NB Francophone G3 Math cheat sheet

A 3-digit number is written as hundreds + tens + ones: 472 = 400 + 70 + 2.

In 638, the digit 6 has value 600, the 3 has value 30, and the 8 has value 8.

Place-value positions from right to left are ones, tens, hundreds; each position is 10 times the one to its right.

Comparing numbers: compare the hundreds digit first, then the tens, then the ones; the first difference decides.

Ordering: ascending means smallest to largest; descending means largest to smallest.

Standard form 905, expanded form 900 + 5, and words 'nine hundred five' name the same number.

A number just before 300 is 299 and just after is 301; there is no greatest whole number.

Even numbers end in 0, 2, 4, 6, or 8; odd numbers end in 1, 3, 5, 7, or 9.

Addition and subtraction are inverse operations: if 348 + 276 = 624, then 624 − 276 = 348.

When adding or subtracting, line up digits by place value and regroup by 10 ones = 1 ten, 10 tens = 1 hundred.

Commutative property of addition: a + b = b + a; subtraction is not commutative.

Mental strategy for +9: add 10 then subtract 1; for +19: add 20 then subtract 1.

Mental strategy for −9: subtract 10 then add 1 back.

Multiplication a × b means a groups of b; 4 × 6 = 6 + 6 + 6 + 6 = 24.

Division c ÷ d answers 'how many groups of d in c'; 24 ÷ 4 = 6 because 4 × 6 = 24.

Multiplying by 10 appends a zero: 7 × 10 = 70; dividing by 10 removes a zero when the number ends in 0.

A fraction a/b: b is the number of equal parts in one whole, a is how many parts are taken.

Halves: 1/2 = 2/4; fourths: 1/4, 2/4, 3/4, 4/4 = 1 whole.

Thirds: 1/3, 2/3, 3/3 = 1; tenths: 1/10 through 10/10 = 1.

With the same denominator, the larger numerator is the larger fraction: 3/4 > 1/4.

With the same numerator, the larger denominator gives the smaller fraction: 1/3 > 1/5.

One half is greater than one third because splitting into 3 parts makes each part smaller.

Decimal notation for tenths: 1/10 = 0.1, 3/10 = 0.3, 10/10 = 1.0; 1/2 = 0.5.

A fraction equal to one whole has numerator equal to denominator, such as 5/5 or 8/8.

A repeating pattern has a core that repeats: in A B B A B B A B B the core is A B B.

A growing pattern increases by a constant amount each step: 3, 6, 9, 12 grows by +3.

A shrinking pattern decreases by a constant amount: 20, 16, 12, 8 shrinks by −4.

Pattern rule states the start and the change: 'start at 5, add 4 each time' gives 5, 9, 13, 17.

Find a missing term by applying the rule to the term before it.

An equation is balanced; the unknown is the value that makes both sides equal.

Solve □ + 7 = 15 by subtracting: □ = 15 − 7 = 8.

Solve 4 × □ = 20 by dividing: □ = 20 ÷ 4 = 5; check by substituting back.

Length units: millimetre (mm), centimetre (cm), metre (m), kilometre (km); 1 cm = 10 mm, 1 m = 100 cm, 1 km = 1000 m.

Mass units: gram (g) and kilogram (kg); 1 kg = 1000 g.

Capacity units: millilitre (mL) and litre (L); 1 L = 1000 mL.

Time: 1 minute = 60 seconds, 1 hour = 60 minutes, 1 day = 24 hours.

Temperature is measured in degrees Celsius (°C); water freezes at 0 °C and boils at 100 °C.

Choose the unit by object size: a pencil in cm, a room in m, a bag of flour in kg, a spoon of syrup in mL.

Perimeter is the total distance around a shape: add all side lengths; a 5 cm by 3 cm rectangle has perimeter 5 + 3 + 5 + 3 = 16 cm.

A ruler is used for length, a balance scale for mass, a measuring cup for capacity, and a clock for time.

Polygons are named by side count: triangle 3, quadrilateral 4, pentagon 5, hexagon 6, octagon 8.

A square has 4 equal sides and 4 right angles; a rectangle has 4 right angles and opposite sides equal.

A 3-D object has faces (flat surfaces), edges (where faces meet), and vertices (corners).

A cube has 6 square faces, 12 edges, and 8 vertices.

A line of symmetry divides a shape into two matching halves; a square has 4 lines of symmetry.

Position is described with terms such as above, below, left, right, beside, and between.

