AfL Questions for assessing Strand One: Using and Applying
Objectives
LEVEL ONE
Solve problems involving counting, adding, subtracting, doubling
or halving in the context of numbers, measures or money, for
example to 'pay' and 'give change'
AfL questions
Which dominoes in the set have a total of six spots?
How can you solve this puzzle?
I think of a number and add 2. My answer is 14. What was my number?
How do you know you need to add/subtract?
How could you work it out? What could you use to help? Could you put something on paper to help you
remember?
How could you check your answer?
I picked up 12 beads with two hands. That was double the number that Hannah picked up on her first try. How
many did Hannah pick up?
Apples cost 6 pence each. How much do two apples cost altogether?
How can you get started? What could you use to help you with the numbers? How do you know that you need to
double/halve the number?
Could you use beads/coins to show how you know you are right?
Can you make up a problem where you would use 'double 10 20' to solve it?
How are you going to tackle this?
What is the important information that you have?
What approach are you going to use? Why?
How did you do the calculations?
What if you used different numbers or coins, would that change your way of working?
How much money is in the money box?
How did you find out which of these two objects was the lighter, shorter, held the least amount, ...?
I am giving each of you six paper strips. Find two strips in your set which are the same length. Show them to me.
Now find a strip in your set which is longer than this one.
What is each of these coins worth?
In how many different ways can you make 10p using only 2p and 1p coins?
Which of these:
containers holds the most water?
ribbons is the longest?
packages is the heaviest?
How do you know? How could you check?
Look at the five paper strips. Put all your five strips in order, from longest to shortest.
Now put your longest strip on its own on the table. Find two strips which, put together, are the same length as your
longest strip.
Show me how to find half of this strip of paper. How do you know it is exactly half?
At the shop, all packets of crisps cost the same. Hannah buys two packets. She pays 40 pence. How much does
one packet cost?
In how many different ways can you make 30p using only silver coins?
Put this box on one side of the balance (scales). Find two other boxes that together balance this one. [Point to the
box on the balance.] Tell me when both sides balance.
Use the balance (scales) to find out which of these three boxes is heaviest, which is the lightest, and which is in
between.
[Use statements like:
The taller the container, the more water it holds.
The larger the package, the heavier it is.]
Do you agree? Can you find an example that shows that the statement is wrong?
How many different pairs of numbers can you remember that have a total of 10? How can you be sure you have
told me them all?
There were 24 biscuits in a packet. Jack put 7 biscuits on a plate. How many biscuits were left in the packet? How
did you work it out?
LEVEL ONE
Look at this puzzle (or problem). What do you have to find out or do?
What does your drawing tell us?
I have three green grapes and two red grapes. How many grapes do I have altogether? Show me how you worked
it out.
If I wanted ten grapes altogether, how many more grapes would I need?
Look at the grapes on your plate and on mine. How many more grapes do you have than me?
Make up another problem using grapes. Now tell me how to work it out.
There are six people on the bus. Three more get on. How many people are on the bus now? Use these cubes.
Show me how to work out the answer.
Give me a number between 6 and 12. Is it closer to 6 or 12? Show me how you know using this number line.
How many animals altogether are there in the three fields? Explain how you worked out your answer.
Are there any other resources or drawings that would help your description?
Show me that 12 blocks plus 3 blocks is 15 blocks. Show me that 11 cubes minus 3 cubes is 8 cubes.
Make up a story that would mean you need to work out
15 4, 19 - 3.
I want to buy one banana. I have 20p. The banana costs 35p. How much more money do I need? Explain your
method.
I am going to choose two stickers for each of you to buy. Tell me how much it will cost to pay for both stickers.
Now find the right coins to pay for the stickers.
LEVEL ONE
How could you find out which objects are heavier than the bag of sand? What did you use to find out?
Where do the objects that are heavier than the bag of sand belong on the diagram? Why is the box of paper clips
here on the diagram?
What information did you need? What equipment did you use?
How does your table show the things that you found out?
What information did you need? What equipment did you use?
How does your table show the things that you found out?
Describe a puzzle or problem using numbers, practical
materials and diagrams; use these to solve the problem and set
the solution in the original context
Answer a question by selecting and using suitable equipment,
and sorting information, shapes or objects; display results
using tables and pictures
LEVEL ONE
Describe simple patterns and relationships involving numbers
or shapes; decide whether examples satisfy given conditions
Can you see a pattern in the number of objects? Is there a pattern in the shapes? How do you know what comes
next?
