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IM: 6.5.3: Adding and Subtracting Decimals with Few Non-Zero Digits (Lesson)

By Newsela Staff
Last updated 2 months ago
16 Questions
3.1: Do the Zeros Matter?
1.

Evaluate mentally: 1.009 + 0.391

Decide if each equation is true or false. Be prepared to explain your reasoning.
2.

34.56000 = 34.56

3.

25 = 25.0

4.

2.405 = 2.45

3.2: Calculating Sums
Andre and Jada drew base-ten diagrams to represent 0.007 + 0.004. Andre drew 11 small rectangles. Jada drew only two figures: a square and a small rectangle.

5.

If both students represented the sum correctly, what value does each small rectangle represent? What value does each square represent?

6.

Draw or describe a diagram that could represent the sum 0.008 + 0.07.

7.

Here are two calculations of 0.2 + 0.05. Which is correct? Explain why one is correct and the other is incorrect.

Compute each sum. If you get stuck, consider drawing base-ten diagrams to help you.

  • The applet has tools that create each of the base-ten blocks. This time you need to decide the value of each block before you begin.
  • Select a Block tool, and then click on the screen to place it.
  • Click on the Move tool (the arrow) when you are done choosing blocks.
  • Subtract by deleting with the delete tool (the trash can), not by crossing out.
https://curriculum.illustrativemathematics.org/MS/students/1/5/3/index.html
[Scroll to the tool under "3.2: Calculating Sums"]
8.

9.

0.209 + 0.01

10.

10.2 + 1.1456

3.3: Subtracting Decimals of Different Lengths
To represent 0.4 - 0.03, Diego and Noah drew different diagrams. Each rectangle represented 0.1. Each square represented 0.01.

  • Diego started by drawing 4 rectangles to represent 0.4. He then replaced 1 rectangle with 10 squares and crossed out 3 squares to represent subtraction of 0.03, leaving 3 rectangles and 7 squares in his diagram.
  • Noah started by drawing 4 rectangles to represent 0.4. He then crossed out 3 of rectangles to represent the subtraction, leaving 1 rectangle in his diagram.

11.

Do you agree that either diagram correctly represents 0.4 - 0.03? Discuss your reasoning with a partner.

12.

To represent 0.04-0.003, Elena drew another diagram. She also started by drawing 4 rectangles. She then replaced all 4 rectangles with 40 squares and crossed out 3 squares to represent subtraction of 0.03, leaving 37 squares in her diagram. Is her diagram correct? Discuss your reasoning with a partner.

Find each difference. If you get stuck, you can use the applet to represent each expression and find its value.

Be prepared to explain your reasoning.

  • The applet has tools that create each of the base-ten blocks. This time you need to decide the value of each block before you begin.
  • Select a Block tool, and then click on the screen to place it.
  • Click on the Move tool (the arrow) when you are done choosing blocks.
  • Subtract by deleting with the delete tool (the trash can), not by crossing out.
https://curriculum.illustrativemathematics.org/MS/students/1/5/3/index.html

[Scroll to the tool under "3.3: Subtracting Decimals of Different Lengths"]
13.

0.3-0.05

14.

2.1-0.4

15.

1.03-0.06

16.

0.02-0.007