NB Grade 5 Math cheat sheet

Place value: each position is 10 times the value of the position to its right, so 4 in 47 000 means 40 000 and 4 in 4 700 means 4 000.

Rounding: find the target place, look at the digit to its right; 5 or more rounds up, 4 or less keeps the digit.

Comparing decimals: line up decimal points, then compare digits left to right; 0.6 is greater than 0.58 because 6 tenths beats 5 tenths.

Equivalent fractions: multiply or divide numerator and denominator by the same nonzero number, so 3/4 = 9/12.

Adding and subtracting fractions with unlike denominators: rewrite both with a common denominator, then combine numerators only.

A fraction of a set: divide the set by the denominator, then multiply by the numerator; 3/5 of 40 is 40 ÷ 5 × 3 = 24.

Multiplying by powers of 10 shifts each digit left; dividing shifts each digit right; 3.6 × 100 = 360 and 3.6 ÷ 10 = 0.36.

Factors multiply to give a number and divide it exactly; multiples are products of the number with whole numbers, so 6 is a factor of 18 and 18 is a multiple of 6.

Arithmetic patterns change by a constant difference; find it by subtracting consecutive terms, then extend by adding it.

Geometric patterns multiply by a constant ratio; find it by dividing a term by the previous term.

Two-part rules alternate or combine operations, such as add 3, add 5, add 3, add 5; describe each step separately.

A pattern rule has a starting value and an operation, for example start at 7 and add 4 each time gives 7, 11, 15, 19.

Input-output tables: check whether the rule is multiply, add, or a combination; test the rule on at least two rows before trusting it.

A variable is a letter standing for an unknown number; an expression such as 3n + 2 is evaluated by substituting the value of n.

Equality means both sides have the same value, so 5 + 4 = 3 × 3 is true and an unknown can be solved by keeping both sides balanced.

Growing shape patterns: count tiles or squares per stage, record the numbers in a table, then look for the constant increase.

Perimeter of a rectangle: P = 2 × (length + width); perimeter is the total distance around the outside.

Area of a rectangle: A = length × width; area is measured in square units such as cm².

Area of a triangle: A = base × height ÷ 2, where the height is perpendicular to the chosen base.

A parallelogram's area equals base × height; the height is the perpendicular distance between parallel sides, not the slanted side.

Volume of a rectangular prism: V = length × width × height, measured in cubic units such as cm³.

Angle facts: a right angle is 90°, a straight angle is 180°, and the angles in any triangle add to 180°.

Unit conversions: 1 m = 100 cm, 1 km = 1000 m, 1 kg = 1000 g, 1 L = 1000 mL, 1 hour = 60 minutes.

A polygon is regular when all sides and all angles are equal; a quadrilateral has four sides and its angles total 360°.

Mean is the sum of the values divided by the number of values; the mean of 4, 6, 8, 10 is 28 ÷ 4 = 7.

Median is the middle value when the data are ordered; with an even count, average the two middle values.

Mode is the value that appears most often; a data set can have no mode or more than one mode.

Range is the greatest value minus the least value and measures how spread out the data are.

In a bar graph, bars must have equal width and equal spacing, with a labelled scale and title.

In a line graph, the horizontal axis usually shows time and the vertical axis shows the quantity being tracked.

Probability of an event = favourable outcomes ÷ total equally likely outcomes; a probability of 0 is impossible and 1 is certain.

The probabilities of all outcomes in a simple experiment add to 1, so the chance of an event not happening is 1 minus its probability.

Four-step approach: understand the problem, plan a strategy, carry out the plan, then check whether the answer is reasonable.

Choose a strategy by structure: draw a diagram for geometry, make a table for patterns, work backwards when the end result is given.

Estimate first by rounding to friendly numbers, then compare the exact answer with the estimate to catch errors.

Check subtraction by adding the difference to the subtrahend; check division by multiplying the quotient by the divisor and adding the remainder.

Multi-step word problems: identify the question, list the given information, and decide the order of operations needed.

Order of operations: do work inside brackets first, then multiplication and division left to right, then addition and subtraction.

Explain reasoning with words, numbers, and a diagram, and state why the chosen operation matches the situation.

Answers to measurement problems need units; a number without units does not fully answer the question.