Jump! What if? Stage 3

This resource focusses on developing flexible multiplicative strategies to calculate distance.

Syllabus

Syllabus outcomes and content descriptors from Mathematics K–10 Syllabus © NSW Education Standards Authority (NESA) for and on behalf of the Crown in right of the State of New South Wales, 2023

• MAO-WM-01
• MA3-MR-01
• MA3-GM-02

Collect resources

You will need:

• measuring tools (for example, a ruler, tape measure, mug, handspan or a teaspoon)

• an object to indicate your height (a stick, spoon or rope)

• writing materials (paper and pencil) .

Watch

Watch the Jump! What if? part 1 video (6:27).

Investigate ways to measure height using informal units.

This video was created with Kimberley from Mullumbimby PS, Kelly from Keiraville PS, Michelle from Lake Heights PS and Olivia from Summer Hill PS.

Transcript of Jump! What if? part 1

[White text on a navy-blue background reads ‘Jump! What if? (Stage 3) From reSolve’. Further white text below reads ‘NSW Mathematics Strategy Professional Learning team (NSWMS PL team)’. In the bottom right corner, the NSW Government red ‘waratah’ logo. In the bottom right corner, the NSW Government red ‘waratah’ logo.]

[Black text on a white background reads ‘You will need...’ Bullet points below (read by speaker). Below, in a still colour image, a purple ruler, 2 tape measures and a spotted mug.]

Female speaker

For today's activity, you will need measuring tools, for example, a ruler, tape measure, mug, handspan or a teaspoon. You will need an object to indicate your height like a stick, spoon or rope. And you will also need some writing materials like some paper and a pencil. Let's play!

[White text on a blue background reads ‘Let’s play!’.]

[On a wooden desktop, a white piece of paper has a plastic kangaroo, a yellow frog, a green grasshopper and a black dot on it. Above each one, handwritten text reads, respectively, ‘Kangaroo 4 times’; ‘Frog 20 times’; ‘Grasshopper 30 times’; and ‘Flea 200 times’.]

Female speaker

Hi, mathematicians. Did you know that a kangaroo can jump 4 times its height? A frog can jump 20 times its height. A grasshopper, 30 times its height. And this little speck here, that's resembling a flea, can jump 200 times its height. And it got me wondering, how far could I jump if I were a kangaroo, a frog, a grasshopper, and a flea? So, today we're going to investigate how far we could jump if we were these animals.

[On a double sheet of white paper, a colour paper cut-out of a kangaroo. A line at the top has an arrow on each end and a number ‘0’ in the top left. Further steps explained by speaker.]

Female speaker

I've been thinking about what it means when somebody says 4 times as many because the fact is that a kangaroo can jump 4 times its height. So, I have this picture of a kangaroo here, and I'm going to show what 4 times a kangaroo's height would look like.

I have ruled an empty number line on a blank piece of paper. My number line starts here at zero, and this arrow lets me know that it keeps going down this way. And this arrow lets me know it keeps going up this way. To measure your height, you measure from your top of your head to the bottom of your feet. I'm going to lay the kangaroo on its tummy, and I'm going to line its feet up with where I've marked zero, and then I'm just going to use a marker to draw a line at the top of its ears. Oops.

I'm going to translate this kangaroo and repeat what I just did, lining up its feet, at my last mark, and drawing a line at the tip of its ears. Here, we can see the kangaroo's height being measured out one time. And here, we can see the kangaroo's height being measured out 2 times. Now, what I know about 4 is that double 2 is 4. So, I must repeat this process 2 more times, or double it, and then I will have 4 times the kangaroo's height.

[The 4 marks on the line are converted into rectangles. Text inside each rectangle reads ‘One time’, ‘Two times’; ‘Three times’ and ‘Four times’.]

Female speaker

Here is the final picture showing the kangaroo's height being measured out 4 times. First, we measured the kangaroo's height one time. And it looks like this.

[The speaker uses a black marker to draw a dotted line in an arc to each of the different measurement points.]

