Schoolsweb
Listen

Link to the DfCFS home page
The Standards Site - Raising Standards

This website is changing: Find out more.

Year 5 Block E - Securing number facts, relationships and calculating Unit 3

Objectives

Children's learning outcomes are emphasised 		Assessment for learning
  • Represent a puzzle or problem by identifying and recording the information or calculations needed to solve it; find possible solutions and confirm them in the context of the problem

    I can break a problem into steps and say the calculation I need to do to work out each step I can check that my answers are sensible

How many calculations are needed to solve this problem? What is the first step towards solving this problem? How will you record your working for this step? What does this answer tell you? Roughly, what answer do you expect from this question?

  • Solve one-step and two-step problems involving whole numbers and decimals and all four operations, choosing and using appropriate calculation strategies, including calculator use

    I can decide and justify what calculations to do to solve a problem and whether I will do these mentally, using a written method or with a calculator

How will you solve this problem? Will you use a mental, written or calculator method? Why did you choose this method?
Change the numbers in the problem to ones where you would choose to use a mental method.
How do you know whether you need to add, subtract, multiply or divide? What clues do you look for?

  • Express a smaller whole number as a fraction of a larger one (e.g. recognise that 5 out of 8 is five eights); find equivalent fractions (e.g. seven tenths = fourteen twentieths, or nineteen tenths = 1nine tenths); relate fractions to their decimal representations

    I can give the decimal equivalent of a simple fraction such as three tenths and explain how I know

What is one fifth of 20? One third of a number is 7. What is the number? What fraction of £1 is 30p? Explain how you know. Complete this statement in different ways:

square is 1/4 of square

Find the missing number

Three over a missing number equals twelve sixteenths

Which number represents the shaded part of the figure?

10 bars with 2 shaded

A 2.8 B 0.5 C 0.2 D 0.02
Write four tenths as a decimal number.
What is three quarters as a decimal?
Write 0.23 as a fraction.

  • Understand percentage as the number of parts in every 100 and express tenths and hundredths as percentages

    I know that 'per cent' means 'parts in every 100', so 1% = one hundredth I can give a simple fraction such as one tenth as a percentage

What percentage of the bar is shaded?

10 bars with 4 shaded

40% of a class of children are boys. What percentage are girls?
Rick says that 3% is equivalent to three tenths. Is he right? How do you know?
A test has 50 marks. Rory gets 40 marks. What is his percentage score?

  • Refine and use efficient written methods to multiply and divide HTU × U, TU × TU, U.t × U and HTU ÷ U

    I can use a written method to divide a three-digit number by a one-digit number and explain each step

Find a number between 350 and 360 that gives a remainder of 5 when divided by 8. Work out 261 ÷ 3. Explain each step. These division calculations have errors. What are the errors? Explain how to put them right. 25 × 18 is more than 24 × 18. How much more?

A 1
B 18
C 24
D 25

  • Use sequences to scale numbers up or down; solve problems involving proportions of quantities (e.g. decrease quantities in a recipe designed to feed six people)

    I can use the relationships between numbers to solve ratio and proportion questions

A recipe gives amounts to feed 2 people. Explain how you would change the amounts to feed 6 people. A pattern of tiles is organised so that there are 2 red tiles for every 3 blue tiles. How many blue tiles are needed for a pattern that contains 12 red tiles? How did you work this out? Paul uses 5 tomatoes to make half a litre of tomato sauce. How much sauce can he make from 15 tomatoes? A One and a half litres B Two litres C Two and a half litres D Three litres

  • Find fractions using division (e.g. 1/100 of 5kg), and percentages of numbers and quantities (e.g. 10%, 5% and 15% of £80)

    I can tell you what calculations I will do to find a fraction of a quantity I can tell you what calculations I will do to find a percentage of a quantity

Find one hundredth of 3km. Tell me how to find three quarters of £60. Kate says: 'To find 10% of an amount, you divide it by 10. So to find 20% of an amount, you divide it by 20.' Is Kate correct? How do you know? What calculations would you do to find 15% of £150? What percentage of the whole numbers from 1 to 10 are even?

