Lesson 6 Ten Times as Many

- Let’s represent “10 times as many.”

Warm-up Choral Count: 12, 15 and 24

Count by 12 starting at 12.

Activity 1 Ten Times as Many

Problem 1

Here is a diagram that represents two quantities, A and B.

diagram. two rectangles. bottom rectangle, B. partitioned into 10 equal parts. Top rectangle, A. Same size as one of the 10 parts of the bottom rectangle.

What are some possible values of A and B?
Select the equations that could be represented by the diagram.
1. $15 \times 10 = 150$
2. $16 \times 100 = 1, 600$
3. $30 \div 3 = 10$
4. $5, 000 \div 5 = 1, 000$
5. $80 \times 10 = 800$
6. $12, 000 \div 10 = 1, 200$

Problem 2

For the equations that can’t be represented by the diagram:

Explain why the diagram does not represent these equations.
How would you change the equations so the diagram could represent them?
Compare your equations with your partner’s. Make at least two observations about the equations you and your partner wrote.

Activity 2 What Remains the Same?

Problem 1

Use the diagram to complete the table.
value of A
value of B
$14$
$1, 000$
$160$
$850$
$1, 000$
$2, 070$
$3, 900$

Problem 2

Select some values from your table to explain or show:

How you found the value of B when the value of A is known.
How you found the value of A when the value of B is known.

Practice Problem

Problem 1

If diagram A represents 15, what does diagram B represent? Explain your reasoning.
If diagram B represents 100, what does diagram A represent? Explain your reasoning.