Female speaker

Then, we measured the kangaroo's height 2 times, and 2 times the kangaroo's height looks like this. Next, we measured what 3 times the kangaroo's height would be, and that looks like this.

[The speaker places extra cut-out kangaroos for each different measurement on the paper.]

Female speaker

Finally, we measured what 4 times the kangaroo's height would be to show how far it could jump because it can jump 4 times its height. And 4 times the kangaroo's height looks like this. So that means that if this kangaroo were real, it could jump this far. Wow! That is a really long jump.

OK. Over to you, mathematicians, to go and work out your height.

[A blonde woman stands against a wall with her arms by her side. A green piece of paper is stuck on the wall behind her head and a line has been drawn across it to mark the top of her head.]

Female speaker

The first thing I'm going to need to do is find out how tall I am or my height. One thing I know about measuring height is that the measure will stay the same whether I'm standing up or laying down.

[The blonde woman lies on a beige carpet floor. A bright green dog lead is folded up at the top of her head.]

Female speaker

It's easier to measure myself when I'm laying down. So today, I'm laying on the floor with my feet against the wall, and I've placed a lead at the top of my head.

[She uses a mug to measure the space between the lead and the wall.]

Female speaker

I'm now using a mug to measure the distance, from the lead to the wall, and this will tell me my height.

[The speaker holds a white mug above a sheet of blank white paper.]

Female speaker

I've just measured my height, using this mug. And I was 16 mugs and a little bit. Now I need to work out how tall I am using this knowledge.

[The speaker places the mug down and uses a blue marker to write on the paper (as read by speaker).]

Female speaker

If I was 16 mugs and a little... or and a little bit, and I estimated or I estimate...this mug is 10 cm long, I know that 16 10s is 160. And I'm going to record the centimetres because I'm recording my height. And I was about this little bit. I can use my relational knowledge that half of 10 is 5, so is...5 would be around here, I'm going to estimate this little bit as 2 cm. Using this knowledge, I can see I've worked out that I'm around 162 cm tall. Using this knowledge, I can see I've worked out that I'm around 162 cm tall.

[White text on a blue background reads ‘Over to you!’.]

Female speaker

Alright, mathematicians. Now it's over to you to go and work out your height, and then come on back, and we'll talk about what's next.

[The NSW Government waratah logo turns briefly in the middle of various circles coloured blue, red, white and black. A copyright symbol and small blue text below it reads ‘State of New South Wales (Department of Education), 2021.’]

[End of transcript]

Instructions

• Measure your height by lying on the floor with your feet against the wall and placing an object (for example, a stick, spoon or rope) at the top of your head to mark your height.

• Measure the distance from the wall to your object using a formal unit such as a ruler or tape measure. If you don't have a ruler or tape measure, use an informal unit such as a mug or teaspoon to measure your height.

• Record your height on a piece of paper. If you are using informal units, estimate the length of your informal unit and use this to calculate your estimated height. For an example see the image below.

Watch

Watch the Jump! What if? part 2 video (6:32).

How far would you jump if you were a kangaroo?

This video was created with Kimberley from Mullumbimby PS, Kelly from Keiraville PS, Michelle from Lake Heights PS and Olivia from Summer Hill PS.

Transcript of Jump! What if? part 2

[On a white sheet of paper, handwritten blue text reads ‘My height is 162cm.’]

Female speaker

I've just calculated that my height is 162cm tall. So now that I know what my height is, let's remind ourselves of the problem we're trying to solve.

[A second sheet of white sheet of paper has handwritten purple text (as read by speaker)]

Female speaker

A kangaroo can jump 4 times its height. How far could you jump if you were a kangaroo? So the next thing I need to do is work out what 4 times my height is, because a kangaroo can jump 4 times its height.

[The speaker uses a blue marker to write the additional questions onto the white sheet of paper.]

Female speaker

What is 4 times 162 cm? Now, I actually don't know 4 times 162cm, but one thing I know about mathematicians is that they use what they know to work out what they don't know or to solve a problem. And one thing I know about 4 is that double 2 is 4. So I think I'm going to use doubling today to help me solve what 4 times 162cm is. To help me keep track of my thinking, I'm going to be recording my progress in a table.

