- Questions that draw from Lower Key Stage 2 often see lower success rates. Here is a ‘select a response’ example from 2017 where insecure knowledge about types of lines, and perhaps not looking carefully enough for more than one possible answer, resulted in many children missing out on a mark.
Making fact files, revision posters or other ideas for retrieval practise can really help children remember facts and so fluently recall them when required.
2. Check that understanding and application of place value is secure
Children need to have secure understanding of place value for ordering, rounding, scaling and calculating etc. so do look at the relevant sections in Achieve to support this. However, we also require children to recognise how they can use place value along with known facts to help them calculate more efficiently. Let’s look at applying facts within 10 to powers of 10. What connections do we want children to make?
Children can then use their fluency along with reasoning to see, for example, that 5400 ÷ 9 is 54 hundreds divided by 9 which equals 6 hundreds.
3. Encourage children to describe numbers in different ways
- Describing whole numbers in different ways and thinking about their position in the linear number system gives children skills for both estimating and calculating. Challenge learners to see how many different ways they can describe them e.g. we can say that 445:
- is made up of the place value parts 4 hundreds, 4 tens and 5 ones
- is also 445 ones or 4 hundreds and 45 more ones or 44 tens and 5 more ones etc.
- can be partitioned as 400 + 40 + 5 or as 400 + 30 + 15 or as 300 + 145 etc.
- is 10 times the size of 44.5 but one-tenth of the size of 4450 (or 10 times as small)
- is 5 less than 500 or 5 less than double 250 or 5 less than one-quarter of 200
- is a little less than halfway between 400 and 500 on a number line but is exactly halfway between 440 and 450 etc.
We can also describe fractions and decimals in different ways. How might describing 0.23 not only as 2 tenths and 3 more hundredths, but also as 23 hundredths help with the question below?
4. Focus on mathematical language and reading
- Questions on the reasoning papers can be wordy with a lot of information to process. You can use mathematics problems for group or whole class reading activities. Ask questions, such as: What is the problem about? Which words or information are important?
- The number of ‘explain how you know’ questions has been gradually increasing over time but they are still not answered very successfully.
Try using the ‘Explain how you know’ questions from Achieve and from past papers for shared writing opportunities and a focus on concise and effective explanations. A good starting point is to make use of explanations in the mark schemes and ask children to rank them on a scale. How would you rate this explanation for the question above?
5. Model how to be a mathematician – fluency, reasoning and problem solving
- The tests assess mathematical fluency, reasoning and problem solving skills. By sharing our mathematical thinking and discussing the decisions we make when solving calculations and problems, we can support children’s development of meta-cognition. This provides them with a repertoire of strategies to choose from and the skills to select the most suitable strategy for a given task.
Here are just a few prompts to guide discussion:
- Children can also rank examples of calculations and solved problems in terms of accuracy, efficiency and flexibility. You could focus feedback on working mathematically.
- The steps in the Achieve Revision books will provide further ideas for this and help children move towards greater independence.
- Focus on making connections e.g. children may know how to find common factors but do they know when this might be useful, such as simplifying fractions? Remember to think about the way that manipulatives and pictorial representations expose connections between mathematical ideas.
You can find lots more top tips for children in the Achieve revision series.
Steph King is a mathematics education adviser and author with more than 25 years’ experience in primary education, including senior leadership, subject leadership and 10 years as mathematics adviser for a local authority, before working independently in her own company, AK Mathematical Solutions Ltd.
Steph is an NCETM Professional Development Accredited Lead and writes and presents CPD for schools. She has also been involved in national events for NACE, Rising Stars UK and UKLA.
Steph is an author for publishers Hodder Education, Rising Stars UK, Harper Collins, Pearson, Oxford University Press (OUP), MacMillan Education, GL Assessment and Keen Kite. She works on both national and international writing projects.