This morning I wanted to get to know my new year seven maths group. Having rarely taught mixed ability before I wanted a lesson that made sure every student was engaged, able to succeed and challenged.
Rather than working towards a single learning objective I wanted an activity that would assess their knowledge of place value and use of a calculator while encouraging teamwork and setting the rules and routines. I encouraged the use of calculators rather than mental arithmetic or written methods to increase the pace of the lesson. We would be learning about written methods in future lessons.
The challenge was to arrange the digits 1 to 9 in the diagram and find the greatest difference between the sum of the vertical and horizontal numbers. The students were encouraged to work in small groups but also allowed to work on their own if they wanted to.
At the start of the activity the most common approach was to place the numbers in the diagram at random with the hope of achieving the largest difference by luck rather than skill. Little thought was given to any strategy or use of place value. Once the groups had completed their first attempt I stopped the class to talk through one of their examples.
At this point I didn’t want us to get to distract by negative numbers. Just as long we all understood -54 to be less than the difference in my first example of 594.
We began to form a simple strategy by identifying the need for the sum of the vertical numbers to be greater than the sum of the horizontals. I asked the class to consider how we could increase the value of 124 in the second column be rearranging the digits. An immediate response was to switch the 4 and 1 to make 421 rather than 124. One student suggested we could switch the 1 and 9 in the top row to decrease the value of the horizontals.
I now asked the class to suggest other changes on their mini-whiteboards. From their response it was clear the majority were ready to work independently.
For the next five minutes the students worked more strategically to create the greatest difference. The most able students realised the importance of numbers in the first column and the second two in the top row.
I used this time to observe who could work well together, who felt comfortable using a calculator or became embedded with written methods, who needed support beyond that provided by their peers and who needed a further challenge. The further challenge was to make the smallest number possible and investigate any symmetry between the two.
To keep the kids engaged and maintain the pace of the lesson I decided to add a competitive element using the school’s reward policy. I stopped the class and asked which group thinks they have achieved the greatest difference. One student believed they had the greatest difference of 832. However, if, in the next five minutes anyone achieved a greater difference they would earn the reward. The class responded to the challenge! At the end of the activity the greatest difference was found to be 1350 as verified by the group.
The remainder of the lesson consisted of similar problem solving activities with number.
Throughout their first week with me i’ll use a similar approach to get to know my students with problems on shape, timetables and further use of a calculator.
Problem solving lesson on two-way tables and frequency trees.
Three typical exam questions to revise on plotting quadratic, cubic and reciprocal graphs.
Linking cumulative frequency graphs to ratio, percentages and financial mathematics.