Can you talk about the pattern in your own words?
Describe the pattern so that your partner can make it.
Tell me how to continue the pattern.
Make a string of beads for me. First a red one, then a blue one. Carry on threading one red, one blue. What colour
is the sixth bead on your string? What colour will the tenth bead be? The twentieth bead? How do you know?
Can you make a different pattern using the same numbers/shapes?
What comes next? How did you work that out?
Look at these shapes.
Which two of the shapes would fit together to make the shape below? Tick the two shapes.
What is special about the way I have ordered these counters?
Can you make a different pattern using the same counters?
Tell me how to continue this pattern.
Can you make a pattern where the third counter is blue? Is that the only way it could be done?
What is wrong with this pattern? Can you put it right?
LEVEL ONE
How did you find out how many more pencils were needed so that the children had one each?
What did you have to do to check that we had the same number of coins before and after the children worked with
the till?
What did you need to know? How did you work it out? What did you use to help?
How did you solve the problem? Why did you decide to add/subtract? How did the apparatus/your recording help
you? How do you know that your answer makes sense?
How did you get started?
How did you check that your solution works?
How did you find out which of these would hold the most water? How did you begin? How did you decide what you
needed to do?
How could you show someone else that this one holds most?
How does your picture/diagram show what you did and what you found out?
LEVEL TWO
What do you look for when deciding the best order for adding numbers?
Mina and Ben play a game. Mina scores 70 points. Ben scores 42 points. How many more points does Mina score
than Ben? Show me on the 100-square how to work out the answer. Now show me on an empty number line.
Anna has 54p. She buys as many pencils as she can.
Describe ways of solving puzzles and problems, explaining
choices and decisions orally or using pictures
Solve problems involving addition, subtraction, multiplication or
division in contexts of numbers, measures or pounds and pence
How much money will she have left? Use the coins to show me how to work out the answer.
Rosie spent 24p. She spent 8p more than Suzy. How much did Suzy spend? What calculation is needed? How did
you decide?
How did you work out the calculation? How did you record it?
Look at this next problem. What do you need to find out? How do you know you need to
add/subtract/double/halve? What clues are there?
Look at the number line. It shows the sum that Peter did.
Which of these sums did Peter do? Tick it.
5 7 2 = 14
5 6 3 = 14
5 5 4 = 14
5 8 1 = 14
Ella's dad washes some cars. He uses 12 buckets of water. Each bucket has 5 litres of water. How many litres of
water does he use altogether? Show me how to use cubes to work out the answer. Now show me how to work out
the answer using a number line.
There are 60 sweets in a bag. 20 sweets are red. 16 sweets are yellow. The rest are green. How many sweets are
green? Show me how you worked out the answer.
Make up a story that would mean that you needed to work out 2 × 9 then add 16.
Solve these problems. What calculations are needed? How did you decide?
Mina and Ben play a game. Mina scores 70 points. Ben scores 42 points. How many more points does Mina score
than Ben?
I think of a number then halve it. The answer is 9. What was my number?
Rosie spent 48p. Suzy spent 36p more than Rosie. How much did Suzy spend?
How much money is in the hand?
Choose three of these numbers: 14, 15, 16, 17. Add them up. What different totals can you make?
Using coins if necessary, show me how to find the total of 29p and 36p.
Solve these problems. What calculations are needed? How did you decide?
These beads weigh 2 kg. What would a quarter of them weigh?
Susan bought three chocolate bars at 15p each. How much change from 50p did she get?
Jo has three 20p and two 15p stamps. What values can he make using one or more of the stamps?
How many different ways can you find to pay 50p using only silver coins?
A week has 7 days. How many weeks are there in 35 days?
Ellen has a £5 note. She spends £1.99. Draw a ring around each coin she gets in her change.
Write the two missing amounts in this sequence. The same amount is added each time.
£2.95
£3.15
£2.65 £2.75
Look at these [two-step] problems. Tell me what calculations you will do. Show me how to do those
calculations.There are 38 bean bags. Kerry takes 15 and Paul takes 11. How many are left?
There are 60 sweets in a bag. 20 sweets are red. 16 sweets are yellow. The rest are green. How many sweets are
green?Make up a story that would mean that you need to work out 2 × 9 then add 16.
