NL Grade 6 Math cheat sheet
NL Grade 6 Math · Keep the key ideas within reach.
Number
Place value: each position is 10 times the value of the position to its right; in 4,706,352 the 7 stands for 700,000.
Rounding rule: look at the digit one place to the right; 5 or more rounds up, 4 or less keeps the digit the same.
Multiplying by powers of 10 shifts digits left: ×10, ×100, ×1000 add 1, 2, 3 zeros; dividing shifts digits right.
Order of operations: brackets first, then exponents, then × and ÷ left to right, then + and − left to right.
A fraction is a division: 3/4 = 3 ÷ 4 = 0.75; to compare fractions, rewrite with a common denominator or convert to decimals.
A percent is a fraction out of 100: 45% = 45/100 = 0.45; to find 15% of 80, compute 0.15 × 80 = 12.
Divisibility: by 2 if the last digit is even; by 3 if digit sum is divisible by 3; by 5 if the last digit is 0 or 5; by 9 if digit sum is divisible by 9.
A ratio compares two quantities; equivalent ratios come from multiplying or dividing both parts by the same nonzero number (2:3 = 6:9).
Integer operations: adding a negative moves left on the number line; subtracting a negative is the same as adding (5 − (−3) = 8).
Patterns and Relations
Arithmetic sequence: each term changes by a constant difference d; next term = current term + d.
Rule for an arithmetic sequence: term n = first term + (n − 1) × d, so 4, 7, 10, ... has term n = 4 + 3(n − 1) = 3n + 1.
To find the rule from a table, check whether the output changes by a constant amount per unit increase in input; that amount is the multiplier.
A relation is a set of ordered pairs (input, output); a variable is a letter standing for a number that can change.
An expression has no equals sign (3n + 2); an equation states two expressions are equal (3n + 2 = 14).
Solve one-step equations by applying the inverse operation to both sides: n + 7 = 15 gives n = 8; 4n = 20 gives n = 5.
Preserve balance: whatever operation is done to one side of an equation must be done to the other side.
Growing patterns can be described by the number of tiles added per step; the constant term is the number of tiles at step 0.
Shape and Space
Perimeter of a rectangle = 2 × (length + width); area of a rectangle = length × width.
Area of a triangle = ½ × base × height, where height is perpendicular to the base; area of a parallelogram = base × height.
Volume of a rectangular prism = length × width × height; volume is measured in cubic units.
Angle facts: angles on a straight line sum to 180°; angles around a point sum to 360°; vertically opposite angles are equal.
Triangle angle sum = 180°; an equilateral triangle has three 60° angles, and an isosceles triangle has two equal base angles.
A quadrilateral's interior angles sum to 360°; a rectangle has four right angles and opposite sides equal.
Transformations: a translation slides a shape without turning or flipping; a reflection flips it over a line; a rotation turns it about a point.
1 cm = 10 mm, 1 m = 100 cm, 1 km = 1000 m; 1 L = 1000 mL; 1 kg = 1000 g.
Congruent shapes have the same size and shape; similar shapes have the same shape but may differ in size.
Statistics and Probability
Mean = sum of all values ÷ number of values; median is the middle value when data are ordered; mode is the most frequent value.
Range = greatest value − least value; range measures spread, not center.
With an even number of data values, the median is the mean of the two middle values.
Outliers are values far from the rest; they pull the mean toward them but do not affect the median as much.
Probability of an event = number of favourable outcomes ÷ total number of equally likely outcomes.
Probabilities range from 0 (impossible) to 1 (certain); the probabilities of an event and its complement add to 1.
A bar graph compares categories; a line graph shows change over time; a circle graph shows parts of a whole as percents summing to 100%.
In a fair experiment each outcome is equally likely, so the probabilities of all outcomes sum to 1.
Number
Place value: each position is 10 times the value of the position to its right; in 4,706,352 the 7 stands for 700,000.
Rounding rule: look at the digit one place to the right; 5 or more rounds up, 4 or less keeps the digit the same.
Multiplying by powers of 10 shifts digits left: ×10, ×100, ×1000 add 1, 2, 3 zeros; dividing shifts digits right.
Order of operations: brackets first, then exponents, then × and ÷ left to right, then + and − left to right.
A fraction is a division: 3/4 = 3 ÷ 4 = 0.75; to compare fractions, rewrite with a common denominator or convert to decimals.
A percent is a fraction out of 100: 45% = 45/100 = 0.45; to find 15% of 80, compute 0.15 × 80 = 12.
Divisibility: by 2 if the last digit is even; by 3 if digit sum is divisible by 3; by 5 if the last digit is 0 or 5; by 9 if digit sum is divisible by 9.
A ratio compares two quantities; equivalent ratios come from multiplying or dividing both parts by the same nonzero number (2:3 = 6:9).
Integer operations: adding a negative moves left on the number line; subtracting a negative is the same as adding (5 − (−3) = 8).
Patterns and Relations
Arithmetic sequence: each term changes by a constant difference d; next term = current term + d.
Rule for an arithmetic sequence: term n = first term + (n − 1) × d, so 4, 7, 10, ... has term n = 4 + 3(n − 1) = 3n + 1.
To find the rule from a table, check whether the output changes by a constant amount per unit increase in input; that amount is the multiplier.
A relation is a set of ordered pairs (input, output); a variable is a letter standing for a number that can change.
An expression has no equals sign (3n + 2); an equation states two expressions are equal (3n + 2 = 14).
Solve one-step equations by applying the inverse operation to both sides: n + 7 = 15 gives n = 8; 4n = 20 gives n = 5.
