These documents have been produced to support teachers in assessing children with aspects of mathematics identified within the National Curriculum Level Descriptions
and the Assessing Pupils Progress materials.
The ‘Assessment Criteria’ give the breadth of understanding necessary for children to demonstrate a thorough understanding of each aspect of the mathematics curriculum.
The ‘Sample Questions’ offer possible ways to support teachers in assessing children’s competence and understanding of the assessment criteria at the appropriate level.
The questions and ideas have been taken from the Levelopaedia documents from the Gloucestershire Mathematics Team website
http://www.kangaroomaths.com/kenny3.php?page=KassessKS3#lp and also from the Pitch and Expectations documents from the Primary Framework for Mathematics.
The documents can be used in a variety of ways and should be used flexibly to fit in with the structure of the classroom and assessment procedures within the school.
Assessing Pupil Progress – Exemplification for Ma2 Number Level 2
Assessment Criteria
counting sets of objects reliably
- group objects in tens, twos or fives to count them
- uses efficient methods such as counts in sets of two to make groups of ten and then count
groups
begins to understand the place value of each digit, use this to order numbers up to 100
- know the relative size of numbers to 100
- use 0 as a placeholder
- demonstrate knowledge using a range of models/images
- can say what each digit represents in a two-digit number
- know the value of each digit in a two-digit number
- position numbers on a number line
- use knowledge of the relative value of numbers to position them on a partially marked
number line
- order random numbers
- can use base 10 materials to represent a two-digit number
- can use place value cards to represent a two-digit number
- can compare two or more different two-digit numbers and say which is the largest /
smallest
recognise sequences of numbers, including odd and even numbers
- continue a sequence increasing/decreasing in regular steps
- recognise numbers in sequences where the step size is ten or two
- recognise missing numbers in a sequence, where these are: at the beginning; at the end; in
the middle; more than one adjacent missing number
- recognise if given numbers would appear in the sequence when continued
- recognise sequences that start from any number including those which are not multiples of
the count
AF1 – Numbers and the number system
Sample questions
 Have two different arrays of e.g. 10 objects. Ask what is the same
and what is different about these sets.
 How can you change this set so it has the same number (more/less)
than this one?
 How can you sort these sets of objects so that they are grouped in
the same way (e.g. in 2s, 5s, 10s)?
 Convince me that I can’t sort 13 toys into groups of 2.
 How could you count this set of toys? Could you do it in a different
way? Does it matter where you start?
 Show me:
- a number that has more/less tens/units than this number
- using arrow cards the numbers represented by this bead
string/abacus.
 What is wrong with this:
- 27 is bigger than 67?
- 68 is made up of 8 tens and 6 units?
 What is the same and different about these two numbers e.g. 13
and 31?
What is different about these two numbers e.g. 30 and 300? What
do the 0s mean?
 Always, sometimes, never true: A number with 9 units is bigger
than a number with 6 units.
 Convince me that 20 is less than 27.
 Show me a sequence that has 20 in it.
 The number 67 will be in this sequence: 5, 10, 15, 20,…
 Show me two sequences that increase with the same step but start
at different numbers e.g. 1, 3, 5, 7, 9 or 2, 4, 6, 8, 10. What is the
same and different about these? What do you notice about these
sequences? Why?
AF2 - Fractions
begin to use halves and quarters
- understand that a fraction describes part of a whole
- understand that the denominator describes the number of equal parts within a whole unit
- understand that the numerator describes how many of the equal parts are required
- use the concept of a fraction of a number in practical contexts such as sharing sweets
between two to get ½ each, among four to get 1/4 each
- understand that halving is sharing into two equal groups or dividing by 2
- understand that finding a quarter is sharing into four equal groups or dividing by 4
- work out halves of numbers up to 20 and begin to recall them
relate the concept of half of a small quantity to the concept of half of a shape
 shade one half or one quarter of a given shape including those divided into equal regions
 shade in a given fraction of a shape e.g. four squares to represent a ½ of a regular and
irregular shape split into 8 equal parts
 What is wrong: Half of 19 is 9?
 Always, sometimes, never true: 17 divided by 2 is impossible? (You
can share 17 bananas equally between 2 people, but you cannot
sort 17 children equally into 2 groups).
