Lesson 10 Ten Times As Much

    • Let’s write equations to show the relationship between the digits in multi-digit numbers.

Warm-up Number Talk: Related Numbers

Find the value of each expression mentally.

Activity 1 Alike but Not the Same

  1. Complete the table with the value of the 8 in each number.

    number

    value of the 8

    180,000

    108,000

    100,800

    100,080

    100,008

  2. Describe the relationship between the value of the 8 in each number.

  3. Write a multiplication or division equation to represent the relationship between the values of the 8 in two different numbers in the table.

Activity 2 More and More Money

Diego’s class is counting collections of play money during a math class. There are four types of bills: tens, hundreds, thousands, and ten-thousands.

Diego found 9 of each type of bill. He organized each type into a stack, creating four stacks.

image of play money

Problem 1

How much money is in each stack of bills?

  1. 9 tens

  2. 9 hundreds

  3. 9 thousands

  4. 9 ten-thousands

Problem 2

Describe the relationship between the values of each stack of bills.

Problem 3

How is the value of the stack of thousands related to the value of the stack of ten-thousands? Write an equation for that relationship.

Problem 4

Clare had 21 bills of each type. How much money is in each stack of bills Clare has?

  1. 21 tens

  2. 21 hundreds

  3. 21 thousands

  4. 21 ten-thousands

Problem 5

What is the value of the 2 in each stack of bills?

Problem 6

How is the value of the 2 in the stack of thousands related to the value of 2 in the stack of ten-thousands? Write an equation for that relationship.

Practice Problem

Problem 1

  1. What is the value of the 6 in 65,247?

  2. What is the value of the 6 in 16,803?

  3. Write multiplication and division equations to represent the relationship between the value of the 6 in 65,247 and the value of the 6 in 16,803.