School math
Follow the working, one step at a time.
Division
Long Division
Every step of the division bracket, with the multiplication you need shown right when you need it.
Long Division with 2-Digit Divisors
The harder version — estimating the quotient when the divisor has two digits.
Dividing Decimals
Move the decimal point in the divisor first — then it is ordinary long division.
Fraction to Decimal
A fraction is a division problem. Divide the top by the bottom and watch it turn into a decimal.
Multiplication
Long Multiplication
Including the placeholder zero on the second row — the step almost every kid forgets.
Multiplying Decimals
Multiply as if the points were not there, then count the places to put the point back.
Area Model (Box Method)
The method your child is taught at school and you probably were not. Split by place value, multiply, add.
Multiply & Divide by 10, 100, 1000
Watch the decimal point slide. It never was about “adding zeros”.
Addition & Subtraction
Addition with Carrying
Column addition with the carried digits written where they actually go.
Subtraction with Borrowing
Regrouping shown the way it is written on paper — crossed out, with the new number above.
Subtracting Across Zeros
When the neighbour is a zero it has nothing to lend, so you keep going left. The hardest one in the unit.
Adding Decimals
Line up the points, fill the gaps with zeros, then add like normal.
Subtracting Decimals
The same lining-up rule, plus borrowing across the decimal point.
Fractions
Adding & Subtracting Fractions
Unlike denominators, with the common denominator found by counting multiples — the step that is normally invisible.
Multiplying Fractions
Cancel diagonally first, then multiply straight across. No common denominator needed.
Dividing Fractions
Keep, change, flip — and this one actually shows you why flipping works.
Subtracting Mixed Numbers
Borrowing a whole one and turning it into fraction pieces. The hardest thing in the fraction unit.
Simplifying Fractions
Find the greatest common factor from the actual factor lists, then divide once.
Mixed & Improper Fractions
Both directions, with a picture of why the whole number turns into pieces.
Comparing Fractions
Which one is bigger? Cross multiply, and see both drawn as bars.
Equivalent Fractions
The same amount written five different ways, drawn side by side so you can see it is the same.
Fraction, Decimal & Percent
All three are the same number. This shows how to walk between them.
Factors & Multiples
Prime Factorization
A factor tree that grows branch by branch, with the reason each prime was chosen.
Greatest Common Factor (GCF)
The ladder method — divide both numbers together until nothing is left in common.
Least Common Multiple (LCM)
Same ladder as the GCF, but you multiply in an L shape — down the side and along the bottom.
Divisibility Rules
Test one number against every rule at once, and see why each one works.
Factor Pairs
Every pair that multiplies to your number — and why you only test up to the square root.
Expressions & Equations
Order of Operations (PEMDAS)
One operation at a time, with the reason that one goes next. Brackets, exponents, then × ÷, then + −.
Evaluating Expressions
Put a number in for x, then work through it in the right order.
Two-Step Equations
Undo the addition first, then the multiplication — doing the same thing to both sides every time.
Adding & Subtracting Integers
Walk it out on a number line — including why subtracting a negative moves you right.
Percent & Ratio
Percent of a Number
What is 15% of 80? Turn the percent into a decimal, then multiply — with a 10% sanity check.
Percent Increase & Decrease
The trap is what goes on the bottom. It is always the number you started with.
Solving Proportions
Two ratios that match, one number missing. Cross multiply and it falls out.
Unit Rate
Cost for one. Once everything is “per 1” you can compare any two deals.
Measurement & Geometry
Metric Conversions
The metric staircase. Every step is ten, so converting is just sliding the decimal point.
Customary Conversions
Inches, feet, pounds, cups. No pattern to lean on — so go down to the smallest unit and back up.
Elapsed Time
Count on to the next whole hour, then the hours, then the leftover minutes. Works every time.
Perimeter & Area
The two get mixed up constantly. One is the walk around the edge, the other is the space inside.
Area of Composite Figures
An L-shape is just two rectangles. Slice it, do each piece, add them up.
Volume of a Rectangular Prism
One layer of cubes, then stack the layers. That is all volume ever is.
Angles
See the angle drawn, name it, and find what it pairs with to make 90° or 180°.
Data & Number Sense
Mean, Median, Mode & Range
Mean, median and mode from one sorted list — plus the range, which measures spread rather than average.
Rounding on a Number Line
“Five or more, round up” is a picture before it is a rule. Here is the picture.
Place Value & Expanded Form
The same digit is worth a different amount depending on where it sits.
Roman Numerals
Built one letter at a time, with the subtractive pairs like IV and CM explained as they appear.
Estimating
Round first, work it out in your head, then check the real answer is close.
Absolute Value
Not “make it positive” — it is the distance from zero, and distance is never negative.
Ratio Tables
Scale both columns by the same amount and the ratio survives. That is the whole idea.