BrainiLab Academy · Numbers & logic
Maths from zero: little numbers, big ideas
Short maths lessons from counting and equal sharing to squares, prime numbers and the difference between mean and median. Optional quizzes included.
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What you’ll explore
Begin with a small pile of counters and an empty space. Learn to count, build tens, add, subtract and share equally. Then grow a square, count factors and discover how a very full biscuit tin can change an average.
Each short lesson adds one idea. Read at your own pace; optional quizzes stay tucked away until you want them.
One discovery at a time
Your lessons, step by step
- 1
Read →2 min read · Quick quiz
Counting and zero: what’s in an empty cup?
Count each object once and give an empty pile its number.
Ready when you are - 2
Read →2 min read · Quick quiz
Why 23 means two tens and three ones
Bundle ten counters and see what each digit means.
Ready when you are - 3
Read →2 min read · Quick quiz
What does adding actually mean?
Join two piles and discover what the plus sign means.
Ready when you are - 4
Read →2 min read · Quick quiz
How does subtraction work?
Remove counters and check what is left.
Ready when you are - 5
Read →2 min read · Quick quiz
Multiplication starts with equal groups
Connect equal groups to a multiplication fact.
Ready when you are - 6
Read →2 min read · Quick quiz
How division works: sharing equally
Share equal amounts and explain what is left over.
Ready when you are - 7
Read →2 min read · Quick quiz
What is a square number? Start with nine tiles
Explain a square number with equal rows and columns, then spot the odd-number gaps.
Ready when you are - 8
Read →2 min read · Quick quiz
Prime numbers: why does 1 get left out?
Identify prime and composite numbers by their different positive factors, and explain why 1 is neither.
Ready when you are - 9
Read →2 min read · Quick quiz
Mean vs median: the biscuit tin that changes the average
Calculate a mean and a median, then explain how one unusually large value changes the story.
Ready when you are
A few words worth knowing
- Add
- Put amounts together to find a total.
- Subtract
- Find what remains when an amount is taken away.
- Equal groups
- Groups that each contain the same amount.
- Zero
- The number we use for none.
- Square number
- The result of multiplying a whole number by itself.
- Factor
- A whole number that divides another whole number exactly, with no remainder.
- Prime number
- A whole number greater than 1 with exactly two different positive factors: 1 and itself.
- Mean
- The total of the values divided by how many values there are.
- Median
- The middle value in an ordered list; with an even number of values, the mean of the middle pair.
Curious to dig deeper?
- OpenStax — Add Whole Numbers
- OpenStax — Subtract Whole Numbers
- OpenStax — Multiply Whole Numbers
- OpenStax — Exponents and exponential notation
- University of Cambridge NRICH — Picturing Square Numbers
- OpenStax — Prealgebra 2e: Find Multiples and Factors
- OpenStax — Contemporary Mathematics: Prime and Composite Numbers
- OpenStax — Mean, Median and Mode
- OpenStax — Measures of Center and the Effect of Outliers
Follow the sources, explore a little further, or tell us if something needs a correction. Suggest a correction.