Standard #: MA.5.AR.2.1

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

• MA.5.NSO.1
• MA.5.NSO.2.1
• MA.5.NSO.2.2
• MA.5.NSO.2.3
• MA.5.AR.3.1
• MA.5.M.1.1

 

Terms from the K-12 Glossary

• Expression

 

Vertical Alignment

Previous Benchmarks

• MA.4.AR.2.2

 

Next Benchmarks

• MA.6.AR.1.1

 

Purpose and Instructional Strategies

The purpose of this benchmark is for students to translate between numerical and written mathematical expressions. This builds from previous work where students wrote equations with unknowns in any position of the equation in grade 4 (MA.4.AR.2.2). Algebraic expressions are a major theme in grade 6 starting with MA.6.AR.1.1. Students continue to deepen their understanding of operations with whole numbers (MA.5.NSO.2.1

/MA.5.NSO.2.2).

• During instruction, teachers should model how to translate numerical expressions into words using correct vocabulary. This includes naming fractions and decimals correctly. Students should use diverse vocabulary to describe expressions. 
  • For example, in the expression 4.5 + (3 × 2) could be read in multiple ways to show its operations. Students should explore them and find connections between their meanings (MTR.3.1, MTR.4.1, MTR.5.1). 
    • 4 and five tenths plus the quantity 3 times 2  
    • 4 and 5 tenths plus the product of 3 and 2 
    • The sum of 4 and 5 tenths and the quantity 3 times 2 
    • The sum of 4 and 5 tenths and the product of 3 and 2 
• The expectation of this benchmark is to not use exponents or nested grouping symbols. Nested grouping symbols refer to grouping symbols within one another in an expression, like in 3 + [5.2 + (4 × 2)]. Explain to students that parentheses make the expression clearer, but they are not necessary when multiplication comes before addition, as seen in the example.

• Instruction of this benchmark helps students understand the order of operations, the expectation of MA.5.AR.2.2. 
• Teachers can encourage and motivate students to utilize properties to rewrite expressions. Instruction includes a review of the distributive, associative, and commutative properties of addition and multiplication. Reinforce the concept that the distributive property involves the distribution of multiplication over addition, while the commutative property entails a change in the order of the terms.

 

Common Misconceptions or Errors

• Students can misrepresent decimal and fraction numbers in words. This benchmark helps students practice naming numbers according to place value. 
• Some students can confuse the difference between what is expected in the expressions 5(9 + 3) and 5 + (9 + 3). Students need practice naming the former as multiplication (e.g., 5 times the sum of 9 and 3) and understanding that in that expression, both 5 and 9 + 3 are factors.
• Students may have confusion with parentheses. Misplacement or omission of parentheses can lead to incorrect interpretations of expressions. Students might forget to use parentheses where necessary or include unnecessary ones, altering the meaning of the expression. 
• Additional misinterpretations include misunderstanding the order of operations, where a student mistakenly performs an operation over another (e.g. addition before multiplication with no parentheses present).

 

Strategies to Support Tiered Instruction

• Instruction includes opportunities to name fractions and decimals correctly according to place value. The teacher provides students a place value chart to support correctly naming decimals. Students use appropriate terminology for naming fractions. 

o For example, write 8.601 in standard form and word form in a place value chart. 

 

• For example, students write 10.36 in standard form and word form in a place value chart. 

• For example, students write 2.47 in standard form and word form in a place value chart using place value disks. Place value disks can be used as a visual representation in addition to the place value chart.

• For example, students write $\frac{\text{5}}{\text{12}}$ in word form (five twelfths). 
• For example, students write 2 $\frac{\text{7}}{\text{8}}$ in word form (two and seven eighths). This is repeated with additional fractions and decimals. 
• Instruction includes opportunities to correctly translate numerical expressions into words using appropriate vocabulary.
  • For example, the teacher has students read aloud the following expression and write in word form. Next, the teacher models one way of reading aloud and has students provide alternate ways while using questioning to facilitate the conversation about the multiple ways the expression can be read aloud to show its operations. 

• Eighteen and forty-nine hundredths minus the quotient of twenty-seven divided by three.
• 18 and 49 hundredths minus the quantity 27 divided by 3.
• The difference between 18 and 49 hundredths and the quotient of 27 divided by 3. 
• The difference between 18 and 49 hundredths and the quantity 27 divided by 3. 

 

Instructional Tasks

Instructional Task 1 (MTR.4.1) 

• Nadia sees the numerical expression 6.5 + $\frac{\text{1}}{\text{2}}$ (4-2). She translates the expression as, “6 and five tenths plus 1 half times 4, minus 2."
• Part A: Is her translation correct? Explain. 
• Part B: Evaluate the expression.

 

Instructional Task 2 (MTR.3.1) 

Translate the written mathematical description below into a numerical expression: Divide the difference of 20 and 5 by the sum of 4 and 1. 

a. Draw a model that represents 6×(6+4).
b. How much times greater is the value of 6×(6+4) than 6+4?

Instructional Task 5