19
20
Apply various
strategies to multiply
by 3
•
Flex Day (Instruction Based on Data)
Recommended Resources:
“Engage NY Lesson 3.20” (Appendix C)
“Multiples of Ten Multiply” (Appendix C)
My Math Chapter 6 Check My Progress (Page 325 – 326)
My Math Chapter 6 Problem Solving Investigation (Pages 327 – 332)
My Math Fluency Practice (Pages 351 – 352)
My Math Chapter 6 Review (Pages 353 – 356)
My Math Chapter 7 “Am I Ready?” (Page 359)
1. There are 6 bags of chocolate chip
Students may benefit from using the
cookies. Each bag has 3 cookies. How
strategy of multiplying by 2 and then
many cookies are there in all?
adding 1 more group.
a. Write an equation with a ? to
represent the unknown.
b. Draw a picture to solve.
c. Write the inverse equation to
check your work.
2. In the multiplication chart below, shade
the column of numbers that show the
products with a factor of 3.
My Math
Chapter 7 Lesson 1
“Engage NY
Lesson 1.8”
(Appendix C)
3. Describe the pattern of even and odd
products.
16 | P a g e 21
Apply various
strategies to divide by
3
1. Show two different ways to find the
quotient of:
36 divided by 3
22
Multiply by 4 using
skip counting, arrays,
and by doubling a
known fact
•
•
•
17 | P a g e Students should be able to explain the
strategy of doubling a double (or
doubling the x2 facts they have
memorized).
Students should be able to define a
“known fact” as a fact they have
memorized. They should be able to
“decompose” 4 into equal addends of 2 +
2.
Teaching Tip: encourage students to
reason about the “doubling a known fact”
strategy and why it is particularly helpful
when multiplying by 4 (i.e. because ½ of
4 is 2 and we can fluently multiply by
2’s!)
2. Andrea has is using apple slices to
decorate pies. She uses 3 apple slices to
decorate each pie. She has 21 apple
slices. How many pies can she
decorate?
a. Write an equation with a ? to
represent the unknown.
b. Draw a picture or a number line
to solve.
c. Write the inverse equation to
check your work.
1. For every bowl of guacamole he makes, a
chef uses 3 avocadoes. How many
avacadoes does he use to make four bowls?
Model and solve this problem using:
a. array:
b. doubling a known fact:
2. In the multiplication chart below, shade the
row of numbers that show the products with
a factor of 4.
My Math
Chapter 7 Lesson 2
“Engage NY
Lesson 1.13”
(Appendix C)
“Engage NY
Lesson 1.14”
(Appendix C)
My Math
Chapter 7
Lessons 3-4
*Note – the bulk of
student practice
should be with
lesson 4 (use
examples from
lesson 3 as needed
to model
decomposing an
even factor)
3. Describe the pattern of even and odd
products. Use what you learned about
decomposing 4 to explain the pattern.
23
24
Use repeated
subtraction, arrays and
the inverse relationship
between multiplication
and division in order to
divide by 4.
Explore arithmetic
patterns to solve and
explain problems with
multiplication and
division by 1 and o
Mr. Thomas organizes 16 binders into stacks of
4. How many stacks does he make?
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.
•
The Concept Development section of
EngageNY Module 3, Lesson 16 provides
a script for teachers to guide students in
inferring the Identity Property.
•
Students should be able to define
“Identity Property” and “Zero Property”
•
Students should be able to explain in
writing and orally what happens when
you multiply and divide by 0 and 1
1. There are 11 students in Mr. Macy’s
class. To play a game, each person
needs 1 playing piece. How many
playing pieces are needed for the class
to play the game?
a. Write an equation with a ? to
represent the unknown.
b. Draw a picture or a number line
to solve.
c. Write the inverse equation to
check your work.
My Math
Chapter 7 Lesson 5
“Engage NY
Lesson 1.17”
(Appendix C)
My Math
Chapter 7
Lessons 7 & 8
“Engage NY
Lesson 3.16”
(Appendix C)
2. Ms. Green has 8 flower pots, with 1
flower in each pot. How many flowers
does Ms. Green have in all?
a. Write an equation with a ? to
represent the unknown.
b. Draw a picture or a number line
to solve.
c. Write the inverse equation to
check your work.