How did you know it was a multiplication/division? How did you work it out?
If you had three 5p coins, how much money would you have? How could you write that down? What sort of
calculation is it? What if, instead of three 5p coins, you had four 5p coins. How would your number sentence
change? How would the answer change?
Make up a story that would mean that you need to work out:
15 24, 18 ÷ 3,
9 5.
LEVEL TWO
Identify and record the information or calculation needed to
solve a puzzle or problem; carry out the steps or calculations
and check the solution in the context of the problem
What do you think the problem or puzzle wants you to do? What information will you use?
Explain how you recorded your solution.
How could you work out the cost of 3 pencils each costing 5p? How could you write this in a number sentence?
What does this mean? 2 2 2 2 2 2
Is there another way of recording this?
Make up another problem like this and tell me how to work it out.
What do you need to find out? How do you know that you need to add/multiply/double/halve?
What helped you to decide how to do this calculation? Could you do it another way?
Tell me how you solved the puzzle.
Why did you write that number sentence? Is there another way you could write it?
Write as many different ways as you can of making 12.
Record your working so that a friend can follow it. How could you check that you have found all the possibilities?
Sam goes to the shop for some buttons. There are two red buttons and four blue buttons on each card of buttons.
How many buttons are there on ten cards?
What do you need to find out?
What was the question that you were asked? So does your answer make sense? How do you know?
Could 20 be the answer? Or 40? How do you know?
There are 15 apples in a tray. Ling has 4 trays of apples.
LEVEL TWO
Follow a line of enquiry; answer questions by choosing and using
suitable equipment and selecting, organising and presenting
information in lists, tables and simple diagrams
How many apples does Ling have altogether?
Show how you work it out.
Which soft drink should we serve at our sports day? What information do you need to answer the question?
Is this a good way to present information? Why?
How could you make the table? What headings do you need?
How could you make the list? Would it help to put the information in order?
Which of these ways of presenting the information helps us best to answer the question?
Someone said that children in our class are in bed by half past 7. How could we find out if that is true?
What do you think we will find? Why?
What information do we need?
How are we going to collect it?
LEVEL TWO
Describe patterns and relationships involving numbers or
shapes, make predictions and test these with examples
Show me the shapes that have: at least one rectangular face, one curved face, eight corners, ...
We have worked out that 3 5 = 8 and 13 5 = 18. Without calculating, tell me what 23 5 will be. What about 63
5?
Write the missing digits to make this correct.
What is special about the way I have ordered these counters?
Can you make a different pattern using the same counters? Can you make me a pattern where the eighth counter
is blue? Is that the only way it could be done?
What is wrong with this pattern? Can you put it right?
Is this picture/object symmetrical? How can you check?
I have begun to make a symmetrical shape with these coloured blocks. Can you complete the shape? How can
you check that it is symmetrical?
Investigate different ways of making 50p using only silver coins.
How many different ways can you find?
Record each different way of doing it.
LEVEL TWO
Present solutions to puzzles and problems in an organised way;
explain decisions, methods and results in pictorial, spoken or
written form, using mathematical language and number
sentences
How did you solve the problem?
How did you decide which information to use?
How did you know which calculations to do?
Explain how you did your calculation.
you draw something or use a number line to help us understand what you did?
What information did you use to solve the problem?
Could you have solved it in a different way?
How is your method different from Judi's method?
How did you know what information to use?
Where did you decide to start? Is there a pattern in your results?
Could you record your results in order to help you see patterns? Have you found all of the ways?
Is there a different way to solve the problem?
Kiz worked out the answer to 7×3 on a number line. Show how Kiz could have worked out the answer on this
number line.
Mr Bell had three pots with four crayons in each pot. How many crayons did he have altogether?
Which one of these would you use to work out the answer to the question?
A4 4
B3 3
C4×3
D3 4
Sita worked out the correct answer to 9 × 5. Her answer was 45. Show how she could have worked out her
answer.
Harry worked out the correct answer to 20 ÷ 5. His answer was 4. Show how he could have worked out his
answer.
LEVEL THREE
Solve one-step and two-step problems involving numbers,
money or measures, including time; choose and carry out
appropriate calculations, using calculator methods where
appropriate
Tell me how to start to solve this problem.
I think of a number and add 12 to it. My total is 38. What is my number?
Show me how to solve the problem using an empty number line, or a 100-square. Write down the calculation that
you would do.
