*For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.*

**Subject Area:**Mathematics

**Grade:**4

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

**Cluster:**Level 1: Recall

**Cluster:**Understand decimal notation for fractions, and compare decimal fractions. (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

**Assessed:**Yes

**Assessment Limits :**

Denominators must be either 10 or 100. Decimal notation may not be assessed at this standard.**Calculator :**No

**Context :**Allowable

**Test Item #:**Sample Item 1**Question:**Create a fraction with a denominator of 100 that is equivalent to .

**Difficulty:**N/A**Type:**EE: Equation Editor

**Test Item #:**Sample Item 2**Question:**Which fraction is equivalent to ?

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

**Test Item #:**Sample Item 3**Question:**An equation is shown.

What is the missing fraction?

**Difficulty:**N/A**Type:**EE: Equation Editor

**Test Item #:**Sample Item 4**Question:**Melvin mows a lawn. The fraction of the lawn that Melvin has mowed so far is represented by the shaded model shown.

Melvin will mow more of the lawn before he takes his first break.

What fraction of the lawn will Melvin have mowed when he takes his first break?

**Difficulty:**N/A**Type:**EE: Equation Editor

## Related Courses

## Related Access Points

## Related Resources

## Assessments

## Formative Assessments

## Lesson Plans

## Original Student Tutorial

## Problem-Solving Tasks

## Tutorials

## STEM Lessons - Model Eliciting Activity

In this open-ended real world problem, students will work in groups to determine a procedure for ranking playground equipment to help a school purchase new equipment for their playground. Students will need to find like denominators, make decisions based on a data table, and write a letter to the school providing evidence for their decisions. Students will need to trade off between the cost of the equipment, its safety rating and student opinions.

In this MEA, students will work in collaborative groups to solve multi-step problems with whole numbers, fractions, decimals and percent by using different mathematical operations. The students will be asked to assist an ice cream shop owner, who is planning a promotional program "Flavor of the Month," to rank the ice cream flavors based on the data provided. Students will need to read a data table, rank the flavors, convert the fraction amount to a percent and decimal and per serving costs to a decimal as well. A twist is added to the problem when one of the flavors is too expensive to make because of seasonal availability but two new flavors are added to be calculated. An additional twist is given by adding an adult survey to the second data table. The students will need to recalculate the new percent and decimals for the additional flavors.

## 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 being with a focus on tenths and hundredths. Each part of this task emphasizes a unique aspect of 4.NF.5.

Type: Problem-Solving Task

The purpose of this task is for students to finish the equations to make true statements. Parts (a) and (b) have the same solution, which emphasizes that the order in which we add doesn't matter (because addition is commutative), while parts (c) and (d) emphasize that the position of a digit in a decimal number is critical. The student must really think to encode the quantity in positional notation. In parts (e), (f), and (g), the base-ten units in 14 hundredths are bundled in different ways. In part (e), "hundredths" are thought of as units: 14 things = 10 things + 4 things. Part (h) addresses the notion of equivalence between hundredths and tenths.

Type: Problem-Solving Task

Students may not articulate every detail, but the basic idea for a case like the one shown here is that when you have equivalent fractions, you have just cut the pieces that represent the fraction into more but smaller pieces. Explaining fraction equivalences at higher grades can be a bit more involved (e.g. 6/8=9/12), but it can always be framed as subdividing the same quantity in different ways.

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

The purpose of this task is to help students gain a better understanding of fractions through the use of dimes and pennies.

Type: Problem-Solving Task

## Tutorials

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

Type: Tutorial

In this Khan Academy video a fraction is converted from tenths to hundredths using grid diagrams.

Type: Tutorial

## Parent Resources

## Problem-Solving Tasks

The purpose of this task is adding fractions being with a focus on tenths and hundredths. Each part of this task emphasizes a unique aspect of 4.NF.5.

Type: Problem-Solving Task

The purpose of this task is for students to finish the equations to make true statements. Parts (a) and (b) have the same solution, which emphasizes that the order in which we add doesn't matter (because addition is commutative), while parts (c) and (d) emphasize that the position of a digit in a decimal number is critical. The student must really think to encode the quantity in positional notation. In parts (e), (f), and (g), the base-ten units in 14 hundredths are bundled in different ways. In part (e), "hundredths" are thought of as units: 14 things = 10 things + 4 things. Part (h) addresses the notion of equivalence between hundredths and tenths.

Type: Problem-Solving Task

Students may not articulate every detail, but the basic idea for a case like the one shown here is that when you have equivalent fractions, you have just cut the pieces that represent the fraction into more but smaller pieces. Explaining fraction equivalences at higher grades can be a bit more involved (e.g. 6/8=9/12), but it can always be framed as subdividing the same quantity in different ways.

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

The purpose of this task is to help students gain a better understanding of fractions through the use of dimes and pennies.

Type: Problem-Solving Task