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IM: 6.5.2: Using Diagrams to Represent Addition and Subtraction (Lesson)

By Newsela Staff
Last updated 2 months ago
25 Questions
2.1: Changing Values
Here is a rectangle.


1.
What number does the rectangle represent if each small square represents:
  1. 1 _______
  2. 0.1 _______
  3. 0.01 _______
  4. 0.001 _______
Here is a square.

2.
What number does the square represent if each small rectangle represents:
  1. 10 _______
  2. 0.1 _______
  3. 0.00001 _______
2.2: Squares and Rectangles
You may be familiar with base-ten blocks that represent ones, tens, and hundreds. Here are some diagrams that we will use to represent digital base-ten units. A large square represents 1 one. A rectangle represents 1 tenth. A small square represents 1 hundredth.

The applet has tools that create each of the base-ten blocks.

https://curriculum.illustrativemathematics.org/MS/students/1/5/2/index.html

[Scroll to the tool under "2.2: Squares and Rectangles"]
Select a Block tool, and then click on the screen to place it.


One








Tenth








Hundredth
Click on the Move tool when you are done choosing blocks.

3.

Here is the diagram that Priya drew to represent 0.13.

Draw a different diagram that represents 0.13 in the applet. Explain why your diagram and Priya’s diagram represent the same number.

4.

Here is the diagram that Han drew to represent 0.25.

Draw a different diagram that represents 0.25 in the applet. Explain why your diagram and Han’s diagram represent the same number.

For each of these numbers, draw or describe two different diagrams that represent it.

5.

0.1

6.

0.02

7.

0.43

Use diagrams of base-ten units to represent the following sums and find their values. Think about how you could use as few units as possible to represent each number.
8.

0.03 + 0.05

9.

0.06 + 0.07

10.

0.4 + 0.7

2.3: Finding Sums in Different Ways
Here are two ways to calculate the value of 0.26+0.07. In the diagram, each rectangle represents 0.1 and each square represents 0.01.

Use what you know about base-ten units and addition of base-ten numbers to explain:
11.

Why ten squares can be “bundled” into a rectangle.

12.

How this “bundling” is reflected in the computation.

The applet has tools that create each of the base-ten blocks. Select a Block tool, and then click on the screen to place it.
https://curriculum.illustrativemathematics.org/MS/students/1/5/2/index.html

[Scroll to the tool under "2.3: Finding Sums in Different Ways "]
Select a Block tool, and then click on the screen to place it.


One








Tenth








Hundredth
Click on the Move tool when you are done choosing blocks.

13.

Find the value of 0.38 + 0.69 by drawing a diagram. Can you find the sum without bundling? Would it be useful to bundle some pieces? Explain your reasoning.

14.

Calculate 0.38 + 0.69. Check your calculation against your diagram in the previous question.

Find each sum. The larger square represents 1, the rectangle represents 0.1, and the smaller square represents 0.01.
15.

16.

2.4: Representing Subtraction
Here are diagrams that represent differences. Removed pieces are marked with Xs. The larger rectangle represents 1 tenth. For each diagram, write a numerical subtraction expression and determine the value of the expression.
17.

18.

19.

Express each subtraction in words.
20.

0.05 - 0.02

21.

0.024 - 0.003

22.

1.26 - 0.14

Find each difference by drawing a diagram and by calculating with numbers. Make sure the answers from both methods match. If not, check your diagram and your numerical calculation.
23.

0.05 - 0.02

24.

0.024 - 0.003

25.

1.26 - 0.14