The Grade 4 IAR math test asks Illinois students to apply and extend skills they learned in Grade 3 to larger numbers, more complex fractions, and new geometric concepts. Grade 4 represents the year where computation becomes more demanding and fraction reasoning becomes central. Students who enter Grade 4 with strong multiplication and place value foundations typically progress well — but those with gaps in those areas often struggle with every new topic in Grade 4.
This post provides aligned practice problems across the major Grade 4 IAR math domains, with solutions included for each problem set.
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Domain 1: Operations and Algebraic Thinking
Grade 4 students apply multiplication and division to multi-step word problems and interpret remainders in context. They also learn about factors and multiples, and identify prime and composite numbers.
Practice Problems
1. A school orders 8 boxes of markers. Each box has 24 markers. How many markers are ordered in all?
Solution: 8 × 24 = 192 markers.
2. 156 students are divided equally into 4 classrooms. How many students are in each classroom?
Solution: 156 ÷ 4 = 39 students per classroom.
3. Is 36 a prime or composite number? List all its factors.
Solution: Composite. Factors: 1, 2, 3, 4, 6, 9, 12, 18, 36.
4. Which of the following is a multiple of 7: 42, 45, 48, 51?
Solution: 42. (42 ÷ 7 = 6)
Domain 2: Number and Operations in Base Ten
Grade 4 students work with numbers through the millions, use standard algorithms for multi-digit addition and subtraction, multiply up to 4-digit numbers by 1-digit numbers, and divide up to 4-digit numbers by 1-digit divisors.
Practice Problems
5. What is the value of the digit 7 in the number 374,825?
Solution: 70,000 (ten-thousands place).
6. 4,526 + 2,789 = ?
Solution: 7,315.
7. Multiply: 6 × 1,347
Solution: 6 × 1,000 = 6,000; 6 × 300 = 1,800; 6 × 40 = 240; 6 × 7 = 42. Total: 8,082.
8. Divide with remainder: 1,258 ÷ 3
Solution: 419 R 1. (3 × 419 = 1,257; 1,258 − 1,257 = 1)
Domain 3: Number and Operations — Fractions
This is the most heavily tested domain in Grade 4 on the IAR. Students work with equivalent fractions, compare fractions with different denominators, add and subtract fractions and mixed numbers with like denominators, and multiply a fraction by a whole number.
Practice Problems
9. Write two fractions equivalent to 2/3.
Solution: 4/6 and 6/9 (multiply numerator and denominator by the same number).
10. Compare: 3/4 ☐ 5/8. Write >, <, or =.
Solution: 3/4 = 6/8 > 5/8. Answer: 3/4 > 5/8.
11. 2 3/5 + 1 4/5 = ?
Solution: Add whole numbers: 3. Add fractions: 3/5 + 4/5 = 7/5 = 1 2/5. Total: 3 + 1 2/5 = 4 2/5.
12. A recipe needs 3/4 cup of sugar. If you are making 5 batches, how much sugar do you need?
Solution: 5 × 3/4 = 15/4 = 3 3/4 cups.
Domain 4: Measurement and Data
Grade 4 students convert units within the same measurement system (inches to feet, etc.), measure and record angles with a protractor, and interpret data from line plots that include fractions.
Practice Problems
13. How many inches are in 3 feet 7 inches?
Solution: 3 × 12 = 36 inches + 7 inches = 43 inches.
14. A right angle measures 90°. An angle measures 35°. What is the angle needed to complete the right angle?
Solution: 90° − 35° = 55°.
15. Is a 130° angle acute, right, obtuse, or straight?
Solution: Obtuse (between 90° and 180°).
Domain 5: Geometry
Students classify two-dimensional figures by their properties (parallel sides, right angles, equal side lengths). They understand lines of symmetry and can identify whether a figure is symmetric.
Practice Problems
16. How many lines of symmetry does a rectangle have?
Solution: 2 lines of symmetry (horizontal and vertical through the midpoints of opposite sides).
17. Name a quadrilateral that has exactly one pair of parallel sides.
Solution: Trapezoid.
18. Is a square a special rectangle? Explain.
Solution: Yes. A square has all the properties of a rectangle (4 right angles, opposite sides equal) and the additional property that all four sides are equal. So every square is a rectangle, but not every rectangle is a square.
Common IAR Grade 4 Math Mistakes
- Adding denominators when adding fractions: 1/4 + 2/4 ≠ 3/8. The denominator stays the same when denominators are equal. Only the numerators are added.
- Place value errors in multi-digit multiplication: When multiplying 6 × 347 and forgetting to carry the tens digit, errors compound quickly. Encourage students to show each partial product separately.
- Interpreting remainders: On division word problems, a remainder must be interpreted in context — not just written as “R 1.” If the problem asks how many complete buses are needed, a remainder means an extra bus is required.
- Confusing prime and composite: The number 1 is neither prime nor composite. The number 2 is the only even prime. These are common trick questions on the IAR.
IAR Grade 4 Math Resources from ViewMath
ViewMath offers Grade 4 math workbooks, practice test books, and study guides aligned to the Common Core State Standards — the same content framework underlying the Illinois Learning Standards. All books include full answer keys. Explore the Grade 4 collection in the sidebar.
ViewMath is an independent publisher. Our materials are not official IAR or ISBE materials.
