Maths - Lessons with Grandpa

20th April 2012 at 01:00
Keeping it real in maths can lead to unexpected problems

Students often choose to interpret questions in ways that differ greatly from those imagined by the question-setter. Take this problem on sequences: Grandma gives Henry #163;5 on his third birthday and then increases this amount by #163;2 for each subsequent birthday.

I looked at the question as it shimmered on my whiteboard, and my thoughts ran obediently along the lines prescribed by the setter: "This is about arithmetic sequences."

But what were my students thinking? As I surveyed the room, I could see little appreciation of the mathematics of the situation. The word that had captured them was "Grandma".

For each of my students, that word was summoning up pictures of their own grandmothers. How did the Grandma of the problem compare with their own? In the question, her rule seemed to speak of financial fidelity, of an increasing monetary commitment mirroring a growing love for her grandchild.

But then the question goes on to embrace Grandpa: Grandpa gives Henry #163;5 on his first birthday and then increases this amount by 10 per cent for each subsequent birthday.

Rachel gasped, but failed to see the economic parallel: "So he gets one present from Grandma and another from Grandpa!"

The human aspect of this tale began to take over the lesson. Have Grandma and Grandpa conferred about their gifts? Does the separateness of their giving reflect some deep division in their marriage? Once the first few terms of Grandpa's giving are calculated, it is agreed that he is a bit odd. #163;5, #163;5.50, #163;6.05, #163;6.66, #163;7.32 ...

"So if I say, 'I've seen a scarf for #163;7.33 that I really like, Grandpa'," said Emily, "then he will say, 'Sorry, you are only getting #163;7.32. I have a system, you know.'"

"That's what you get for having a grandparent who's a maths teacher," muttered Lewis.

"And for Christmas, Henry," said Teala, putting on a stern voice, "you will be getting a radian pounds!"

I did my best to drag the class back to the question. On which birthday does the total amount received by Henry from Grandma first exceed #163;650? The answer turned out to be the 26th.

"My grandparents disowned me when I was 15!" cried Daniel.

I am all for real-life problems appearing in classrooms, but does the above question qualify? The question is "real", yet strangely unreal at the same time, which led to my students being distracted from the maths. It was an interesting lesson, but perhaps not in the way that the setter had intended.

Jonny Griffiths teaches at a sixth-form college.


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