# Equivalent Fraction Models

Videos, examples, solutions, and lessons to help Grade 3 students learn how to generate simple equivalent fractions by using visual fraction models and the number line.

Common Core Standards: 3.NF.3a, 3.NF.3b, 3.NF.3c

New York State Common Core Math Grade 3, Module 5, Lesson 22, Lesson 23
Grade 3, Module 5, Lesson 22 Worksheets
Grade 3, Module 5, Lesson 23 Worksheets

Lesson 22 Application Problem
Mr. Ramos wants to nail the TV cord against the wall so no one trips. He puts 7 nails equally spaced along the cord. Draw a number line representing the cord. Label it from 0 at the start of the cord to 1 at the end. Mark where Mr. Ramos puts each nail with a fraction.
a. Build a number bond with unit fractions to 1 whole.
b. Write the fraction of the nail that is equivalent to ½ the cord.

Lesson 22 Concept Development

1. Using your fraction strips, name the fraction that is equivalent to 1 third.
2/6
2. Now name the fractions that are equivalent to 1 half.
2/4, 4/8, 3/6
3. Look at 2/3 and 4/6. Do you notice any relationship between the numbers in these fractions?
3 is half of 6. And 2 is half of 4.
4. Now look at 3/4 and 6/8. Does the same pattern you just noticed apply to these fractions? Yes

Lesson 22 Homework

1. Write what fraction of the figure is shaded in the blanks then match the equivalent fractions.
2. Complete the fractions to make true statements.
3. Why does it take 3 copies of 1/6 to show the same amount as 1 copy of 1/2? Explain your answer in words and pictures.
4. How many ninths does it take to make the same amount as 1/3? Explain your answer in words and pictures.
5. A pie was cut into 8 slices equally. If Ruben ate 3/4 of the pie, how many slices did he eat? Write the answer in eighths. Explain your answer using a number line and words.

New York State Common Core Math Grade 3, Module 5, Lesson 23
Lesson 23 Application Problem
The soccer player stood at the corner of a 100 meter field and kicked the ball to her teammate. She kicked it 20 meters. The commentator said she kicked it a quarter of the way across the field.
Is that true? If not, what fraction should the commentator have said? Prove your answer by using a number line.

Concept Development
Create the following index cards and distribute one card to each pair per group:
Group A: Intervals 3-5, thirds and sixths
Group B: Intervals 1-3, sixths and twelfths
Group C: Intervals 3-5, halves and fourths
Group D: Intervals 1-3, fourths and eighths
Group E: Intervals 4-6, sixths and twelfths
Group F: Intervals 6-8, halves and fourths

Make a number line with your given intervals. Then estimate to partition into your given unit by folding your sentence strip. Label the endpoints and the unit fractions. Rename the wholes.
Compare number lines to find equivalent fractions. Record all possible equivalent fractions in your math journals.

Lesson 23 Homework

1. On the number line above, use a colored pencil to divide each whole into 3 unit fractions and label each one above the line.
2. On the number line above, use a different colored pencil to divide each whole into 6 unit fractions and label each one.
3. Write the fractions that name the same place on the number line below.
4. Using your number line to help, name the fraction equivalent to 20/6. Name the fraction equivalent to 12/3.
Draw the part of the number line that would include these fractions below and label it.
5. Write two different fraction names for the dot on the number line. You may use halves, thirds, fourths, fifths, sixths, eighths, or tenths.
6. Danielle and Mandy each ordered a large pizza for dinner. Danielle’s pizza was cut into sixths, and Mandy’s pizza was cut into twelfths. Danielle ate 2 sixths of her pizza. If Mandy wants to eat the same amount of pizza as Danielle, how many slices of pizza will she have to eat? Write the answer as a fraction. Draw a number line to explain your answer.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 