Standard #: MA.3.FR.2.2

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

• MA.3.FR.2.1

Terms from the K-12 Glossary

• Number Line

Vertical Alignment

Previous Benchmarks

• MA.2.NSO.1.2

Next Benchmarks

• MA.4.FR.1.3 
• MA.4.FR.1.4

Purpose and Instructional Strategies

• The purpose of this benchmark is for students to identify equivalent fractions both on appropriately scaled number lines and on area models, and to justify how they know (MTR.2.1, MTR.4.1). 
• Instruction should prioritize tasks that allow for students to reason why fractions are equivalent using the models instead of the algorithm. Students are not expected to generate equivalent fractions until Grade 4 (MTR.2.1).

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

Strategies to Support Tiered Instruction

• Instruction includes opportunities to use concrete models and drawings to solidify understanding of fraction equivalence. Students use models to describe why fractions are equivalent or not equivalent when referring to the same-size whole. 
  • For example, when looking at $\frac{\text{2}}{\text{8}}$ and $\frac{\text{4}}{\text{8}}$, conversation includes that both fraction 88 models are the same size, so when comparing them we are comparing the same size whole. Students can see that 2 out of the 8 are shaded in the first model and 4 out of the 8 are shaded in the second model, making the $\frac{\text{4}}{\text{8}}$ greater than $\frac{\text{2}}{\text{8}}$ . 

• Instruction includes opportunities to use concrete models and drawings to solidify understanding of fraction equivalence. Students use models to describe why fractions are equivalent or not equivalent when referring to the same-size whole. Instruction includes partitioning shapes with halves, thirds, and fourths and then comparing the pieces used. 
  • For example, students partition a shape into halves. 

• Conversation includes observations about the shape partitioned into two equal pieces. The teacher models writing the fractional parts of $\frac{\text{1}}{\text{2}}$ so that students can make the connection of the denominator representing the number of pieces. Students then practice partitioning shapes into thirds and fourths for this same understanding.

Instructional Tasks

Instructional Task 1 

• Plot the fractions 6/4 and 3/2. Use your number line to determine whether the fractions are equivalent. Justify your argument in words.