Exemplification
Examples of what children should be able to do, in relation to each (boxed) Programme of Study statement
solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts
Answer problems such as:
 Here is a recipe for pasta sauce.
Pasta sauce
300 g tomatoes
120 g onions
75 g mushrooms
Sam makes the pasta sauce using 900 g of tomatoes. What weight of onions should he use? What weight of mushrooms?
 A recipe for 3 portions requires 150 g flour and 120 g sugar. Desi’s solution to a problem says that for 2 portions he needs 80 g flour and 100 g sugar. What might Desi have done wrong? Work out the correct answer.

This map has a scale of 1 cm to 6 km.
The road from Ridlington to Carborough measured on the map is 6.6 cm long. What is the length of the road in kilometres?
solve problems involving the calculation of percentages (e.g. of measures) such as 15% of 360 and the use of percentages for comparison
Find simple percentages of amounts and compare them. For example:
 A class contains 12 boys and 18 girls. What percentage of the class are girls? What percentage are boys?
 25% of the apples in a basket are red. The rest are green. There are 21 red apples. How many green apples are there?
solve problems involving similar shapes where the scale factor is known or can be found
 Solve simple problems involving direct proportion by scaling quantities up or down, for example:
Two rulers cost 80 pence. How much do three rulers cost?
 Use the vocabulary of ratio and proportion to describe the relationships between two quantities solving problems such as:
Two letters have a total weight of 120 grams. One letter weighs twice as much as the other. Write the weight of the heavier letter.
The distance from A to B is three times as far as from B to C. The distance from A to C is 60 centimetres. Calculate the distance from A to B.
solve problems involving unequal sharing and grouping using knowledge of fractions and multiples
Relate fractions to multiplication and division (e.g. 6 ÷ 2 = ½ of 6 = 6 × ½), simplify fractions by cancelling common factors, find fractions of wholenumber quantities and solve problems such as:
 What fraction is 18 of 12
 What fraction is 500ml of 400ml?
 What is ^{14}⁄_{35} in its simplest form? ⅖
 What ⅓ × 15? What about 15 × ⅓? How did you work it out?
 What is two thirds of 66?
 What is three quarters of 500?