Fraction Equivalence: Happy by Design

Learning Resource Type

Learning Activity

Subject Area

Mathematics

Grade(s)

Overview

Students will work in groups to solve a task involving a 10x10 grid. They will be asked to represent the same amount in both tenths and hundredths, making connections between equivalent fractions with 10 and 100 as the denominator.

This activity results from the ALEX Resource Development Summit.

Phase

Before/Engage

Mathematics (2019) Grade(s): 4

MA19.4.17
Express, model, and explain the equivalence between fractions with denominators of 10 and 100.

Vocabulary

Equivalence
Denominator
Fraction model
Tenths
Hundredths
Sum

Knowledge

Students know:

Strategies for generating equivalent fractions.
Strategies for adding fractions with like denominators.

Skills

Students are able to:

Express a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100.
Use models to illustrate equivalency between fractions with denominators of 10 and 100.
Explain equivalency between fractions with denominators of 10 and 100.
Use equivalency to add two fractions with denominators of 10 and 100.

Understanding

Students understand that:

equivalent fractions are fractions that represent equal value.

Learning Objectives

Students will be able to create equivalent fractions with denominators of 10 and 100 using a model.

Activity Details

Begin by telling the students that they will be working together to solve a problem. If students are not sitting in groups, put them in groups of 3-4.
Display Slide 2 on the “Happy by Design” slideshow. Read the problem aloud and give students time to look at the design. Ask students if they can answer the problem -- if they immediately answer yes or no, ask them if they can justify their answer.
Display Slide 3. Part A asks the students to figure out exactly how much of the figure is shaded -- they should count and realize there are 40 squares out of 100 that are shaded. This might be enough to answer the question about Malik’s discount, but we can explain and justify our answer by representing the shaded amount as a fraction (40/100). Malik does get the discount because 40/100 is less than half, which would be 50/100.
After students have discussed Part A, direct their attention to Part B. How can we represent the shaded part in a different way besides 40/100? Encourage students to think outside the box. We’re looking for 4/10, but other answers may be correct also.
If students are struggling, ask them if we could rearrange the shaded squares. Provide students with copies of a hundred-grid and encourage them to shade in 40 squares all together, instead of the design that Malik used. It might be helpful to model this on a document camera if students need extra support.
Close the activity by emphasizing that Malik’s design had 40 squares out of 100 shaded in, which is 40/100 and also four columns out of 10 shaded in, which is 4/10.

Assessment Strategies

Observe students and see if they are able to explain the equivalence between 40/100 and 4/10. To get a quick check, write the fraction 20/100 on the board and ask students to create an equivalent fraction using 10 as the denominator.

Variation Tips

Some students might need to see a grid that is only divided into tenths to make the connection between the rows/columns on the 10x10 grid. As an extension, students can make a design on a 10x10 grid by shading in exactly 30 squares. After making the design, ask them to represent the amount with two different equivalent fractions.

Background / Preparation

You will need to have a projector and board to display the slideshow.

Have copies of blank hundred-grids available for students to use.

https://docs.google.com/presentation/d/1yf9xubjokwukQ6iw7bm2W2D0rOKGEq3UqWv_Sl9…

Approved Date

2020-07-01

Owner (Author)

seasley

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