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Unit 5 - Lesson 4 - Grade 5: Illustrative Mathematics

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Grade 5 Unit 5
Lesson 4: Explore Place Value Relationships
CC BY 2021 Illustrative Mathematics
Grade 5 Unit 5
Lesson 4: Explore Place Value Relationships
CC BY 2021 Illustrative Mathematics
Lesson: Explore Place Value Relationships

Notice and Wonder: Maintain Your Balance (Warm Up)

1.

What do you notice?

2.

What do you wonder?

Balance the Weight

For each problem, you have a balance and weights of 0.1 ounce, 0.01 ounce, and 0.001 ounce.
A gold nugget weighs 0.2 ounces.
3.

What is one set of weights you could use to balance the nugget? Explain or show your reasoning.

4.

What is another set of weights you could use to balance the nugget? Explain or show your reasoning.

5.

How many 0.01 ounce weights would you need to balance the nugget?

What about 0.001 ounce weights?

For each problem, you have a balance and weights of 0.1 ounce, 0.01 ounce, and 0.001 ounce.
Write a decimal number for the weight of the gold nuggets that balanced with:
6.

266 of the 0.001 ounce weights

7.

150 of the 0.01 ounce weights

8.

27 of the 0.1 ounce weights

Weights and Place Values

Weights are used to balance some gold nuggets. Write the weight of each gold nugget in expanded form.
9.

three 0.1 ounce weights, five 0.01 ounce weights, and eight 0.001 ounce weights

10.

six 0.1 ounce weights and two 0.001 ounce weights

11.

two 0.01 ounce weights and six 0.1 ounce weights

Here are the weights of some gold nuggets in word form. Write the weights in expanded form.
12.

two hundred eighty three thousandths of an ounce

13.

four hundred nine thousandths of an ounce

A gold nugget weighs 0.527 ounces.
14.

What is the value of each of the digits in the decimal 0.527?

15.

How does the expanded form of 0.527 show the value of each digit in the decimal?

Comparing Place Values with Weights

16.

How many 0.01 ounce weights will balance one 0.1 ounce weight? Explain or show your reasoning.

17.

How many 0.001 ounce weights will balance a 0.1 ounce weight? Explain or show your reasoning.

The table shows the weights of 3 of the gold nuggets Diego and his friends found panning for gold. Fill in the blanks.
18.
Nugget A weighs_______ times as much as Nugget B.
19.

Explain or show your reasoning.

20.
Nugget A weighs_______ times as much as Nugget C.
21.

Explain or show your reasoning.

22.
Nugget C weighs_______ times as much as Nugget B.
23.

Explain or show your reasoning.

24.
Nugget C weighs_______ times as much as Nugget A.
25.

Explain or show your reasoning.

Cool Down: Worth its Weight in Gold
A gold nugget balances with 2 one hundredth ounce weights and 6 one thousandth ounce weights.
26.

What is the weight of the nugget? Write your answer as a decimal.

27.

What is a different set of weights that will balance the nugget?