  • Present a spoken argument, sequencing points logically, defending views with evidence and making use of persuasive language

    I can describe each stage of my calculation method (e.g. for 186 ÷ 6). I can explain why it is a good method for this calculation
 Make a list of the steps you would take to solve this problem: A pack of frozen peas costs £1.72. Sally bought three packs of frozen peas. How much change did he get from a £10 note? Explain to the class why you solved the problem in that way.

Learning overview

Children use multiplication (and division) to solve problems involving ratio and proportion. They answer questions such as:

Mary posts a package. She uses 10p and 2p stamps. She uses two 2p stamps for every 10p stamp. What could the package cost to post?
There are 25ml of cordial in every 100ml of juice drink. How much cordial is needed to make one half litre of juice drink?

Children scale the ingredients in recipes up or down, for example rewriting a recipe for 8 people so that it would feed 16 or 4 people.
Children use division and multiplication to find fractions and percentages of numbers and quantities, for example:

35% of the children in a class are girls. What percentage are boys?
A shop is selling trainers at 75% of normal price. A pair of trainers usually costs £24. How much will they cost in the sale?
I spend 30% of my £1 pocket money. How much do I have left?
Richard got 40 marks out of 80 in a test. Sarah got 45%. Who had the better score, Richard or Sarah?
Asif buys a 1kg bag of flour. He uses 30% of it to make biscuits and two fifths of it to bake a cake. How much of the flour is left?

Children secure their understanding of the equivalence of fractions. They use a fraction wall or other diagrams and their understanding of scaling to identify families of fractions that are equivalent to, for example, two thirds:

two thirds = four sixths = six ninths = eight twelfths = ten fifteenths = twelve eighteenths = ...

They recognise that the numerator and the denominator of two thirds have both been multiplied by 3 to create the equivalent fraction six nineteenths. They understand that when you multiply (or divide) the numerator and the denominator of a fraction by the same number, you create an equivalent fraction. They use this to find the missing numbers in equations such as:

Four fifths equals missing number over twenty and Sixteen twenty fourths equals missing number over eight

Through practical experience, children establish relationships between common fractions. They know that, for example, one seventh is smaller than one sixth. They recognise that one sixth is half of one third. They use the patterns to predict and test similar relationships such as 'one tenth is half of one fifth.' Children use diagrams, images (such as fraction walls or number lines) or practical equipment to solve problems involving fractions such as:

What fraction lies halfway between three tenths and seven tenths?
Which of these fractions is less than one half?
seven tenths, sixty hundredths, two fifths, one tenths, eleven twentieths, one twentieth
Place these fractions in order, smallest first:
one half, 2, 1three quarters, three halves, one quarter

Children express one amount as a fraction of another. For example, they compare two strips of stickers, one of 2 stickers and one of 10 stickers. They understand that 10 is 5 times 2 and 2 is one fifth of 10. They recognise that there are 5 times as many stickers in the longer strip as in the small, and that the short strip has one fifth of the number of stickers on the long strip. They answer questions such as:

I drink 100ml of a 1 litre bottle of lemonade. What fraction of the lemonade in the bottle have I drunk? What fraction of the lemonade is left?
There are 30 children in a class. 6 children are girls. What fraction of the class are the girls? What fraction of the class are boys?

