### Examples

The fraction is to the right of the fraction on a number line so is greater than .### Clarifications

*Clarification 1:*Instruction includes making connections between using a ruler and plotting and ordering fractions on a number line.

*Clarification 2:*When comparing fractions, instruction includes an appropriately scaled number line and using reasoning about their size.

*Clarification 3:* Fractions include fractions greater than one, including mixed numbers, with denominators limited to 2, 3, 4, 5, 6, 8, 10 and 12.

**Subject Area:**Mathematics (B.E.S.T.)

**Grade:**3

**Strand:**Fractions

**Date Adopted or Revised:**08/20

**Status:**State Board Approved

## Benchmark Instructional Guide

### Connecting Benchmarks/Horizontal Alignment

### Terms from the K-12 Glossary

- Number Line

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

The purpose of this benchmark is for students to plot and order fractions with the same numerator (e.g., $\frac{\text{3}}{\text{4}}$, $\frac{\text{3}}{\text{2}}$, $\frac{\text{3}}{\text{8}}$) or fractions with the same denominator (e.g., $\frac{\text{3}}{\text{5}}$, $\frac{\text{10}}{\text{5}}$, $\frac{\text{7}}{\text{5}}$) to compare them by their location on a number line.- During instruction, teachers should provide students opportunities to practice using the
number line, which will assist students with understanding the difference in size when fractions have the same numerator (the size of the parts) and with comparing fractions with the same denominator (number of parts)
*(MTR.2.1).* - Through making connections to rulers, students see that appropriately scaled number lines allow for comparisons of fraction size. Students should also utilize open number lines as to practice creating their own appropriately scaled number lines
*(MTR.2.1).* - Instruction should model that fractional units on a number line represent intervals that are its unit fraction in size. For example, $\frac{\text{5}}{\text{3}}$ on a number line is represented by 5 units from 0
that are each one-third in length. Second, number lines help students see comparisons of fractions to the same whole and will continue as students compare fractions with different numerators and denominators in Grade 4. Finally, number lines reinforce Clarification 3 for MA.3.FR.1.3, that fractions are numbers
*(MTR.2.1, MTR.5.1).*

### Common Misconceptions or Errors

- Students can be confused that when numerators are the same in fractions, larger denominators represent smaller pieces, and smaller denominators represent larger pieces.
- When fraction comparisons are made using area models, students may be confused that the size of the whole for each model must be the same size.

### Strategies to Support Tiered Instruction

- Instruction includes opportunities to use concrete models and drawing of number lines to connect learning with fraction understanding.
- For example, students plot fourths on the number line. Utilizing fraction strips or tiles, students can connect fractional parts to the measurement on a number line.

- Conversation includes what students notice about the fraction on the number line. “How many fourths are in three-fourths? What do we notice about the size of $\frac{\text{1}}{\text{4}}$ compared to $\frac{\text{3}}{\text{4}}$?” Students have opportunities to describe the distance from the 0 as well as the distance from other benchmark fractions.
- Instruction includes opportunities to use fraction manipulatives, concrete models, and
drawings. The teacher begins instruction by modeling fractional pieces with their fraction name. It is important that students see that the fractions that they are building and comparing refer to the same size whole.
- For example, students build fractions tiles or models to equal the same size one whole like below.

### Instructional Tasks

*Instructional Task 1 *

### Instructional Items

*Instructional Item 1 *

*Instructional Item 2 *

*or*>.

**The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.*

## Related Courses

## Related Access Points

## Related Resources

## Formative Assessments

## Image/Photograph

## Lesson Plans

## Original Student Tutorials

## Problem-Solving Tasks

## MFAS Formative Assessments

Students compare two pairs of fractions and record their comparisons using the *less than or greater than *symbols.

Students are asked to locate five-eighths on a number line that has been anchored by zero and one, but that has not yet been scaled.

Students are asked to use a number line that includes the location of zero and one-sixth to find the location of four-sixths.

