# Balancing numbers 2

A thinking mathematically targeted teaching opportunity, focussed on exploring equivalence using collections of objects and a balance arm

These videos are inspired by the work of Dan Meyer, Three-Act Tasks.

## 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
• MAE-RWN-01
• MAE-RWN-02
• MAE-CSQ-01
• MAE-CSQ-02

• MAO-WM-01
• MA1-NSM-01
• MA1-RWN-01
• MA1-RWN-02

## Collect resources

You will need:

• a pencil
• something to write on.

## Watch

Watch Balancing numbers 2 part 1 (0:54).

Investigate quantities needed to balance the mass of objects.

### Transcript of Balancing numbers 2 Part 1

[No sound in the beginning. The Hulk is placed on one side of the balance and 4 bundles of 10 ice block sticks are placed on the other side. The scale begins to wobble.]

How many ice block sticks are needed to balance the mass of the Hulk?

What's an estimate that's way too high? What's an estimate that's way too low, and what's a reasonable estimate?

[End of transcript]

## Instructions

Estimate the number of ice block sticks needed to balance the mass of The Hulk.

• What's an estimate that is way too high?
• What's an estimate that is way too low?
• What's an estimate that you think is reasonable?

## Watch

Watch Balancing numbers 2 part 2 (1:20).

Investigate quantities needed to balance the mass of objects.

### Speaker

Let's see, how many paddle pop sticks are needed to balance the mass of the Hulk?

5 tens is too heavy, 4 tens is too light. What would you do to solve this problem?

How many paddle pop sticks are needed to balance the mass of the Hulk?

Over to you mathematicians!

[End of transcript]

## Instructions

• What would you do to solve this problem?
• Share your thinking with a fellow mathematician or write down your ideas.
• Revise your estimate: how many paddle pop sticks are needed to balance the mass of The Hulk?

## Watch

Watch Balancing numbers 2 part 3 (2:57).

Investigate quantities needed to balance the mass of objects.

### Transcript of Balancing numbers 2 Part 3

[No sound in the beginning. The Hulk is placed on one side of the balance and 4 bundles of 10 paddlepop sticks are placed on the other side. The scale begins to wobble. When the 5th bundle is added the scale tips the other way. The 5th bundle is broken up and six individual paddle pop sticks are added. Then 15 small bears are added to one side of the balance and The Hulk is added to the other side and they balance. Then the bears are removed and 46 paddle pop sticks are added to balance The Hulk. Then The Hulk is removed and the bears are picked up and carried towards the scale.]

What do you think will happen to the balance scale?

Draw a picture to communicate your thinking.

[End of transcript]

## Instructions

• What do you think will happen to the balance scale?
• Draw a picture to communicate your thinking.

## Watch

Watch Balancing numbers 2 part 4 (0:54).

Investigate quantities needed to balance the mass of objects.

### Transcript of Balancing numbers 2 Part 4

[No sound at the beginning. The scale has 46 paddlepop sticks on one side. 15 bears are picked up and held above the other side of the scale. Then the bears are placed on the scale and it balances.]

What can we say about the mass of the Hulk, the collection of bears, and the collection of paddle pop sticks? Here's what they look like.

Record your thoughts in your maths book or on a piece of paper or share them with a fellow mathematician.

Over to you mathematicians!

Draw a picture to communicate your thinking.

[End of transcript]

## Share or submit

• What can we say about the mass of The Hulk, the collection of bears and the collection of paddle pop sticks?