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

5th Grade math test solutions: Numerical Expressions and Order of Operations – Maths PDF

Cover of the book Grade 5 Math Tests with Answer Keys (PDF)

Download as a PDFThe Grade 5 tests book with answer keysPrintable PDFSee the book ›

Sommaire

This grade 5 expressions test answers for 5th Grade covers numerical expressions and order of operations (Common Core 5.OA.A.1, 5.OA.A.2), with a free PDF to print.

Use this answer key to grade the order of operations test. Each solution shows the steps and a scoring guide. Award partial credit as described. The total is 20 points. A score of 16 or more shows strong understanding of grouping symbols and the order of operations.

Grade 5 · Common Core State Standards: 5.OA.A.1, 5.OA.A.2

Grade 5 expressions test answers: worked solutions

Question 1 – Evaluate two expressions [2 pts]

(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.

Question 2 – Left to right and brackets [2 pts]

(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.

Question 3 – Braces [2 pts]

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

Answer: 4

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

Question 4 – Write the expression [2 pts]

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

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

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

Question 5 – Greater or less [2 pts]

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).

Question 6 – Insert parentheses [2 pts]

(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.

Question 7 – Noah at the store [3 pts]

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

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

Steps for Noah.

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

Question 8 – Little League snacks [3 pts]

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

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

Steps for the oranges.

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

Question 9 – Mei's mistake [2 pts]

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.

Correct work.

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

Total score

Total

20 points

Key facts behind this grade 5 expressions test answers

Key facts

Do grouping symbols ( ), [ ] and { } first, from the inside out.
Multiplication and division share one level: work left to right.
Addition and subtraction share one level: work left to right.
Words like add first, then multiply need parentheses when you write them as an expression.
An expression like 3 × (5 + 7) is 3 times as large as 5 + 7.

How to use this grade 5 expressions test answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

All Grade 5 chapters: Grade 5 math.

Voter.. post

Free printable PDF