Primary 4 Mathematics

A number from 10000 to 99999, made of five digits.

The 5th place from the right; each 1 means 10000.

The 4th place from the right; each 1 means 1000.

The 3rd place from the right; each 1 means 100.

The 2nd place from the right; each 1 means 10.

The 1st place from the right; it counts ones.

10 thousands make ten thousand (10000).

Writing a number stretched out, e.g. 24531 = 20000 + 4000 + 500 + 30 + 1.

The rules for mixed calculations: brackets, then ×÷, then +−.

( ), the part calculated first.

× and ÷ come before + and −, worked left to right.

+ and − are worked last, also left to right.

One expression with both +− and ×÷, e.g. 2 + 3 × 4.

A line of numbers and operation signs, e.g. 18 ÷ 3 + 2.

Equal-level operations go in order: in 8 ÷ 2 × 3, do 8÷2 first.

A written problem needing a mixed expression to solve correctly.

A number that divides another exactly, e.g. 2 is a factor of 6.

A number times 1, 2, 3…, e.g. 6, 9, 12 are multiples of 3.

Dividing with no remainder, e.g. 12 ÷ 3 = 4.

Find factors in multiplication pairs: 12 = 1×12 = 2×6 = 3×4.

Countable to the end; a number's factors are finite.

Never ends; multiples go on forever.

18 is divisible by 3, so 3 is a factor of 18.

Shared by both, e.g. 6 is a factor of both 12 and 18.

Fractions with the same bottom number, e.g. 27 and 37.

The top number; adding and subtracting happen here.

The bottom number; it never changes in these sums.

Dividing top and bottom by the same number, e.g. 48 = 12.

A whole plus a fraction, e.g. one and a half (1 12).

Numerator equal to or bigger than the denominator, e.g. 76.

To subtract from 1, rewrite it, e.g. 1 = 77.

After working, see if the answer simplifies, e.g. 39 = 13.

Adding two decimals, e.g. 1.25 + 3.4.

Subtracting decimals, e.g. 5 − 2.4.

Line the dots up in a column so places match.

Add zeros to match lengths, e.g. write 3.4 as 3.40.

The first place after the dot, the 0.1 place.

The second place after the dot, the 0.01 place.

Same as whole numbers: carry at ten, borrow when short.

Roughly predict the answer first to sanity-check your work.

Multiplying digit by digit in vertical column form.

When a product reaches 10, pass the tens part left.

Multiply from the ones place upward, digit by digit.

Predict the size first, e.g. 1234 × 3 is a bit over 3600.

×10 appends one 0; ×100 appends two 0s.

Split a 2-digit multiplier into two rows and add, e.g. 23 = 20 + 3.

1200 × 3 ≈ 3600, so 3702 is sensible.

E.g. one box holds 1234 beads; how many in 3 boxes?

Step-by-step column division, starting from the left.

The answer of the division, written on top.

What is left over; always smaller than the divisor.

Pull the next digit down to keep dividing.

The total being divided, e.g. the 848 in 848 ÷ 4.

The number dividing, e.g. the 4 in 848 ÷ 4.

Unlike adding, division starts at the highest place.

Quotient × divisor (+ remainder) must equal the dividend.

Fractions with different bottom numbers, e.g. 12 and 14.

A shared bottom number both fractions can use, e.g. 4.

Rewriting with the same value but a common denominator: 12 = 24.

Whatever you do to the bottom, do to the top: 12 = 24.

Fractions of equal value, e.g. 12 = 24 = 48.

Helps pick the common denominator: LCM of 2 and 4 is 4.

Reduce the answer to lowest terms, e.g. 28 = 14.

Draw bars with different divisions to see the combined amount.

A factor shared by both numbers, e.g. 1 and 2 for 6 and 8.

The biggest common factor; HCF of 6 and 8 is 2.

A multiple shared by both, e.g. 12 for 4 and 6.

The smallest common multiple; LCM of 4 and 6 is 12.

List them all, circle the shared ones, pick the biggest/smallest.

Divide top and bottom by the HCF to simplify in one step.

Use the LCM as the common denominator when converting.

Biggest equal groups → HCF; when things coincide again → LCM.

Finding a fraction of an amount, e.g. 14 of 12.

14 of 12 means 14 × 12.

12 ÷ 4 = 3, then 3 × 1 = 3 — easy steps.

Formally: numerator × whole over the same denominator, e.g. 25 × 3 = 65.

Multiplying by a whole number never changes the denominator.

65 becomes 1 15; 48 simplifies to 12.

A fraction with numerator 1, e.g. 14 — the easiest case.

Eating 14 of 12 sweets means eating 3 sweets.

Calculations like 0.5 × 3 or 1.2 × 4.

First multiply as whole numbers: 5 × 3 = 15.

Then place the dot: count the decimal places in the original number.

0.8 has one decimal place, so 0.8 × 3 keeps one place.

0.5 × 3 = 0.5 + 0.5 + 0.5 = 1.5 — check by adding.

A pen costs $3.5; two pens cost $7.

1.5 × 2 = 3.0, usually written simply as 3.

1.2 × 4 is a bit over 4, so 4.8 is sensible.