 Convince me that half of 20 sweets is more than half of 10 sweets.
 How many of these 12 squares must I colour in to have coloured
half / quarter?
 Given a number of shapes split into a different number of equal
sections, which of these shapes would help you to find half /
quarter of 16?
Group assessment notes
AF3 – Operations and relationships between them
use the knowledge that subtraction is the inverse of addition
 given three numbers, make all related addition and subtraction number sentences (fact
families), e.g.
6 + 8 = 14, 14 – 8 = 6,
8 + 6 = 14, 14 – 6 = 8
 use the knowledge of fact families to solve number sentences with missing numbers in
different places
 understand that multiplication is repeated addition
 understand that division as grouping is repeated subtraction
 understand that multiplication is the inverse of division and vice versa
understand halving as a way of ‘undoing’ doubling and vice versa
 recognise that halving is the inverse of doubling
 when given the double of a number can work backwards to find the original half or vice
versa
 Show me an addition with an answer of 20. Now show me a
number sentence with the inverse operation.
 Give me a number story/word problem for these number
sentences:
- 3+8=?
- 6 + ? = 15
- 17 – 5 = ?
- ? = 12 – 8
- ? – 9 = 13
- 4x5=?
- 15 ÷ 5 = ?
 Sarah thinks of a number and when she doubles it the answer is 14.
What number did Sarah first think of?
 What is the same/different about:
4 x 2, 4 + 4, double 4?
half of 4, halve 4, ½ of 4, 4 ÷ 2, 2 ÷ 4?
AF4 – Mental methods
use mental recall of addition and subtraction facts to 10
- use addition/subtraction facts to 10 and place value to add or subtract multiples of 10, e.g.
use known facts such as 3 + 7 = 10 and place value to derive 30 + 70 = 100
- use known facts to solve 46 + 3 = 49 using the addition fact of 6 + 3
use mental calculation strategies to solve number problems including those involving money
and measures
– recall doubles to 10 + 10 and other significant doubles, e.g. double 50p is 100p
or £1
- use knowledge of doubles to 10 + 10 to derive corresponding halves
- can choose and use an appropriate mental strategy
 Show me an addition/subtraction number fact with the answer 8.
 Always, sometimes, never true: I can say two addition number
sentences to make any answer up to 10.
 Convince me that 10 take away 4 is not 5.
 What is wrong: To add 1 pound and 30p, I do 1 add 30 which is
31p?
 How can you change this calculation 23 + 8 = 31 so it will help you
answer this problem? I have 33p then I find 8p more, how much
have I got now?
 Always, sometimes, never true: To find the total weight of two
objects I need to add their weights together.
 Convince me that 34p + 58p = 92p
choose the appropriate operation when solving addition and subtraction problems, e.g.
– use their knowledge of addition to solve multiplication problems through
repeated addition
– begin to use repeated subtraction or sharing equally to solve division problems
– given a number sentence and can create a related word problem
– represent a problem practically or using pictures or diagrams to support identification of
the calculation required
 Tell me a story that you would solve by using this addition
16 + 7 = 23. Tell me another.
Tell me a story that you would solve by adding 7. Tell me another.
 15, 19, 4: Order these numbers and add the appropriate operation
so it shows this problem: There were 19 people on the bus then 4
got off. How many were left?
 Always, sometimes, never true: When I need to work out the
change in a money problem, I use subtraction.
 Convince me that you need to use addition/subtraction to solve
this problem.
 Ella’s dad washes some cars. He uses 12 buckets of water. Each
bucket holds 5 litres of water. How much water did he use
altogether?
 Desi and Ella share some money equally. How much do they each
get if there were two 20p coins, two 10p coins and two 5p coins?
AF5 – Solving numerical problems
solve number problems involving money and measures, e.g.
– add/subtract two-digit and one-digit numbers, bridging tens where necessary in
contexts using units such as pence, pounds, centimetres
AF6 – Written methods
record their work in writing, e.g.
– record their mental calculations as number sentences
– record with pictures and diagrams
Show me a jotting/picture/sentence/number sentence that shows
what is happening in this story: A shop had 25 ice creams, then 8 were
sold and there were 17 left.
Always, sometimes, never true: I need to use all the numbers in a
problem to help me find the answer.