Primary Framework contact | Primary Framework site map
Primary Framework search
In this learning overview are suggested assessment opportunities linked to the assessment focuses within the Assessing Pupils’ Progress guidelines. As you plan your teaching for this unit, draw on these suggestions and on alternative methods to help you to gather evidence of attainment, or to identify barriers to progress, that will inform your planning to meet the needs of particular groups of children. When you make a periodic assessment of children’s learning, this accumulating evidence will help you to determine the level at which they are working.
To gather evidence related to the three Ma1 assessment focuses (problem solving, reasoning and communicating), it is important to give children space and time to develop their own approaches and strategies throughout the mathematics curriculum, as well as through the application of skills across the curriculum.
In this unit the illustrated assessment focuses are:
Children double and halve decimal numbers, using their knowledge of doubling and halving whole numbers and decimal place value. They find, for example, double 0.47 and half of 7.2. They answer questions such as:
Find a number whose double lies between 1.3 and 1.4.
What number lies halfway between 2.47 and 2.83 on a number line?
Children count in fractions. For example, they count from 0 in steps of 1/4 initially using improper fractions (0, 1/4, 2/4, 3/4, 4/4, 5/4, ...) and then using mixed numbers (0, 1/4, 2/4, 3/4, 1, 11/4, ...). They record the count on a number line to establish equivalent pairs, e.g. 23/4 = 11/4. They discuss how to find equivalent pairs without a number line, establishing that 1 whole is equivalent to 4 quarters, so 2 wholes is 8 quarters (4 quarters × 2), and 23/4 is equivalent to 8 quarters + 3 quarters, or 11 quarters. They use diagrams where they are helpful to confirm the equivalent improper fraction for a given mixed number and vice versa.
Assessment focus: Ma2, Fractions, decimals, percentages, ratio and proportion
Look for evidence of children using diagrams to relate improper fractions to mixed numbers, for example:
23/6 = 35/6
Look out for those children who begin use division to convert improper fractions to mixed numbers.
Children relate fractions to their decimal equivalents. They recognise that fractions with a denominator of 10 or 100 can be converted to their decimal equivalent by placing the digits of the numerator in the appropriate column, for example 3/10 = 0.3, 7/100 = 0.07, 13/100 = 0.13. They use number lines (or the ITP 'Fractions') to establish the decimal equivalent of fractions such as 2/5 or 1/20.
For example, they use a 0 to 1 number line marked in steps of 0.1, divide it into fifths and mark 1/5, 2/5, ... on it. They use this to establish that 1/5 = 0.2, 2/5 = 0.4, ... They use the patterns in such sequences to predict other equivalents, predicting, for example, that 4/5 will be equivalent to 0.8. Children understand how to use a calculator to convert a fraction to a decimal. They appreciate that 4/5 is equivalent to 4 ÷ 5. They appreciate that when they key this calculation into a calculator it will give them the answer in decimal form. So one way to find the decimal equivalent of 4/5 is to key 4 ÷ 5 into a calculator. Children solve problems involving fractions, including some for which the calculations merit use of a calculator. For example, they find 2/3 of 150ml by dividing 150ml by 3 to find 1/3, then multiplying the answer by 2 to find 2/3.
Assessment focus: Ma2, Operations, relationships between them
Look for children who relate finding a unit fraction of a number to division, for example, children who calculate 1/5 of 125 as 125 ÷ 5. Look for children who understand how finding a fraction such as 3/5 of 125 relates to division and multiplication and can be calculated as 125 ÷ 5 × 3.
Children solve problems such as:
Jay buys a 2 litre bottle of pop. He drinks 1/4 of the bottle and spills 2/5 of the bottle. How many millilitres are left?
A mile is 1760 yards. I have walked 5/11 of a mile. How many yards is this?
Find different ways to complete:
Children understand percentage as the number of parts in every 100. They represent particular percentages using practical resources, such as money ( £1, 10p and 1p coins) or images such as a 10 by 10 square grid, for example shading 35 squares in the grid to represent 35%. To find the percentage equivalent for simple fractions such as 3/4 they shade this fraction of a 10 by 10 grid and consider what percentage this represents. Children appreciate that 10% is equivalent is 1/10, so to find 10% of an amount they can divide it by 10. They find 10% of numbers and measures such as £2.00, 150, 25, 700 ml, 3 kg. They begin to use 10% of an amount to find 5% , then 20% , 30% , ... They use this method to work out percentages of quantities such as 20% of 1 kg, 30% of 200 ml, 5% of £80.