Show me how to solve this problem using an empty number line.
Ling got into the swimming pool at 10:30. She got out at 11:20. How long was she in the pool?
What is the answer to 20÷5? Can you make up a problem that means you need to work out 20÷5 to solve it?
Write down the calculations that you need to do to solve this problem.
Three buns cost 24 pence. What do two buns cost?
Look at this problem.
I buy two comics that cost 30p each. How much change will I get from £1?
Wayne starts to solve the problem by working out 30 2=60. What does this answer tell us? What does he need to
do next?
Eggs are bought in boxes of six. How many boxes do I need to buy if I want 18 eggs?
How would you work out this problem?
What are the answers to 8 4, 8÷4? Make up a problem to match each calculation.
A box holds 35 nuts.
John eats 17 nuts. How many nuts are left?
How many people can have 5 nuts each?
How many nuts are there in 3 boxes?
What calculation did you do each time?
Anna has a 50p coin and three 20p coins. How much is this altogether?
Show how you worked out the answer. How did you decide what calculations to do?
What is the first calculation you will do to solve this problem? What does this answer tell you? What will you do
next?
Look at this problem.
Ella buys a 6p lolly. She pays with a 50p piece. How much change does she get?
Which calculation will you do to solve this problem?
50 6
50 - 6
50 × 6
50 ÷ 6
How did you choose the correct calculation? What unit is the answer in?
Look at this problem.
Ella buys one toy costing 35p and another costing 48p. She pays with a £5 note. How much change does she get?
What two calculations do you need to do to answer this problem? What does the answer to the first calculation tell
you?
Make up a word problem that would lead to the calculation 8×4. How do you recognise that this problem involves
multiplication?
Look at this problem.
There are 20 legs. How many zebras is this?
What calculation did you do? What was it about the problem that made you decide to use this operation?
Make up your own word problem that would lead you to working out the calculation 32 ÷ 4. How do you recognise
that this problem involves division?
Look at this problem.
15 grapes are shared equally onto 3 plates. How many grapes are there on each plate?
What calculation would you do to answer it? Draw a picture to represent the problem. Now look at this problem.
How many bunches of 3 grapes can you get from 15 grapes?
What calculation would you do to answer it? Draw a picture of this problem.
Write your own word problem that involves sharing. Write the calculation that you need to do to solve it.
These are the prices of coconuts and bananas.
Josh buys one coconut and half a kilogram of bananas. How much does he spend altogether?
Explain what you did to get your answer.
How did you know what operation(s) to use?
Could you have done it in a different way? Did you use a calculator? Why/why not?
A piece of rope 204 cm long is cut into 4 equal pieces. Which of these gives the length of each piece in
centimetres?
A. 204 ÷ 4, B. 204 × 4, C. 204 - 4, D. 204 4
How did you know whether to add, subtract, multiply or divide? What clues did you look for in the problem?
What are the important things to remember when you solve a word problem?
Look at this problem:
Jenny can walk 103 metres in 1 minute.
How far can she walk in 2 minutes?
Explain what you should do to get your answer. Show me how to record any calculations you need to do to solve
the problem.
It takes Chris 4 minutes to wash a window. He wants to know how many minutes it will take him to wash 8
windows at this rate. He should:
A multiply 4 × 8
B divide 8 by 4
C subtract 4 from 8
D add 8 and 4
How did you know which of these to choose?
Maria has half a litre of orange juice. She fills some glasses by pouring 100 ml of orange juice into each of them.
How many glasses does Maria fill?
What calculation did you do? Did you use a calculator? Why/why not?
Did you have to do anything to your answer to make it fit with the problem? Tell me what you did.
LEVEL THREE
Represent a puzzle or problem using number sentences,
statements or diagrams; use these to solve the problem;
present and interpret the solution in the context of the
problem
Tell me how you solved this problem. Did you make any notes or drawings to help you? Describe them to me.
Find the total of 3, 4, 5, 6 and 7. Jot down how you work it out. Which numbers did you start with? Why? Explain
what you wrote down.
A number line 48, missing number, 55 with plus 2plus 5 in between the 3 numbers,
Jay drew this number line to work out 48 7. What is the missing number? Why did he split the 7 into 2 then 5?
What do you think the answer to 38 7 would be?
Tell me how you solved this problem. Did you make any notes or drawings to help you? Can you describe them to
me?