3. How many legs do 6 snakes have?
Explain your answer using the Zero
Property of Multiplication.
18 | P a g e 25
Use decomposition,
Students should relate multiplication by 6 to
arrays, and skip
multiplication by 4 (doubling a known fact).
counting to multiply by
6
1. Ray is selling magazine subscriptions.
Each subscription costs $8. If Ray sells
6 subscriptions, how much money will
he make?
a. Write an equation with a ? to
represent the unknown.
b. Double a known fact to solve
and draw an array to model your
answer.
My Math
Chapter 8 Lesson 1
26
Use decomposition,
arrays, and skip
counting to multiply by
7
1. Carmella was trying to solve the
problem 7 x 7. She decided to break
down one of the factors to help make
the problem easier. Here’s what she
has so far:
My Math
Chapter 8 Lesson 2
(7 x 3) + ( _____ x ______ )
Help Carmella finish the problem by filling in
the blanks in the parenthesis, then solve.
2.
Michael is building robots for his
science experiment. Each robot has 6
wheels on the bottom. If he is going to
build 7 robots, how many wheels will
he need?
Show how to solve this problem using two
different strategies:
19 | P a g e 27
Use repeated
subtraction and the
inverse relationship
between multiplication
and division to divide
by 6s and 7s
28
Use the distributive
property as a strategy
to multiply and divide
by 6 and 7
29
Multiply by 8 using
arrays, the
Commutative Property
and known facts
20 | P a g e 1. There are 24 pencils in a box. Ms.
Smith shares them equally with 6
students. (She does not keep any for
herself.) How many pencils does each
student get?
a. Write an equation with a ? to
represent the unknown.
b. Draw a picture or a number line
to solve.
c. Write the inverse equation to
check your work.
•
The Concept Development section of
EngageNY Module 3, Lesson 6 provides
a helpful script for introducing the
Distributive Property.
•
Students will probably be most
comfortable decomposing 7 into the
addends 5 and 2, because they have spent
the most time practicing these facts.
•
Students should be encouraged to explore
apply various strategies for different
problems
1) A parking lot has space for 42 cars.
Each row has 7 parking spaces. How
many rows are there?
o Write an equation with a ? to
represent the unknown.
o Draw an array to solve.
o Use the following template and your
array to decompose the addend from
part a and write an inverse equation
to check your answer: (__ x __) +
(__ x __) = 42
2) Malia solves 6 x 7 using (5 x 7) + 7.
Leonidas solves 6 x 7 using (6 x 5) + (6 x 2).
Who is correct? Use arrays to help you explain
your answer.
1. Double a known fact to solve 3 x 8.
2. Use the distributive property to solve 7 x 8.
Draw an array to support your answer.
3. Fill in the blanks to complete a fact that you
would use the Commutative Property of
Multiplication to solve. Explain your
reasoning.
___ x 8 = ___
My Math
Chapter 8 Lesson 3
“Engage NY
Lesson 3.6”
(Appendix C)
My Math
Chapter 8 Lesson 4
30
31
32
Identify patterns in a
multiplication chart
when multiplying by 9
Subtract from a known
10s fact and apply
previously learned
strategies to multiply
by 9 (i.e. arrays,
commutative property,
distributive property
when multiplying by
an even factor, etc.).
Apply various
strategies to divide by
8 and 9
Interpret the unknown
in multiplication and
division models to
solve problems
21 | P a g e •
Students should take time to explore the
numerous patterns in the multiplication
chart with factors of 9. See Example 2 in
My Math Chapter 8, Lesson 5 and the
Concept Development section of
EngageNY Module 3, Lesson 13.
