🧠 Brain Lab · Reasoning

Counting & Arrangements in kindergarten to grade 5

How many ways something can happen, counted systematically rather than listed. Daily Academy tracks it as its own skill, separately from the 9 others in brain lab, so it can never be averaged away by a subject score.

Check it tonight

“Three shirts and two pairs of pants — how many outfits, without listing them?”

What to watch for

Listing every possibility and counting the list. That works at six and collapses at sixty; the multiplying is the part that scales.

Real counting & arrangements questions from the library

2 activities currently target this skill. These are actual questions, shown at the difficulty they are served at, with the explanation a child sees after answering.

Difficulty 4.6 — mid grade 4
A shop has 3 flavours of ice cream and 2 kinds of cone.
How many different single-scoop orders are possible?
Hint shown after a miss: For each flavour, how many cones could go with it?
Explanation: Each of the 3 flavours can go with either cone, so 3 × 2 = 6. Multiplying works because every choice of the first is available with every choice of the second.
Difficulty 4.6 — mid grade 4
You have a red, a blue and a green shirt, and black or grey trousers.
How many different outfits can you make?
Hint shown after a miss: Three shirts, and two options for each.
Explanation: 3 × 2 = 6. Notice it is the same arithmetic as the ice cream — different story, identical structure, which is the point of learning the structure.
Difficulty 4.8 — mid grade 4
In how many different orders can three friends — Ada, Bo and Cy — line up?
Hint shown after a miss: Whoever is first, there are two ways to arrange the remaining two.
Explanation: 3 choices for first place, then 2 for second, then 1 for last: 3 × 2 × 1 = 6. Each choice shrinks the pool, which is what makes this different from the outfits.

The other 9 skills in Brain Lab

Each one is estimated separately, which is what lets the parent dashboard name a specific gap rather than report a subject average.

Sequencing“What would go wrong if you put your boots on before your socks?”PatternsShow a pattern: “what’s the rule?” — not “what comes next?”ClassificationSort four things by an unstated rule and ask which one does not belong — and why.Spatial Reasoning“If you turn this shape a quarter turn, what does it look like?”DeductionGive two clues about three things and ask what must be true.StrategyIn any game: “what are you going to do after that?”Algorithms“Tell me how to draw a square — and I will do exactly what you say, nothing else.”Logical ArgumentAfter any claim: “could that be true and your reason still be wrong?”Systems ThinkingAbout any rule they propose: “if everyone did that, what happens next?”

Common questions

How do I know if my child has counting & arrangements secure?

“Three shirts and two pairs of pants — how many outfits, without listing them?” Listing every possibility and counting the list. That works at six and collapses at sixty; the multiplying is the part that scales.

Which grade is counting & arrangements taught in?

It appears in both. Daily Academy does not gate skills by year group — a child is placed on a continuous difficulty scale during a five-minute intake, and counting & arrangements is then served at whatever level they are actually at, adjusted separately from every other skill.

Practice by grade

Grade 2 critical thinking and logic activitiesLogic puzzles for 7 and 8 year olds — patterns, deduction, sorting and spatial reasoning — set at the right difficulty and framed as a game rather than a test.Grade 3 critical thinking and logic activitiesLogic and reasoning practice for 8 and 9 year olds — multi-step patterns, elimination puzzles, spatial reasoning and strategy — adapted to each child’s level.Grade 1 critical thinking and logic activitiesLogic puzzles for 6 and 7 year olds — sequencing, patterns, sorting and two-clue deduction — kept small enough that they measure reasoning rather than memory.Grade 4 critical thinking and logic activitiesLogic puzzles for 9 and 10 year olds — conditional reasoning, systematic counting, nets and multi-step planning — where the first plausible answer is usually wrong.Grade 5 critical thinking and logic activitiesLogic puzzles for 10 and 11 year olds — elimination, systematic counting, and telling a valid argument from a conclusion that happens to be true.Kindergarten logic and thinking activitiesThinking puzzles for 4 and 5 year olds — odd one out, repeating patterns, first, then, last, and two-clue riddles — short enough to be about reasoning rather than memory.

See where your child stands on counting & arrangements

A five-minute intake places them on a continuous scale, and the skill map shows every skill separately from the first week. The daily mission is free.

Start free See the parent dashboard