Work out 47 29. Show me how you worked it out on a number line.
How many wheels are there on seven cars? What did you write down/draw to help you work this out?
Think of a problem that this picture could represent.
A spider has eight legs. How many legs do six spiders have?
How did you find the answer? What did you write down or draw?
Anna is 118 cm tall. Her brother is 97 cm tall. How much taller is Anna?
Draw a picture or use a number line to help you to find the answer.
Ali had 50 apples. He sold some and then had 20 left. Which of these is a number sentence that shows this?
A
20 = 50
= 50
B 20
C
50 = 20
= 20
D 50
What did you write down to help you answer this problem?
Look at this problem.
Two snakes are 56 cm and 83 cm long. What is the difference in their lengths?
Draw a picture that will help you to solve the problem. What part of your picture shows the difference?
Becky has three £1 coins and four 1p coins in her purse. Write down the amount of money she has altogether.
Consider this problem.
Jack bought some butter for 87p, some flour for £1.27 and some sugar for £2.15. What did he pay altogether?
Explain what you did to get your answer. What made you decide which calculation to do? How would you work out
Jack's change from a £10 note?
Make up a word problem that would lead to each calculation:
9 × 5 63 ÷ 9 54 - 17 48 19 27
What are the important things to remember when you solve a word problem?Sort these problems into those you
would do mentally and those you would do with pencil and paper. Explain why
John wanted to use his calculator to add 463 and 319. He entered 263 319 by mistake. What could he do to
correct his mistake?
A Add 200.
B Add 2.
C Subtract 2.
D Subtract 200.
What could you write down or draw to help you to think about this problem?
How can you check that your answer makes sense?
Jan is 9 years old. Her mother is 31 years old.
How many years older is Jan's mother?
Which of these could you use to work out the answer?
40 - 31 31 9 31 × 9 31 - 9 40 - 9
What could you write down or draw to help you to think about this problem?
One length of the swimming pool is 25 metres.
Jane swims 5 lengths of the pool.
How far does Jane swim altogether?
How can you check that your answer makes sense?
Look at this problem.
Jan is 9 years old. Her mother is 31 years old.
How many years older is Jan's mother?
Circle which of these you could use to work out the answer.
40 31
31 9
31 × 9
31 9 40 9
There are 10 girls and 20 boys in Jill's class. Jill said that there is one girl for every two boys. Her friend Amanda
said that means of all the children in the class are girls.
Is Jill right? Use words or pictures to explain why.
Is Amanda right? Use words or pictures to explain why.
A piece of rope 204 cm long is cut into four equal pieces. Which of these gives the length of each piece in
centimetres?
A 204 ÷ 4 B 204 × 4 C 204 - 4 D 204 4
Sita worked out the correct answer to 16 × 5. Her answer was 80.
Show how she could have worked out her answer.
Harry worked out the correct answer to 70 ÷ 5. His answer was 14.
Show how he could have worked out his answer.
LEVEL THREE
What are you trying to find out? What information are you aiming to collect? How?
What do you think the result will be? Why?
Why have you chosen to collect that information? What will it tell you?
Gulab says that most children in our class walk to school. What data would you suggest that he collects to find out
whether he is right?
What are you trying to find out? What information are you aiming to collect? How?
Why have you chosen to collect that information? What will it tell you?
Your class has collected data about the distances that children travel to school and the type of transport they use.
What questions could you ask to find out more from this data?
What are you trying to find out? What information are you aiming to collect? How?
Why have you chosen to collect that information? What will it tell you?
Imagine that the class is going to organise a tea party for parents. What information would you need to find out?
What are the simplest ways that you can find the information?
LEVEL THREE
Sort the numbers 1 to 20 into two groups: 'multiples of 5' and 'not multiples of 5'. What do you notice? Tell me a
number bigger than 100 that would go in each group.
9 3=6. What is 90 30, and 900 600? How do you know?
What addition calculation would you use to work out 13 8? Why can you use addition to work out subtraction?
16 =9. How would you find the missing number?
All the shapes on this table except one are prisms. Which shape does not belong? How did you recognise the odd
one out?
What fact can help you to work out 60 61?
14 3=17, 14 13=27, 14
=37 . What is the missing number? How do you know?
Mark multiplies 7 by 4 to get 28. What operation will now turn 28 into 7?
Shade more squares so that this rectangle has one line of symmetry.