Students are given four number line diagrams and asked to choose the one that correctly shows the location of one-third.

Students are asked to scale a number line from zero to one so that they can find the location of three-fourths.

## Original Student Tutorials Mathematics - Grades K-5

Joey learns about the location of unit fractions on a number line while at camp in this interactive tutorial.

Joey uses his knowledge of fractions to win games at camp by knowing where fractions greater than one are located on number lines, in this interactive tutorial.

Learn to use number lines to represent fractions as Emmy explores nature in this interactive tutorial.

## Student Resources

## Original Student Tutorials

Joey uses his knowledge of fractions to win games at camp by knowing where fractions greater than one are located on number lines, in this interactive tutorial.

Type: Original Student Tutorial

Learn to use number lines to represent fractions as Emmy explores nature in this interactive tutorial.

Type: Original Student Tutorial

Joey learns about the location of unit fractions on a number line while at camp in this interactive tutorial.

Type: Original Student Tutorial

## Problem-Solving Tasks

This task is meant to address a common error that students make, namely, that they represent fractions with different wholes when they need to compare them. This task is meant to generate classroom discussion related to comparing fractions.

Type: Problem-Solving Task

The purpose of this task is for students to compare fractions using common numerators and common denominators and to recognize equivalent fractions.

Type: Problem-Solving Task

How students tackle the problem and the amount of work they show on the number line can provide insight into the sophistication of their thinking. As students partition the interval between 0 and 1 into eighths, they will need to recognize that 1/2=4/8. Students who systematically plot every point, even 9/8, which is larger even than 1 may still be coming to grips with the relative size of fractions.

Type: Problem-Solving Task

The goal of this task is to help students gain a better understanding of fractions and their place on the number line.

Type: Problem-Solving Task

This simple-looking problem reveals much about how well students understand unit fractions as well as representing fractions on a number line.

Type: Problem-Solving Task

This task includes the seeds of several important ideas. Part a presents the student with the opportunity to use a unit fraction to find 1 on the number line. Part b helps reinforce the notion that when a fraction has a numerator that is larger than the denominator, it has a value greater than 1 on the number line.

Type: Problem-Solving Task

The purpose of this task is to extend students' understanding of fraction comparison and is intended for an instructional setting.

Type: Problem-Solving Task

In every part of this task, students must treat the interval from 0 to 1 as a whole, partition the whole into the appropriate number of equal sized parts, and then locate the fraction(s).

Type: Problem-Solving Task

## 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

This task is meant to address a common error that students make, namely, that they represent fractions with different wholes when they need to compare them. This task is meant to generate classroom discussion related to comparing fractions.

Type: Problem-Solving Task

The purpose of this task is for students to compare fractions using common numerators and common denominators and to recognize equivalent fractions.

Type: Problem-Solving Task

How students tackle the problem and the amount of work they show on the number line can provide insight into the sophistication of their thinking. As students partition the interval between 0 and 1 into eighths, they will need to recognize that 1/2=4/8. Students who systematically plot every point, even 9/8, which is larger even than 1 may still be coming to grips with the relative size of fractions.

Type: Problem-Solving Task

The goal of this task is to help students gain a better understanding of fractions and their place on the number line.

Type: Problem-Solving Task

This simple-looking problem reveals much about how well students understand unit fractions as well as representing fractions on a number line.

Type: Problem-Solving Task

This task includes the seeds of several important ideas. Part a presents the student with the opportunity to use a unit fraction to find 1 on the number line. Part b helps reinforce the notion that when a fraction has a numerator that is larger than the denominator, it has a value greater than 1 on the number line.

Type: Problem-Solving Task

The purpose of this task is to extend students' understanding of fraction comparison and is intended for an instructional setting.

Type: Problem-Solving Task

In every part of this task, students must treat the interval from 0 to 1 as a whole, partition the whole into the appropriate number of equal sized parts, and then locate the fraction(s).

Type: Problem-Solving Task