# MA.4.FR.2.3

Explore the addition of a fraction with denominator of 10 to a fraction with denominator of 100 using equivalent fractions.

### 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.

General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Fractions
Status: State Board Approved

## Benchmark Instructional Guide

• 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.

Determine the equivalent fraction.
• $\frac{\text{5}}{\text{10}}$ = $\frac{\text{}}{\text{100}}$
• $\frac{\text{31}}{\text{100}}$ + $\frac{\text{5}}{\text{10}}$

### Instructional Items

Instructional Item 1

An expression is shown. What is the value of the expression?
• $\frac{\text{3}}{\text{10}}$+ $\frac{\text{32}}{\text{100}}$

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

## Related Courses

This benchmark is part of these courses.
5012060: Mathematics - Grade Four (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7712050: Access Mathematics Grade 4 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
5012055: Grade 3 Accelerated Mathematics (Specifically in versions: 2019 - 2022, 2022 and beyond (current))
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022, 2022 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.4.FR.2.AP.3: Explore the addition of a fraction with denominator of 10 to a fraction with denominator of 100 using visual models to find equivalent fractions.

## Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

## Formative Assessments

Tenths and Hundredths:

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.

Type: Formative Assessment

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.

Type: Formative Assessment

Hundredths and Tenths:

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

Type: Formative Assessment

Seven Tenths:

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.

Type: Formative Assessment

## Original Student Tutorial

Fractions at the Fair: Equivalent Tenths and Hundredths:

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

Type: Original Student Tutorial

## Perspectives Video: Expert

B.E.S.T. Journey:

What roles do exploration, procedural reliability, automaticity, and procedural fluency play in a student's journey through the B.E.S.T. benchmarks? Dr. Lawrence Gray explains the path through the B.E.S.T. maththematics benchmarks in this Expert Perspectives video.

Type: Perspectives Video: Expert

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

Expanded Fractions and Decimals:

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.

## Tutorial

Adding Two Fractions with Denominators 10 and 100:

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

Type: 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.

Hundredths and Tenths:

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

Seven Tenths:

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.

Tenths and Hundredths:

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

Fractions at the Fair: Equivalent Tenths and Hundredths:

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

## Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

## Original Student Tutorial

Fractions at the Fair: Equivalent Tenths and Hundredths:

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

Type: Original Student Tutorial

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

Expanded Fractions and Decimals:

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.

## Tutorial

Adding Two Fractions with Denominators 10 and 100:

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

Type: Tutorial

## Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.