Many parents are aware that mathematics has been a focus at MTS for the last few years. Students know that mathematicians don’t find a solution to a problem easily. They have to work with friends so need good communication and team skills. They need to propose solutions and work through their solutions and if they come up with an answer they need to prove it works in all cases.
An example of this happened when I taught four Magenta recently. Mrs Partridge and I designed some tasks to lead into the teaching of perimeter and area. The problem we presented was called that patio problem. I have reproduced it below.
Tiling A Patio
Alfredo Gomez is designing patios. Each patio has a rectangular garden area in the centre. Alfredo uses black tiles to represent the soil of the garden. Around each garden he designs a border of white tiles. The pictures shown below show the three smallest patios that he can design with black tiles for the garden and white tiles for the border.
Draw patio 4 and patio 5. How many white tiles are in patio 4? Patio 5? Can you work out an efficient or quick way of working how many would be in patio 10? Patio 20? Patio 50? Patio 100?
The children worked in pairs and were simply given the problem and some manipulatives to assist. Many started by using tiles to recreate the patios or drew the patios but soon realised beyond patio 10 it was very difficult to continue with the pattern. Some began by using tables to record their results. Both teachers circulated and asked questions to move their thinking along. Many groups soon saw that totalling the top and bottom rows and adding two (the white tiles from the middle row) assisted. Again we asked them think about how they could explain it as a formula or rule. The answers they came up with were: 2 x L + 2 and 2B + 6.
In this week’s lesson we asked to see if they could come up with a rule for the perimeter of the patios. The responses were P = W + 4; P = 2B + 10 and 2L + 2 W. This then lead to a look at the rule for all rectangles and perimeters.
When we initially designed the task we thought it may be beyond them and had a fall back plan should it be too difficult. We were both amazed by the way the students engaged with the task and the solutions they came up with. It reinforces the idea that we need to have high expectations of our students and they will rise to meet the challenge.
Not all of our maths are investigations or problem solving. Explicit teaching still takes place often during an investigation, and always in a context meaningful for the students.
I know wonderful maths lessons are taking place across the school and that events such as the parent sessions, staff numeracy lunches, involvement in the Primary Maths Challenge amongst many other initiatives have helped lift the profile of mathematics at MTS and made it more challenging yet rewarding for our students.
I thank Mrs Williams for driving this change at Mother Teresa and the teachers for trying new strategies and opening up the doors of their wonderful classrooms.
Congratulations to Cooper Power (5 Pearl) who won this week’s prize. This week’s problem is below.
Think carefully about the question.
Joe ate ½ of a pizza.
Ella ate ½ of another pizza.
Joe said that he ate more pizza than Ella, but Ella said they both ate the same amount. Use words and pictures to show that Joe could be right.