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Year 6 Block E - Securing number facts, relationships and calculating Unit 3

Objectives

Children's learning outcomes are emphasised 		Assessment for learning
  • Tabulate systematically the information in a problem or puzzle; identify and record the steps or calculations needed to solve it, using symbols where appropriate; interpret solutions in the original context and check their accuracy

    I can record the calculations needed to solve a problem and check that my working is correct

When have you seen symbols used in everyday life?
When would you use them to explain a calculation?
What is your first step going to be in solving this puzzle?
Explain how making a table could help you to solve this problem.

Here are five number cards.
5 number cards, 3 marked A, two B
A and B stand for two different whole numbers. The sum of all the numbers on all five cards is 30. What could be the values of A and B?
  • Solve multi-step problems, and problems involving fractions, decimals and percentages; choose and use appropriate calculation strategies at each stage, including calculator use

    I can work out problems involving fractions, decimals and percentages using a range of methods

Give me an example of a percentage increase that you would find:

entirely in your head
using jottings
using a written method
using a calculator
using a combination of these strategies.
  • Use knowledge of place value and multiplication facts to 10 × 10 to derive related multiplication and division facts involving decimals (e.g. 0.8 × 7, 4.8 ÷ 6)

    I can use place value and my tables to work out multiplication and division facts

Ten times a number is 86. What is the number?
Divide 4.2 by 6.
If you know 42 ÷ 6 = 7, what else do you know?
What number multiplied by 8 equals 4.8?
How else could you make an answer of 4.8?
What is half of 6.3?

  • Use efficient written methods to add and subtract integers and decimals, to multiply and divide integers and decimals by a one-digit integer, and to multiply two-digit and three-digit integers by a two-digit integer

    I can use standard written methods to add, subtract, multiply and divide whole numbers and decimals

Explain how you will work out the answer to this problem without using a calculator.

Shenaz buys a pack of 24 cans of cola for £6.00.
24 cans in a box marked £6.00
What is the cost of each can?
  • Use a calculator to solve problems involving multi-step calculations

    I can work out problems involving fractions, decimals and percentages using a calculator

What steps would you take to work out these problems?

Some children do a sponsored walk.
Jason is sponsored for £1.25 for each lap.
He does 23 laps. How much money does he raise?
Lynne wants to raise £200
She is sponsored for £6.50 for each lap. What is the least number of whole laps she must do?
A calculator shows 19.428 571 42... What answer would you give if it related to pounds, metres, litres, hours?
Write in the missing digits: 323 × square7 = 15 18square
  • Express a larger whole number as a fraction of a smaller one (e.g. recognise that 8 slices of a 5-slice pizza represents eight fifths or 1 three fifths pizzas); simplify fractions by cancelling common factors; order a set of fractions by converting them to fractions with a common denominator

    I can write a large whole number as a fraction of a smaller one and simplify fractions and put them in order of size

What do the fractions six ninths, fourteen twentyfirsts and eighteen twentysevenths have in common?
Arrange these numbers in order: 1 three quarters, fifteen eighths, 1.6

with a calculator
without a calculator.
Which way of working do you prefer? Why?
  • Relate fractions to multiplication and division (e.g. 6 ÷ 2 = one half of 6 = 6 × one half); express a quotient as a fraction or decimal (e.g. 67 ÷ 5 = 13.4 or 13 two fifths); find fractions and percentages of whole-number quantities (e.g. five eighths of 96, 65% of £260)

    I can find fractions and percentages of whole numbers

The result of dividing one number by another is 4 three quarters. What were the two numbers? Are there any other possibilities?
Explain the steps you would take to find 35% of an amount without a calculator.
How would you find 35% of an amount using a calculator?
Three-quarters of a number is 48. What is the number?
What is twenty per cent of sixty pounds?
What is two percent of three hundred?

  • Express one quantity as a percentage of another (e.g. express £400 as a percentage of £1000); find equivalent percentages, decimals and fractions

    I can work out a quantity as a percentage of another and find equivalent percentages, decimals and fractions

Organise these numbers into two or more groups, giving reasons for your grouping:
40%, 125%, 0.4, five fourths, two fifths, 1.25.
Add at least one more fraction to each of your groups.
Circle the two fractions that are equivalent to 0.6.