Movement on a grid is described by direction and number of squares, for example 'right 3, up 2'.

A prism has two matching parallel bases; a pyramid has one base and triangular faces meeting at a point.

A tally mark stands for one item; tallies are grouped in fives with a diagonal stroke across four.

A pictograph uses a key, such as one symbol = 2 books, so half a symbol = 1 book.

A bar graph has a title, labelled axes, a scale, and bars of equal width.

The mode of a data set is the value that appears most often.

The range is the greatest value minus the smallest value.

Likelihood words: impossible (0 chance), unlikely, equally likely, likely, certain (always happens).

An event with more favourable outcomes is more likely: a bag with 7 red and 2 blue counters is more likely to give red.

Read a graph by matching the bar or symbol height to the scale on the axis, not by bar width.

Four-step process: understand the problem, plan a strategy, carry out the plan, check the answer.

Key words: 'in all' and 'altogether' suggest addition; 'how many more' and 'left' suggest subtraction.

Equal-sharing words such as 'shared equally' signal division; 'groups of' signals multiplication.

A two-step problem is solved in order: first compute the intermediate amount, then apply the second operation.

Estimate first by rounding to tens or hundreds, then compare the exact answer with the estimate.

Check subtraction by adding the difference to the number subtracted: 82 − 47 = 35 because 35 + 47 = 82.

Perimeter problems: find missing sides from symmetry or given equal sides before adding.

Explain a solution by naming the operation used and giving the numbers and result, for example '624 − 276 = 348 because 348 + 276 = 624'.

In 507, the 0 in the tens place means zero tens; the number is 500 + 7.

Skip counting by 5, 10, 25, and 100 builds number sense: 100, 200, 300 or 25, 50, 75, 100.

A number can be represented with base-ten blocks: flats = 100, rods = 10, units = 1.

Comparison symbols: > means greater than, < means less than, = means equal.

Rounding to the nearest ten: look at the ones digit; 4 or less rounds down, 5 or more rounds up.

The greatest 3-digit number is 999 and the smallest is 100.

Doubles facts help mental math: 7 + 7 = 14, so 7 + 8 = 15 (one more).

Making ten: 8 + 5 = 8 + 2 + 3 = 10 + 3 = 13.

Subtraction by counting up: 63 − 58 = 5 because 58 + 5 = 63.

Multiplication facts connect to arrays: 3 rows of 4 counters show 3 × 4 = 12.

Any number multiplied by 1 stays the same; any number multiplied by 0 is 0.

Division by 1 leaves the number unchanged; a number divided by itself equals 1.

Equal parts matter: a shape cut into 4 unequal parts does not show fourths.

Two halves make one whole; four fourths make one whole; three thirds make one whole.

A unit fraction has numerator 1: 1/2, 1/3, 1/4, 1/10.

One tenth is smaller than one fourth because tenths are smaller parts of the whole.

Money links to decimals: 50 cents = 0.50 dollar = 1/2 dollar; 25 cents = 0.25 dollar = 1/4 dollar.

Patterns can use numbers, shapes, colours, or sounds; the rule describes how the pattern changes.

Find the rule by comparing consecutive terms: 2, 4, 8, 16 doubles each time.

A fact family links operations: 3 + 5 = 8, 5 + 3 = 8, 8 − 5 = 3, 8 − 3 = 5.

Balance reasoning: if both sides of an equation change equally, the equation stays true.

Estimate before measuring, then measure with a ruler starting at the 0 mark.

1 metre is about the width of a doorway; 1 kilogram is about the mass of a large textbook.

Elapsed time is found by counting forward from the start time to the end time.

A square with side 6 cm has perimeter 4 × 6 = 24 cm.

A regular polygon has all sides equal and all angles equal.

A cylinder has 2 circular faces and 1 curved surface; a cone has 1 circular face and 1 vertex.

Symmetry can be checked by folding: if the halves match exactly, the fold line is a line of symmetry.

Shapes can be sorted by attributes such as number of sides, number of vertices, or presence of right angles.

Collect data with a survey question and record each response once.

A frequency table lists each category with its count.

A spinner with equal sections gives equally likely outcomes for those sections.

Probability is between impossible (0) and certain (1); it cannot be negative or greater than 1.

Draw a diagram or make a table to organize information in a multi-step problem.

Work backward from the answer when the end result and operations are known.

Check that the answer answers the question asked and includes the correct unit.

Justify an estimate by naming the rounded numbers used, such as 198 + 305 ≈ 200 + 300 = 500.