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

Last updated 11 months ago

16 questions

3.1: Do the Zeros Matter?

Evaluate mentally: 1.009 + 0.391

3.2: Calculating Sums

3.3: Subtracting Decimals of Different Lengths

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

Last updated 11 months ago

16 questions

3.1: Do the Zeros Matter?

Evaluate mentally: 1.009 + 0.391

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

34.56000 = 34.56

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.

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

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

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"]

0.209 + 0.01

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.

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

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"]

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

Evaluate mentally: 1.009 + 0.391

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

Evaluate mentally: 1.009 + 0.391

34.56000 = 34.56

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

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

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

0.209 + 0.01

10.2 + 1.1456

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

0.3-0.05

34.56000 = 34.56

25 = 25.0

2.405 = 2.45

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

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

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

0.209 + 0.01

10.2 + 1.1456

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

0.3-0.05

2.1-0.4

1.03-0.06

0.02-0.007

25 = 25.0

2.405 = 2.45

2.1-0.4

1.03-0.06

0.02-0.007