Lesson 11
Objective: Model division as the unknown factor in
multiplication using arrays and tape diagrams.
Application Problem (5 minutes)
Rosie puts 2 lemon slices in each cup of iced tea. She uses
a total of 8 slices. How many cups of iced tea does Rosie
make?
Note: Students may have solved the problem as shown, or
using division (8 ÷ 2 = 4). This problem leads into modeling
with tape diagrams, which is introduced in the concept
development.
Lesson 12
Objective: Interpret the quotient as the number of groups
or the number of objects in each group using units of 2.
Application Problem (5 minutes)
A chef arranges 4 rows of 3 red peppers on a tray. He adds
2 more rows of 3 yellow peppers. How many peppers are
there altogether?
Note: Students might solve using an array to model the
distributive property (Lesson 10) or the tape diagram
(Lesson 11). If they use the latter strategy, it is likely their
first use of a tape diagram to solve multiplication. The
problem is a review and provides an exploratory
opportunity for students to select and use appropriate
tools.
Lesson 13
Objective: Interpret the quotient as the number of groups or the
number of objects in each group using units of 3.
Mark spends $16 on 2 video games. Each game costs the
same amount. Find the cost of each game.
Notes: This problem reviews equal groups division from
Lesson 12 where the unknown is the number of objects in
each group.
Lesson 14
Objective: Skip-Count objects in models to build fluency with
multiplication facts using units of 4.
Application Problem (5 minutes)
Jackie buys 21 pizzas for a party. She places 3 pizzas on
each table. How many tables are there?
Note: This problem reviews equal groups division from
Lesson 13 where the unknown is the number of groups. In
preparation for today’s lesson, students solve by skipcounting to add units until they reach the total of 21.
When directions are not specified, students may use any
model of their choice to solve.
Lesson 15
Objective: Relate arrays to tape diagrams to model the
commutative property of multiplication.
Application Problem (5 minutes)
A cell phone is about 4 inches long. About how long are 9
cell phones laid end to end?
Note: This problem reviews multiplication using units of
four from Lesson 14. It provides an opportunity to review
using tape diagrams as tools for solving multiplication
problems, which students further explore in today’s
lesson.
Lesson 16
Objective: Use the distributive property as a strategy to find
related multiplication facts.
Application Problem (5 minutes)
Ms. Williams draws the array below to show the class
seating chart. She sees the students in 4 rows of 7 when
she teaches at Board 1. Use the commutative property to
show how Ms. Williams sees the class when she teaches at
Board 2.
Bonus: On Monday, six of Ms. Williams’ students are
absent. How many students are in class on Monday?
Lesson 17
Objective: Model the relationship between multiplication and
division.
Application Problem (5 minutes)
Mrs. Peacock bought 4 packs of yogurt. She had exactly
enough to give each of her 24 students 1 yogurt cup. How
many yogurt cups are there in 1 pack?
Note: This problem is designed to lead into the concept
development. In Problem 1, students will analyze how a
number bond represents the division sentence, 24 ÷4.
Lesson 18
Objective: Apply the distributive property to decompose
units.
Application Problem (5 minutes)
A parking structure has 10 levels. There are 3 cars parked
on each level. How many cars are parked in the structure?
Lesson 19
Objective: Apply the distributive property to decompose
units.
Application Problem (5 minutes)
Henrietta works in a shoe store. She uses 2 shoelaces to
lace each pair of shoes. She has a total of 24 laces. How
many pairs of shoes can Henrietta lace?
Lesson 20
Objective: Solve two-step word problems involving multiplication
and division and assess the reasonableness of answers.
Application Problem (8 minutes)
Red, orange, and blue scarves are on sale for $4 each. Nina
buys 2 scarves of each color. How much does she spend
altogether?
Note: This problem reviews multiplication using units of
four. It also leads into Problem 1 of the Concept
Development.
Lesson 21
Objective: Solve two-step word problems involving all four
operations and assess the reasonableness of answers.
Application Problem (5 minutes)
There are 4 boxes with 6 binders in each one. 3 brothers
share the binders. How many binders does each brother
get?
Note: This two-step problem reviews Lesson 20’s
emphasis. To solve application problems, students selfselect an approach and independently solve them.
Practicing a two-step problem here scaffolds the
difference between the structured practice in Lesson 20
and the open-ended practice in Lesson 21. Prepare
students for today’s exploration by guiding them to
evaluate their methods for solving and assessing the
reasonableness of their answer.