Unit 1 Introducing Multiplication — Unit Plan

TitleAssessment
Lesson 1
Make Sense of Data
Describe and Ask

A group of students were asked, “How do you get home from school each day?”

Their responses are shown in this bar graph:

<p>Bar graph. How We Get Home. Vertical axis from 0 to 10 by ones. Horizontal axis labeled bike, walk, bus, car. Height of bar: Bike, 6. Walk, 4. Bus, 8. Car, 2.</p>

Based on the data shown on the graph:

  1. Write one fact you learned about how the students get home.
  2. Write one question that can be answered by reading the graph.
Show Solution

Sample responses:

  1. More students take the bus home than ride bikes. Eight students take the bus home. Two students ride in a car.
  2. How many more students take the bus than walk home? How many students ride their bikes home?
Lesson 2
Represent Data and Solve Problems
Questions About a Bar Graph

A group of students were asked, “Where is your favorite place to read?”

Their responses are shown in this bar graph:

Bar graph. Favorite Place to Read. Vertical axis labeled number of students from 0 to 10 by 1s. Horizontal axis labeled place: park, home, school, library. Height of bar: park, 8. home, 5. school, 4. library, 2.

  1. How many more students chose the park than home as their favorite place to read?
  2. True or false: More students chose the school or library than the park. Explain or show your reasoning.
Show Solution
  1. 3 more students
  2. False. Sample response: 6 students (4+24+2) chose the school or library, and 8 students chose the park.
Lesson 3
Scaled Picture Graphs
Birds in the Park

Jada collects data about 4 types of birds she sees on her way home.

The data is shown in this picture graph:

Picture Graph. Birds I saw on the way home. Key: check mark represents 2 birds. Cardinals, 1 check mark. Blue Jays, 3 check marks. Pigeons, 6 check marks. Sparrows, 5 check marks.

Based on the data in the graph:

  1. How many sparrows did Jada see on the way home?

  2. Write one question you could ask about the birds Jada saw on the way home.
Show Solution
  1. 10 sparrows
  2. Sample responses: How many birds did Jada see on the way home? How many blue jays and cardinals did Jada see on the way home?
Lesson 4
Create Scaled Picture Graphs
Complete the Picture Graph

A group of students were asked, “Which way would you like to travel?”

Their responses are shown in this picture graph:

Picture Graph. Ways We Would Like to Travel. Key: smiley represents 2 students. Car, 5 smileys. Train, 1.5 smileys. Boat, 3 smileys. Balloon, 1.5 smileys. Plane, 0.5 smileys. Helicopter, 1 smiley.

Four students were absent when this data was collected. They would like to travel by plane.

Add their data to the graph.

Show Solution
Students draw two more smiley faces in the plane column.
Lesson 5
Represent Data in Scaled Bar Graphs
Complete a Scaled Bar Graph

Students were asked, “Which is your favorite animal at the zoo?”

Their responses are shown in this table:

animal number of students
elephant 17
tiger 10
giraffe 14
otter 4

Use the data in the table to complete the scaled bar graph.

<p>Bar graph. Favorite Animals at the Zoo. Vertical axis labeled number of students from 0 to 25 by 5s. Horizontal axis labeled type of animal: elephant, tiger, giraffe, otter. Height of bar: elephant, 17. tiger, no bar. giraffe, 14. otter, no bar.</p>

Show Solution

Student bar graphs show 10 students chose tigers and 4 students chose otters.

Bar graph.

Lesson 6
Choose a Scale
Reflection on Bar Graphs and Scale

  1. How did you decide on the scale for your graph in the last activity?

  2. What was the most important thing you learned today that will help when you make your next scaled bar graph?

Show Solution
  1. Sample response: I chose a scale of 5 so I would have fewer numbers to write on my scale.
  2. Sample response: I learned to think about the numbers in my data to help me choose a scale.
Lesson 7
Answer Questions about Scaled Bar Graphs
Favorite Sports

A group of students were asked, “Which is your favorite sport?”

Their responses are shown in this bar graph: 

<p>Bar graph. Favorite Sports. Vertical axis labeled number of students from 0 to 70 by 5s. Horizontal axis labeled football, soccer, basketball, hockey. Height of bar: football, 28. soccer, 61. basketball, 35. hockey, 22.</p>

Use the graph to answer the questions.

  1. How many more students chose soccer than football? Show your thinking using expressions or equations.
  2. How many fewer students chose hockey than basketball? Show your thinking using expressions or equations.
Show Solution

Answers may vary by 1 or 2 because students may read some of the data slightly differently for bars that represent numbers that are not multiples of 5.

