Comparing D

# Compare fractions with like numerators or like denominators using models and symbols

# Comparing Fractions with Like Numerators or Like Denominators

#### Description

This is a set of prompts consisting of purposely paired fractions to elicit the use of various strategies. The prompts may be used on different occasions for either Minds-On activities or for Action tasks depending on student readiness. Repeated practice and exploration in making comparisons between fractions will deepen student understanding. These prompts are presented symbolically and without context. Encourage students to build models/representations and create contexts to support visualization of fractions, which in turn supports meaning-making.

#### Mathematics

Research shows that it is beneficial to spread fraction learning throughout the year and embed it in other strands. These prompts progress in complexity from comparisons of equivalent fractions, to examples that include same denominators, to comparisons of very close fractions with different numerators and denominators. Students are encouraged to develop a range of different strategies and to use them strategically, based on the situation.

#### Curriculum Connections

Students will:

- present, compare and order fractional amounts using a variety of tools

#### Instructional Sequence

- Partner students and introduce the task. Post the selected prompt (select from the given options) on the black/whiteboard or interactive whiteboard, or distribute on a handout.
- Provide students time to complete the task. Encourage them to use graph paper, rulers, and manipulatives (concrete or virtual, such as the tools at mathies.ca).
- Highlight different strategies that students used by purposely choosing students that solved the problem using different strategies. Have students identify the similarities and differences between the strategies.

##### Prompt #1

Which is greater: ^{7}⁄_{8} or ^{5}⁄_{8}?
How do you know?

##### Prompt #2

Which is greater: ^{5}⁄_{7} or ^{3}⁄_{7}?
How do you know?

##### Prompt #3

Which is greater: ^{2}⁄_{12} or ^{2}⁄_{10}?
How do you know?

##### Prompt #4

Which is greater: ^{17}⁄_{12} or ^{17}⁄_{7}?
How do you know?

#### Highlights of Student Thinking

Students may:

- construct accurate models to compare two or more fractions
- rely on the algorithm for determining equivalent fractions
- consider only the numerators or only the denominators
- use benchmarks to make estimates for comparison
- consider the size of the unit fractions (as indicated by the denominators)
- consider the proximity of the fraction to 1 by identifying the ‘missing piece’ (complement)
- be purposeful about the strategy for comparison based on the fractions given

#### Key Questions

- Did you think of contexts to help you visualize the fractions? How did this help you?
- Share how you visualized the fractions.
- How did your representation help you to compare the fractions?
- What strategy did you find most helpful? Why?
- What manipulatives can you use to help you?

#### Materials

Make tools available such as paper and markers, grid paper, paper strips for folding, and/or manipulatives such as relational rods.