100+ Free New Hampshire NH SAS Mathematics Grade 5 Practice Questions

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2026 Statistics

Key Facts: New Hampshire NH SAS Mathematics Grade 5 Exam

NHDOE

State Agency

New Hampshire Department of Education, Office of Assessment

34 operational items (38-42 total)

Official Test Length

NH SAS 2022-23 Technical Report Vol. 2 Part 1

2 hr 15 min

Estimated Testing Time

NH SAS Test Administration Manual, Table 2

English and Spanish

Delivery Languages

NH SAS Test Administration Manual

100 practice questions

Practice Bank Size

OpenExamPrep

Prepare for the NH SAS Math Grade 5 test with 100 practice questions weighted to the official blueprint — Operations and Algebraic Thinking 24-32%, Base Ten and Fractions 41-50%, and Measurement, Data and Geometry 26-32% — with worked explanations for every answer.

Sample New Hampshire NH SAS Mathematics Grade 5 Practice Questions

Try these sample questions to test your New Hampshire NH SAS Mathematics Grade 5 exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Evaluate the expression (8 + 2) × 3.

A.30

B.14

C.26

D.48

Explanation: First add the numbers inside the parentheses: 8 + 2 = 10. Then multiply by 3, giving 10 × 3 = 30. Parentheses tell you to complete that sum before multiplying.

2Evaluate 2 × [3 + (4 − 1)].

A.12

B.9

C.13

D.10

Explanation: Work from the innermost grouping outward. First 4 − 1 = 3, so the brackets become 3 + 3 = 6. Finally multiply: 2 × 6 = 12.

3Evaluate the expression {(6 − 2) × 3} + 5.

A.17

B.5

C.21

D.32

Explanation: Inside the braces, 6 − 2 = 4, then 4 × 3 = 12. Add the outside 5 to get 12 + 5 = 17. The braces group the subtraction and multiplication together before the final addition.

4Evaluate 50 − [3 × (4 + 2)].

A.32

B.40

C.282

D.36

Explanation: Inside the parentheses, 4 + 2 = 6. Then 3 × 6 = 18 inside the brackets. Subtract from 50: 50 − 18 = 32.

5Which expression represents the phrase "add 7 and 5, then multiply the sum by 4"?

A.(7 + 5) × 4

B.7 + 5 × 4

C.7 × 5 + 4

D.(7 × 5) + 4

Explanation: The phrase says to add 7 and 5 first, so those numbers must be grouped in parentheses. Then the sum is multiplied by 4, giving (7 + 5) × 4. Without parentheses, 7 + 5 × 4 would multiply first and add second.

6Which expression represents "subtract 3 from 10, then divide by 2"?

A.(10 − 3) ÷ 2

B.10 − 3 ÷ 2

C.(10 ÷ 3) − 2

D.10 ÷ (3 − 2)

Explanation: Subtracting 3 from 10 first must be grouped in parentheses, giving 10 − 3 = 7. Then divide the result by 2, so the expression is (10 − 3) ÷ 2. Without parentheses, division would happen before subtraction.

7Which expression represents "multiply 8 by 3, then add 5 to the product"?

A.8 × 3 + 5

B.(8 + 3) × 5

C.8 × (3 + 5)

D.8 + 3 × 5

Explanation: Multiplication is stated first: 8 × 3 gives the product 24. Then add 5 to that product, giving 8 × 3 + 5. Order of operations already does multiplication before addition, so no parentheses are needed.

8Pattern A starts at 0 and follows the rule "add 3". Pattern B starts at 0 and follows the rule "add 6". What is the relationship between corresponding terms?

A.Each term in Pattern B is 2 times the corresponding term in Pattern A

B.Each term in Pattern B is 3 more than the corresponding term in Pattern A

C.Each term in Pattern B is 6 more than the corresponding term in Pattern A

D.Each term in Pattern B is equal to Pattern A plus 3

Explanation: Pattern A gives 0, 3, 6, 9, 12 and Pattern B gives 0, 6, 12, 18, 24. Each B term is exactly twice the matching A term (for example, 6 = 2 × 3 and 12 = 2 × 6), because the add-6 rule grows twice as fast as add-3.

9Pattern x uses the values 1, 2, 3, 4, 5. Pattern y follows the rule y = 4x. What ordered pair corresponds to x = 4?

A.(4, 16)

B.(4, 20)

C.(16, 4)

D.(4, 12)

Explanation: Substitute x = 4 into the rule: y = 4 × 4 = 16. Ordered pairs are written as (x, y), so the pair is (4, 16).

10Pattern A: 2, 4, 6, 8, 10. Pattern B: 4, 8, 12, 16, 20. What is the relationship between corresponding terms?