A number as so many parts out of 100, written %.

% reads percent, e.g. 25% is twenty-five percent.

50% means 50 out of every 100 parts.

One hundredth is the basic unit behind %.

100% is the whole thing: 100100 = 1.

50100 = 12 = 0.5.

Sales use percentages, e.g. 10% off.

Percentages can exceed 100%: 150% is 1.5 times.

Numerator ÷ denominator, e.g. 12 = 1 ÷ 2 = 0.5.

One place goes over 10, two places over 100, then simplify.

0.3 = 310; the denominator is 10.

0.25 = 25100; the denominator is 100.

25100 becomes 14; divide top and bottom by the common factor.

12 = 0.5, 14 = 0.25, 34 = 0.75, 110 = 0.1.

The first decimal place is tenths, so 0.7 is 710.

0.5, 12 and 50% describe the same amount.

A quadrilateral with exactly one pair of parallel sides.

The top parallel side, usually shorter.

The bottom parallel side, usually longer.

The two non-parallel sides on the left and right.

The perpendicular distance between the two bases.

A trapezium whose legs are equal; it looks left-right symmetric.

The trapezium's only pair: upper base parallel to lower base.

Rectangles, squares and parallelograms have two parallel pairs; a trapezium has just one.

A solid with two identical parallel bases and rectangular side faces.

One base with triangular faces meeting at an apex.

The face that names it: triangle base → triangular prism; square base → square pyramid.

The point where all a pyramid's triangular faces meet.

A prism with two triangle bases, like a chocolate bar.

A prism with rectangle bases, e.g. a shoebox.

A square base with four triangular faces, like the pyramids of Egypt.

Flat faces, edges and corners; a cuboid has 6 faces, 12 edges, 8 vertices.

The property of folding exactly onto itself along a line.

The fold line; both sides mirror each other across it.

Cut the shape out and fold to see if the sides match.

The two sides reflect each other like a mirror.

The up-down fold and the left-right fold.

A corner-to-corner fold; a square has two of these.

How many fold lines a shape has: square 4, circle infinite.

Letters like A, H and O have symmetry lines.

Sliding a figure along a straight path without turning or resizing.

Turning a figure around a point, like clock hands.

The fixed point the figure turns around.

The direction clock hands move is clockwise; the reverse is anticlockwise.

A 90° turn, e.g. facing north turning to face east.

A translation states both: 3 squares to the right.

Neither translation nor rotation changes a figure's size or shape.

Reflection flips like a mirror — different from slides and turns.

The surface a rectangle covers = length × width.

The longer side of the rectangle, e.g. 6 cm.

The shorter side, e.g. 4 cm.

Area unit: a 1 cm × 1 cm square.

The unit for floors and courts.

A rectangle with equal sides; area = side × side.

The border length, different from area; unit is cm.

Given area and one side, divide: width = area ÷ length.

The total length of the border around a shape.

Add every side to get the perimeter.

Rectangle perimeter = (length + width) × 2.

Square perimeter = side × 4.

All sides equal: perimeter = side × number of sides.

Perimeter is a length: cm or m, never cm².

Fencing a field means buying its perimeter.

Given the perimeter and other sides, subtract to find the missing one.

The bigger capacity unit; 1 L = 1000 mL.

The smaller unit; a cup of water is about 250 mL.

Changing units: 2.5 L = 2500 mL.

L to mL: append three 0s (or move the dot 3 places right).

mL to L: move the dot 3 places left.

1.5 L means one and a half litres = 1500 mL.

The 500 mL or 1.5 L printed on a bottle.

Match units before comparing or adding.

How much space a solid occupies.

The volume of a 1 cm cube; the unit of volume.

A 1 cm × 1 cm × 1 cm block, used to build and count.

A box-like solid with length, width and height.

Count one layer, then multiply by the number of layers, e.g. 6 × 2.

The cuboid volume formula, built up by counting.

The unit for truck loads and rooms.

Volume in cm³ is space; area in cm² is flat — never swap them.

The side chosen as the bottom; any side can be the base.

The perpendicular distance from the opposite vertex to the base.

The height meets the base at 90°, never at a slant.

Triangle area = base × height ÷ 2.

Two identical triangles combine into a parallelogram.

Parallelogram area = base × height; a triangle is half of it.

A triangle with a 90° corner; its two legs are base and height.

Area answers use square units like cm², m².

The smallest common time unit; one heartbeat is about 1 second.

1 minute = 60 seconds.

1 hour = 60 minutes = 3600 seconds.

The thinnest hand; each small step is 1 second.

A full sweep of 60 marks makes 1 minute.

Multiply by 60: 3 min = 180 sec.

Divide by 60: 240 sec = 4 min.

A watch for short times, showing min and sec — used in races.

Two bars side by side per category, comparing two data sets.

Seeing which set is bigger and by how much.

The key saying which colour stands for which set.

The two bars of one category sit together for direct comparison.

How much each gridline stands for, e.g. one square = 5.

Subtracting the two values, e.g. 12 − 8 = 4.

Both sets (or everything) added together.

Collecting data, e.g. asking the class their favourite sport.