Comparing Fractions: Build Your Own Models

Learning Resource Type

Learning Activity

Subject Area

Mathematics

Grade(s)

Overview

Students will work in groups to create cards using templates. Each card will have a model of the fraction, mixed number, or improper fraction. After making the cards, students will answer questions during a whole-class discussion to compare fractions with different numerators and denominators using visual models or benchmarks.

This activity results from the ALEX Resource Development Summit.

Phase

Before/Engage

Mathematics (2019) Grade(s): 4

MA19.4.14
Compare two fractions with different numerators and different denominators using concrete models, benchmarks (0, $\frac{1}{2}$, 1), common denominators, and/or common numerators, recording the comparisons with symbols >, =, or <, and justifying the conclusions.

Vocabulary

Compare
Equivalent fraction
Numerator
Denominator
Benchmark fraction
Concrete model
Visual model
Length model
Area model

Knowledge

Students know:

Comparing two fractions is only valid if they refer to the same whole.
Meaning of comparison symbols,, or = .
Fractions can be represented by a variety of visual models (length and area).

Skills

Students are able to:

Use concrete models, benchmarks, common denominators, and common numerators to compare two fractions and justify their thinking.
Explain the comparison of two fractions is valid only when the two fractions refer to the same whole.

Understanding

Students understand that:

When comparing fractions they must refer to the same whole.
Benchmark fractions can be used to compare fractions.
Fractions can be compared by reasoning about their size using part to whole relationship.
Fractions can be compared by reasoning about the number of same-sized pieces.
Fractions can be compared by reasoning about their size when there are the same number of pieces.
Fractions can be compared by reasoning about the number of missing pieces.

Learning Objectives

Students will be able to compare fractions with different numerators and denominators using models and benchmarks.

Activity Details

Begin by drawing a rectangle on the board. Invite a student volunteer to shade in three-fourths. As the student works, invite the other students to ask questions. If no one asks, ask the student how they know they have three-fourths.
Repeat the same process with the fraction three-eighths, one and one-third, and five-fourths, making sure students have seen a model for both an improper fraction and a mixed number. It’s okay if the students are not completely comfortable with drawing these models because they will have a chance to practice in the activity.
Put the students in groups of 3-4. Give each group a fraction list, a fraction template sheet, and 3 sheets of copy paper. It’s helpful to give each group a different color of copy paper to keep the cards from getting mixed up, but it’s not necessary. Each group will also need scissors, glue, and something to write with.
Students should fold and cut their blank paper into fourths so that they have 12 cards. Their job is to create a model for the 12 fractions on their list. They should shade in the required number of pieces on the fraction templates and then glue the model onto the card. The last step is to label the models on the card with the fraction.
Rotate around to each group, helping and encouraging participation as needed. If a group finishes early, they can try to sort their cards into groups: less than one/more than one, fraction/mixed number/improper fractions, etc.
After each group gets finished making their cards, have them come back to sit together as a whole group with their groupmates. Explain that you are going to ask a question and the group will have to decide which card to choose as their answer. They should discuss with their groupmates before picking a card and they will need to be prepared to defend their answer.
Ask the students to find a card that fits the following statement:

Show me a fraction that has more than one whole.
Show me a fraction that is less than one half.
Show me a fraction that has an even number of pieces.
Show me a fraction that is bigger than one third.
Show me a fraction that is bigger than seven-eighths.

After each group has chosen a card, choose a group to defend their answer. Be sure to call on groups that are both correct and incorrect to point out any misconceptions. If you have time, choose two groups that chose different cards (both correct) and ask the class to decide which one is correct.
Encourage students to use benchmarks and comparisons about numerators and denominators. For example, students might say that two-thirds is bigger than two-fifths because they both have two pieces but thirds are bigger than fifths. Another possible strategy to highlight is that four-fifths is smaller than seven-eighths because they are both only one piece away from being a whole but the missing fifth is bigger than the missing eighth. It might be helpful to draw/show the models on a document camera to further illustrate these ideas as they are discussed.

Assessment Strategies

Monitor the students as they are building the cards and answering the class discussion questions to ensure students are able to correctly compare fractions with different numerators and denominators. Student conversations will give insight into the strategies that students are using to compare the fraction models. You can use a checklist with student names to keep track of who needs extra help or enrichment.

Variation Tips

One option is to turn the discussion at the end into a competition. As each group chooses a card, they can earn a point for their team if it matches the description. The winning team is the group that has the most points.

Background / Preparation

You will need to make copies of the fraction lists and fraction template sheet for each group. Each group will also need copy paper (white or colored), scissors, glue, and something to write with.

https://drive.google.com/file/d/1q4xhbxua3MR8xpUFlCvDP8_7g7Tyy3nQ/view?usp=shar…

Approved Date

2020-06-18

Owner (Author)

seasley