### Clarifications

**Examples of Opportunities for In-Depth Focus**

Extending fraction equivalence to the general case is necessary to extend arithmetic from whole numbers to fractions and decimals.

**Subject Area:**Mathematics

**Grade:**4

**Domain-Subdomain:**Number and Operations - Fractions

**Cluster:**Level 3: Strategic Thinking & Complex Reasoning

**Cluster:**Extend understanding of fraction equivalence and ordering. (Major Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

**Date Adopted or Revised:**02/14

**Date of Last Rating:**02/14

**Status:**State Board Approved - Archived

**Assessed:**Yes

**Assessment Limits :**

Denominators of given fractions are limited to: 2, 3, 4, 5, 6, 8, 10, 12, 100. For items with denominators of 10 and 100, focus may not be on equivalence between these 2 denominators, since this is addressed specifically in standards MAFS.4.NF.5 – 7, but should focus on equivalence between fractions with denominators of 2, 4, and 5, and fractions with denominators of 10 and 100, e.g., , etc.Fractions must refer to the same whole, including in models. Fraction models are limited to number lines, rectangles, squares, and circles. Fractions can be fractions greater than 1 and students may not be guided to put fractions in lowest terms or to simplify. Equivalent fractions also include fractions .

**Calculator :**No

**Context :**Allowable

**Test Item #:**Sample Item 1**Question:**Select all the models that have been shaded to represent fractions equivalent to

**Difficulty:**N/A**Type:**MS: Multiselect

**Test Item #:**Sample Item 2**Question:**Corey tried to find a fraction equivalent to . His work is shown.

Which statement describes Corey's error?

**Difficulty:**N/A**Type:**MC: Multiple Choice

**Test Item #:**Sample Item 3**Question:**Kari represented a fraction by shading parts of the model shown.

Select all the models that have been shaded to represent fractions equivalent to Kari’s fraction.

**Difficulty:**N/A**Type:**MS: Multiselect

## Related Courses

## Related Access Points

## Related Resources

## Formative Assessments

## Image/Photograph

## Lesson Plans

## Original Student Tutorials

## Problem-Solving Tasks

## Tutorial

## Virtual Manipulatives

## MFAS Formative Assessments

Students partition squares to model two fractions and then determine if the fractions are equivalent.

Students draw a visual fraction model to determine whether two fractions are equivalent.

Students use a number line to explain that one-half is equivalent to two-fourths.

Students scale number lines to locate given fractions, find equivalent fractions, and explain the relationship between equivalent fractions.

## Original Student Tutorials Mathematics - Grades K-5

Learn how to create equivalent fractions and visually see how they are equivalent in this interactive tutorial.

This is part 1 of a 2-part series. Click **HERE **to open Part 2.

Learn how to find equivalent fractions in a multiplication table in this interactive tutorial.

This is part 2 of a 2 part series. Click **HERE** to open Part 1.

## Student Resources

## Original Student Tutorials

Learn how to create equivalent fractions and visually see how they are equivalent in this interactive tutorial.

This is part 1 of a 2-part series. Click **HERE **to open Part 2.

Type: Original Student Tutorial

Learn how to find equivalent fractions in a multiplication table in this interactive tutorial.

This is part 2 of a 2 part series. Click **HERE** to open Part 1.

Type: Original Student Tutorial

## Problem-Solving Tasks

The purpose of this task is to provide students with an opportunity to explain fraction equivalence through visual models in a particular example. Students will need more opportunities to think about fraction equivalence with different examples and models, but this task represents a good first step.

Type: Problem-Solving Task

The purpose of this task is for students to compare two fractions that arise in a context. Because the fractions are equal, students need to be able to explain how they know that. Some students might stop at the second-to-last picture and note that it looks like they ran the same distance, but the explanation is not yet complete at that point.

Type: Problem-Solving Task

## Tutorial

This Khan Academy video illustrates that fraction a/b is equivalent to fraction (a *x* n)/(b x n).

Type: Tutorial

## Virtual Manipulatives

Match shapes and numbers to earn stars in this fractions game.

- Match fractions using numbers and pictures
- make the same fractions using different numbers
- Match fractions in different picture patterns
- Compare fractions using numbers and patterns

Type: Virtual Manipulative

This virtual manipulative allows individual students to work with fraction relationships. (There is also a link to a two-player version.)

Type: Virtual Manipulative

## Parent Resources

## Image/Photograph

Illustrations that can be used for teaching and demonstrating fractions. Fractional representations are modeled in wedges of circles ("pieces of pie") and parts of polygons. There are also clipart images of numerical fractions, both proper and improper, from halves to twelfths. Fraction charts and fraction strips found in this collection can be used as manipulatives and are ready to print for classroom use.

Type: Image/Photograph

## Problem-Solving Tasks

The purpose of this task is to provide students with an opportunity to explain fraction equivalence through visual models in a particular example. Students will need more opportunities to think about fraction equivalence with different examples and models, but this task represents a good first step.

Type: Problem-Solving Task

The purpose of this task is for students to compare two fractions that arise in a context. Because the fractions are equal, students need to be able to explain how they know that. Some students might stop at the second-to-last picture and note that it looks like they ran the same distance, but the explanation is not yet complete at that point.

Type: Problem-Solving Task

## Virtual Manipulative

Match shapes and numbers to earn stars in this fractions game.

- Match fractions using numbers and pictures
- make the same fractions using different numbers
- Match fractions in different picture patterns
- Compare fractions using numbers and patterns

Type: Virtual Manipulative