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What tasks your child solves

Every MathTrail task belongs to one topic. Here are all of them, what their tasks are like, and how some topics stand on others.

Comet
Grade 3
Rank 3of 11
43% of the way to the next rank
  • Ranks 1–4, the current one among them: tasks of grades 1–2.
  • Ranks 5–7: tasks of grades 3–4.
  • Ranks 8–11: tasks of grades 5–6.

For parents: the scale shows roughly which grades' tasks the child can manage. The tasks here are olympiad ones, so this is not a school mark.

Next — rank 4. Right answers move the bar forward, mistakes a little back.

Next up

Enumeration, once more

The rank in each topic

  • OrderingMasteredaheadRank 4
  • EnumerationevenRank 3
  • Gaps and boundariesevenRank 3
  • Parity and alternationbehindRank 2
  • Knights and liarsbehindRank 2

The progress as a chat shows it, with a rank in every topic. The child and the numbers are an example.

How the topics link

Some topics stand on others. Enumeration is needed for the pigeonhole principle and for knights and liars alike. When a child is stuck, it helps to step back to the topic a hard one stands on.

Step 1

Foundations

Almost no prior knowledge.

Step 2

Rules

Reasoning by hand becomes a rule.

Step 3

Hard problems

Several ideas to hold in mind at once.

OrderingEnumerationGaps and boundariesClocksParity and alternationArithmetic with a trickKnights and liarsPigeonhole principleFigures on a square gridCalendar and ageGames with a winning strategyParts and sharesWeighing and pouringOverlapping groupsDivisibility and remaindersPercentagesRatios and sharing

Point at a topic, or reach it with Tab, to light up what it stands on and what it opens.

Ordering · first: nothing, it is a foundation · opens: Knights and liars

Knights and liars · first: Ordering, Enumeration · opens: nothing, it is a summit

Enumeration · first: nothing, it is a foundation · opens: Knights and liars, Pigeonhole principle, Weighing and pouring, Figures on a square grid, Overlapping groups, Games with a winning strategy

Gaps and boundaries · first: nothing, it is a foundation · opens: Calendar and age, Figures on a square grid, Divisibility and remainders

Clocks · first: nothing, it is a foundation · opens: nothing, it is a summit

Calendar and age · first: Gaps and boundaries · opens: Divisibility and remainders

Pigeonhole principle · first: Enumeration · opens: Weighing and pouring, Overlapping groups

Parity and alternation · first: nothing, it is a foundation · opens: Divisibility and remainders, Games with a winning strategy

Arithmetic with a trick · first: nothing, it is a foundation · opens: Parts and shares, Percentages, Ratios and sharing

Weighing and pouring · first: Enumeration, Pigeonhole principle · opens: nothing, it is a summit

Parts and shares · first: Arithmetic with a trick · opens: Percentages, Ratios and sharing

Percentages · first: Arithmetic with a trick, Parts and shares · opens: nothing, it is a summit

Ratios and sharing · first: Arithmetic with a trick, Parts and shares · opens: nothing, it is a summit

Figures on a square grid · first: Enumeration, Gaps and boundaries · opens: nothing, it is a summit

Divisibility and remainders · first: Gaps and boundaries, Calendar and age, Parity and alternation · opens: nothing, it is a summit

Overlapping groups · first: Enumeration, Pigeonhole principle · opens: nothing, it is a summit

Games with a winning strategy · first: Enumeration, Parity and alternation · opens: nothing, it is a summit

  • First
  • Topic
  • Then

Logic

Reasoning: suppose, draw the consequence, find the contradiction.

Ann > Ben > Kate

Ordering

Who is taller, older, faster: line everyone up from a few clues.

Opens: Knights and liars

Grades 1–6More →

A: "I am a knight"
B: "A is lying"

Knights and liars

Some always tell the truth, the others always lie. Work out who is who from what they say.

Builds on: Ordering, Enumeration

Grades 3–6More →

( A ( 3 ) B )

Overlapping groups

Some children go to two clubs at once. How not to count them twice.

Builds on: Enumeration, Pigeonhole principle

Grades 5–6More →

Counting and enumeration

Count every case, and leave none out.

12 13 21 23 31 32

Enumeration

List every case in order, so that none is lost and none counted twice.

Opens: Knights and liars, Pigeonhole principle, Weighing and pouring, Figures on a square grid, Overlapping groups, Games with a winning strategy

Grades 1–6More →

|--3--|--3--|--3--|

Gaps and boundaries

Posts and spans, floors and stairs: when to add one, and when not to.

Opens: Calendar and age, Figures on a square grid

Grades 1–6More →

[● ●] [●] [●]

Pigeonhole principle

With more pigeons than holes, some hole is bound to hold two.

Builds on: Enumeration

Opens: Weighing and pouring, Overlapping groups

Grades 1–6More →

+---+---+---+
|   |   |   |
+---+---+---+

Figures on a square grid

Area and perimeter by the squares. Cut, fit together, and count without missing one.

Builds on: Enumeration, Gaps and boundaries

Grades 5–6More →

Time

Clocks, days of the week and years, and what changes with them.

11:50 + 20 min = 12:10

Clocks

How much time has passed, and what the time will be: the hands, the dial, going past noon.

Grades 1–6More →

Mum 30   Ann 6
+5 yrs   +5 yrs

Calendar and age

Days of the week, months and ages. A gap in age never changes, and the week comes round again.

Builds on: Gaps and boundaries

Opens: Divisibility and remainders

Grades 1–6More →

Numbers with a trick

Numbers where the idea matters more than the speed of counting.

25 × 7 × 4 = 7 × 100

Arithmetic with a trick

Count cleverly: reorder, group, and spot the easy way before working it out.

Opens: Parts and shares

Grades 1–6More →

● ○ ● ○ ● ○

Parity and alternation

Even and odd, every other one: what can be known without counting it all.

Opens: Divisibility and remainders, Games with a winning strategy

Grades 1–6More →

17 = 5 · 3 + 2

Divisibility and remainders

Whether a number divides evenly, and what is left over when it does not.

Builds on: Calendar and age, Parity and alternation

Grades 5–6More →

Parts of a whole

A whole cut into parts: shares, percentages and ratios.

■ ■ ■ □ = 3/4

Parts and shares

A half, a third, a quarter: a part of the whole, and the whole from its part.

Builds on: Arithmetic with a trick

Opens: Percentages, Ratios and sharing

Grades 5–6More →

10% of 50 = 5

Percentages

How much that is in percent, and of what. A percent is one hundredth.

Builds on: Parts and shares

Grades 5–6More →

□ □ : □ □ □

Ratios and sharing

Share in the ratio 2 to 3, and find how much one part is.

Builds on: Parts and shares

Grades 5–6More →

Strategies and games

Find the plan that works whatever the other player or the scales do.

||||| ||||| |||||
take 1 to 3

Games with a winning strategy

Who takes the last match? Look for the positions that win whatever the other player does.

Builds on: Enumeration, Parity and alternation

Grades 5–6More →

[● ● ●] = [● ● ●]
5 l · 3 l → 4 l

Weighing and pouring

Find the fake coin in the fewest weighings, or measure out water with jugs that have no marks.

Builds on: Enumeration, Pigeonhole principle

Grades 3–6More →