4 fractions: six tenths, one sixtieth, sixty hundredths and one sixth

Write in the missing numbers.
30% of 60 is square.
30% of square is 60.

  • Solve simple problems involving direct proportion by scaling quantities up or down

    I can solve problems using ratio and proportion

Six cakes cost one pound eighty. How much do ten cakes cost?
Here is part of a number line. Write the two missing numbers in the boxes.

A number line with calibrations at intervals of 5, 960 and 980 are marked. The missing numbers are 955 and 1030

In a country dance there are 3 boys and 2 girls in every line.

Children in a line

42 boys take part in the dance. How many girls take part?
For a different dance there are 45 children. How many boys are there?

  • Use a range of oral techniques to present persuasive arguments

    I can discuss mathematical ideas and persuade others

Let's discuss ideas for solving this problem.
What links can you see between fractions and ratios?

Learning overview

Children draw on their knowledge of multiplication and division facts and of place value to work out mentally calculations involving fractions, decimals or percentages. They use jottings where appropriate to respond to questions such as:

Subtract nought point seven five from six.
Estimate the value of nine point two multiplied by two point nine.
Multiply eight point seven by two.
What is one half added to three quarters?
What is three fifths of forty pounds?
What is fifty per cent of twenty pounds?
What is ninety-nine per cent of two hundred?

Children consolidate and extend their use of efficient written methods. They use standard column procedures to add and subtract integers and decimals, and to multiply two- and three-digit integers by a one- or two-digit integer; they extend division to dividing three-digit by two-digit integers.

Children understand equivalence and simplify fractions to their lowest form. They compare and order fractions, decimals and percentages.

They continue to identify and record the calculations needed to solve problems. They interpret solutions in the original context and check their accuracy. They use symbols where appropriate to explain their reasoning and conclusions. Children solve multi-step problems by breaking each problem down into steps, identifying and recording the calculation needed for each step. They decide whether to use a written method or a calculator to solve problems such as:

20% of the area of this flag is blue. What area of the flag is blue?

A rectangle 125cm by 60cm with a hexagon inside

A shop has a sale offering a 20% discount. A cooker normally costs £362. How much will it cost in the sale?
A 250 g box of washing powder costs £1.48. A 1.1 kg box of the same washing powder costs £7. Which box is the better value for money?
50 000 people visited a theme park in one year. 15% of the people visited in April and 40% of the people visited in August. How many people visited the park in the rest of the year?
What is the total cost of 3 spades at £9.55 each and 2 buckets at £4.73 each?

Children use the vocabulary of ratio and proportion to describe the relationships between two quantities. They begin to use ratio notation. For example, from the knowledge that orange paint is made from 3 tins of red paint to 2 tins of yellow paint, children write the ratio of red paint to yellow paint as 3 : 2, They work out, say, that if they have 21 tins of red paint that they will need 14 tins of yellow paint to make orange paint. They solve problems such as:

Here is a rectangle with six identical shaded squares inside it. The width of the rectangle is 7.2 centimetres. Calculate the length of the rectangle.

A rectangle 7.2cm wide with 6 squares shaded

This map has a scale of 1 cm to 6 km.

A map showing Ridlington and Carborough

The road from Ridlington to Carborough measured on the map is 6.6 cm long. What is the length of the road in kilometres?
Sapna makes a fruit salad using bananas, oranges and apples. For every one banana, she uses two oranges and three apples. Sapna uses 24 fruits. How many oranges does she use?
Cheddar cheese costs £7.50 for 1 kg. Marie buys 200 grams of cheddar cheese. How much does she pay?
Cream cheese costs £3.60 for 1 kg. Robbie buys a pot of cream cheese for 90p. How many grams of cream cheese does

Resource links to existing published material

Mathematical challenges for able Key Stages 1 and 2
Activities PDF 1MB
Activity 71 - Pet shop
Intervention programmes

Objectives for Springboard intervention unit

Springboard unit

Use a calculator to convert a fraction to its decimal equivalent and to find a fraction of a quantity

Springboard 6 Unit 10 (PDF 1.4MB)

Supporting children with gaps in their mathematical understanding (Wave 3)
Diagnostic focus Resource
Is not confident in making reasonable estimates for multiplication and division 4 Y6 ×/÷
DfES 1162-2005 (PDF 111KB)

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
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