New Jersey Grade 5 Math Study Guide for NJSLA: Topics, Practice, and Books

The New Jersey Grade 5 math assessment is now part of the New Jersey Student Learning Assessments-Adaptive (NJSLA-Adaptive) program. For Grade 5, the most important math review areas are fractions, decimals, volume, coordinate geometry, and algebraic thinking. Knowing which topics matter most and where students commonly struggle is the starting point for an effective study plan.

This guide walks through the key NJSLS (New Jersey Student Learning Standards) topics for Grade 5, provides practice problems with answers, and offers a four-week study plan families and teachers can use at home or in the classroom.

ViewMath is an independent publisher and is not affiliated with or endorsed by the New Jersey Department of Education or any state assessment program.

Official source checked: The New Jersey Department of Education lists NJSLA-Adaptive mathematics for grades 3 through high school and shows the Spring 2026 NJSLA-Adaptive window as April 27-May 29, 2026. NJDOE’s adaptive-assessment FAQ says the updated assessments are designed to align with the 2023 New Jersey Student Learning Standards. Check your district calendar for the exact school testing dates. See the NJDOE statewide assessment schedule and NJSLA-Adaptive FAQ.

NJSLA Grade 5 Math: Key Topics by Standard Domain

Operations and Algebraic Thinking

Fifth graders in New Jersey are expected to write and evaluate simple numerical expressions using parentheses, brackets, and braces, and to analyze and generate patterns.

• Evaluate expressions with grouping symbols: (2 + 3) × 4
• Generate numerical patterns from a rule and identify relationships between two patterns

Number and Operations in Base Ten

This domain covers the full place value system through thousandths and fluency with multi-digit whole number and decimal operations.

• Place value: reading and writing decimals to thousandths
• Comparing decimals using >, =, <
• Multiplying multi-digit whole numbers
• Dividing up to 4-digit dividends by 2-digit divisors
• Adding, subtracting, multiplying, and dividing decimals to hundredths

Number and Operations — Fractions

This is the most tested domain in Grade 5. Students move from comparing and ordering fractions to performing all four operations with fractions and mixed numbers.

• Adding and subtracting fractions and mixed numbers with unlike denominators
• Multiplying fractions and mixed numbers
• Dividing unit fractions by whole numbers and whole numbers by unit fractions
• Interpreting fraction division in context

Measurement and Data

• Converting measurement units within the same system (miles, yards, feet; kilograms, grams)
• Understanding volume: counting unit cubes, applying V = l × w × h
• Line plots with fractional data values

Geometry

• The coordinate plane: plotting ordered pairs in the first quadrant
• Classifying 2D figures in a hierarchy based on properties
• Understanding that a square is a special rectangle; a rectangle is a special parallelogram

Grade 5 Math Practice Problems with Answers

Fractions

Problem 1. Find the sum: 2/3 + 3/4.

Solution: LCD of 3 and 4 is 12. 2/3 = 8/12; 3/4 = 9/12. Sum = 17/12 = 1 5/12.

Problem 2. Multiply: 3/5 × 2/3.

Solution: (3 × 2) / (5 × 3) = 6/15 = 2/5.

Problem 3. A jar holds 1/2 cup of flour. How many full jars are needed to measure 3 cups?

Solution: 3 ÷ 1/2 = 3 × 2 = 6 jars.

Decimals

Problem 4. Write 4.076 in words and identify the value of the digit 7.

Solution: “Four and seventy-six thousandths.” The 7 is in the hundredths place; its value is 0.07.

Problem 5. Multiply: 3.4 × 2.5.

Solution: 34 × 25 = 850. Two decimal places total: 8.50.

Volume

Problem 6. A rectangular box is 5 inches long, 4 inches wide, and 3 inches tall. What is the volume?

Solution: V = 5 × 4 × 3 = 60 cubic inches.

Problem 7. A fish tank is made by stacking unit cubes in a 6 × 4 × 2 arrangement. How many unit cubes are in the tank?

Solution: 6 × 4 × 2 = 48 unit cubes.

Coordinate Plane

Problem 8. A point is located 3 units to the right of the origin and 5 units up. Write the ordered pair for this point.

Solution: (3, 5).

Problem 9. Plot the points A(2, 3) and B(6, 3) on a coordinate plane. What is the distance between them?

Solution: Both points share the same y-coordinate (3), so the distance = |6 − 2| = 4 units.

Patterns

Problem 10. Pattern A starts at 0 and adds 3 each time. Pattern B starts at 0 and adds 6 each time. List the first 5 terms of each pattern. What do you notice about corresponding terms?

Solution: Pattern A: 0, 3, 6, 9, 12. Pattern B: 0, 6, 12, 18, 24. Each term of Pattern B is twice the corresponding term in Pattern A.

Four-Week NJSLA Grade 5 Math Study Plan

Common Mistakes in Grade 5 Math

• Adding fractions without a common denominator: 2/3 + 3/4 ≠ 5/7. Always find the LCD first.
• Forgetting to simplify fractions after multiplying: 6/15 should be reduced to 2/5.
• Placing the decimal point incorrectly in multiplication: Count the total decimal places in both factors and apply that count to the product.
• Confusing length × width × height with length + width + height: Volume is multiplication, not addition.
• Reversing coordinates: In an ordered pair (x, y), x always comes first (horizontal) and y comes second (vertical).

ViewMath Resources for NJ Grade 5 Math

ViewMath publishes Grade 5 math workbooks and practice test books designed for self-study. Each book includes topic-by-topic practice with full answer keys and worked solutions. The resources listed on this page are aligned to the Grade 5 content standards tested on the NJSLA. They are well-suited for after-school review, tutoring sessions, or independent summer study.