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Explore maths in Year 6 with Gina: calculation and order of operations, fractions, decimals and percentages, ratio and proportion, and more.
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Choose mental or written methods according to the numbers. In an expression, calculate brackets first, then powers, then multiplication and division from left to right, then addition and subtraction from left to right. Estimate and use inverse operations to check.
Try it: Write two expressions with the same numbers but different bracket positions and explain the results.
Convert to a useful equivalent form before calculating or comparing. Dividing by a whole number can make fractional parts smaller. Multiplying by a proper fraction finds a proportion. Percentages can be assembled from easy amounts.
Try it: Compare three offers expressed as a fraction, decimal and percentage.
A ratio compares amounts in parts. Scaling every part by the same factor preserves the ratio. Ratio is different from a fraction of the total: in a 2:3 ratio there are five parts altogether.
Try it: Create a ratio with counters and show two equivalent scaled versions.
A letter can stand for an unknown number or a changing quantity. Keep both sides of an equation equal. A sequence follows a rule, which should explain every step rather than just one example.
Try it: Invent a growing sequence and explain its rule using words and a letter.
Triangles have interior angles totalling 180°. Area and volume formulas depend on the shape and chosen units. A triangle’s area is half the area of a rectangle with the same base and perpendicular height.
Try it: Explain why a triangle’s area uses half of base times perpendicular height.
The mean is a total divided by the number of values. The range is the largest value minus the smallest. Graphs can emphasise or hide differences through their scales, so inspect labels and intervals before interpreting them.
Try it: Collect a small numerical dataset, show it clearly, and explain its mean and range.
A ratio compares quantities multiplicatively. Equivalent ratios multiply or divide every part by the same factor. The order of the labels matters. A ratio of red to blue 2:3 does not mean two fifths blue.
Try it: Model two equivalent ratios with coloured counters.
A letter can represent a number. An expression describes a calculation; an equation states equality. Use the same value for the same variable within a problem. Inverse operations can find an unknown while preserving equality.
Try it: Create an equation and verify its solution by substitution.
A multi-step problem needs an ordered plan. Identify units, choose operations and estimate before calculating. Keep intermediate results clear and check the final answer in context. There may be more than one valid method.
Try it: Solve a two-step story in two different ways.
Each chapter brings together teaching, an example, practice and a practical discovery. Use the material with discussion and suitable offline activities. Choose a comfortable starting point and revisit explanations as needed.
Open this subject in the Academy for Gina’s explanations, examples and activities. The Academy supports shared learning and practical work; it is not independently certified as a complete home-education curriculum.
Continue in the app →Heartwing AcademyExplore maths in Year 1 with Gina: counting and place value, addition, subtraction and number bonds, sharing and equal groups, and more.
Explore →Heartwing AcademyExplore maths in Year 2 with Gina: tens, ones and ordering, adding and subtracting in steps, multiplication and division, and more.
Explore →Heartwing AcademyExplore maths in Year 3 with Gina: hundreds and place value, addition and subtraction with exchange, multiplication and division strategies, and more.
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