage NY
Lesson 1.6”
(Appendix C)
9
Apply the inverse
relationship between
multiplication and
division to write and
solve equations based
on a given fact family
Students should understand that an
equation (unlike an expression) has an
equals sign. Either an equation or an
expression may include a variable to
stand in for an unknown.
Students should relate the terms
“dividend,” “divisor,” and “quotient” to
the terms “factor” and “product.”
Students should learn the definition of
“inverse operations.”
10
Match expressions
with multiplication and
division situations.
Create a visual model
to accompany the
expression
11 | P a g e Students should use the Commutative
Property of Multiplication as a
foundation for their understanding of
fact families.
• Students should define an
“expression” as a number or
combination of numbers and
operations without an equals sign
(My Math Chapter 9, Lesson 5).
•
Attend to precision when
distinguishing between addition and
multiplication expressions, as well as
between division and subtraction
•
Students should recognize “each” as
a key word indicating multiplication
or division.
•
Students should be justifying their
answers with language of repeated
groups or partitioning into equal
groups.
1. Write four different number sentences using
the following numbers: 2, 4, and 8. In one
equation, label the factors and the product.
In a different equation, label the dividend,
divisor, and quotient.
2. For a school field trip, 72 students will be
traveling in 9 vans. Each van will hold an
equal number of students. The equation
below shows one way to determine the
number of students that will be in each van:
72 ÷ 9 = ?
Write an equation using a different operation to
show the number of students in each van.
Using words and an array, explain why
multiplication and division are inverse operations.
My Math
Chapter 5 Lesson 5
“Engage NY
Lesson 1.11”
(Appendix C) (#1 and #2 are sample PARCC EOY assessment
My Math
questions)
Chapter 9
1. Which three statements can be represented
Lessons 5-7
by the expression 24 ÷ 4?
a. Jake makes 24 muffins. He gives
away 4 muffins.
b. Collin has 24 toy trucks. He sorts
them into groups of 4 trucks each.
c. Amira has 24 trading cards. She puts
them into piles containing 4 cards
each.
d. Rosemary puts 24 stickers in each
book. She uses enough stickers to
fill 4 books.
e. Steven fills a new bookshelf with 24
books. He puts the same number of
books on each of the 4 shelves.
2. For one of the three statements you chose for
#1, use words, numbers, and pictures to
explain why the statement represents 24 ÷ 4.
11
Make sense of and
•
persevere in solving
real world problems
involving
multiplication and
division. Model these
problems using visuals,
manipualtives, arrays,
and/or equations.
•
•
12 | P a g e 3. Which two statements can be represented by
the expression 4 x 8?
a. A teacher puts 8 chairs at each of 4
tables.
b. Tom buys 4 red markers and 8 black
markers.
c. Marie shares her 8 marbles equally
among 4 friends.
d. There are 4 rows of flowers. There
are 8 flowers in each row.
e. There are 8 ducks in the pond. Then,
4 more ducks join them.
For one of the statements you did not choose for #3,
use words, numbers, and pictures to explain why the
statement does not represent 4 x 8.
1. Lucy has 28 craft sticks. She needs 7 sticks
Students should ask themselves
to make a puzzle. How many puzzles can
questions to determine whether to
Lucy make? Write an equation to represent
use multiplication or division for
the situation, and then use your favorite
word problems, such as Do I know
strategy to solve.
the total amount? Do I know the
2. Maria makes 6 blueberry muffins. Each
number of groups? Do I know the
muffin has 5 blueberries. How many
size of each group? By modeling
blueberries did she use in all? Write an
and making sense of problems,
equation to represent the situation, and then
students will be able to reason about
use your favorite strategy to solve.
which operation is necessary because
3. Explain in complete sentences how you are
able to decide whether to use multiplication
Students should begin to write the
or division to solve a single-step word
number sentence of the inverse
problem.
operation as a way to check their
work.
My Math
Chapter 5 Lesson 6
“Making Up Multiplication” (Appendix C) Students should also practice
multiplication and division word
problems with money.
Flex Day (Instruction Based on Data)
Recommended Resources:
Arrays on the Farm (Appendix C)
Array Picture Cards (Appendix C)
Sharing or Grouping? (Appendix C)
Sharing Marbles Equally (Appendix C)
Number Story Arrays (Appendix C)
Division as Unknown Factor Problems (Appendix C)
My Math Chapter 5 Review (Pages 283 – 286)
12
13
Through repeated
observations, infer the
pattern in products
when multiplying by 2.
Use skip counting,
arrays, visual models
and repeated addition
to multiply by 2 with
fluency.
•
•
•
•
•
•
•
13 | P a g e Tip: Prior to this lesson (or on the do
now), assess students’ prerequisite skills
of identifying even/odd numbers
Teaching Tip: Design this as an inquiry
based lesson by:
Begin with #3 (Independent practice) on
page 297 – ask students to color in the
row that shows the products of 2 and to
identify a pattern and make a prediction
Then, allow students to put their theory to
the test using visual models,
manipulatives and/or arrays
For instance, if they predict that any
number x 2 will always be even, they can
use models to represent 11 x 2 or 15 x 2,
and so on to “test” their theory
Then, begin instruction by confirming
that any number with a factor of 2 is in
fact an even number. Encourage students
to think about how this understanding
helps them as mathematicians (i.e. it
helps us judge the reasonableness of our
work – if I ever multiply by 2 and get an
odd number, I know I made a mistake!)
emphasize fluency through skip-counting
1. Julia plants 2 rows of lilies. There are
9 lilies in each row. How many lilies
are there altogether?
a. Write an equation with a ? to
represent the unknown.
b. Draw an array to solve.
c. Write the inverse equation to
check your work.