Preserve balance: whatever operation is done to one side of an equation must be done to the other side.
Growing patterns can be described by the number of tiles added per step; the constant term is the number of tiles at step 0.
Shape and Space
Perimeter of a rectangle = 2 × (length + width); area of a rectangle = length × width.
Area of a triangle = ½ × base × height, where height is perpendicular to the base; area of a parallelogram = base × height.
Volume of a rectangular prism = length × width × height; volume is measured in cubic units.
Angle facts: angles on a straight line sum to 180°; angles around a point sum to 360°; vertically opposite angles are equal.
Triangle angle sum = 180°; an equilateral triangle has three 60° angles, and an isosceles triangle has two equal base angles.
A quadrilateral's interior angles sum to 360°; a rectangle has four right angles and opposite sides equal.
Transformations: a translation slides a shape without turning or flipping; a reflection flips it over a line; a rotation turns it about a point.
1 cm = 10 mm, 1 m = 100 cm, 1 km = 1000 m; 1 L = 1000 mL; 1 kg = 1000 g.
Congruent shapes have the same size and shape; similar shapes have the same shape but may differ in size.
Statistics and Probability
Mean = sum of all values ÷ number of values; median is the middle value when data are ordered; mode is the most frequent value.
Range = greatest value − least value; range measures spread, not center.
With an even number of data values, the median is the mean of the two middle values.
Outliers are values far from the rest; they pull the mean toward them but do not affect the median as much.
Probability of an event = number of favourable outcomes ÷ total number of equally likely outcomes.
Probabilities range from 0 (impossible) to 1 (certain); the probabilities of an event and its complement add to 1.
A bar graph compares categories; a line graph shows change over time; a circle graph shows parts of a whole as percents summing to 100%.
In a fair experiment each outcome is equally likely, so the probabilities of all outcomes sum to 1.
Number
Place value: each position is 10 times the value of the position to its right; in 4,706,352 the 7 stands for 700,000.
Rounding rule: look at the digit one place to the right; 5 or more rounds up, 4 or less keeps the digit the same.
Multiplying by powers of 10 shifts digits left: ×10, ×100, ×1000 add 1, 2, 3 zeros; dividing shifts digits right.
Order of operations: brackets first, then exponents, then × and ÷ left to right, then + and − left to right.
A fraction is a division: 3/4 = 3 ÷ 4 = 0.75; to compare fractions, rewrite with a common denominator or convert to decimals.
A percent is a fraction out of 100: 45% = 45/100 = 0.45; to find 15% of 80, compute 0.15 × 80 = 12.
Divisibility: by 2 if the last digit is even; by 3 if digit sum is divisible by 3; by 5 if the last digit is 0 or 5; by 9 if digit sum is divisible by 9.
A ratio compares two quantities; equivalent ratios come from multiplying or dividing both parts by the same nonzero number (2:3 = 6:9).
Integer operations: adding a negative moves left on the number line; subtracting a negative is the same as adding (5 − (−3) = 8).
Patterns and Relations
Arithmetic sequence: each term changes by a constant difference d; next term = current term + d.
Rule for an arithmetic sequence: term n = first term + (n − 1) × d, so 4, 7, 10, ... has term n = 4 + 3(n − 1) = 3n + 1.
To find the rule from a table, check whether the output changes by a constant amount per unit increase in input; that amount is the multiplier.
A relation is a set of ordered pairs (input, output); a variable is a letter standing for a number that can change.
An expression has no equals sign (3n + 2); an equation states two expressions are equal (3n + 2 = 14).
Solve one-step equations by applying the inverse operation to both sides: n + 7 = 15 gives n = 8; 4n = 20 gives n = 5.
Preserve balance: whatever operation is done to one side of an equation must be done to the other side.
Growing patterns can be described by the number of tiles added per step; the constant term is the number of tiles at step 0.
Shape and Space
Perimeter of a rectangle = 2 × (length + width); area of a rectangle = length × width.
Area of a triangle = ½ × base × height, where height is perpendicular to the base; area of a parallelogram = base × height.
Volume of a rectangular prism = length × width × height; volume is measured in cubic units.
Angle facts: angles on a straight line sum to 180°; angles around a point sum to 360°; vertically opposite angles are equal.
Triangle angle sum = 180°; an equilateral triangle has three 60° angles, and an isosceles triangle has two equal base angles.
A quadrilateral's interior angles sum to 360°; a rectangle has four right angles and opposite sides equal.
Transformations: a translation slides a shape without turning or flipping; a reflection flips it over a line; a rotation turns it about a point.
1 cm = 10 mm, 1 m = 100 cm, 1 km = 1000 m; 1 L = 1000 mL; 1 kg = 1000 g.
Congruent shapes have the same size and shape; similar shapes have the same shape but may differ in size.
Statistics and Probability
Mean = sum of all values ÷ number of values; median is the middle value when data are ordered; mode is the most frequent value.
Range = greatest value − least value; range measures spread, not center.
With an even number of data values, the median is the mean of the two middle values.
Outliers are values far from the rest; they pull the mean toward them but do not affect the median as much.
Probability of an event = number of favourable outcomes ÷ total number of equally likely outcomes.
Probabilities range from 0 (impossible) to 1 (certain); the probabilities of an event and its complement add to 1.
A bar graph compares categories; a line graph shows change over time; a circle graph shows parts of a whole as percents summing to 100%.
In a fair experiment each outcome is equally likely, so the probabilities of all outcomes sum to 1.