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Classroom Notes

Step-by-step math lessons with worked examples: fractions, long division, percentages, ratios, exponents, primes, order of operations and mental math.

All · 30Math at Home · 14Classroom Notes · 16Math explained · 15For parents · 11
A kitchen counter with apples on a red weighing scale, stacks of coins, a measuring jug of water, a paper grocery bag with a long receipt and a calculator.
Classroom Notes· 11 min read

Multiplying and dividing decimals: count the places, move the point

How to multiply decimals by counting decimal places, how to divide a decimal by a whole number or by another decimal, the powers-of-ten shift, money and measurement examples, and the four mistakes behind most wrong answers.

By Laura Bennett, MathIt
A frosty winter window with a mug of hot chocolate, a thermometer between it and a sunny window with a potted plant, and a basement with stairs and crates below the ground floor.
Classroom Notes· 10 min read

Negative numbers explained: how to add, subtract, multiply and divide them

What negative numbers are, how the number line, opposites and absolute value work, the rules for adding, subtracting, multiplying and dividing negative numbers, why a negative times a negative is positive, and the mistakes that cost the most marks.

By Laura Bennett, MathIt
A kitchen table with a lattice berry pie missing one slice, the slice on a plate with a fork, a jug and a glass of lemonade, and a stack of colored wooden blocks on a cutting board.
Classroom Notes· 10 min read

Subtracting fractions step by step: unlike denominators, whole numbers and mixed numbers

How to subtract fractions with like and unlike denominators, find the least common denominator, subtract a fraction from a whole number, regroup mixed numbers and check every answer by adding back.

By Laura Bennett, MathIt
A pan of brownies cut into a grid of squares on a wooden board, part of it frosted, with a hand cutting it with a knife, colorful fraction circles, a notebook and a pencil beside it.
Classroom Notes· 9 min read

How to multiply fractions: the rule, the area model and mixed numbers

The three-step rule for multiplying fractions, why it works on an area model, how to cancel first, how to multiply fractions with whole numbers and mixed numbers, and the mistakes that cause most wrong answers.

By Laura Bennett, MathIt
A kitchen counter with two cups of milk, three cups of flour, a mixing bowl with a whisk, two jars of blue paint and one jar of yellow paint beside a few drops of green.
Classroom Notes· 10 min read

Ratios explained: what a ratio is and how to find equivalent ratios

What a ratio is, part-to-part versus part-to-whole, how to simplify ratios and find equivalent ones, the cross-multiplication test, unit rates, scaling a recipe and the four mistakes that cause most wrong answers.

By Laura Bennett, MathIt
Six paper bags in two rows on a table, each holding the same three red apples and four oranges, showing fruit shared into equal groups.
Classroom Notes· 11 min read

Greatest common factor and least common multiple: how to find them

What the GCF and the LCM are, three ways to find them with worked examples, the GCF × LCM shortcut, when to use which, and the four mistakes that cost marks.

By Laura Bennett, MathIt
A pie cut into eight slices on a plate, with one slice lifted on a pie server, next to a set of four nested measuring cups.
Classroom Notes· 9 min read

How to divide fractions with keep-change-flip, and why it works

What 3 ÷ 1⁄2 means, the keep-change-flip steps, the common-denominator proof of why they work, fractions divided by whole numbers, mixed numbers, and the four mistakes children make.

By Laura Bennett, MathIt
Three cubes built from small blocks on a table: a single yellow block, a blue cube two blocks on each side and a larger orange cube three blocks on each side, with two loose green blocks beside them.
Classroom Notes· 10 min read

Exponents explained: what the small number means and the rules that follow from it

What the base and the exponent mean, how powers of 10 connect to place value, the five laws of exponents with worked examples, why any number to the power of 0 is 1, and the mistakes that cost marks.

By Laura Bennett, MathIt
A rectangle cut once across and once down into four colored parts of different sizes.
Classroom Notes· 10 min read

Long multiplication explained: the order that makes it stick

The order that makes long multiplication stick: the times-table check, 36 × 24 as an area model, the placeholder zero, and the four mistakes that ruin the second row.

By Laura Bennett, MathIt
Ten bars of different heights in a row, with a dashed line drawn across them at the average height.
Classroom Notes· 10 min read

Mean, median and mode explained, with worked examples

Three summaries of the same list of numbers give three different answers, and all of them are correct. Here is how to find the mean, the median and the mode, with worked examples, the even-count rule and the mistakes that cost marks.

By Laura Bennett, MathIt
Three groups of counters on a table: twelve arranged in a rectangle, eight in a rectangle and nine in a square, while seven counters fit only in one straight line.
Classroom Notes· 11 min read

Prime numbers explained: how to spot them and why they matter

What makes a number prime, why 1 is left out, the square-root test that settles any number under 100, prime factorization with factor trees, and the six mistakes children make.

By Laura Bennett, MathIt
Flat illustration on a deep purple background of an adult holding a shopping bag and a phone calculator, next to an abstract pie chart and a large percent-like shape.
Classroom Notes· 7 min read

How to calculate percentages: three formulas and the mental shortcuts

Every percentage question is one of three calculations. Here are the three formulas with a worked example each, the 10% trick for doing them in your head, and the mistakes that make a sale price or a news headline come out wrong.

By Laura Bennett, MathIt