Seesaw shenanigans
A group of animals has made a seesaw in the woods. How can you make the seesaw balance?
Problem
A group of mice, robins, hedgehogs and owls have made a seesaw in the woods.
Use the interactive seesaw below to have a play with them.
To put an animal on the seesaw, drag it towards a seat. When the seesaw changes colour slightly, you will know the animal is in the right place.
How can you make the seesaw balance?
Try exploring to find lots of different ways.
What else can you discover?
We would love to hear what you find out.
Getting Started
Choose an animal. What do you think will happen when you put that animal on one side of the seesaw? Why? Try it!
Were you right?
Choose another animal to put on the other side of the seesaw. What do you think will happen? Why? Try it!
Can you describe what happened? Why do you think that happened?
Student Solutions
Mia from King's College School in the UK started off by balancing the same animal on both sides of the seesaw, but later she found that she could balance the seesaw by putting different animals on each side. She drew some pictures and used letters to represent each type of animal on the seesaw:
Well done Mia! The top right picture actually shows an owl on the left and two mice and a bird on the right, which would make the seesaw balance.
Vinnie from the UK says:
The mouse weighs 1. The robin weighs twice as much as the owl, which is 2. That means 2 mice on one side and one robin on the other side will balance. The porcupine (hedgehog) weighs 3. That means that a porcupine on one side (3) will balance with a mouse and a robin on the other side (2+1=3). The owl weighs 4. One owl can balance with a porcupine and a mouse (3+1=4) or with 2 robins (2+2=4)
Thank you for that clear explanation, Vinnie. Have a look at Vinnie's ideas - why has he decided that the mouse weighs 1?
Kimaya from Brentwood Preparatory School noticed a mistake in Vinnie's answer:
It says that "The robin weighs twice as much as the owl". I don't think that is right. The robin weighs twice as much as a mouse. The owl weighs twice as much as a robin. Four mice weigh the same as one owl.
Well spotted, Kimaya!
Vinnie and Mia each found four solutions, but some of their solutions are different. Can you see which ones are different? If you think you've found all the ways of balancing the seesaw, we'd love to hear about it. Please email us with your ideas.
Teachers' Resources
Why do this problem?
This task enables learners to explore ideas associated with equivalence, in an intuitive context that may also be familiar. It provides opportunities to develop young children's language of comparison, for example 'heavier', 'lighter', 'greater', 'smaller', 'same', 'equally heavy', 'equal'...
Possible approach
You may like to read the book 'Balancing Act' by Ellen Stoll Walsh as a precursor to this task.
This problem featured in an NRICH Primary webinar in January 2021.
Begin by setting the scene and telling children about the animals in the wood. You could simply show the image of the seesaw and invite pupils to talk to each other about what they notice and what they wonder. Give opportunities for them to share their observations and questions, trying to value all contributions. At this point, some children may talk about their own experiences of seesaws, and you can refer to this as you pose some challenges.
You could say that you're going to sit an owl on one side of the seesaw (indicate which side by pointing). What do they think is going to happen? Invite suggestions and then demonstrate. Give learners time to talk to a partner about what happened, and offer the chance for some pairs to share their thoughts.
Next, explain that you are going to sit a hedgehog on the other side of the seesaw. Can they talk to their partner about what they think will happen? Once again, demonstrate using the interactivity, and allow learners time to talk with their partner again. As you invite pairs to share their interpretations of what happened, encourage them to try to explain what they saw. Draw attention to any appropriate vocabulary they use and introduce useful language yourself if it is not forthcoming from the children themselves.
Use some further examples with the whole class so that children get a good feel for the context. You may like to encourage them to suggest their own set-ups, but ask everyone to predict what will happen each time before demonstrating.
Next, give pairs of children time to explore the seesaw for themselves. The interactivity could be used on a large child-height whiteboard and/or on laptops/tablets/computers. If you have real balances available in your setting, you can use them to explore the ideas in this task using small world toys, soft toys, cubes or... As children discover relationships, encourage them to record what they have found out. Try not to be too prescriptive about how they do this - they may draw pictures, use words, invent symbols... However they choose to record, try to make time to talk with each pair about their discoveries too.
In the plenary, you could ask some pairs to talk about a particular relationship they have discovered. Alternatively, or in addition, you could spend some time looking at different ways to balance the seesaw. Create a balanced seesaw using the interactivity and ask learners what they think will happen if an owl sits on the left and another owl sits on the right? Why? What will happen if both owls get off the seesaw? Understanding that if the two sides are balanced, and then the same change is made to both sides the seesaw stays balanced, is key.
Key questions
What do you think is going to happen when...?
Can you describe what happened? Why did that happen?
Possible support
Practical experience (through the interactivity or a real balance/seesaw) will help all children access this task.
Possible extension
You may like to introduce mathematical notation in terms of the equals and inequality signs. The Settings menu of the interactivity allows you to 'turn on' symbols so that these become visible at the pivot point of the seesaw.