MA.7.NSO.1.2

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

• MA.7.NSO.2
• MA.7.AR.1.2
• MA.7.AR.3
• MA.7.GR.1
• MA.7.GR.2
• MA.7.DP.1
• MA.7.DP.2

Terms from the K-12 Glossary

• Rational Number

Vertical Alignment

Previous Benchmarks

• MA.6.NSO.1.1
• MA.6.NSO.1.2
• MA.6.NSO.3.5

Next Benchmarks

• MA.8.NSO.1.1
• MA.8.NSO.1.2

Purpose and Instructional Strategies

• When solving problems with numbers written in various forms, students must be able to convert between these forms to perform operations or make comparisons (MTR.2.1).
• Students should begin to develop charts, like the one below, that allow them to find patterns within the different forms of rational numbers. Students should have common fractions, decimals and percentages at their disposal in order to move to ones that are more difficult to determine.
  
  
  
• Students should have practice with and without the use of technology to rewrite rational numbers in different but equivalent forms.
• Students should work with simple problems to showcase how truncating repeated decimals may result in incorrect solutions.
  • For example, using the fractional value of $\frac{\text{1}}{\text{3}}$ may provide a more precise answer than using the truncated decimal of 0.33.
• Students should use reasonableness to determine if it is appropriate to use a specific equivalent form over another one when problem solving (MTR.6.1).

Common Misconceptions or Errors

• Students may not differentiate between terminating decimals, repeating decimals and rounded decimals, and they may not use them appropriately within the given contexts.
• Students may incorrectly truncate repeating decimals when problem solving.
• Students may incorrectly divide when the quotient is not a whole number.
  • For example, students may use the remainder of a problem as a decimal representation.

Strategies to Support Tiered Instruction

• Instruction includes the use of estimation to find the approximate decimal value of a fraction or mixed number before rewriting in decimal form to help with correct placement of the decimal point.
• Teacher provides opportunities for students to explore and discuss the differences between repeating and truncated decimals and the impact of truncating repeating decimals when solving problems.
  • For example, provide students with the equation $y$= $\frac{\text{1}}{\text{3}}$$x$ and have them create a table of values comparing using $\frac{\text{1}}{\text{3}}$, 0.3, 0.333 and 0.33333 as the constant of proportionality. Students can discuss the differences in $y$-values and importance of using exact values in some cases and approximate values in others.
    
    
    
• Instruction includes co-creating a graphic organizer to highlight the differences between terminating decimals, repeating decimals, and rounded decimals.

Instructional Tasks

• Part A. Graph the numbers on a number line to determine increasing order.
  
  
  
  
  
• Part B. Robin plotted her number line using all decimals, whereas Courtney plotted them using the original forms. Describe why both would be acceptable answers.

Instructional Items

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