Stage3-Brainwave5


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Brainwave 5

Liquid Measures

Three containers can hold 2L, 3L and 8L of water each.
Using only these three containers, measure out quantities from 1 litre up to 13 litres?
eg To measure 1 litre: Fill 3 litre container. Pour 2 litres into 2 litre container. There is 1 litre left in the 3 litre container. Two steps are required.

Litres	Explanation	No. of Steps
1
2
3
4
5
6
7
8
9
10
11
12
13

If you try to measure out quantities from 1 litre up to 13 litres, which measures take the most steps to make the required quantity of water?

Feature Solution

The feature solution for the problem came from Thomas, Antonio & Connor from Our Lady of the Nativity

What did you have to find out?
We had to find out how to get the measurements correct.

What materials did you use?
A pencil, paper and three brilliant minds.

How did you think? What strategies did you use? How did you solve this problem?
We used the strategy of pouring water from a smaller container into a bigger container (in our heads).

What answers did you come up with?
1: Fill 3 litre container. Pour 2 litres into 2 litre container. This took 2 steps

2: Pour 2 litres into 2 litre container. This took 1 step.

3: Pour 3 litres into 3 litre container. This took 1 step.

4: Pour 2 litres into 2 litre container. Pour 2 litres into 8 litre container. Repeat last step. This took 4 steps.

5: Pour 2 litres into 2 litre container. Pour that into 8 litre container. Fill 3 litre container and pour into 8 litre container. This took 4 steps.

6: Pour 3 litre into 3 litre container. Pour that into 8 litre container. Repeat last step. This took 4 steps.

7: Pour 3 litres into 3 litre container. Pour that into 8 litre container. Fill 2 litre container. Pour that into 8 litre container. Repeat last step. This took 6 steps.

8: Fill 8 litre container. This took 1 step.

9: Pour 3 litres into the 3 litre container. Pour that into the 8 litre container. Repeat last step. Fill 3 litre container. This took 5 steps.

10: Fill 2 litre container. Fill 8 litre container. This took 2 steps.

11: Fill 3 Litre container. Fill 8 litre container. This took 2 steps.

12: Fill 3 litre container. Pour that into 8 litre container. Fill 2 litre container. Pour that into 8 litre container. Repeat last step. Fill 3 litre container. Fill 2 litre container. This took 8 steps.

13: Fill all the containers. This took 3 steps.

Commendable contributors to the problem were:
Dharshu & Diana; Kevin, Jason, David & Anthony; Jahin from Homebush West Public School
Mitch, Noah, Stephen & Luke; Danielle & Danielle; Jessie; Natalie, Abbey & Maddy from Lord Howe Island Central School
Sakshi; William; Alena; Melissa from St Peters Anglican Primary School

Solutions were also sent in by:
Andrew; Alex; Jack; Hayden from Tottenham Central School
Niamh, Rehan & Jenny from Abbotsford Public School