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IM: 6.4.5: How Many Groups? (Part 2) (Lesson)

By Newsela Staff
Last updated 2 months ago
9 Questions
5.1: Reasoning with Fraction Strips
Write a fraction or whole number as an answer for each question. If you get stuck, use the fraction strips. Be prepared to share your reasoning.


1.
How many 1/2s are in 2? _______

How many 1/5s are in 3? _______

How many 1/8s are in 11/4? _______

1\div \frac{2}{6}=? _______

2\div \frac{2}{9}=? _______

4 \div \frac{2}{10}=? _______
5.2: More Reasoning with Pattern Blocks
Use the pattern blocks in the applet to answer the questions. (If you need help aligning the pieces, you can turn on the grid.)

https://curriculum.illustrativemathematics.org/MS/students/1/4/5/index.html

[Scroll to the tool under "5.2: More Reasoning with Pattern Blocks"]
2.
If the trapezoid represents 1 whole, what do each of these other shapes represent? Be prepared to explain or show your reasoning.

  • 1 triangle _______
  • 1 rhombus _______
  • 1 hexagon _______
3.

Use (or draw) pattern blocks to represent each multiplication equation. Use the trapezoid to represent 1 whole.

  • 3 \cdot 1/3 = 1
  • 3 \cdot 2/3 = 2

4.

Diego and Jada were asked “How many rhombuses are in a trapezoid?”

  • Diego says, “11/3. If I put 1 rhombus on a trapezoid, the leftover shape is a triangle, which is 1/3 of the trapezoid.”
  • Jada says, “I think it’s 11/2. Since we want to find out ‘how many rhombuses,’ we should compare the leftover triangle to a rhombus. A triangle is 1/2 of a rhombus.”

Do you agree with either of them? Explain or show your reasoning.

5.

Select all the equations that can be used to answer the question: “How many rhombuses are in a trapezoid?”

5.3: Drawing Diagrams to Show Equal-sized Groups
For each situation, draw a diagram for the relationship of the quantities to help you answer the question. Then write a multiplication equation or a division equation for the relationship. Be prepared to share your reasoning.
6.

The distance around a park is 3/2 miles. Noah rode his bicycle around the park for a total of 3 miles. How many times around the park did he ride?

7.

You need 3/4 yard of ribbon for one gift box. You have 3 yards of ribbon. How many gift boxes do you have ribbon for?

8.

The water hose fills a bucket at 1/3 gallon per minute. How many minutes does it take to fill a 2-gallon bucket?

Are you ready for more?
9.

How many heaping teaspoons are in a heaping tablespoon? How would the answer depend on the shape of the spoons?