  1. 33 students. Sample response: 28+2=3028 + 2 = 30, 30+31=6130 + 31 = 61, and 2+31=332 + 31 = 33
  2. 13 students. Sample response: 35−22=1335-22 = 13
Lesson 8
More Questions about Scaled Bar Graphs
Reading Time

A group of students were asked, 'Which is your favorite time to read?' Their responses are shown in this bar graph:

Bar graph. Favorite Time to Read. Vertical axis labeled number of students from 0 to 50 by 5s. Horizontal axis labeled morning, lunchtime, afternoon, evenings. Height of bar: morning, 12. lunchtime, 25. afternoon, 23. evenings, 44.

Use the graph to answer the questions.

  1. How many fewer students chose morning than afternoon? Show your thinking using expressions or equations.

  2. How many more students chose evening than morning or lunchtime? Show your thinking using expressions or equations.
Show Solution
  1. Sample response: 11 fewer students. 23−12=1123-12=11
  2. Sample response: 7 more students
  • 12+25=3712+25=37
  • 44−37=744-37=7
Section A Check
Section A Checkpoint
Problem 1

The table shows the number of different coins in a piggy bank. Create a scaled picture graph and a scaled bar graph to represent the data. Use a scale of 2.

coin number
penny 19
nickel 6
dime 10
quarter 15

<p><span>Empty bar graph titled Coins in Piggy Bank. Horizontal axis: penny, nickel, dime, quarter.</span></p>

<span>Empty picture graph titled Coins in Piggy Bank. Horizontal axis: penny, nickel, dime, quarter.</span>

Show Solution

Sample responses:

Bar graph.

Picture graph.

Problem 2

The bar graph and picture graph both show the same data—the number of different animals seen in a park.

<p>Bar graph. Animals in the Park. Vertical axis labeled number of animals from 0 to 50 by fives. Horizontal axis labeled squirrel, duck, sparrow, swan. Height of bar: squirrel, 45. duck, 25. sparrow, 20. swan, 5.</p>

  1. How many squirrels and sparrows were seen altogether? Explain or show your reasoning.
  2. How many more squirrels were seen than sparrows and swans combined? Explain or show your reasoning.
Show Solution
  1. 65. Sample response: 45+20=6545+20=65
  2. 20. Sample response: 20+5=25,45−25=2020+5=25, 45−25=20
Lesson 9
Multiplication for Equal Groups
Represent Equal Groups

Jada has 3 bags. Each bag has 5 bracelets in it.

Represent the situation.

Show Solution

Sample responses:

  • Students make 3 groups of 5 counters or 3 groups of 5 connecting cubes.
  • Students create a drawing of 3 groups with 5 items in each.

Equal groups. 3 groups of 5.

Lesson 10
Situations, Drawings, and Diagrams, Oh My!
Boxes of Shirts

The store has 4 boxes. Each box has 10 shirts in it.

Does this diagram match the situation? Explain your reasoning.

<p>Diagram. A rectangle split into 4 equal parts, each labeled 10.</p>
Show Solution

Yes. Sample response: The 4 parts represent the 4 boxes, and the 10 in each part represents the 10 shirts in each box.

Lesson 11
Multiplication Expressions
Write an Expression

There were 6 envelopes. Each envelope had 2 notes in it.

Write a multiplication expression to represent the situation. Explain or show your reasoning. Create a drawing or diagram if it's helpful.

Show Solution

6×26\times2 or 2×62\times6. Sample response: The 6 represents the 6 envelopes and the 2 represents the 2 notes in each envelope.

Lesson 12
Represent and Solve Multiplication Problems
Ducks in a Pond

There are 4 ponds. Each pond has 5 ducks. How many ducks are there altogether?

Use diagrams, symbols, or other ways to show your thinking.

Show Solution

20 ducks. Sample responses:

  • 4×54\times5
  • 5, 10, 15, 20

Equal groups. 4 groups of 5.

Lesson 13
Multiplication Equations
Match the Equation

Select all the drawings, diagrams, and situations that could represent the equation.

80=8×1080 = 8\times10

  1. 8 groups of 10.

  2. Andre has 8 boxes. Each box has 10 cars in it. He has 80 cars altogether.

  3. 2 arrays. Left array has 2 rows of 5 dots. Right array has 2 rows of 4 dots.

  4. Diagram. 8 equal parts, each labeled 10. Total length, 80.
  5. Andre had 8 boxes. Then, he found 10 more boxes. How many boxes does Andre have?
  6. <p>Diagram. A rectangle split into 2 parts, one labeled 10, the other labeled 8. Total length, 18.</p>
Show Solution

A, B, and D

Lesson 14
Write and Solve Equations with Unknowns
Unknown and a Number
  1. Write an equation to match the diagram. Use a symbol for the unknown.
    Diagram. A rectangle split into 4 equal parts, each labeled question mark. Total length, 40.