Children consolidate their understanding of equivalence between simple fractions, decimals and percentages. For example, they complete a table showing equivalent fractions, decimals and percentages, such as:

Fraction

Decimal

Percentage

one half

 

 

 

0.1

 

 

 

25%

three tenths

 

 

 

 

7%

Children extend written methods for division to include HTU ÷ U, including calculations with remainders. They suggest what they expect the approximate answer to be before starting a calculation and use this to check that their answer sounds sensible. They increase the efficiency of the methods that they are using. For example:

196 ÷ 6 is approximately 200 ÷ 5 = 40

196 divided by 6 calculated by subtracting multiples of 6, first three steps 6 by 10 then 6 by 2196 divided by 6 calculated by subtracting multiples of 6, first three steps 6 by 10 then 6 by 2

Children know that, depending on the context, answers to division questions may need to be rounded up or rounded down. They explain how they decided whether to round up or down to answer problems such as:

Egg boxes hold 6 eggs. A farmer collects 439 eggs. How many boxes can he fill?
Egg boxes hold 6 eggs. How many boxes must a restaurant buy to have 200 eggs?

Children use their understanding of equivalence between fractions and decimals to begin to write the remainder to a division calculation as a fraction and as a decimal. They discuss a practical situation such as:

7 apples are shared out fairly between 4 children. How many apples does each child get?

They realise that the remaining 3 apples can be shared by dividing them into quarters to give each child 1three quarters apples or 1.75 apples. They find the exact answer to other division calculations such as 28 ÷ 5, 37 ÷ 4, 366 ÷ 8, 734 ÷ 5, and to problems such as:

Eight children share equally the cost of a present costing £20. How much does each child pay?
Seven tins of dog food are shared equally between five big dogs. How many tins of dog food does each dog get?

Resource links to existing published material

Mathematical challenges for able pupils in Key Stages 1 and 2
Activities PDF 1MB
Activity 57 - Presents
Activity 63 - Jack's book
Activity 66 - Zids and Zods
Activity 67 - Franco's fast food
Activity 70 - A bit fishy
Intervention programmes

Objectives for Springboard intervention unit

Springboard units

Recognise ½, ¼, 1/10, 1/5 and use them to find fractions of shapes and numbers
Begin to recognise simple equivalent fractions, for example, 5/10 as ½ and 10/10 as 1

Springboard 5 Unit 4 (PDF 283KB)
Develop and refine written methods for multiplication (two- or three-digit x single-digit)
Approximate the answer first		 Springboard 5 Unit 10 (PDF 269KB)
Springboard 5 Unit 10 supplementary (PDF 63KB)
Supporting children with gaps in their mathematical understanding (Wave 3)
Diagnostic focus Resource
Does not apply partitioning and recombining when multiplying and confuses the value of two digit numbers 4 Y4 ×/÷
DfES 1153-2005 (PDF 104KB)
Assumes the commutative law holds for division also 5 Y4 ×/÷
DfES 1154-2005 (PDF 85KB)
Writes a remainder that is larger than the divisor 6a Y4 ×/÷
DfES 1155-2005 (PDF 76KB)
Discards the remainder; does not understand its significance 6b Y4 ×/÷
DfES 1156-2005 (PDF 93KB)
Does not recognise when the remainder is significant when rounding up or down 6c Y4 ×/÷
DfES 1157-2005 (PDF 65KB)
Continues to subtract 2s without using knowledge of times tables 7 Y4 ×/÷
DfES 1158-2005 (PDF 89KB)

Click here for information on different file formats and their usage.

Wave 3 addition and subtraction tracking children's learning charts

PDF 161KB RTF 930KB Word 315KB

Wave 3 multiplication and division tracking children's learning charts

PDF 195KB RTF 1.3MB Word 430KB

Wave 3 Resource sheets and index of games booklet

PDF 500KB
Disclaimer notice
The Department for Children, Schools and Families wishes to make clear that the Department and its agents accept no responsibility for the actual content of any materials suggested as information sources in this document, whether these are in the form of printed publications or on a website. In these materials icons, logos, software products and websites are used for contextual and practical reasons. Their use should not be interpreted as an endorsement of particular companies or their products. The websites referred to in these materials existed at the time of going to print. Tutors should check all website references carefully to see if they have changed and substitute other references where appropriate.