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 use decimal notation in a variety of contexts, such as 3.5 ÷ 7 or 
÷ 5 = 0.4, explaining methods and checking that answers are correct. They apply knowledge of multiplication facts to derive related facts; for example, they state the three other known facts when given 23.4 × 2.5 = 58.5, or work out that since 8 × 7 = 56 then 0.8 × 0.7 = 0.56.
Children multiply and divide decimals to solve word problems such as: How many cups holding 0.2 litres can be filled from three 1.5 litre bottles of lemonade? They approximate first to check that their answers are sensible: 'I estimated that the answer must lie between 21 and 24 so it cannot possibly be 225.' They communicate their reasoning and rectify the error. They use symbols to write a formula for the number of glasses g in y bottles, if one bottle holds 5 glasses.
Children use their calculators to solve problems involving patterns and relationships. They use rounding to find an approximate answer as a check. They record the calculations involved using symbols for unknown numbers where appropriate. They look at an answer in its original context and check that it is reasonable. For example, they use a calculator to find the missing numbers and digits in calculations such as 568.1 ÷ = 24.7, or 14 × 6 = 10 868, and explain their reasoning.
Assessment focus: Ma2, Operations, relationships between them
Look for evidence of children understanding that, for addition and multiplication, order does not matter (i.e. the operations are commutative). Look for evidence of children using division as the inverse of multiplication. Look out for children who use trial and improvement to find the missing number in a sentence such as 442 ÷ = 26, and those children who recognise that 442 ÷ 26 will provide the answer because, for example:
26 ×
= 442 and
442 ÷
Children find the squares of multiples of 10 and answer questions such as:
What is 40 squared?
What number when multiplied by itself gives 900?
They find prime factors of two-digit numbers; for example, they find that the prime factors of 28 are 7 × 2 2. They collaborate to find the number between 0 and 50 with the greatest number of prime factors. They solve problems such as:
Find two prime numbers with a total of 30.
Which prime numbers lie between 20 and 30?
Is 96 a prime number? How do you know?
Explain why 87 is not a prime number.
Children explore patterns, sequences and relationships and explain their method and reasoning, using diagrams where helpful. For example:
What are the missing numbers in this sequence? 10, 25,
Write a formula for the nth term of the sequence 3, 6, 9, 12, 15, ...
A line of counters is set out in a pattern: 5 white, 4 blue, 5 white, 4 blue, ...
What colour is the 65th counter?
Make a pattern with blue and yellow beads so that the 57th bead is yellow.
Children hypothesise and investigate systematically. They explore the patterns made by multiples of 2, 3, 4, 5, ... on a 100-square. They predict the numbers whose multiples will form vertical or diagonal lines, or checkerboard patterns. They change the layout to a nine-column grid, and hypothesise about the patterns that the multiples will make. They predict a number whose multiples will be in vertical lines, or what multiples will form diagonal lines. They continue and extend the investigation, asking 'What if...?' questions and making general statements.
Assessment focus: Ma1, Reasoning
As children work with sequences of numbers, including those that arise as they grow shapes, look for the way in which children express a general rule. Look for children who record in words how to work out numbers that will occur later in the sequence. Look out for those children who begin to use algebra to express the general rule for a sequence.
'It goes up in fours.'
'The 20th shape will have 5 + 19 × 4 squares in it.'
'The pattern in the number of squares goes:
4 + 1, 2 × 4 + 1, 3 × 4 + 1
so the nth shape will have n × 4 + 1 squares.'
Children investigate the line symmetry of polygons. They find assorted shapes with two lines of symmetry. They measure the angle between the lines of symmetry of shapes with 2, 3, 4, 5, ... lines of symmetry. They describe what they have found out, commenting on patterns and relationships. They investigate the properties of quadrilaterals, measuring the angles or using paper-folding to establish which angles in a quadrilateral are equal. They investigate the diagonals of quadrilaterals to discover which of them are perpendicular and which intersect at their mid-points.
Assessment focus: Ma3, Properties of shapes
Look for evidence of children’s knowledge of the properties of 2-D and 3-D shapes. Look for the range of criteria that children use to sort shapes, for example numbers of pairs of parallel sides. Look for children’s increasing knowledge of the diagonals of quadrilaterals, for example, which quadrilaterals have diagonals that intersect at their mid-points, that meet at right angles (i.e. are perpendicular to each other) or that are equal. Look for children who know a complete turn is 360° and begin to use the sum of angles at a point, for example to reason about how shapes might fit together at a point.
|
Objectives Children's learning outcomes are emphasised |
Assessment for learning |
|---|---|
|
 |
|
How could you organise the information to help you? 
How can you make sure that you have counted them all? |
|
Estimate the area of a field 38 m wide by 42 m long. |
|
You know that 72 ÷ 8 = 9. What other division and multiplication facts can you derive from this? |
|
How many distinct prime factors has 16? What about 17? |
|
How do you know that 234 is divisible by 3? |
|
Which three prime numbers multiply to make 231? |
|
What is the same about a rhombus and a kite? What is different? |
|
Give me instructions to get me to draw a rhombus using my ruler and a protractor.  |
|
Does your rule for the relationship between edges, faces and vertices work for cylinders and cones? |
| Activities | PDF 1MB |
| Activity 61 - Make five numbers |
|
Objectives for Springboard intervention unit |
Springboard unit |
|
Use a given relationship expressed in words to develop a sequence and describe in words the rule for a given sequence |
Springboard 6 Unit 21 (PDF 379KB) |
| Diagnostic focus | Resource |
| Is not confident when recalling multiplication facts | 4 Y6 ×/÷ DfES 1150-2005 (PDF 104KB) |
Click here for information on different file formats and their usage.
each stand for a different number.
Channel information • Teaching resources • Streaming video of all programmes