# Broken calculator

A thinking mathematically targeted teaching opportunity focussed on building flexible strategies, reasoning and relationships

## 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
• MA2-AR-01
• MA2-AR-02
• MA2-MR-01
• MA2-MR-02

• MAO-WM-01
• MA3-AR-01
• MA3-MR-01
• MA3-MR-02

## Collect resources

You will need:

• pencils or markers

• something to write on.

## Watch

Watch Broken calculator video (2:41).

Reach the target number on a calculator that has broken buttons.

### Speaker

[Screen reads – Okay, mathematicians…it’s time to warm up our mathematical brains!]

Ok mathematicians, it's time to warm up our mathematical brains.

[Screen shows calculator with 3 broken buttons, 4, 3 and the plus button. In the top right-hand corner, the screen reads, What can I do? And to the left-hand side of the calculator, it reads Goal: 33.]

Now this is one of my favourite challenges from Dan Finkel.

It's called the broken calculator and what our challenges is, is to see if we can get to 33, make the target number of 33, but we have a few obstacles on our way so, here is sometimes how I play.

What I know is that 3 elevens is 33 so I could go, hey I have one already, but there's a problem on my calculator and that is the 3 buttons broken.

[3 elevens equals 33 is now displayed under the words Goal: 33 as an option on how students could get to the target number of 33 and the number 3 button on the calculator is highlighted to show that it is a broken button.]

Yes, so I can't use it so that one doesn't work but hold on the 2 and 1 is there.

[22 plus 11 equals 33 is now displayed under the words Goal: 33 as another option on how students can reach the target number of 33.]

So, I could say 22 plus 11 is 33, which is a number fact.

But the problem is, the plus button doesn't work.

[The plus button on the calculator is highlighted to show that it is a broken button.]

Oh, this pesky broken calculator.

So ok, what about subtraction? Is there look, there's a subtraction button, so 44 - 11 oh. No 4.

[44 minus eleven equals 33 is now displayed under the words Goal: 33 as another option on how students can reach the target number of 33. The number 4 button is now highlighted to show that it is a broken button.]

Ok, I'm going to have to think a bit harder now.

Can you think hard with me? What are you seeing?

And so, our options are we have to use division or multiplication or subtraction and/or all of them.

And we can't use 3 and we can't use 4. Ah yeah, I I can see that idea too. I think this one will work. Look 66 / 2. Is 33.

[66 divided by 2 equals 33 is displayed under the words Goal: 33 as another option on how students can reach the target number of 33.]

Yeah, I can use the 6 button I can use, we can use the division button and we can use the 2.

Yes, that's one that gets us to 33.

[66 divided by 2 equals 33 under the words Goal: 33 is now highlighted green to show that it was a correct option students could use to reach the target number of 33.]

Nice working together mathematicians.

Ok so your challenge is, what are some other ways that you can find to get to 33 on the broken calculator?

[Screen reads – Over to you!]

Over to you to warm up your brains.

[Screen reads – What’s (some of) the mathematics?]

And let's briefly talk about what's some of the mathematics in this task. So, this task gets you to get you into thinking and working like a mathematician pretty quickly. It's great for practicing your skills and applying your knowledge of numbers and operations.