It was too good a chance to miss. The Co-op over the road was offering two small pizzas for £1 and the note I’d scrawled to myself during my last tutoring session with Danny said, “Do decimals – pizzas!”
(If you haven’t encountered Danny in my blog before, you can find out more about him by checking this post.)
Oh we’d tried decimals together many times, Danny and me. I’m sure various school teachers and teaching assistants had made similar attempts. The result was always the same. He’d start to twitch, writhe and wave his hands around. His eyes became both wide and wild.
“I don’t DET decimals!” he would complain frantically. “All weird points and stuff. I don’t det dat!”
As we all know, trying to master a new skill while in a state of blind panic is next to impossible. That’s where the pizzas came in.
As I ushered Danny into the kitchen rather than the study and began unwrapping them, he deduced that Christmas had been delayed but was now well and truly here.
“We doing dooting today?” he asked, hopefully.
“Well we need to cook these before we start on the maths, yes,” I told him. “Because we’re going to be doing maths with pizzas.”
We stood watching the pizzas as they browned and bubbled. It took a mere six minutes – just the right amount of time to prepare Danny for the lesson.
“How many pizzas did we put in?” I asked.
“Two,” he grinned, salivating like one of Mr Pavlov’s canine subjects.
“Well when they’re cooked we’ll be leaving one of them whole and cutting the other one up,” I explained.
“Otay,” Danny nodded. “Day smellin’ dood.”
“Yes, and do you think you’ll have room to eat some of the pieces?” I enquired casually.
Danny expressed a certainty that he would.
“But you will have to concentrate hard on the maths, Danny.”
“Oh, I will. I promise I will,” he assured me.
“Because when we cut one up, it will be in pieces – decimal parts of a pizza.”
He didn’t even flinch. “Otay. Do you dint dey’re done now?”
Danny was as good as his word. He sat in the study, watching silently as I transferred a whole pizza to the first plate and carefully cut the second into ten slices.
“This,” I explained, wafting one piece of pizza in front of him, “is smaller than a whole pizza, isn’t it?”
He agreed that it was.
“There are ten pieces, so each one is a tenth. We also call that zero point one of a pizza. Two tenths would be zero point two. Could you show me zero point six?”
No problem. Danny went on to identify all fractions of a pizza to one decimal place.
Next I places three of the tenths onto the plate with the the whole pizza, showing him the plate now held 1.3 pizzas, while the other plate held 0.7. He caught on instantly. Once he’d shown he could move slices around to create 1.5 and 0.5 pizzas respectively, I asked him to lay out 1.6 and 0.3. He held the left-over slice in his hand. I suggested eating it, since there was nowhere else to put it. Danny happily complied.
The next step was to divide one of the slices into ten minuscule slivers of pizza. A couple disintegrated, so that they too had to be eaten. However once he had been shown that these were hundredths of a pizza, he was able to deal with decimals to two places with no difficulty. Within the space of half an hour, Danny was happily recording and constructing numbers and quantities such as 1.72 and 0.53.
“I think you get decimals now, Danny,” I remarked.
His eyes widened, but he was still calm. “I dint I do,” he agreed.
A few more mouthfuls of pizza and several other maths activities later, I set him a final task. We have been playing the ‘ten game’ for months, with little discernible progress. It involves laying ten counters on the table. I swiftly remove some and he is supposed to tell me – instantly – how many I’ve taken by counting those that remain. Number bonds to ten – another long-term sticking point. Tonight, though, his answers were fast and accurate, for the first time ever.
“How did you suddenly get so good at this, Danny?” I asked.
He smiled slowly. “I’m tellin’ myself dat dey’re bits of pizza!” he announced triumphantly. “When I dee dem lite pizza I dan do dem easily.”
Staring happily into the middle distance he remarked dreamily, “Pizzas dan solve any problem. Dey’re brilliant at maths!”