Keeping a focus on learning in mathematics, underpinned by the aims of the National Curriculum, whilst still preparing children so that they demonstrate their understanding in a test situation, is one of the challenges in Y6. Here are seven things to consider:
1 Number Talks
Use the start or the end of the day for Number Talks. Choose some number talks to start from a test question and focus on reasoning and decision making. For example, use Q18 from Paper 1 2016:
122 456 - 11 999 =
(KS2 SATs 2016)
Once different ways of finding the answer have been shared and discussed, ask the children to judge which they think are efficient and which inefficient and why and then to generate their own example calculations that could be solved efficiently in a similar way.
2 Focus on ‘what you know’
Encourage the children to identify things they know, make a displayed class list of these and keep adding to them throughout the year. Draw the children’s attention to the list on a regular basis so that it becomes a habit for them to look for things they know. Force awareness of this by presenting them with questions which use things they know and asking them to identify what it is that they know that is useful. For example:
“These questions all use one thing we know on our class list – what is the thing we know and how is it useful in each of the questions?
- 37 × 2
- 214 ÷ 2
- A group of seven friends wins £14 million on the lottery; what do they each win?”
Ask the children to make up further questions which use the same fact or a group of questions which use a different fact.
3 Build on what you know
Sometimes children struggle to get started with questions. Use the mantra ‘What do you know? Write it down’ and support the children to identify what they know (both from the content of the question and their own related knowledge) and to record it mathematically as a starting point. This gets children involved in the question and often takes them a significant way towards solving it. For example:
From the question a child might record:
6 small bricks = 5 large bricks
1 small brick = 2.5kg
Then from their own related knowledge they might record:
2 small bricks = 5kg
so 6 small bricks = 15kg
They are now halfway to solving the problem.
4 Demonstrate understanding of structures and relationships
In Digging Deeper we identify that noticing things is a key part of fluency. Work with the children to notice things and then to generate their own related examples. For example, the following question involves no actual calculating:
326 ÷ 1 =
(KS2 SATs, 2016)
The children could generate further examples, using all the operations and combinations of operations, challenging themselves to devise what look like complicated calculations and questions but are in fact very simple, for example:
45 678 × 3 722 × 0
27 696 + 38 758 – 27 697
5 Reinforce understanding of place value
Understanding number and our number system is crucial to problem-solving and calculating. Use images such as place value charts, place value mats, place value counters and base ten to explore the multiplicative relationship between different parts of the number system. Make a clear link between understanding whole numbers and understanding decimal numbers; base ten can act as a bridge between the two, with the thousand cube used to represent both 1000 and 1, in a relevant context such as 1000ml = 1l.
Provide opportunities for the children to identify how understanding place value is important in different problems, often in combination with a known fact. For example,
(KS2 SATs 2016)
6 Use models/pictures to make sense of a problem so that it can be solved
Encourage the children to draw something to model a problem and help them solve it and then discuss/share different ways and how effective they are. For example,
A child might draw:
Another child might draw:
A third child might draw:
The children can identify what is the same and what is different about the drawings, consider how each one helps to make sense of the problem and find a solution and try using the different models they have identified as effective to solve further problems.
7 Decide and justify when to use a written method
Present the children with a range of calculations and ask them to identify if there are any for which they would use a formal written method and why. Expect them to make this the last choice they make rather than the default choice, so that they start from what they notice and consider:
- Do I know the answer, because it is something I can recall or because of what I understand about the operation?
- Is the answer obvious because of what I understand about place value/our number system?
- Can I use what I know to find the answer easily?
- Can I use what I know and understand to find the answer, jotting down or modelling my route to help keep track?
- Are the numbers too awkward for working in any of the ways above and a written method is best?
Each time ask the children to generate further examples of calculations which match the ones presented, distinguishing between how they would solve each of them and justifying why.