Maths education adviser Steph King suggests some activities for key stage 2 students who are high achievers in maths
In my role as a mathematics education adviser for a local authority I am frequently asked to provide training for schools focused on the more able mathematicians. In too many cases these pupils leave key stage 1 above or well above national expectation, then make insufficient progress at key stage 2 and fall short of their potential. Here are my key considerations when supporting more able students in mathematics at key stage 2.
Even the able learners have weaknesses
The first step that we so often forget is that even the more able pupils have weaknesses in their mathematics. It is vital to identify these as well as their strengths. There are a range of indicators that I use to help teachers identify more able pupils in the primary phase such as “needs fewer steps in each process”, “enjoys increased pace” and “thrives on independent study”. I always try to be careful that the identification of these behaviours is fair and transparent, without discriminating against particular groups.
Don’t rely on the column method
As children advance through key stage 2, many are taught algorithms (for example, column methods), a step-by-step procedure to calculate the correct answer. In my experience, I find there is an over-reliance on column methods. For example, in one year 6 lesson, the children had the task of finding the difference between 400 and 250 as the first step in a problem. Virtually every child carried out their workings using a column method of subtraction. While this is certainly one way of answering the question, is not the most efficient and should be challenged by teachers.
Choosing the right tool for the job
Aim to challenge new methods and explore a range of strategies that allow children to make choices about the efficient method to use, depending on the numbers involved and their stage in learning. Ensure that children understand how the mathematics they have learned is going to help them in a particular context; choosing the right tool for the job.
Would the children use a mental method or written method to calculate the following sums?
246.29 – 10.29
124 x 501
266 – 283 + 24
64 x 2.5
630 ÷ 35
2/5 of 700
Playing with numbers
From this point I always recommend exploring how to encourage learners to play with numbers and become problem-solvers rather than simply followers of rules.
One activity to support this is to ask the students how many different ways they can solve a calculation, such as 36 x 25. I encourage them to think about all the relationships and connections to help them.
The discussion afterwards may reveal that they recognised that 25 is one quarter of 100, so they calculated 36 x 100 and then found one quarter by halving and halving again.
Others may have rearranged the calculation to find 30 x 25 using their knowledge of 3 x 25 and then multiplying the product by 10 before adding 6 x 25 by using 3 x 25 (already found) and doubling, for example; 750 + 150.
Ways to develop problem solving and reasoning skills
I then try to create opportunities on a regular basis for all pupils to ‘play’ with numbers and operations so they can discover the effect they have on each other.
Solving problems requires students to; make sense of the problem; find a starting point by deciding what needs to be done; have a go, but recognise when you have gone down an incorrect path; recognise when a problem has more than one possible solution and to check that your solution makes sense in the context of the question.
One example of a problem solving activity is to say to the children “I am thinking of a number. When I round my number to the nearest hundred, it rounds to 200. However, when I subtract 10 from my number and round it again to the nearest hundred, it now rounds to 100. What could my number be and is there more than one possibility?” I ensure that each child explains their thinking process.
Another example of a supporting activity would be to ask the children to explain what the next two terms in this sequence are or perhaps reason as to why the next two terms could/might not be say, 40 and 32.
75, 65, 56, 48, _ , _
The application of knowledge and skills
Another example of how children can be challenged to use and apply knowledge and skills through a problem-solving approach is by using a question, such as the KS2 test example below. This question has been chosen to encourage children to think about all the possible relationships and connections to help them solve the problem in different ways.
In a supermarket storeroom there are:
7 boxes of tomato soup
5 boxes of pea soup
4 boxes of chicken soup
There are 24 tins in every box. How many tins are there altogether?
You may initially find that many children either add up the total number of boxes and multiply by 24 or sum the number of tins of each flavour using a variety of column methods.
Prompt the class to consider tools such as rounding, doubling and halving, partitioning in different ways, knowledge of place value and multiplying/dividing by 10, and so on, to guide any further possible methods. Commonly, the floodgates opened and reasoning such as, “Well, we know 10 times the number of tins, so we can simply halve this amount for five times the number of tins” and “24 is nearly 25 and I know there are 4 lots of 25 in 100 so I can adjust my answer” will ensue.
Steph King is a mathematics education adviser for a local authority. She has more than 20 years’ experience in primary education, including senior leadership, subject leadership and more than nine years in her current role. She has extensive knowledge and understanding of mathematics progression and pedagogy and has recently written the latest Essential CPD online training course entitled Supporting the more able in Mathematics at Key Stage 2, in partnership with Rising Stars and Guardian Teacher Network.
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