Suggest a line of enquiry and the strategy needed to follow it;
collect, organise and interpret selected information to find
answers
Identify and use patterns, relationships and properties of
numbers or shapes; investigate a statement involving numbers
and test it with examples
What is special about the shaded numbers in the grid? Suggest some other numbers that would be shaded.
Look at this set of 2-D shapes. Identify the shapes in the set that have one right angle, two right angles, more than
two right angles.
What are the missing numbers in this pattern? How did you find them? 83, 78, , 68, 63, 58,
Find
of 16. Find
of 16. Find
of 16. What do you notice?
Sam says: 'When you count from zero in fours, every number is even.' Is he right? How do you know?
Tell me some numbers that will divide exactly by 2, by 5, by 10. How do you know?
Tell me a number that will divide exactly by 4. How do you know that a number will divide exactly by 4?
Continue this number sequence in both directions.
What are the two missing numbers in this sequence?
Look at these coins.
Which of these amounts can you make using only two coins each time?
61p 52p 20p £1.05 80p
Name a multiple of 6 that is also a multiple of 9.
Using the numbers 6, 8 and 48, create some sentences using the vocabulary product, factor, multiplied by and
multiple of.
Here are some polygons. Decide on a property and classify them according to your property. Explain your
decisions to me.
What colour is each shape? Write it on the shape.
Clues
Red is not next to grey.
Blue is between white and grey.
Green is not a square.
Blue is on the right of pink.
LEVEL THREE
Report solutions to puzzles and problems, giving explanations
and reasoning orally and in writing, using diagrams and symbols
How did you solve this problem?
If you had to solve it again would you do anything differently? Why?
Suppose the problem had these numbers. Would that change the way you would solve the problem?
What diagram did you draw to help you to solve the problem? Did anyone use a different diagram? Which diagram
is more helpful? Why?
What information did you use to solve this problem? Why?
Tell me why you chose this way to record your solution to the problem. Could you have done it differently?
Make up a word problem that could be solved using each calculation: 6 × 5, 30 ÷ 3, 30 7, 26 19
Sort these problems into those you would do mentally and those you would do with pencil and paper. Explain your
decisions.
This grid has two shaded shapes.
Leon says: 'Shape A has a larger area than shape B.' Explain how he could have worked this out.
What have you found out? Does anything surprise you? Why?
What evidence do you have to support your conclusions?
What other questions could you ask now that you have finished your enquiry?
What would you do differently if you carried out the enquiry again?
LEVEL FOUR
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
A fruit pie costs 55 pence. What is the cost of three fruit pies?
Some children go camping. It costs £2.20 for each child to camp each night. They go for 6 nights.
How much will each child have to pay for the 6 nights?
There are 70 children. Each tent takes up to 6 children. What is the least number of tents they will need?
The table shows the cost of coach tickets to different cities.
What is the total cost for a return journey to York for one adult and two children?
How much more does it cost for two adults to make a single journey to Hull than to Leeds?
What information did you use to solve the problem?
How did you decide what calculations to do?
Solve a problem such as:
Three prize pigs weigh 850kg altogether. The heaviest pig is 378kg. The lightest pig is half the mass of the
heaviest pig. How heavy is the middle-sized pig?
How did you work out your answer?
The answer is 15.4kg. What was theb question?
Solve these problems:
A spoonful is 5ml. How many spoonfuls can you get from a bottle that holds one quarter of a litre?
A tin of baked beans weighs 400 grams.
How many grams less than 1 kilogram is this?
Did you have to change any of the information to help you solve the problem, e.g. convert units of measurement?
Did you need to use the calculator to solve the problem? What key sequence did you use? Write instructions for a
friend to solve the problem.
What estimates did you make before you worked out the calculations?
How did you check your answer? Could you have checked it in a different way? How?
Write another problem using the information in this problem.
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.
LEVEL FOUR
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
Tanya has read the first 78 pages in a book that is 130 pages long. Which number sentence could Tanya use to
find the number of pages she must read to finish the book? A 130 78 =
B - 78 = 130
C 130 ÷ 78 =
D 130 - 78 = Tilly's parcel cost 55p to post. She stuck on eight stamps. Each stamp was either 10p or 5p. How
many of each stamp did Tilly stick on her parcel? Show how you worked out your answer.
How did you decide which calculations to do? How did you know whether to add, subtract, multiply or divide? What
clues did you look for?