Assessment focus: Ma2, Fractions, decimals, percentages, ratio and proportion
Look for evidence of children relating decimal numbers to fractions expressed in tenths and hundredths, and to percentages. For example, look for children who convert a decimal number such as 0.35 to 35/100 and recognise that this can be recorded as 35%. Look out for children who convert decimal numbers with one or two decimal places in this way.
Children recognise and interpret the vocabulary of ratio and proportion, using diagrams or objects to represent the situation. They understand that scaling involves increasing a quantity by a given factor.
Multiplication by 5 means scaling a number or quantity by a factor of 5, and making it 5 times as big.
They use pairs of number lines to show scaling, for example by a factor of 3:
They scale up a relationship such as 'There are 3 red sweets in every pack of 10' to establish that there would be 6 red sweets in every 20 sweets, 9 red sweets in every 30 sweets, and so on. They solve problems such as:
At the gym club there are 2 boys for every 3 girls. Suggest some numbers of boys and girls that there might be at the club.
A mother seal is fed 5 fish for every 2 fish for its baby. Alice fed the mother seal 15 fish. How many fish did she feed to the baby?
Paul uses 3 tomatoes for every 1/2 litre of sauce. How much sauce can he make from 15 tomatoes? How many tomatoes would he need for 2 litres of sauce?
Assessment focus: Ma1, Reasoning
Look for evidence of children identifying patterns as they work, in order to find a solution to a problem; for example, they might identify multiples of different numbers to help with scaling problems. Look out for children who use these patterns to check solutions and to justify their answers.
| Objectives Children's learning outcomes are emphasised | Assessment for learning |
|---|---|
|
How many calculations are needed to solve this problem? |
|
Prepare a two-way Venn diagram showing 'multiples of 10' and 'numbers greater than 100'. Put the numbers 42, 90, 105, 171, 200 in the correct regions. Explain what this diagram shows. |
|
Here is a chocolate bar.
Bill eats 3 pieces and Ann eats 2 pieces.
Tell me two fractions that are the same as 0.2. |
|
Shade 10% of this grid.
Which is bigger: 65% or 3/4? How do you know? |
|
18 is 6 times as many as 3.
What number is 6 times as many as 9? |
|
A number when doubled gives 9.2. What is the number? |
|
1/3 of 75 is 25. Write this as a division statement. |
|
What calculation would you key into a calculator to find 3/20 as a decimal? Use a calculator to establish whether 27/40 is bigger or smaller than 0.75. What two numbers have a product of 912? Are there any other possibilities? |
|
Why did you decide to use a mental/written/calculator method for this calculation? Why did you decide to change all the units to litres rather than millilitres? |
| Activities | PDF 1MB |
| Activity 54 - Joins | |
| Activity 53 - Square it up | |
| Activity 55 - Money bags | |
| Activity 57 - Presents | |
| Activity 58 - Spot the shapes 2 | |
| Activity 60 - Three digits | |
| Activity 63 - Jack's book | |
| Activity 64 - Flash Harry | |
| Activity 66 - Zids and Zods | |
| Activity 69 - Coins on the table | |
| Activity 70 - A bit fishy | |
| Activity 74 - Anyone for tennis |
|
Objectives for Springboard intervention unit |
Springboard units |
|
Know by heart: all +/- facts for each number up to 20, all pairs of multiples of 100 with a total of 1000, all pairs of multiples of 5 with a total of 100, all pairs of numbers with a total of 100 |
Springboard 5 Unit 3 (PDF 305KB) |
| Springboard 5 Unit 3 supplementary (PDF 85KB) | |
| 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) |
| Diagnostic focus | Resource |
| Does not make sensible decisions about when to use calculations laid out in columns | 3 Y4  /-DfES 1130-2005 (PDF 101KB) |
| Has difficulty with adding three numbers in a column | 4 Y4 /- DfES 1131-2005 (PDF 95KB) |
Click here for information on different file formats and their usage.
Channel information • Teaching resources • Streaming video of all programmes