  2. Find the number that makes the equation true. Rewrite the equation with that number. Explain your reasoning.
Show Solution
  1. 4×?=404\times {?} = 40 or ?×4=40{?} \times4 = 40
  2. 4×10=404\times10 = 40 or 10×4=4010\times4 = 40. Sample response: If I count by ten 4 times, I get 40. So, the unknown number is 10.
Lesson 15
More Factors, More Problems
Solve the Problem

Solve each problem. Explain or show your reasoning.

  1. There are 4 boxes. Each box has 10 toys. How many toys are there?
  2. Elena has 10 socks. She puts them in piles of 2. How many piles does she make?
Show Solution
  1. 40 toys. Sample response:
    Diagram.
  2. 5 piles. Sample response: 10=?×210={?}\times2. I know that 5×25\times2 is 10.
Section B Check
Section B Checkpoint
Problem 1

Jada has 2 bowls. Each bowl has 3 apples. Select all representations of Jada’s apples.

A. 
<p>Diagram. Rectangle partitioned into 2 equal parts, each labeled 3.</p>
B. 
3 Dot cubes with 2 dots each.
C. 
Diagram. Rectangle partitioned into 3 equal parts, each labeled 6.
D.

2×32 \times 3

E.

2+32 + 3

F. 
2 dot cubes of 3.

Show Solution
A, D, F
Problem 2
  1. There are 3 bunches of grapes. Each bunch has 10 grapes. How many grapes are there? Explain or show your reasoning.
  2. There are 30 people in some cars. Each car has 5 people in it. How many cars are there? Explain or show your reasoning.
Show Solution
  1. 30 grapes. Sample responses:
    • 3×10=303 \times 10 = 30
    • 10×3=3010 \times 3 = 30
    • Diagram.
  2. 6 cars. Sample response: I counted 5, 10, 15, 20, 25, 30 and that’s 6 times to get to 30. So, there are 6 cars.
Lesson 16
Arrange Objects into Arrays
Array Arrangement

Arrange 12 cubes into an array.

Explain or show how the array is related to multiplication.

Show Solution

Sample response: It’s related to multiplication because there are 4 cubes in each row, which is like 3 equal groups.

Lesson 17
Match and Draw Arrays
Draw and Describe
  1. Redraw the equal groups as an array.
  2. Describe how the drawing and the array are related.
Show Solution
  1. Students create a 4×54\times5, 5×45\times4, 2×102\times10, or 10×210\times2 array.
  2. Sample response: There are 5 dots in each group and there are 5 dots in each row. There are 4 groups and there are 4 rows. They both have 20 dots.
Lesson 18
Represent Arrays with Expressions
Array Situation

There are 2 rows of plants. Each row has 5 plants.

  1. Draw an array to represent the situation.

  2. Write a multiplication expression to represent the situation.
Show Solution
  1. Sample response:
    Array.
  2. 2×52\times5 or 5×25\times2
Lesson 19
Solve Problems Involving Arrays
Clare’s Cards

Clare has 3 rows of baseball cards. Each row has 10 cards. How many cards does she have?

  1. Write an equation with a symbol for the unknown number to represent the situation.
  2. Find the number that makes the equation true. Explain or show your reasoning.
Show Solution
  1. Sample response: 3×103\times10 = ? or 10×310\times3 = ?
  2. 30. Sample response: 30 because 3 rows of 10 is 10, 20, 30.
Lesson 20
The Commutative Property
Multiplication Reflection

Summarize what you learned about multiplication today.

Show Solution
Sample response: If we switch the order of the numbers we're multiplying, we get the same product.
Lesson 21
Game Night Seating Plan
No cool-down
Section C Check
Section C Checkpoint
Problem 1

Draw an array that represents the expression 3×43 \times 4. Explain or show your reasoning.

Show Solution
Sample responses:
  • Students draw an array with 3 rows and 4 columns.
  • There are 3 rows of 4 dots, so that’s 3×43 \times 4 dots.
  • Students draw an array with 3 columns and 4 rows.
  • There are 4 rows of 3 dots, so that’s 3×43 \times 4 dots.
Problem 2

There are 5 rows of chairs in the room. Each row has 7 chairs. How many chairs are there?

  1. Draw an array to represent the situation.
  2. Write an equation to represent the situation. Use a symbol for the unknown.
  3. Solve the problem. Explain or show your reasoning.
Show Solution
  1. Students draw a 5 by 7 array or 7 by 5 array.
  2. 5×7=?5 \times 7 = {?} or 7×5=?7 \times 5 = {?}
  3. 35 chairs. Sample response:
    7+7=1414+14=2828+7=35\begin{array}{l} 7 + 7 = 14\\ 14 + 14 = 28 \\ 28+7=35\end{array}