We included **HMH Into Math Grade 4 Answer Key**** PDF** **Module 11 Lesson 3 Explain Fraction Equivalence Using Visual Models** to make students experts in learning maths.

## HMH Into Math Grade 4 Module 11 Lesson 3 Answer Key Explain Fraction Equivalence Using Visual Models

I Can use a visual model to show that two fractions are equivalent and explain why they are equivalent.

**Spark Your Learning
**Compare Jason’s and Kym’s turns. Whose turn is closer to being a full turn? Use the visual model of each turn to explain.

Answer:

Both are close to turn closer to being a full turn because both turns are same.

Explanation:

Jason’s turns:

Number of shaded turns of Jason = 3.

Total number of turns of Jason = 4.

Number of turns Jason makes = Number of shaded turns of Jason ÷ Total number of turns of Jason

= 3 ÷ 4 or \(\frac{3}{4}\)

Kym’s turns:

Number of shaded turns of Kym = 6.

Total number of turns of Kym = 8.

Number of turns Kym makes = Number of shaded turns of Kym ÷ Total number of turns of Kym

= 6 ÷ 8 or \(\frac{6}{8}\)

= \(\frac{6}{8}\) ÷ \(\frac{2}{2}\) = \(\frac{3}{4}\)

**Turn and Talk** How do the number and size of parts compare in the visual models for Jason’s and Kym’s turns?

Answer:

Total number of turns(size of parts) and number of turns they made (shaded part) are compare in the visual models for Jason’s and Kym’s turns

Explanation:

Number of shaded turns of Jason = 3.

Total number of turns of Jason = 4.

Number of turns Jason makes = \(\frac{3}{4}\)

Number of shaded turns of Kym = 6.

Total number of turns of Kym = 8.

Number of turns Kym makes = \(\frac{6}{8}\)

**Build Understanding
**1. Sam wants to paint a skateboard ramp with a cool design. He has just enough paint to cover half of the ramp. Show different designs Sam can use. Divide the last two rectangles into a different number of equal parts. Shade each of the last three rectangles to show \(\frac{1}{2}\).

**Complete the table to record your findings.
**

Look at the first fraction you wrote in the table.

A. How does the size of the parts compare to those in \(\frac{1}{2}\)?

____________________________

B. How does the number of parts and the number of shaded parts compare to those in \(\frac{1}{2}\) ?

____________________________

Answer:

Explanation:

\(\frac{1}{2}\)

\(\frac{1}{2}\) = \(\frac{1}{2}\) × \(\frac{3}{3}\) = \(\frac{3}{6}\)

\(\frac{1}{2}\) = \(\frac{1}{2}\) × \(\frac{5}{5}\) = \(\frac{5}{10}\)

\(\frac{1}{2}\) = \(\frac{1}{2}\) × \(\frac{2}{2}\) = \(\frac{2}{4 }\)

**Turn and Talk** Look for patterns in your table. How does the numerator and denominator for each fraction compare to those in \(\frac{1}{2}\) ?

Answer:

\(\frac{1}{2}\) < \(\frac{7}{2}\).

Explanation:

Fraction is a number that represents a portion of a whole number. Some fractions are larger than others.

Fraction = Numerator by Denominator.

Given Fraction = \(\frac{1}{2}\)

For example:

Which is bigger \(\frac{1}{2}\) and \(\frac{7}{2}\)

\(\frac{1}{2}\) < \(\frac{7}{2}\) because we check denominators and numerators.

If denominators are same , the value high in numerator is big.

If Numerators are same , the value small in denominators is big.

**Step It Out
**

**Connect to Vocabulary**

Two or more fractions that name the same amount are called equivalent fractions.

2. Write an equivalent fraction for \(\frac{1}{2}\).

A. Compare the rectangle with 2 parts that shows \(\frac{1}{2}\) in Task 1 to the rectangle with 6 parts you shaded to show \(\frac{1}{2}\). Complete the equation.

