Grade 6 math

Solve one-step equations by doing the same inverse operation to both sides, with worked examples, common mistakes, and practice problems with full solutions.

Solve one-step inequalities the same way as equations, plus the one rule that changes: why the sign flips when you multiply or divide by a negative.

How to add and subtract decimals by lining up the decimal points, why the alignment matters, and how to handle numbers with different lengths.

How to divide by a decimal by shifting both numbers until the divisor is whole, why that shift is allowed, and how to divide a decimal by a whole number.

How to multiply decimals by ignoring the points, multiplying as whole numbers, then counting the decimal places — and why that count is what it is.

What an exponent means, why it is repeated multiplication and not repeated addition, how to read powers aloud, and where exponents sit in order of operations.

How to divide fractions by multiplying by the reciprocal, why flipping the second fraction works, and how to divide with whole numbers and mixed numbers.

How to decide whether a fraction word problem needs addition, subtraction, multiplication or division, with the signal words and worked solutions for each.

Two ways to turn a fraction into a decimal, how to tell in advance whether it will terminate or repeat, and how to convert a decimal back into a fraction.

Why the area of a triangle is half base times height, what counts as the height, and how to handle triangles where the height falls outside the shape.

Why the volume of a box is length times width times height, why the units are cubed, and how the base-times-height form works for any prism.

What absolute value means, why it is never negative, how it differs from a statement about order, and how to use it to find the distance between two numbers.

How to compare negative numbers using the number line, what the inequality signs really say about position, and how to order a mixed list of integers and decimals.

How to plot and read ordered pairs in all four quadrants, what the signs tell you about which quadrant a point is in, and how to find the distance between two points.

What negative numbers mean, how opposites work, where integers sit on the number line, and why zero needs no sign of its own.

How to find what percent one number is of another: divide the part by the whole and multiply by 100, and how to tell which number is the whole.

Three ways to find a percent of a number: convert to a decimal and multiply, use a fraction, or build it from 10% and 1% in your head.

What percent means, why it is out of one hundred, and how to move between a percent, a fraction and a decimal without memorising three separate rules.

How to evaluate an algebraic expression by substituting a value for the variable, why brackets matter when the value is negative, and how order of operations applies.

How to break an expression into terms, name the coefficient and constant, and describe a whole expression as a sum, product, quotient or difference.

The commutative, associative, distributive and identity properties, what each one permits, and how to check whether two expressions are equivalent.

What a variable is, how to write an algebraic expression from a sentence, why 3n means multiplication, and how an expression differs from an equation.

How to turn a worded problem into an equation or inequality, what solving actually asks, which words signal each inequality sign, and how two quantities relate.

How to convert between units by multiplying by a ratio equal to 1, why the unwanted unit cancels, and how to decide which way up the conversion factor goes.

How to find equivalent ratios by multiplying or dividing both parts, how to build and read a ratio table, and how to fill in a missing value.

What a unit rate is, how to find one by dividing, how to use unit price to compare two deals, and the difference between a rate and a ratio.

What a ratio means, the three ways to write one, the difference between part-to-part and part-to-whole ratios, and why the order of the numbers matters.

How to build a box plot from the five-number summary, what the box and whiskers each show, how to spot skew from the median line, and how to compare two groups.

How to read and build a dot plot and a histogram, why a histogram's bars touch, how bin width changes what you see, and what a statistical question is.

How to find the mean, median and mode of a data set, what each one measures, and how to choose between them when an outlier pulls the mean away from the middle.

How to measure how spread out a data set is using range, interquartile range and mean absolute deviation, and why two sets with the same mean can be nothing alike.