5 Math Kangaroo Practice Problems (Grades 3-4)

The 2026 Math Kangaroo competition is on March 19 — just weeks away. If your child is in 3rd or 4th grade, they’ll face 24 multiple-choice questions in 75 minutes, each with 5 answer choices (A through E). The questions start easy and get progressively harder, split into three tiers: 3-point, 4-point, and 5-point.

Here are five original practice problems that mirror the style and difficulty of the real test. We’ve included two easy problems (3-point level), two medium problems (4-point level), and one hard problem (5-point level). Let your child try them all before scrolling down to the solutions.

Need a refresher on the full competition format? Check out our complete Math Kangaroo format guide.

The Problems

Try all five before checking the solutions below!

Remember: there’s no penalty for wrong answers on Math Kangaroo, so your child should always make their best guess — even on the hard ones.

Problem 1: The Hopping Frog (3 points)

A frog sits on the number 3 on a number line. It hops forward 4 spaces, then backward 2 spaces. It keeps repeating this pattern — forward 4, backward 2 — over and over.

After 6 hops, what number is the frog on?

(A) 7   (B) 9   (C) 11   (D) 13   (E) 15

Problem 2: The Garden Border (3 points)

Anna is making a border for her garden using square tiles. Her garden is a rectangle that is 5 tiles long and 3 tiles wide. She only needs tiles for the outside edge — not the inside.

How many tiles does Anna need for the border?

(A) 8   (B) 10   (C) 12   (D) 14   (E) 15

Problem 3: The Birthday Handshakes (4 points)

Five friends meet at a birthday party. Each friend shakes hands with every other friend exactly once.

How many handshakes happen in total?

(A) 5   (B) 8   (C) 10   (D) 15   (E) 20

Problem 4: The Mystery Number (4 points)

I am a two-digit number. My tens digit is 3 more than my ones digit. The sum of my digits is 9.

What number am I?

(A) 36   (B) 54   (C) 63   (D) 72   (E) 81

Problem 5: The Staircase (5 points)

Leo builds a staircase pattern with small square blocks.

• Step 1 uses 1 block
• Step 2 uses 3 blocks total
• Step 3 uses 6 blocks total
• Step 4 uses 10 blocks total

If Leo continues this pattern, how many blocks does Step 6 use?

(A) 15   (B) 18   (C) 20   (D) 21   (E) 24

Solutions

Problem 1: The Hopping Frog — Answer: (B) 9

The trick is to track the frog’s position after each hop:

Strategy tip: Every pair of hops (forward 4, backward 2) moves the frog a net of 2 spaces forward. After 6 hops (3 pairs), the frog has moved 3 × 2 = 6 spaces forward from 3, landing on 9. Recognizing this shortcut saves time — and that kind of pattern-spotting is exactly what Math Kangaroo rewards.

Problem 2: The Garden Border — Answer: (C) 12

Picture the rectangle:

■ ■ ■ ■ ■
■ □ □ □ ■
■ ■ ■ ■ ■

The ■ squares are the border. The □ squares are the inside.

One way to count: the top row has 5 tiles, the bottom row has 5, and the two sides each have 1 tile (the corners are already counted). That’s 5 + 5 + 1 + 1 = 12.

Another way: the entire rectangle uses 5 × 3 = 15 tiles. The inside is 3 × 1 = 3 tiles. Border = 15 − 3 = 12.

Strategy tip: Drawing a picture is one of the most powerful tools on Math Kangaroo. Many geometry and counting problems become much easier once you can see them.

Problem 3: The Birthday Handshakes — Answer: (C) 10

The key is to count systematically so you don’t double-count. Let’s call the friends A, B, C, D, and E:

• A shakes hands with B, C, D, E → 4 handshakes
• B already shook with A, so: C, D, E → 3 new handshakes
• C already shook with A and B, so: D, E → 2 new handshakes
• D already shook with A, B, C, so: E → 1 new handshake
• E has already shaken with everyone → 0 new

Total: 4 + 3 + 2 + 1 = 10

Why (E) 20 is a trap: You might think “each of 5 friends shakes 4 hands,” giving 5 × 4 = 20. But that counts every handshake twice — once for each person involved. Dividing by 2 gives the correct answer: 5 × 4 ÷ 2 = 10.

Strategy tip: When counting pairs, a common technique is to list them in order and avoid repeats. This systematic counting approach shows up often on Math Kangaroo.

Problem 4: The Mystery Number — Answer: (C) 63

We know two things:

1. The tens digit is 3 more than the ones digit
2. The digits add up to 9

Let’s call the ones digit x. Then the tens digit is x + 3.

Setting up the equation: x + (x + 3) = 9, which gives us 2x + 3 = 9, so 2x = 6, and x = 3.

The ones digit is 3, the tens digit is 6. The number is 63.

Check: 6 is indeed 3 more than 3 ✓ and 6 + 3 = 9 ✓.

Why the other answers are tempting: Every answer choice has digits that sum to 9 — (A) 3+6=9, (B) 5+4=9, (D) 7+2=9, (E) 8+1=9. But only 63 has a tens digit that is exactly 3 more than its ones digit.

Strategy tip: On Math Kangaroo, you can also solve this by testing each answer choice instead of using algebra. That’s a perfectly valid approach, especially for younger students.

Problem 5: The Staircase — Answer: (D) 21

Look at the pattern of how many blocks are added at each step:

Each step adds one more block than the previous step. Step 5 adds 5 blocks (10 + 5 = 15), and Step 6 adds 6 blocks (15 + 6 = 21).

These numbers — 1, 3, 6, 10, 15, 21 — are called triangular numbers because they form a triangle pattern when you arrange dots:

Step 1:  •

Step 2:  •
         • •

Step 3:  •
         • •
         • • •

Why this is a 5-point problem: You need to figure out the pattern (each step adds one more), extend it past what’s given (Steps 5 and 6), and resist choosing (A) 15, which is only Step 5 — a common trap for students who stop one step too early.

Strategy tip: On harder Math Kangaroo problems, always look at the differences between consecutive numbers. The pattern in the differences is often simpler than the pattern in the numbers themselves.

What These Problems Practice

These five problems cover skills that come up again and again on Math Kangaroo:

• Pattern recognition (Problems 1 and 5) — spotting a repeating rule and extending it
• Spatial reasoning (Problem 2) — visualizing shapes and counting carefully
• Systematic counting (Problem 3) — organizing your work to avoid over-counting
• Logical deduction (Problem 4) — using clues to narrow down possibilities
• Number sense (all problems) — understanding how numbers behave

The best way to build these skills? Short, consistent practice. Even 15 minutes a day with a few problems like these can make a real difference by competition day.

Want more practice at this level? Our Math Kangaroo Preparation Guide for Grades 3–6 has topic-by-topic explanations, additional practice problems with full solutions, and test-taking strategies designed specifically for the Math Kangaroo format.

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