Standard #: MA.4.FR.2.1

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

• MA.4.FR.1.3
• MA.4.AR.1.2

 

Terms from the K-12 Glossary

• Expression

 

Vertical Alignment

Previous Benchmarks

• MA.3.FR.1.1
• MA.3.FR.1.2

 

Next Benchmarks

• MA.5.FR.2.1

 

Purpose and Instructional Strategies

The purpose of this benchmark is to build students’ understanding from grade 3 that each fraction is composed of the sum of its unit fractions. Decomposing fractions becomes the foundation for students to make sense of adding and subtracting fractions, much like decomposing whole numbers provided the foundation for adding and subtracting whole numbers in the primary grades.

• During instruction, students should show multiple ways to decompose a fraction into equivalent addition expressions with the support of models (e.g., objects, drawings, and equations).

 

Common Misconceptions or Errors

• Students may have difficulty decomposing mixed numbers and fractions greater than one because of misunderstanding of flexible fraction representations (e.g., $\frac{\text{4}}{\text{4}}$ is equivalent to 1). It is helpful when students’ expressions are accompanied by a model that justifies them.

 

Strategies to Support Tiered Instruction

• Instruction includes fraction tiles or fraction kits to physically place and see equivalent fractions of a model.
  • Example: 

• The teacher provides instruction that models how fractions can be decomposed in multiple ways.
  •  For example, using the same fraction tiles as above, students decompose $\frac{\text{1}}{\text{2}}$ multiple ways with the understanding that the value doesn't change: $\frac{\text{1}}{\text{2}}$= $\frac{\text{1}}{\text{8}}$ + $\frac{\text{1}}{\text{8}}$ + $\frac{\text{1}}{\text{8}}$ + $\frac{\text{1}}{\text{8}}$or $\frac{\text{1}}{\text{2}}$ = $\frac{\text{1}}{\text{8}}$ + $\frac{\text{1}}{\text{8}}$ + $\frac{\text{2}}{\text{8}}$ or $\frac{\text{1}}{\text{2}}$ = $\frac{\text{1}}{\text{8}}$ + $\frac{\text{3}}{\text{8}}$. 
  • For example, using fraction circles, students combine 4 one-quarter circles and then see that there are 4 pieces that make up the whole circle. Equations are accompanied by a model that justifies them.

 

Instructional Tasks

Instructional Task 1 (MTR.2.1) 

• Part A. Use a visual fraction model to show one way to decompose $\frac{\text{5}}{\text{9}}$. Make sure to label each fraction part in the model, and write an equation to show how you decomposed $\frac{\text{5}}{\text{9}}$.
• Part B. Show how you could decompose $\frac{\text{5}}{\text{9}}$in a different way using a visual fraction model. Again, make sure to label each fraction part in the model, and write an equation to show how you decomposed $\frac{\text{5}}{\text{9}}$.

 

Instructional Items

Instructional Item 1 

• Which sums show ways to express $\frac{\text{8}}{\text{3}}$?

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