5th Grade Numerical Expressions and Order of Operations Test Solutions and Scoring (PDF)

(a) \(6\times3=18\), then \(14+18=32\). 32

(b) \(14+6=20\), then \(20\times3=60\). 60

Scoring: 1 point for each correct value.

(a) \(54\div9=6\), then \(6\times2=12\). 12

(b) \(10-7=3\), \(4+3=7\), then \(5\times7=35\). 35

Scoring: 1 point for each correct value.

\(2+2=4\); \(3\times4=12\); \(20-12=8\); \(8\div2=4\).

Answer: 4

Scoring: 1 point for correct grouping order (inside out), 1 point for the correct value.

(a) \((30-8)\times2\)

(b) \((12+9)\div7\)

Scoring: 1 point for each expression. Parentheses are required. Do not give credit for answers like \(30-8\times2\).

The first expression is 5 groups of \(87+142\), so it is 5 times as large. It is greater.

Scoring: 1 point for “greater”, 1 point for a correct explanation (5 times as large).

(a) \((3+4)\times5=7\times5=35\). \((3+4)\times5=35\)

(b) \(24\div(2+4)=24\div6=4\). \(24\div(2+4)=4\)

Scoring: 1 point for each correct placement.

(a) \(4\times3+2\times2\)

(b) \(4\times3=12\) and \(2\times2=4\), so \(12+4=16\). Noah pays \(\$16\).

Scoring: (a) 1 point. (b) 1 point for both products, 1 point for the correct total with a dollar sign.

(a) \((5\times8-4)\div9\)

(b) \(5\times8=40\); \(40-4=36\); \(36\div9=4\). Each player gets 4 oranges.

Scoring: (a) 1 point; parentheses around the first part are required. (b) 1 point for 36, 1 point for 4.

After the parentheses, Mei subtracted \(25-3\) before multiplying. Multiplication must come before subtraction.

Correct: \(3\times6=18\), then \(25-18=7\). The correct value is 7.

Scoring: 1 point for naming the mistake, 1 point for the correct value 7.