A.Each term in Pattern B is 2 times the corresponding term in Pattern A

B.Each term in Pattern B is 2 more than Pattern A

C.Each term in Pattern B is 4 more than Pattern A

D.Each term in Pattern B is half of Pattern A

Explanation: Comparing matching positions: 4 vs 2, 8 vs 4, 12 vs 6, each B term is exactly twice the A term. Pattern B grows by adding 4 while Pattern A grows by adding 2, so B is always 2 × A.

About the New Hampshire NH SAS Mathematics Grade 5 Exam

The New Hampshire Statewide Assessment System (NH SAS) Mathematics assessment at Grade 5 measures proficiency on the New Hampshire College and Career Ready Standards. It is a computer-adaptive test administered online through the NH SAS Portal (Cambium Assessment) each spring, and NHDOE offers a Spanish presentation of the Mathematics session in addition to English. This 100-question practice bank is an English-language four-option MCQ study adaptation weighted to the official reporting categories.

Assessment

One online computer-adaptive Mathematics session delivered through the NH SAS Portal (Cambium Assessment), drawing 34 operational items from a grade-level pool plus 6-8 embedded field-test items. This local bank contains 100 English four-option practice MCQs across the three official reporting categories.

Time Limit

Not timed; NHDOE estimates 2 hours 15 minutes

Passing Score

No pass mark. Four achievement levels are reported (Level 1 through Level 4); Levels 3 and 4 count as proficient and above. Scale score ranges differ by grade and subject.

Exam Fee

No fee to students (New Hampshire Department of Education (NHDOE))

New Hampshire NH SAS Mathematics Grade 5 Exam Content Outline

24-32%

Operations and Algebraic Thinking

Order of operations with parentheses, brackets and braces; writing and interpreting expressions without evaluating; and numerical patterns and ordered pairs.

41-50%

Number and Operations — Base Ten and Fractions

Powers of ten and place value, decimal comparison and rounding, multi-digit multiplication and division, decimal arithmetic, fractions with unlike denominators, fractions as division, multiplication as scaling, and unit-fraction division.

26-32%

Measurement and Data, and Geometry

Unit conversion, line plots with fractions, volume by counting and by formula, composite volume, the first-quadrant coordinate plane, and the hierarchy of two-dimensional figures.

How to Pass the New Hampshire NH SAS Mathematics Grade 5 Exam

What You Need to Know

Passing score: No pass mark. Four achievement levels are reported (Level 1 through Level 4); Levels 3 and 4 count as proficient and above. Scale score ranges differ by grade and subject.
Assessment: One online computer-adaptive Mathematics session delivered through the NH SAS Portal (Cambium Assessment), drawing 34 operational items from a grade-level pool plus 6-8 embedded field-test items. This local bank contains 100 English four-option practice MCQs across the three official reporting categories.
Time limit: Not timed; NHDOE estimates 2 hours 15 minutes
Exam fee: No fee to students

Keys to Passing

Work through all 100 available questions
Review every answer and explanation
Track weak areas and revisit them
Use our AI tutor for tough concepts

New Hampshire NH SAS Mathematics Grade 5 Study Tips from Top Performers

1Work from the innermost grouping symbol outward on every order-of-operations item.

2Read expression items carefully: some ask you to interpret an expression rather than evaluate it.

3Line up place values before adding or subtracting decimals, and estimate to place the decimal point after multiplying.

4Rewrite fractions with a common denominator before adding or subtracting unlike fractions.

5For volume, count layers of unit cubes as a check on the length times width times height formula.

Frequently Asked Questions

What is the NH SAS Math Grade 5 test?

It is the New Hampshire Statewide Assessment System Mathematics assessment for Grade 5, a computer-adaptive test administered online through the NH SAS Portal (Cambium Assessment) each spring.

How many questions are on the real NH SAS Math test?

The published blueprint sets 34 operational items plus 6-8 embedded field-test items, about 38-42 items in total. Because the test is computer-adaptive, the exact items differ from student to student.

Is the NH SAS Math test only multiple choice?

No. Alongside multiple-choice and multiple-select items, students construct equations, plot on grids, and complete tables. This practice bank uses four-option MCQs as a study aid, not as a format simulation.

Is the NH SAS Math test available in Spanish?

Yes. NHDOE offers a Spanish presentation for the Mathematics and Science sessions, with a toggle back to English. This practice bank is English-language only.

How are NH SAS results reported?

There is no pass mark. NHDOE reports four achievement levels (Level 1 through Level 4), with Levels 3 and 4 counted as proficient and above.

100+ Free New Hampshire NH SAS Mathematics Grade 5 Practice Questions

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