What does the answer to this step tell you?
You need six drinking straws each the same length. Cut two of them in half. You now have eight straws, four long
and four short. You can make two squares from the eight straws like this.
Arrange your eight straws to make three squares, all the same size. Draw a diagram to show your solution.
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?
LEVEL FOUR
What are you trying to find out? What information are you aiming to collect? How?
What other questions could you ask now that you have finished your enquiry?
What would you do differently if you carried out the enquiry again?
LEVEL FOUR
What is the same about these two numbers (or shapes)? What is different?
Look at this shape (or a shape that is drawn on a square grid). Tell me whether each of these statements is true or
false.
The shape has exactly two right angles.
The shape has two pairs of parallel lines.
The shape has one line of symmetry.
The shape is a quadrilateral.
Look at these four numbers (or shapes). Think of a property which is true for two of them and false for the other
two. Now think of some different properties.
Ella says: 'The sum of two even numbers is always a multiple of 4.' Is she correct? Give some examples to justify
your answer.
Two square tiles are placed side by side. How many tiles are needed to surround them completely?
Plan and pursue an enquiry; present evidence by collecting,
organising and interpreting information; suggest extensions to
the enquiry
Explore patterns, properties and relationships and propose a
general statement involving numbers or shapes; identify
examples for which the statement is true or false
What if three square tiles were laid side by side? Four tiles? Five tiles? How many tiles would be needed if 100
tiles were laid side by side? Explain your answer.
'A number that ends in the digits 52 is always divisible by 4.' Give me an example where the statement is true. Can
you find an example where the statement is false? Why not?
LEVEL FOUR
Explain reasoning using diagrams, graphs and text; refine ways
of recording using images and symbols
Tell me how you solved this problem.
What does this calculation/diagram tell you?
If I doubled this number, what would you have to change?
Tell me how you solved this problem
How was Ann's method different from yours?
What would you do differently if you were to solve this problem again?
Tell me how you solved this problem
What does this calculation/diagram tell you?
What does the answer to this calculation tell you?
Asim and Mike both buy 12 cans of lemonade.
Asim buys 3 packs of 4 cans at £1.20 for each pack.
Mike buys 2 packs of 6 cans at £1.70 for each pack.
Mike says to Asim: 'You paid 50p more than me.'
Is Mike correct? Circle Yes or No.
Explain how you know.
On Sports Day children get points for how far they jump.
Joe jumped 138cm. How many points does he get?
Sam said: 'I jumped 1.5 metres. I get 4 points.' Give a reason why Sam is correct
What does the data tell you about your original question?
Why did you choose this type of table, graph or chart?
What did you find out? What evidence do you have to support your conclusions?
Are your results what you expected or were there any surprises?
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.
Draw a different diagram to show the same information.
What mixed number is equivalent to 1 ? How do you know?
How many sevenths are there in three wholes? What calculation does this involve?
Find an improper fraction that lies between 3 and 4.
. Explain how he found the numerator 13.
Sam says that 2 is equivalent to
LEVEL FIVE
Solve multi-step problems, and problems involving fractions,
decimals and percentages; choose and use appropriate
calculation strategies at each stage, including calculator use
How do you know whether you need to add, subtract, multiply or divide? What clues do you look for?
How did you decide what to do first?
Make up a word problem that could be solved using these calculations:
2 m - (24.2 cm × 5)
(£30.35 £47.11) ÷ 6
2 hours - 45 minutes
What are important things to remember when you solve word problems?
What clues do you look for in the wording of questions? What words mean you need to add, subtract, multiply or
divide?
Make up two different word problems for each of these calculations. Try to use a variety of words.
(17 5) × 6
12.5 ÷ 5 - 0.25
Each tile is 4 centimetres by 9 centimetres.
Here is a design made with the tiles.
Calculate the width and height of the design.
Write down the calculations that you did. Did you use a written method or a calculator? Explain why.
Mr Singh buys paving slabs to go around his pond.
He buys 4 rectangular slabs and 4 square slabs. What is the total cost of the slabs he buys?
Mr Singh says: 'It would cost more to use square slabs all the way round.' Explain why Mr Singh is correct.
How did you decide whether Mr Singh was right or wrong? What calculations did you do?
What clues do you look for in the wording of questions? What words mean you need to add, subtract, multiply or
divide?
This fence has three posts, equally spaced.