B. How can you use multiplication to describe the relationship between the numerators? Between the denominators?

C. Complete the equation to show how to write a fraction equivalent to \(\frac{1}{2}\).

D. Complete the statement about any fraction.

To write an equivalent fraction, multiply the numerator and ____ of the fraction by ____

Answer:

Equivalent fraction for \(\frac{1}{2}\) = \(\frac{3}{6}\)

Explanation:

Equivalent fraction for \(\frac{1}{2}\):

\(\frac{3}{3}\) × \(\frac{1}{2}\) = \(\frac{3}{6}\)

**Turn and Talk** Look at the other fractions you wrote in Task 1. Do they agree with the statement in Part D? Explain.

Answer:

Yes, they agree with the statement in Part D. \(\frac{1}{2}\) = \(\frac{3}{6}\) both are same

Explanation:

Task 1: Fraction \(\frac{1}{2}\)

Part D: Fraction \(\frac{3}{6}\)

**Check Understanding Math Board
**Question 1.

Jason makes a \(\frac{5}{6}\) turn on his skateboard. Samantha makes a \(\frac{10}{12}\) turn. Did they make the same-sized turn? Use the visual models to explain.

Answer:

They make the same-sized turn.

Explanation:

Number of turns on his skateboard Jason makes = \(\frac{5}{6}\)

Number of turns on his skateboard Samantha makes = \(\frac{10}{12}\)

\(\frac{5}{6}\) = \(\frac{5}{6}\) × \(\frac{2}{2}\) = \(\frac{10}{12}\)

\(\frac{10}{12}\) = \(\frac{10}{12}\) ÷ \(\frac{2}{2}\) = \(\frac{10}{12}\)

**On Your Own
**Question 2.

Are the fractions \(\frac{3}{4}\) and \(\frac{6}{8}\) equivalent? Use the visual models to explain how you know.

Answer:

Yes, they are the fractions \(\frac{3}{4}\) and \(\frac{6}{8}\) equivalent

Explanation:

\(\frac{3}{4}\) = \(\frac{3}{4}\) × \(\frac{2}{2}\) = \(\frac{6}{8}\) .

\(\frac{6}{8}\) = \(\frac{6}{8}\) ÷ \(\frac{2}{2}\) = \(\frac{3}{4}\)

**Model with Mathematics** Complete the equation to show how the two fractions are equivalent.

Question 3.

Answer:

Explanation:

\(\frac{2}{3}\) = \(\frac{2}{3}\) × \(\frac{2}{2}\) = \(\frac{4}{6}\)

\(\frac{4}{6}\) = \(\frac{4}{6}\) ÷ \(\frac{2}{2}\) = \(\frac{2}{3}\)

Question 4.

Answer:

Explanation:

\(\frac{2}{3}\) = \(\frac{2}{3}\) × \(\frac{4}{4}\) = \(\frac{8}{12}\)

\(\frac{8}{12}\) = \(\frac{8}{12}\) ÷ \(\frac{4}{4}\) = \(\frac{2}{3}\)

Question 5.

**Reason** A recipe asks for \(\frac{1}{4}\) teaspoon of salt. Jonas only has a \(\frac{1}{8}\)—teaspoon measuring spoon. He fills that spoon two times to get \(\frac{1}{4}\) teaspoon of salt. Use visual models to explain why this works.

Answer:

Explanation:

Quantity of teaspoon of salt a recipe asks =\(\frac{1}{4}\)

Quantity of teaspoon measuring spoon Jonas has = \(\frac{1}{8}\)

\(\frac{1}{8}\) = \(\frac{1}{8}\) × 2 = \(\frac{2}{8}\) = \(\frac{1}{4}\)

**I’m in a Learning Mindset!
**Did the practice help me master how to use visual models to explain equivalent fractions? Why or why not?

____________________________________

Answer:

Yes, this practice has helped the master to use visual models to explain equivalent fractions because its easy to understand the figures.

Explanation:

Visual models makes headway in identifying as well as representing equivalent fractions easily.