5 Math Kangaroo Practice Problems (Grades 5-6)

Math Kangaroo is held once a year, on the third Thursday in March — check the official site for this year’s exact date. If your child is in 5th or 6th grade, the test is a step up from the younger levels. Grades 5-6 students face 30 multiple-choice questions in 75 minutes, each with 5 answer choices. The questions are split into three tiers: ten 3-point questions, ten 4-point questions, and ten 5-point questions, for a maximum score of 120.

Here are five original practice problems that match the style and difficulty your child will see on test day. We’ve included two easy (3-point), two medium (4-point), and one hard (5-point). Have your child try them all before looking at the solutions.

For a full breakdown of how the competition works, see our Math Kangaroo format guide.

The Problems

Try all five before checking the solutions below!

No penalty for wrong answers on Math Kangaroo — so always make a guess, even on the tough ones.

Problem 1: The Year (3 points)

When the number 2026 is divided by 9, what is the remainder?

(A) 0   (B) 1   (C) 2   (D) 5   (E) 8

Problem 2: The Garden Plot (3 points)

A rectangular garden has a perimeter of 26 meters. Its length is 3 meters longer than its width.

What is the area of the garden?

(A) 30 m²   (B) 35 m²   (C) 40 m²   (D) 45 m²   (E) 48 m²

Problem 3: The Shared Pie (4 points)

Maria eats 1/3 of a whole pie. Then her brother eats 1/4 of what is left.

What fraction of the original pie is still remaining?

(A) 5/12   (B) 1/2   (C) 7/12   (D) 2/3   (E) 3/4

Problem 4: The Test Scores (4 points)

Four students — Anna, Ben, Celia, and Dan — each scored a different grade on a math test. The four scores were 85, 90, 95, and 100. Here’s what we know:

• Anna scored higher than Ben.
• Celia scored 95.
• Dan scored higher than Celia.

Who scored 100?

(A) Anna   (B) Ben   (C) Celia   (D) Dan   (E) Cannot be determined

Problem 5: The Toothpick Triangles (5 points)

Maya is building a row of triangles using toothpicks. Each triangle shares one side with the triangle next to it.

• Shape 1 (one triangle) uses 3 toothpicks
• Shape 2 (two triangles) uses 5 toothpicks
• Shape 3 (three triangles) uses 7 toothpicks

How many toothpicks does Maya need to build Shape 20?

(A) 39   (B) 40   (C) 41   (D) 42   (E) 60

Solutions

Problem 1: The Year — Answer: (B) 1

You could do the long division: 2026 ÷ 9 = 225 with a remainder of 1 (since 225 × 9 = 2025).

But there’s a faster way. The divisibility rule for 9 says that a number has the same remainder when divided by 9 as the sum of its digits. Add up the digits of 2026:

2 + 0 + 2 + 6 = 10

Since 10 ÷ 9 = 1 remainder 1, the answer is 1.

Strategy tip: Divisibility rules are a huge time-saver on Math Kangaroo. The rules for 9 and 3 (sum of digits) come up especially often. Knowing them means you can skip long division entirely.

Problem 2: The Garden Plot — Answer: (C) 40 m²

The perimeter of a rectangle is 2 × (length + width). We know the perimeter is 26, so:

length + width = 26 ÷ 2 = 13

We also know the length is 3 more than the width. If we call the width w, then:

w + (w + 3) = 13 2w + 3 = 13 2w = 10 w = 5

So the width is 5 meters and the length is 8 meters. The area is 5 × 8 = 40 m².

Quick check: Perimeter = 2(5 + 8) = 2 × 13 = 26 ✓

Strategy tip: When a problem gives you the perimeter, start by finding the half-perimeter (length + width). This simplifies the numbers right away and is a technique that works on many geometry problems.

Problem 3: The Shared Pie — Answer: (B) 1/2

This problem rewards careful reading. Maria eats 1/3, then her brother eats 1/4 of what’s left — not 1/4 of the original pie.

Step 1: Maria eats 1/3. What’s left: 1 − 1/3 = 2/3

Step 2: Her brother eats 1/4 of 2/3:

1/4 × 2/3 = 2/12 = 1/6

Step 3: What’s remaining: 2/3 − 1/6 = 4/6 − 1/6 = 3/6 = 1/2

Why (A) 5/12 is a trap: If you misread the problem and compute 1 − 1/3 − 1/4, you get 12/12 − 4/12 − 3/12 = 5/12. That treats the brother as eating 1/4 of the whole pie, not 1/4 of what was left. Reading carefully makes the difference between a right and wrong answer.

Strategy tip: On Math Kangaroo, “fraction of what remains” is different from “fraction of the whole.” Circle or underline key phrases when you read a problem — it helps prevent careless mistakes.

Problem 4: The Test Scores — Answer: (D) Dan

Let’s work through the clues one at a time.

Clue 2 is the most specific, so start there: Celia scored 95.

That leaves 85, 90, and 100 for Anna, Ben, and Dan.

Clue 3: Dan scored higher than Celia (95). The only available score above 95 is 100, so Dan scored 100.

That leaves 85 and 90 for Anna and Ben.

Clue 1: Anna scored higher than Ben. So Anna = 90 and Ben = 85.

Strategy tip: In logic problems, always start with the most specific clue — the one that pins down an exact value. Then work outward. This approach is faster and less error-prone than trying to juggle all the clues at once.

Problem 5: The Toothpick Triangles — Answer: (C) 41

Look at the pattern:

Each new triangle adds exactly 2 toothpicks (because it shares one side with the previous triangle, so only 2 new sides are needed).

We can write a formula: Toothpicks = 2n + 1, where n is the shape number.

Check it:

• Shape 1: 2(1) + 1 = 3 ✓
• Shape 2: 2(2) + 1 = 5 ✓
• Shape 3: 2(3) + 1 = 7 ✓

Shape 20: 2(20) + 1 = 41

Another way to see it: start with 3 toothpicks, then add 2 for each additional triangle. That’s 3 + 2 × 19 = 3 + 38 = 41.

Why (E) 60 is a trap: If you think each triangle uses 3 toothpicks and multiply 3 × 20 = 60, you’ve forgotten that neighboring triangles share a side. Each shared side saves one toothpick, and there are 19 shared sides, so 60 − 19 = 41.

Strategy tip: When a pattern grows by a constant amount, you can find any term without listing them all. Just figure out the starting value and the rule, then jump ahead. This is one of the most powerful techniques on Math Kangaroo — and the harder problems often require extending a pattern to the 50th or 100th term.

What These Problems Practice

These five problems target skills that Math Kangaroo tests heavily at the grades 5-6 level:

• Number sense and divisibility (Problem 1) — quick mental math shortcuts
• Geometry with algebra (Problem 2) — translating word clues into equations
• Fraction operations (Problem 3) — reading carefully and computing with fractions
• Logical deduction (Problem 4) — using clues to eliminate possibilities
• Pattern generalization (Problem 5) — finding a rule and applying it far beyond the given data

At this level, the biggest challenge isn’t usually the math itself — it’s reading the problem carefully, managing time, and choosing the right strategy. Practicing with problems like these builds all three.

Looking for more structured preparation? Our Math Kangaroo Preparation Guide for Grades 3–6 covers every major topic area with explanations, practice problems, and test-day strategies — all designed to match the real competition format.

This guide is not affiliated with or endorsed by Math Kangaroo USA or Kangourou sans Frontières.