Imaginesis: printable Year 6 Ratio and Proportion maths worksheets for England (National Curriculum) — Solving Proportions with Missing Values, Using Map Scales to Find Real Distances, Finding a Fraction of a Number: word problems with hints, answers and worked solutions as PDF, also as an A/B test.
A photography store sells 4 identical padded camera pouches for £32 altogether. How much do 7 of these pouches cost at the same price?
Hint: First work out the price of one padded camera pouch by sharing the £32 equally among the 4 pouches, then use that price to find the cost of 7 pouches.
Answer: 56
A map of the moon base has the scale 1 : 500. On the map, the landing pad and the greenhouse dome are 3 cm apart. How many metres apart are they in reality?
Hint: One centimetre on the moon base map stands for the second number of the scale, in real centimetres. Change the result into metres at the end.
Answer: 15
In the bakery display case sit 56 brioche rolls. Exactly 3/7 of the rolls contain dried cherries. How many rolls contain dried cherries?
Hint: First divide the 56 brioche rolls into 7 equal groups to find the size of one part. Then count how many rolls are in 3 of those groups.
Answer: 24
Children learn to calculate an unknown quantity in a proportion by using whole-number multiplication and division facts to scale values up or down.
KS3.R.7 relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functionsKS3.R.9 solve problems involving direct and inverse proportion, including graphical and algebraic representationsY6.R.1 solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts
At this stage, children compare the relative sizes of two quantities and find missing values using integer multiplication and division facts. They learn to spot the relationship between known amounts—such as identifying that one quantity has been doubled, tripled, or halved—and apply that same multiplier or divisor to determine the unknown amount.
A common hurdle is confusing multiplicative change with addition. For instance, if a recipe changes from 2 eggs to 6 eggs, a child might notice the difference of 4 and add 4 to the flour amount, rather than multiplying by 3. Children also occasionally apply the operation in the wrong direction, multiplying when they need to divide to scale down.
Worksheet tasks focus on these skills through two main formats:
Children learn to use a given scale factor to convert between measurements on a map and actual distances in the real world.
KS3.GM.3 draw and measure line segments and angles in geometric figures, including interpreting scale drawingsKS3.R.2 use scale factors, scale diagrams and mapsY6.R.3 solve problems involving similar shapes where the scale factor is known or can be found
Children learn to connect ratio and scaling to maps and scale drawings. Using a known scale factor, they multiply to scale a map measurement up to its real-world length or divide to scale an actual distance down to map size.
A frequent error occurs when pupils apply the wrong operation, such as multiplying when converting a real distance back onto the page, producing a map length that is impossibly large. Children also commonly struggle when shifting between units of measurement, losing track of how centimetres relate to metres or kilometres during the calculation.
Worksheet tasks based on Distance on a map and in reality provide a clear scale, such as 1 cm representing a set number of metres. Children are given either the map measurement or the real-world distance and calculate the missing value using multiplication or division.
Children learn to calculate unit and non-unit fractions of whole numbers to solve sharing and grouping problems where the result is a whole number.
KS3.N.11 interpret fractions and percentages as operatorsKS3.R.6 understand that a multiplicative relationship between two quantities can be expressed as a ratio or a fractionY3.F.2 recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominatorsY3.F.7 solve problems that involve all of the above.Y4.F.3 solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole numberY6.R.4 solve problems involving unequal sharing and grouping using knowledge of fractions and multiples.
In Year 6, children calculate unit and non-unit fractions of quantities where the answer is a whole number. Building on basic division, they use their knowledge of fractions and multiples to split quantities into equal parts and solve problems involving unequal sharing and grouping.
A common mistake occurs when working with non-unit fractions: children frequently remember to divide by the denominator to find one part, but forget to multiply that answer by the numerator. Another typical error is confusing the two steps entirely by dividing by the top number and multiplying by the bottom.
Tasks using the Find a fraction of a number template present direct arithmetic problems, such as calculating 3/8 of 40 or 2/3 of 18. Children divide the whole number by the denominator to find a unit fraction, then multiply that result by the numerator to reach the final whole-number amount.