1) Marlon buys 9 packs of hot dogs. There
are 6 hot dogs in each pack. How many
hot dogs does he have?
o Show three different ways to
represent and solve this problem:
•
1. Mrs. Aquino pours 36 liters of water
equally into 9 containers. How much
water is in each container?
a. Write an equation with a letter to
represent the unknown.
b. Choose a strategy to solve and
model your answer.
c. Write the inverse equation to
check your work.
4. Write the inverse equation to check
your work.
Engage NY Exit Tickets
My Math
Chapter 8 Lesson 5
“Engage NY Lesson 3.12 & 3.13” (Appendix C) My Math
Chapter 8
Lesson 6
“Engage NY
Lessons 7, 11 and
15”
(Appendix C)
*Modify by
combining
resources to allow
students to practice
solving unknowns
with facts 6-9
33
34
Use patterns, models
and previously learned
strategies to multiply
by 11 and 12
Use models, repeated
subtraction and inverse
reasoning to divide by
11 and 12
35
•
Begin with an inquiry-based approach
that asks students to identify patterns
when skip counting by 11 on a
multiplication chart
•
Students should recognize that 12 can be
decomposed into addends of 10 and 2,
both factors that they should be
comfortable working with using the
Distributive Property.
Students can use repeated subtraction with or
without a number line, inverse operations, or
manipulatives.
My Math
1. Marina bought 8 packs of eggs. The
Chapter 8 Lesson 8
eggs came in packages of 12. How
many eggs did Marina buy?
a. Write an equation with a letter to
represent the unknown.
b. Choose a strategy to solve and
model your answer.
5. Megan forgot some of her 12s facts.
She wants to find 6 x 12, but all she can
remember is 5 x 12 = 60. How can she
use this to find 6 x 12? Explain.
My Math
1. Alex has 66 pictures that she wants to
put in a photo album. Each page of the Chapter 8 Lesson 9
album holds 6 pictures. How many
pages will she use?
a. Write an equation with a letter to
represent the unknown.
b. Choose a strategy to solve and
model your answer.
c. Write the inverse equation to
check your work.
6. How can you think of dividing by 11 or
12 as an unknown factor problem?
Flex Day (Instruction Based on Data)
Recommended Resources:
“Find the Unknown Number” (Appendix C)
“Use What You Know” (Appendix C)
“Finding Factors with Arrays” (Appendix C)
My math Chapter 8 Problem Solving Investigation (Pages 469 – 474)
My Math Chapter 8 Fluency Practice (Pages 487 – 488)
My Math Chapter 8 Review (Pages 489 – 492)
22 | P a g e 36
Use arrays to model
the distributive
property
Be sure to have students cut out their “hard”
fact array on graph paper, so that they can
physically break it apart and put it back
together.
Students should begin to recognize
multiplication facts and arrays in the form of
equations. For example:
Adapted from “Making the ‘Hard’ Facts Easy”:
1. Choose a hard fact: __________ and
use the distributive property to find the
product.
2. Which of the following is not another
way to solve 6 x 7? Explain
a. 6 x 3 = 18
6 x 4 = 24
b. 3 x 6 = 18
4 x 6 = 24
c. 3 x 6 = 18
3x1=3
d. 3 x 7 = 21
3 x 7 = 21
2. Debra cannot remember 6 x 4, but she
remembers her 3s facts. Explain how
she can use the distributive property to
find the product.
My Math
Chapter 9 Lesson 1
“Making the “Hard”
Facts Easy”
(Appendix C)
4 x 13
4 x (5 + 7)
37
(4 x 5) + (4 x 7)
Find products using the • Students should recognize that there are
distributive property.
various ways to decompose any given
factor.
1. Find the product of 4 x 12:
a. Using an array:
b. Using the distributive property:
2. Show another way you could
decompose the factors of 4 and 12 to
find their product using the distributive
property:
23 | P a g e My Math
Chapter 9 Lesson 2
Upward Extension:
“Decompose a
Factor”
(Appendix C)
38
Find products using the
associative property
My Math
Chapter 9
Lessons 3-4
39
Represent real world
scenarios involving all
four operations with an
equation
Make sense of and
persevere in solving
multi-step real world
problems by modeling
and representing each
situation with an
equation.