Each post is 15 centimetres wide. The length of the fence is 153 centimetres. Calculate the length of one gap
between two posts.
Show me the calculations that you did. Did you use a written method or a calculator? Explain why.
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.
LEVEL FIVE
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
How could you organise the information to help you?
How many triangles can you see in this diagram?
How can you make sure that you have counted them all?
Imagine you have 25 beads. You have to make a three-digit number on an abacus. You must use all 25 beads for
each number you make.
How many different three-digit numbers can you make? How can you be sure that you have counted them all?
How will you organise the information in this problem?
Two boys and two girls can play tennis.
Yasir said: 'I will only play if Holly plays.'
Holly said: 'I won't play if Ben is playing.'
Ben said: 'I won't play if Luke or Laura plays.'
Luke said: 'I will only play if Zoe plays.'
Zoe said: 'I don't mind who I play with.'
Which two boys and which two girls play tennis?
What could you draw to help you solve this?
Does your answer make sense?
How do you know you have identified the maximum number of intersections for 5 streets?
Explain how making a table could help you to solve this problem.
Parveen has the same number of 20p and 50p coins. She has £7.00. How many of each coin does she have?
Compare your table or diagram with those of others around you. Discuss the different representations you have
used. Which do you think is more effective?
Explain how making a table could help you to solve this problem.
30 children are going on a trip. It costs £5 including lunch. Some children take their own packed lunch. They pay
only £3. The 30 children pay a total of £110. How many children take their own packed lunch?
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.
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?
LEVEL FIVE
What information will you need to collect to pursue your enquiry? How will you collect it?
What does this graph tell you? What makes the information in the graph easy or difficult to interpret?
What were the advantages of using a computer?
What does the data tell you about your original question?
What further information could you collect to pursue your enquiry question more fully?
What are you trying to find out? What information are you aiming to collect? How?
What other questions could you ask now that you have finished your enquiry?
What would you do differently if you carried out the enquiry again?
LEVEL FIVE
Describe the relationship between terms in this sequence:
2, 3, 8, 63, ...
Make the ITP '20 cards' generate this sequence of numbers:
1, 3, 7, 13, ...
Suggest, plan and develop lines of enquiry; collect, organise and
represent information, interpret results and review methods;
identify and answer related questions
Represent and interpret sequences, patterns and relationships
involving numbers and shapes; suggest and test hypotheses;
construct and use simple expressions and formulae in words
then symbols (e.g. the cost of c pens at 15 pence each is 15c
pence)
Explain why a square number always has an odd number of factors.
The first two numbers in this sequence are 2.1 and 2.2. The sequence then follows the rule: 'to get the next
number, add the two previous numbers'. What are the missing numbers?
2.1 2.2 4.3 6.5
and each stand for a different number.
= 34
=
What is the value of ? Now make up another problem like this.
How could you use symbols to help you to solve this problem?
Each shape stands for a number. The numbers shown are the totals of the line of four numbers in the row or
column. Find the remaining totals.
Draw the next two terms in this sequence:
Describe this sequence to a friend using words. Describe it using numbers.
How many small squares would there be in the 10th picture?
I want to know the 100th term in the sequence. Will I have to work out the first 99 terms to be able to do it? Is there
a quicker way? How?
How would you change an amount of money from pounds sterling to euros? Record it for me using symbols.
LEVEL FIVE
Explain reasoning and conclusions, using words, symbols or
diagrams as appropriate
Here is a repeating pattern of shapes. Each shape is numbered.
The pattern continues in the same way. What will the 35th shape be? Explain how you can tell.
I am thinking of a number. If you add 3 to my number and then multiply the result by 5, the answer is 35. What is
my number? Show me how you worked it out.
Nadia is working with whole numbers. She says: 'If you add a two-digit number to a two-digit number you cannot
get a four-digit number.' Is she correct? Explain why.
The rule for this sequence of numbers is 'add 3 each time'.
1, 4, 7, 10, 13, 16 ...
The sequence continues in the same way. I think that no matter how far you go there will never be a multiple of 3
in the sequence. Am I correct? Explain how you know.
What is the value of 4x 7 when x = 5? Explain how you know.
Give children a completed table, e.g. for the number of handshakes made between a given number of people.]
What does this table represent? How would you explain this table to other children?
Give me a sentence that explains the general rule.
Can you write that algebraically (using symbols)?