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| Objectives Children's learning outcomes are emphasised |
Assessment for learning |
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There are 10 girls and 20 boys in Jill's class. Jill said that there
is one girl for every two boys. Her friend Amanda said that means Is Jill right? Use words or pictures to explain why. Is Amanda right? Use words or pictures to explain why. A piece of rope 204 cm long is cut into four equal pieces. Which of these gives the length of each piece in centimetres? A 204 ÷ 4 B 204 × 4 C 204 - 4 D 204 4
Sita worked out the correct answer to 16 × 5. Her answer was 80. Show how she could have worked out her answer. Harry worked out the correct answer to 70 ÷ 5. His answer was 14. Show how he could have worked out his answer. |
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How many different multiplication and division facts can you make using what you know about 56? What if you started with 560? |
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Tell me some division questions that have the answer 15. How did you go about working this out? Make up some division questions that have a remainder of 3. How did you do it? Talk me through the method that you used to calculate 56 × 7. Is this division correct? How do you know? How could we put it right? Parveen buys 3 small bags of peanuts. She gives the shop keeper £2 and gets 80p change. What is the cost in pence of one bag of peanuts? Tell me how you worked out the answer to this problem. |
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Tell me some fractions that are equivalent to How do you know that two fractions are equivalent? Two of these shapes have three quarters shaded. Point to them. Explain how you know.
Tell me some fractions that are greater than
I ate more than What would you prefer: 3 pizzas shared between 4 people or 6 pizzas shared between 10 people? Explain why. |
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Which of these decimals means A 70 B 7 C 0.7 D 0.07 Which of these fractions is the same as nought point four?
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Which would you rather have:  of £24 or  of £49? Why? |
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One in every three of these beads is red. What fraction of the beads is red? Create a word problem that uses the words 'in every'. In this diagram, 2 out of every 3 squares are shaded.
Which diagram has 3 out of every 4 squares shaded?
In a book of stamps, there are 2 red stamps to every 5 green stamps. There are 15 green stamps in the book. How many red stamps are there? For every soft drink that Fred collected, Maria collected 3. Fred collected a total of 9 soft drinks. How many did Maria collect? A 3 B 12 C 13 D 27Create a word problem that uses the words 'to every'. |
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This set of cards has mixed numbers written on them. In your group, put the cards in order. |
Using number lines and fraction walls, children begin to recognise the relative sizes of different fractions. They sort a set of fractions into those less than and those greater than a half. They notice that for fractions less than a half the numerator is less than half the denominator. They count on and back in halves, quarters, fifths and tenths. They recognise that fractions are numbers and place a set of fractions such as multiples of 
on a number line. Working in groups they order a set of mixed numbers such as 3 
, 4, 2
and place them on a number line, deciding among themselves how to distribute the tasks and resources effectively.
Children continue to use shapes and other diagrams to explore the equivalence between sets of fractions such as fifths and tenths.
Children continue to reinforce the equivalence of one half, one quarter, three quarters, tenths and hundredths, and their decimal representations. On a 0 to 2 number line they place tenths represented as fractions and then do the same using decimals. Children explore further the fraction and decimal equivalence of hundredths. Using a blank 100-square they label the squares 
, 
, 
, and so on. They then label the squares using decimal notation to help them to see the equivalence. They recognise that 0.25 is 25 hundredths, and that this is one quarter.
Children find fractions of numbers, shapes and quantities, responding to questions such as:
What fraction of 1 metre is 25 cm?
What is one fifth of £1?
There are 300 children in Bigham School. Four fifths of the children went on a school visit. How many children were left at school?
There are 36 children in the class. In their lunch boxes, half of them have a red apple and one third of them have a green apple. The rest have no apple. How many children have an apple?
Children continue to count forwards and backwards in different steps. They recall or can derive quickly all multiplication and division facts up to 10 
10. They continue to use place value to derive related facts, such as 540 ÷ 9.
They refine their written methods for multiplying and dividing TU by U, including remainders.
38 × 7 = (30 × 7)
(8 × 7) = 210 56 = 266
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Answer: 13 R 5 |
Children are introduced to the vocabulary of ratio and proportion. They relate fractions to finding a proportion. They describe a proportion using the language of 'in every', for example 'I spend 5 days in every week in school', recognising that this means 'I spend 10 days in every 2 weeks at school'. Children meet the vocabulary 'for every' and 'to every' in everyday statements such as 'I have 1 thumb for every 4 fingers' or 'There are 2 apples to every 1 banana in the bowl'. They recognise that the bowl of fruit has twice as many bananas as apples but that there could be 2 apples and 1 banana, 4 apples and 2 bananas, 6 apples and 3 bananas, and so on. Using two colours, they design a repeating pattern of coloured squares such as blue, blue, red, blue, blue, red, ... They notice there are 2 blue squares to/for every 1 red square, 4 blue squares to/for every 2 red squares, and so on. They notice also that 1 in every 3 squares is
red and that 2 in every 3 squares are blue. They establish that there are twice as many blue squares as red squares. They use fractions to state these proportions, since 
of the squares are red and 
are blue. They go on to consider: If there are 5 red squares in my repeating pattern, how many blue squares would there be?
Children solve problems such as:
Rosie spent £2 on 10p and 20p stamps. She bought three times as many 10p stamps as 20p stamps. How many of each stamp did she buy?
They represent the problem using patterns of numbers, number sentences or diagrams. They recognise that for every 20p stamp Rosie buys three 10p stamps, and that one group of the stamps would cost 20p 10p 10p 10p = 50p. This helps them to find the solution of four 20p stamps and twelve 10p stamps, which they then check in the context of the problem.
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Activities |
PDF 923KB |
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Activity 42 - Stickers |
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Activity 44 - More Stamps |
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Springboard units |
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None currently available |
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Wave 3 section |
Pages |
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Is not confident when recalling X facts |
1 Y4 ×/÷ |
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Does not apply partitioning and recombining when multiplying and confuses the value of 2 digit numbers |
4 Y4 ×/÷ |
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Has difficulty interpreting a remainder as a fraction |
2 Y6 ×/÷ |
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Interprets division as sharing but not grouping |
3 Y6 ×/÷ |
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Discards the remainder: does not understand its significance |
6b Y4 ×/÷ |
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Writes a remainder that is larger than the divisor |
6a Y4 ×/÷ |
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of all the children in the class are girls.
and 
, or 
and 
); interpret mixed numbers and position them on a number line (e.g. 3 
)
. How do you know? Are there any others? What about 
?
.What fraction could I have eaten?
as 0.25 and 
or as 0.1 and that one hundredth can be written as 
or 0.01
is the same as 0.25. It is also the same as 
?
of 30 plums, 
of a 6 by 4 rectangle)
of £10
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