My Math
Chapter 9 Lesson 7
40
•
Students should use their work with
expressions, fact families/inverse
operations, and number sentences
(lessons 8-10) as a foundation for writing
multi-step equations.
•
This objective is allocated two days so
that students have ample opportunities to
practice working with multi-step word
problems.
•
Emphasize the importance of MP1 and
MP4 so that students learn to make sense
of problems through modeling (as
opposed to simplify identifying “signal”
words)
41
•
Sample PARCC EOY assessment
question:
1. Write an equation to represent the
sentence: 12 feet more than 3 equal
groups of 2 feet is p.
2. Carol plays a ball game. She gets 7
points each time her ball hits a target. If
she hits the target at least 5 times in a
row, she can get an extra 25 points.
What is the total number of points Carol
gets if she hits the target 5 times in a
row?
a. Write an equation to represent
the problem using any letter for
the unknown.
b. Solve: ____ points
My Math
Chapter 9 Lesson 8
“Engage NY
Lesson 3.18”
(Appendix C)
LearnZillion:
“Solve two-step
problems using
letters to represent
unknowns”
“Cookie Dough”
(Appendix C)
3. Write a real-world problem that can be
solved using the equation 15 ÷ 3 + 7.
Pablo buys 6 packages of car stamps. Each
package has 6 car stamps. Pablo shares these
car stamps equally among himself and 3
friends. What is the total number of car
stamps that Pablo and each of his 3 friends
receive? ____ stamps
24 | P a g e Flex Day (Instruction Based on Data)
Recommended Resources:
“I Have…Who Has…?” (Appendix C)
“Missing Numbers: Multiplication” (Appendix C)
“Missing Numbers: Division” (Appendix C)
My Math Chapter 9 Problem Solving Investigation (Pages 551 – 556)
My Math Chapter 9 Review (Pages 557 – 560)
42
43
Create and interpret
scaled picture graphs.
•
Teachers can use this as a communitybuilding opportunity by asking students
to gather data about their classmates.
•
Students should be careful to label all
parts of the graph, including a title, the
key, and the x- and y-axes.
•
Students should understand that one
picture does not always represent one unit
or object and connect this to their
understanding of multiplication as equal
groups.
Eliza made a table to show how much time she
spent on chores this week:
Day of the Week
Time Spent on
Chores
Monday
10 minutes
Tuesday
25 minutes
Wednesday
20 minutes
Thursday
15 minutes
My Math
Chapter 12 Lesson 2
“Button Picture Graph” (Appendix C) *Modify to require students to create a scale for their graphs 1.) Eliza wants to display the data in a
picture graph:
a. Use the information in the table
to determine a reasonable scale
for the picture graph:
= _________
b. Use your scale to complete the
picture graph for Monday
through Thursday.
2.) Eliza spent a total of 100 minutes doing
chores during the week. Complete the
picture graph to display Friday’s data.
25 | P a g e 44
Create and interpret
scaled bar graphs.
•
Teachers can use this as a
community-building opportunity by
asking students to gather data about
their classmates.
•
Students should be careful to label all
parts of the graph, including the title,
the key, the categories, and the x- and
y-axes.
•
Students should understand that one
interval does not always represent one
unit and relate this to their
understanding of equal groups.
Ms. Hayden made a table to show the number
of students in the third grade who were wearing
each color of shirt.
My Math
Chapter 12 Lesson 3
“EngageNY
Lesson 6.3”
(Appendix C)
“Button Bar Graph” (Appendix C) *Modify to require students to create a scale for their graphs 1.) Use the information in the table to
complete the bar graph by filling in the
bars to the correct heights.
2.) How many students wore yellow or red
shirts?
3.) Imagine that the fourth grade teacher
collects the following data on her
students’ shirts:
Color of Shirt
Number of
Students
Blue
25
Red
15
Green
20
Yellow
10
Would you use the same scale for a bar graph
about the fourth grade as Ms. Hayden did for
the third grade? If so, why? If not, what scale
would you use and why?
26 | P a g e