### Examples

is equivalent to which is equivalent to .### Clarifications

*Clarification 1:*Instruction includes the use of visual models.

*Clarification 2:* Within this benchmark, the expectation is not to simplify or use lowest terms.

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

**Grade:**4

**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

- NA

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

The purpose of this benchmark is to connect fraction addition to decimal addition through decimal fractions. This will be the first opportunity for students to create common denominators to add fractions. This benchmark continues the work of equivalent fractions (MA.3.FR.1.2) by having students rename fractions with denominators of 10 as equivalent fractions with denominators of 100 (MA.4.FR.1.1). Students who can generate equivalent fractions can adapt this new procedure to develop strategies for adding fractions with unlike denominators in grade 5 (MA.5.FR.2.1).- Instruction may include students shading decimal grids (10 × 10 grids) to support their understanding.

- Subtraction of decimal fractions is not a requirement of grade 4.

### Common Misconceptions or Errors

- Students often will add the numerators and the denominators without finding the like denominator. Students will need visual models to understand what the like denominator means.

### Strategies to Support Tiered Instruction

- Instruction includes opportunities to explore the addition of a fraction with a denominator of 10 to a fraction with a denominator of 100 using visual models to help understand equivalent fractions. Students use visual models to make sense of equivalent fractions when finding like denominators. The teacher provides clarification that students must find the like denominator before adding.
- For example, the teacher displays the problem $\frac{\text{4}}{\text{10}}$ + $\frac{\text{23}}{\text{100}}$ and asks students to share what they notice about this expression. Students identify that the denominators are different. The teacher guides students to shade decimal grids to represent the understanding that $\frac{\text{4}}{\text{10}}$ is equivalent to $\frac{\text{40}}{\text{100}}$. This is repeated with similar addition problems and solved while supporting students as they use the visual models to problems that have denominators of 10 and 100.

- For example, the teacher displays the problem $\frac{\text{24}}{\text{100}}$ + $\frac{\text{3}}{\text{10}}$ , asking students to share what they notice about this expression. Students identify that the denominators are different. The teacher guides students to use place value blocks and shaded decimal grids to represent the problem and solve, having tens rods represent tenths, and one's cubes represent hundredths. Students are supported as they use the visual models to understand that $\frac{\text{3}}{\text{10}}$ is equivalent to $\frac{\text{30}}{\text{100}}$. This is repeated with similar addition problems that have denominators of 10 and 100.

### Instructional Tasks

*Instructional Task 1 *(MTR.5.1)

- $\frac{\text{5}}{\text{10}}$ = $\frac{\text{}}{\text{100}}$

- $\frac{\text{31}}{\text{100}}$ + $\frac{\text{5}}{\text{10}}$ =

### Instructional Items

*Instructional Item 1 *

- $\frac{\text{3}}{\text{10}}$+ $\frac{\text{32}}{\text{100}}$

**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

## Original Student Tutorial

## Perspectives Video: Expert

## Problem-Solving Tasks

## Tutorial

## MFAS Formative Assessments

Students express a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100 and are then asked to add the fraction to another fraction with a denominator of 100.

Students are asked if an equation is true or false. Then students are asked to find the sum of two fractions.

Students express a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100 and are then asked to add the fraction to another fraction with a denominator of 100.

Students are asked if an equation involving the sum of two fractions is true or false. Then students are asked to find the sum of two fractions.

## Original Student Tutorials Mathematics - Grades K-5

Learn about equivalent 10ths and 100ths and how to calculate these equivalent fractions at the fair in this interactive tutorial.

## Student Resources

## Original Student Tutorial

Learn about equivalent 10ths and 100ths and how to calculate these equivalent fractions at the fair in this interactive tutorial.

Type: Original Student Tutorial

## Problem-Solving Tasks

The purpose of this task is adding fractions with a focus on tenths and hundredths.

Type: Problem-Solving Task

The purpose of this task is for students to show they understand the connection between fraction and decimal notation by writing the same numbers both ways. Comparing and contrasting the two solutions shown below shows why decimal notation can be confusing. The first solution shows the briefest way to represent each number, and the second solution makes all the zeros explicit.

Type: Problem-Solving Task

## Tutorial

The Khan Academy tutorial video presents a visual fraction model for adding 3/10 + 7/100 .

Type: Tutorial

## Parent Resources

## Problem-Solving Tasks

The purpose of this task is adding fractions with a focus on tenths and hundredths.

Type: Problem-Solving Task

The purpose of this task is for students to show they understand the connection between fraction and decimal notation by writing the same numbers both ways. Comparing and contrasting the two solutions shown below shows why decimal notation can be confusing. The first solution shows the briefest way to represent each number, and the second solution makes all the zeros explicit.

Type: Problem-Solving Task