3. Describe the pattern that occurs when
you multiply by 2 and provide an
example:
My Math
Chapter 2
Lesson 2
“Engage NY
Lesson 1.7”
(Appendix C)
14
Visually represent
dividing by two to
demonstrate that the
quotient is now ½ of
the dividend.
For each division
problem, write a
related multiplication
fact.
•
•
•
Begin lesson with visual models to
students can actually see that dividing by
two is cutting an amount into two equal
halves
Require students to continue visually
representing division by two using arrays,
hundreds charts, pictures and/or
manipulatives
In this lesson, also emphasize fluency
(students may use hundreds chart)
15
Through repeated
observations, infer the
pattern in products
when multiplying by 5.
Use skip counting,
arrays, visual models
and repeated addition
to multiply by 5 with
fluency.
Students should explore this objective
through the multiplication table and be aware
of skip-counting patterns (the products in
each row and column increase by the same
amount) and the fact that when 5 is a factor,
every other product will end in 0 or 5.
16
Apply patterns in
multiplying by 5s to
determine if a given
number will be
divisible by 5.
•
Divide by 5 with
fluency and for each
division problem, write
a related multiplication
fact.
14 | P a g e •
Introduce the term divisible (when one
number can be divided evenly by another
number and the quotient is one whole
number)
Encourage students to use the patterns
they found in 5 products yesterday to
determine whether or not a number will
be divisible by 5 (tip: use this as a warmup for the day’s lesson using a mix of
numbers that are and are not divisible by
5)
1. There are 14 mints in a box. Cecilia
eats 2 mints each day. How many days
does it take Cecilia to eat all of the
mints in the box?
o Write an equation with a ? to
represent the unknown.
o Draw a number line or a tape
diagram to solve.
o Write the inverse equation to check
your work.
My Math
Chapter 2 Lesson 3
1. Rose has 6 ribbons. Each ribbon is 5
inches long. How many inches of
ribbon does she have in all?
a. Write an equation with a ? to
represent the unknown.
b. Draw a number line or a tape
diagram to solve.
c. Write the inverse equation to
check your work.
2. What is true about all products of 5?
Show/explain:
My Math
Chapter 6 Lesson 4
Garrison collected 45 flags. He displays them
in his room in 5 equal rows. How many flags
does Garrison have in each row?
o Write an equation with a ? to
represent the unknown.
o Draw an array to solve.
o Write the inverse equation to check
your work.
“Engage NY
Lesson 1.12”
(Appendix C)
My Math
Chapter 6 Lesson 5
17
18
Apply skip-counting
strategies and
previously learned
models to solve
problems with
multiplication and
division by 10.
In this lesson, students only need to multiply
10 by 2-12 and divide 20-120 by 10.
Students should explore this objective
through the multiplication table and be aware
of skip-counting patterns (the products in
each row and column increase by the same
amount) and the fact that when 10 is a factor
every product ends in 0.
Use place value
•
understanding and the
Associative Property of
Multiplication to solve
problems with
multiplication by
multiples of 10.
•
15 | P a g e Students should define “multiple” in the
context of multiples of ten. (they can
represent multiples of 10 using multiple
hundreds charts) – encourage students to
describe “how many tens” compose each
multiple
Students may benefit from the use of
place value blocks.
• Sample PARCC EOY assessment
question:
Which two ways show how to find the value
of 7 x 40? Select the two correct answers.
A. 7 x 4
B. 4 x 10
C. 7 x 4 x 10
D. 7 groups of 4 ones
E. 7 groups of 4 tens
1. Byron has 40 pennies. He stacks them
in groups of 10. How many stacks of
pennies can Byron make?
a. Write an equation with a ? to
represent the unknown.
b. Draw a picture or an array to
solve.
c. Write the inverse equation to
check your work.
2. Mia found 3 dimes. How much money
did Mia find?
a. Write an equation with a ? to
represent the unknown.
b. Draw a number line to solve.
c. Write the inverse equation to
check your work.
1. What is true about all products of 10?
Show and explain how you know
1. A small plane (pictured below) has 20
rows of seats. Each row has 4 seats.
My Math Chapter 6,
Lessons 7 & 9
My Math
Chapter 6 Lesson 8
“Engage NY
Lesson 3.19”
Write an equation to find the total number of
seats on the plane.
2. Write a multiplication sentence that
uses a multiple of 10 and has a product
of 160.
(Hint: ___ x ___ x 10 = ___ x ___)
3. Jamila solves 20 x 5 by thinking about
10 tens. Explain her strategy.
https://learnzillio
n.com/lessons/27
61-­‐multiply-­‐by-­‐
mutliples-­‐of-­‐10-­‐
by-­‐breaking-­‐apart-­‐
the-­‐multiple-­‐of-­‐
ten-­‐into-­‐2-­‐factors