[The speaker places a second sheet of smaller white paper alongside the first (further steps explained).]

Female speaker

I'm going to begin by drawing a large rectangle and then getting my eye in to where I think about half is and drawing a vertical line to halve the rectangle. I'm going to call this side 'Times as many' and the right-hand side, 'Distance of jump.' I'm then going to get my eye in and think about where a third is and I know a third is a little less than a half. So if I get my eye in to where about half is and then know that a third is a bit less, I can make my first third.

I then can think about making two-thirds as halving this section. So if I get my eye in and halve where around that is and draw in a line, I now have three-thirds. I'm going to record one time, 2 times and 4 times. And this is because I'm going to use doubling to help me today. So one and one is 2 and 2 2s are 4. I know that inside 162 is 16 10s and 2 ones.

So one times my height is 16 10s and 2 ones.

[A small colour image of a blonde woman lying down appears at the bottom of the screen. Additional images of the blonde woman are added in a line as mentioned.]

Female speaker

To find out what twice my height is, I can double 16 10s and 2 ones. Double 16 is 32, so I will have 32 10s and double 2 is 4, so I will have 4 ones. I'm going to record that now next to ‘Two times’. Two times my height is 32 10s and 4 ones. Finally, to work out what 4 times my height is, I can double 32 10s and 4 ones. Double 32 is 64 10s and double 4 is 8 ones. That means 4 times my height I'll record over here, 64 tens and 8 ones.

I can rename 64 tens as 640 and I can rename 8 ones as 8. And I can calculate that 640 and 8 is 648. So that means that if I were a kangaroo, I could jump 648cm which is also equivalent or the same as 6 metres and 48cm. Wow, that is a really long jump!

Alright. Over to you mathematicians, to go and find how tall you are by measuring your height and then use what you know about doubling to find out what 4 times your height is and then you will know how far you could jump if you were a kangaroo.

[White text on a blue background reads ‘Over to you!’]

Female speaker

Alright mathematicians. It's over to you now to go and work out what 4 times your height is and then you will know how far you could jump if you were a kangaroo.

[Black text on a white background reads ‘How far could you jump if you were a:’ Further text below (read by speaker) along with green frogs, green grasshoppers and a line of dots (when mentioned).]

Female speaker

Alright mathematicians, over to you now to go and work out how far you could jump if you were a frog, which can jump 20 times its height, then go and work out how far you could jump if you were a grasshopper, which can jump 30 times its height. Finally, work out how far you could jump if you were a flea, which can jump 200 times its height.

[Black text on a white background reads ‘What’s (some of) the mathematics?’. Further text below (read by speaker). A colour image of a purple ruler, spotted mug, and 2 measuring tapes.]

Female speaker

What's some of the mathematics we explored today? We can measure and compare lengths using formal and informal units. Today, I used the informal unit of a mug to measure my height. We also learnt that when we hear 4 times as many, we have 4 of something, or 4 groups of something.

[An image of the colour paper cut-outs of kangaroos positioned on a white sheet of paper.]

Female speaker

We can measure and compare lengths using formal and informal units. Today I used the informal unit of a mug to measure my height. We also learnt that when we hear four times as many, we have four of something or four groups of something.

[The NSW Government waratah logo turns briefly in the middle of various circles coloured blue, red, white and black. A copyright symbol and small blue text below it reads ‘State of New South Wales (Department of Education), 2021.’]

[End of transcript]

Instructions

• A kangaroo can jump 4 times its height!
• Using your height, how far could you jump if you were a kangaroo?

• A frog can jump 20 times its height, a grasshopper can jump 30 times its height and a flea can jump 200 times its height!
• Calculate the following:

• How far could you jump if you were a frog?

• How far could you jump if you were a grasshopper?

• How far could you jump if you were a flea?

Discuss

• If somebody else you live with was a kangaroo, how far could they jump?
• What is the difference between your jump and the jump of someone else you live with, if you were both kangaroos?
• How did you work it out?