Lesson 1: Find Fractions of a Set with Arrays

Multiple Choice

Which of the following best describes why counting by halves is important when learning about fractions?

• It helps understand how to divide objects into equal parts.

• It is only useful for addition and subtraction.

• It is not related to fractions at all.

• It is only used in advanced mathematics.

Multiple Choice

How can you express the repeated addition of 1/2 + 1/2 as a multiplication expression?

• 2 × 1/2

• 1 × 1/2

• 1/2 × 2

• 2 × 2

Multiple Choice

Compare the repeated addition of fractions in images 2 and 3. What is the relationship between the number of terms and the multiplication expression?

• The number of terms is the same as the multiplier in the multiplication expression.

• The number of terms is always one less than the multiplier.

• The number of terms is always double the multiplier.

• There is no relationship.

Multiple Choice

What multiplication expression represents the sum 1/3 + 1/3 + 1/3 + 1/3 + 1/3?

• 5 × 1/3

• 3 × 1/3

• 4 × 1/3

• 6 × 1/3

Open Ended

Explain how repeated addition of fractions can be represented as multiplication. Use examples from the images to support your answer.

Multiple Choice

How does the repeated addition of 1/4 five times relate to multiplication?

• It is the same as multiplying 5 by 1/4.

• It is the same as multiplying 4 by 1/5.

• It is the same as multiplying 1/4 by 4.

• It is the same as multiplying 1/5 by 4.

Multiple Choice

What is the result of dividing 9 by 3, as shown in the images?

• 3

• 6

• 1

• 12

Multiple Select

Which of the following fractions is equal to 1? Select all that apply.

• 5/5

• 4/5

• 2/2

• 9/3

Open Ended

Based on the examples provided, explain why dividing a number by itself (such as 5/5) always results in 1.

Multiple Choice

Which of the following best describes how to interpret a fraction as a division problem, based on the examples shown in the images?

• A fraction can be interpreted as the numerator divided by the denominator.

• A fraction can be interpreted as the denominator divided by the numerator.

• A fraction is always equal to 1.

• A fraction is always less than 1.

Multiple Choice

Which mathematical operation does the fraction 20/5 represent?

• Multiplication

• Addition

• Division

• Subtraction

Multiple Choice

How many eggs does Mr. Perez use to make the cake if he uses 1/3 of his 12 eggs?

• 3

• 4

• 6

• 8

Multiple Choice

What is the value of 2/3 of 12?

• 4

• 6

• 8

• 9

Multiple Choice

What is the value of 3/6 of 18?

• 3

• 6

• 9

• 12

Open Ended

How would you explain the process of finding a fraction of a set using an array model?

Multiple Choice

Which of the following is the correct way to find 2/3 of 12 using an array?

• Divide 12 into 3 equal groups and take 2 groups

• Divide 12 into 2 equal groups and take 3 groups

• Multiply 12 by 2/3 directly

• Add 2 and 3 then multiply by 12

Open Ended

How does knowing 1/3 of 27 help you find 4/3 of 27?

Open Ended

What do you notice about Sana’s and Toby’s arrays for showing 3/4 of 12?

Multiple Select

Select all the correct statements about finding a fraction of a set using arrays:

• Arrays help visualize equal groups for fractions

• You can use arrays to find 3/4 of 12 by shading 9 out of 12 circles

• Arrays are only useful for whole numbers, not fractions

• Arrays make it easier to compare different ways to find the same fraction

Open Ended

What is one thing you learned today about finding fractions of a set with arrays?

Open Ended

Is an array helpful when you find a fraction of a set? How?