Seven lessons on scaling in Year 4

The idea of scaling is really important in mathematics, and everywhere in the world, so in Year 4 we've spent seven days exploring it in different ways.

❶ We started off by scaling up shapes drawn on grids. We looked at this:

This is what Rod drew

Then we made some scaled up shapes ourselves.  And we had lots of them (sometimes it went wrong the first time, an we had to re-do it):

❷ The next day we made designs with pattern blocks, with a certain ratio: two triangles to one square. (Thanks to John Golden for this idea.)

There were streets, cats

Here are some of them put on a graph:

and two charts made on paper:

What about a pattern that could carry on forever with the same ratio!

❸ Next up, we looked at A-sizes of paper. We use A4 most of the time, but the wonderful thing about this shape rectangle is that you can cut it in half and it's just the same shape scaled down. So, that's what we did, starting at A2 paper:

❹ In our fourth lesson, we looked at two models of the A380. The real A380 is one hundred times longer than the big model, and five hundred times longer than the small one.

Taking the small one, how long would the runway at Blagnac need to be to be the same scale?

We looked on Google maps:

So, about 4km. We divided this by 500 together, and got...

8 metres!

We made some 8 metre runways (they're a bit too thin, but never mind):

❺ Another approach was to scale up squares of Cuisenaire rods:

  ❻ Next we made chocolate cornflake cupcakes. But we needed to scale up the recipe to make the right number of cupcakes.

We also had a go at scaling up with this website

and scaling down with this:

❼ This one was a bit of a challenge. We looked at a clip from Zoolander:

Thanks to Robert Kaplinski for this lesson.

The real question is how many times would you need to scale this model up to make the real school?
And.... how can you work this out?

We thought about this in groups, and came up with different ideas. But it was a hard question!

Cuisenaire rod patterns in Year 4

Last term, in pairs, Year4 had a go at creating sequences of cubes and understanding them. This week they've been trying a similar thing with Cuisenaire rods. And what a great lot of sequences they've created!

More challenging perhaps, is understanding the patterns and how they grow - and this means understanding them mathematically.

Some of the students got straight into the number crunching:

oops! - this one is not quite right!

Others wanted to draw their sequence first:

They had to think hard about the patterns:

Some of the students were willing to talk about their patterns:

Originally posted on the Year 4 blog

Counting Circles in Year 4

We've been trying out "Counting Circles" in Year 4, and it's starting to get into its stride. Obviously there are lots of ways to count, but we've begun to do it in a very particular way (here described by John Golden, based on Sadie Estrella's lessons). This, for us, involves sitting in a circle, and counting from a chosen number in a certain-sized jump. On the first day we started from zero and jumped up in twos, with the teacher writing down the steps on the whiteboard.

Day 1

Easy enough. Then at a certain point (52 on the first day) we stop and the teacher says:

"What number would Marie (for example) be who's three people after 52? Think about it and put your hand up when you've come up with an answer." 

Then the good bit comes: the explanation. "Who could share the way they worked out that it was 58?"

Usually there are a number of explanations, and a number of ways of getting to the answer. Children explain their thinking, and we note it down on the whiteboard.

Day 2

Day 3

Day 4

Day 5

We've been doing this for perhaps five or ten minutes at the start of some of our lessons, then we leave it and go onto something else. 

This last week we've been looking at time on the analogue clock, so it made sense to do a bit of clock counting, following the way the minutes go ("counting in mod 60"):

Day 9: Clock counting

(Apologies - very shaky video!)

The next day was clock counting with jumps of eight (it took two times round the clock to get back to zero).

The day after, jumps of eleven:

Day 11

There were lots of great ways of getting the person three jumps on's number. James was looking at the vertical pattern all the way across. Alya spotted a diagonal pattern. Rod added three to each digit, rembering that the 6 for sixty became zero. And Samyak added 33 and knew that 68 is actually just 8 in clock counting.

It's early days yet. It's been a good moment for us to share our reasoning and see that we often know more than one good method. We'll keep going with it. We'll try new jumps, and also work on not correcting each other's mistakes, and at listening to each other's explanations really carefully.

PS. See the Year 4 blog to see how we later continued with the clock counting patterns on paper to create Clock Flowers.