Standard #: MA.4.FR.1.4

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

• MA.4.M.1.1 
• MA.4.DP.1.1
• MA.4.DP.1.2

 

Terms from the K-12 Glossary

• NA

 

Vertical Alignment

Previous Benchmarks

• MA.3.FR.2.1

 

Next Benchmarks

• MA.5.NSO.1.4

 

Purpose and Instructional Strategies

The purpose of this benchmark is to understand the relative size of fractions. Students will plot fractions on the appropriate scaled number line, compare fractions using relational symbols, and order fractions from greatest to least or least to greatest. Work builds on conceptual understanding of the size of fractions from grade 3 (MA.3.FR.2.1) where students learned to compare fractions with common numerators or common denominators. 

• Instruction may include helping students extend understanding by generating equivalent fractions with common numerators or common denominators to compare and order fractions.
• Instruction may include number lines, which will make a connection to using inch rulers 1 to measure to the nearest $\frac{\text{1}}{\text{6}}$ of one inch. 
• Instruction may include using benchmark fractions and estimates to reason about the size of fractions when comparing them. Students can compare $\frac{\text{3}}{\text{5}}$ to $\frac{\text{1}}{\text{2}}$ by recognizing that 3 (in the numerator) is more than half of 5 (the denominator) so they can reason that $\frac{\text{3}}{\text{5}}$ > $\frac{\text{1}}{\text{2}}$. 
• Instruction includes fractions equal to and greater than one.

 

Common Misconceptions or Errors

• The student may mistake the fraction with the larger numerator and denominator as the larger fraction. The student may not pay attention to the relationship between the numerator and denominator when estimating.  
• The student incorrectly judges that a mixed number like 1 $\frac{\text{3}}{\text{4}}$ is always greater than an improper fraction like $\frac{\text{17}}{\text{4}}$ because of the whole number in front.

 

Strategies to Support Tiered Instruction

• Instruction includes models that represent different numerators and denominators. 
  • For example, students think about fractions by reasoning about the size of the parts related to the numerator or denominator. Students compare $\frac{\text{1}}{\text{4}}$ to $\frac{\text{1}}{\text{2}}$ by recognizing that 1 (in the numerator) is less than half of 4 (the denominator) so they can reason that $\frac{\text{1}}{\text{4}}$< $\frac{\text{1}}{\text{2}}$. 
    • This can also be shown with a model so that students can see the difference in the sizes of pieces when related to the whole. 

• Instruction includes models and examples where fractions greater than one whole are represented in a mixed number and as an improper fraction. 
  • For example, students might think that $\frac{\text{7}}{\text{3}}$ is greater 1 than $\frac{\text{1}}{\text{4}}$ because of the whole number being represented. Instruction includes models to represent fractions that build conceptual understanding of fractions greater than 1. 

 

Instructional Tasks

Instructional Task 1 (MTR.6.1) 

• Use benchmark fractions and the number line below to compare the fractions $\frac{\text{12}}{\text{5}}$ and 2 $\frac{\text{7}}{\text{8}}$. In the space below the number line, record the results of the comparison using the <, > or = symbol.

 

Instructional Items

Instructional Item 1 

Four soccer players started a game with the exact same amount of water in their water bottles. The table shows how much water each soccer player has left at the end of the game. Who has the least amount of water remaining? 

• a. Jackie 
• b. Laura 
• c. Terri 
• d. Amanda 

 

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