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The whole Atlas

Number & Arithmetic15
Counting18
Geometry & Visualization18
Logic & Deduction11
Patterns & Sequences7
Modeling & Word Problems10
Contest Craft12

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Code is MIT. Problems, skills, and explanations are CC BY-NC-SA 4.0. Practice never requires an account and nothing here is paywalled.

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The Skill Atlas

Every skill Math Kangaroo tests, arranged so that each one sits below what it needs first. 91 skills across seven strands. Follow an arrow downward and you are following what a student can learn next.

The list view holds the same skills and is often the faster way in.

Strands

NUMNumber & Arithmetic
CNTCounting
GEOGeometry & Visualization
LOGLogic & Deduction
PATPatterns & Sequences
MODModeling & Word Problems
CFTContest Craft

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5–6
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9–10
11–12

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NUM-06

Remainders and modular cycles

Number & Arithmetic · Core · levels 3–4, 5–6, 7–8, 9–10, 11–12

When you divide and something is left over, that leftover repeats on a cycle. If today is Tuesday, then 100 days from now depends only on the remainder of 100 divided by 7. Finding the cycle length and the position inside it answers questions about enormous numbers.

Needs first

NUM-04Divisibility rules: 2, 3, 4, 5, 9, 10

Opens up

GEO-18Clock geometry: hands, angles, times NUM-07Last-digit behavior of products and powers PAT-03Repeating cycles and position mod n

Open the skill page12 problems