Numerical Expressions: Grade 5 Math Test Answer Key – PDF Download

Grade 5 Expressions Test Answer Key: questions 1–5

Question 1: Evaluate with parentheses (3 points)

1. 1. Inside the parentheses, subtract: \(15 – 9 = 6\). The expression is now \(4 \times 6\).
   2. Now multiply: \(4 \times 6 = 24\). The expression is now \(24\).

   The value is \(24\).

2. 1. Inside the parentheses, add: \(3 + 4 = 7\). The expression is now \(56 : 7\).
   2. Now divide: \(56 : 7 = 8\). The expression is now \(8\).

   The value is \(8\).

3. 1. Inside the parentheses, multiply: \(8 \times 7 = 56\). The expression is now \(100 – 56\).
   2. Now subtract: \(100 – 56 = 44\). The expression is now \(44\).

   The value is \(44\).

Scoring: 1 point for each correct value (24, 8, and 44). A value found by ignoring the parentheses earns 0 points.

Question 2: Nested grouping symbols (3 points)

1. 1. Inside the parentheses, divide: \(12 : 3 = 4\). The expression is now \(2 \times [9 + 4]\).
   2. Inside the brackets, add: \(9 + 4 = 13\). The expression is now \(2 \times 13\).
   3. Now multiply: \(2 \times 13 = 26\). The expression is now \(26\).

   The value is \(26\).

2. 1. Inside the parentheses, subtract: \(9 – 6 = 3\). The expression is now \(120 : \{4 \times [2 + 3]\}\).
   2. Inside the brackets, add: \(2 + 3 = 5\). The expression is now \(120 : \{4 \times 5\}\).
   3. Inside the braces, multiply: \(4 \times 5 = 20\). The expression is now \(120 : 20\).
   4. Now divide: \(120 : 20 = 6\). The expression is now \(6\).

   The value is \(6\).

Scoring: part (a) 1 point for 26. Part (b) 1 point for working the innermost parentheses and brackets correctly and 1 point for the final value 6.

Question 3: Write expressions (3 points)

1. \(3 \times (9 + 14)\)
2. \(50 – 4 \times 5\). Writing \(50 – (4 \times 5)\) is also correct.
3. \((30 – 12) : 6\)

Scoring: 1 point for each correct expression. Accept equivalent forms that keep the same order of work. For part (a), \(3 \times 9 + 14\) earns 0 points.

Question 4: Interpret without evaluating (2 points)

1. The sum \(25 + 17\) is multiplied by 4, so the expression is 4 times as large as \(25 + 17\).
2. The sum \(24 + 9\) is multiplied by \(\frac{1}{3}\), a number less than 1, so the expression is less than \(24 + 9\). It is one third as large.

Scoring: (a) 1 point for “4 times as large.” (b) 1 point for “less than” with a reason about multiplying by a fraction less than 1.

Question 5: Insert parentheses (2 points)

1. \((3 + 5) \times 4\) \(= 32\), because \(8 \times 4 = 32\).
2. \(18 : (2 + 1)\) \(= 6\), because \(18 : 3 = 6\).

Scoring: 1 point for each correct placement.

Grade 5 Expressions Test Answer Key: questions 6–8

Question 6: Farmers market boxes (3 points)

1. \(5 \times (8 + 3) – 9\)
2. 1. Inside the parentheses, add: \(8 + 3 = 11\). The expression is now \(5 \times 11 – 9\).
   2. Now multiply: \(5 \times 11 = 55\). The expression is now \(55 – 9\).
   3. Now subtract: \(55 – 9 = 46\). The expression is now \(46\).

   The value is \(46\).

   Priya has 46 pieces left.

3. \(8 + 3\) is the number of pieces of fruit in one box.

Scoring: (a) 1 point; the parentheses must show that 8 + 3 is multiplied by 5. (b) 1 point for 46. (c) 1 point for “pieces of fruit in one box.”

Question 7: Noah's notebook (2 points)

Noah dropped the parentheses. He divided 48 by 4 only, then added 4.

1. Noah did not add \(4 + 4\) first, so he divided 48 by 4 instead of by 8.
2. The correct value is 6.

Scoring: (a) 1 point for saying the parentheses were ignored or that \(4 + 4\) should be done first. (b) 1 point for 6.

Question 8: Compare two expressions (2 points)

First: \(5 \times (7 – 2)\)

1. Inside the parentheses, subtract: \(7 – 2 = 5\). The expression is now \(5 \times 5\).
2. Now multiply: \(5 \times 5 = 25\). The expression is now \(25\).

The value is \(25\).

Second: \(5 \times 7 – 2\)

1. Now multiply: \(5 \times 7 = 35\). The expression is now \(35 – 2\).
2. Now subtract: \(35 – 2 = 33\). The expression is now \(33\).

The value is \(33\).

Since \(33\) is greater than \(25\), the second expression is greater.

Scoring: 1 point for both values (25 and 33), 1 point for naming the greater expression.

Scoring summary

How to use this grade 5 expressions test answer key

Use this grade 5 expressions test answer key to score the test fairly and to see which skills need more practice.

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Grade 5 Numerical Expressions test answer key

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