Children love making things move – especially if they move fast! “Young Minds Big Maths” is a collaboration between early childhood educators – ECEs – and University mathematicians in the North East UK. In this project, ramp play is a topic that comes up time and again. Children get engrossed in making an object roll as fast as possible (or at least faster than their friends’) or go as far as possible. They might make a small tweak to their set-up: raising the top of the ramp, choosing a longer plank or a different object, and then try again. Did the object roll faster or slower?
It might look like they’re ‘just playing’, but there’s a huge amount of mathematical thinking going on–and there is potential for even more.
In this blog we highlight three areas of mathematical thinking, using examples from our Ramp Play booklet (which you can download for free from youngmindsbigmaths.co.uk/ramp_play).
Shapes in ramp play
There are two crucial components to ramp play: the ramp, and the object to send down it. How fast the object will go, and whether it will roll or slide, partly depend on the shapes of these two things.
Almost all the ramps we saw the children build were straight, made, for example, using wooden planks or lengths of plastic guttering. In this case, you can think of the ramp as the long side (‘hypotenuse’) of a right-angled triangle.
Usually the horizontal side will be the ground and the vertical side will be the support. Mathematicians usually focus on the angle with the horizontal, but the children tended to notice the angle with the vertical — the ‘top angle’.
In their experimentation (which they thought of as just playing) children were developing intuitive mathematical (and physics) knowledge. To enhance their learning, their teachers introduced vocabulary around angles (‘angle’, ‘right angle’, ‘acute’) and the children began to naturally incorporate these words into their speech and play.
Angles were a new concept for most of the children, and initially, there was some confusion. For instance, some believed that longer lines meant a larger angle. Over time, these misconceptions were addressed through conversations and exposure to varied examples in the context of their play, helping the children develop a clearer understanding.
The shape of the object being sent down the ramp is also important: something round (e.g., a spherical ball or a cylindrical piece of wood) will almost always roll, whereas something with angles might ‘get stuck’ and slide along one of its faces (if it moves at all).
The children quickly understood that whether something would roll, and how fast, depended on lots of factors.
Variables in ramp play
‘Variable’ is a math word for something that can change — like a length, an angle, or a colour. Two important variables in a ramp play scenario are the length of the ramp and its angle with the vertical (or you could think of a different side and angle; in a right-angled triangle everything is fixed by two measurements!). Changing these two variables will almost certainly change how quickly the object moves.
As the children explored the relationships between these variables and the object’s speed, their understanding and confidence steadily increased. They went from noticing and describing what had happened (‘That ramp is steep. The car is going down fast.’) to making general statements and predictions (‘If the ramp is steep, then the car will go fast’). They used their understanding to explain what they saw in terms of the ‘ramp play variables’ and at the same time developed important mathematical vocabulary.
In the left-hand photo above, the boy is pushing things to the limit (an idea mathematicians love!): what happens if you make the ‘top angle’ so big that the vertical side disappears and the ramp triangle collapses to a flat line? The answer is “not much”, unless you push the car. Thankfully, the boy knows exactly what to do to make the car move fast again.
The children took real pride in their explorations and discoveries, and we often saw them exclaim “Watch this!” or “Look!” as they called an adult over to witness the fruits of their hard (but playful) work.
Data in ramp play
As well as wanting their objects to go fast, the children often wanted them to travel far. It’s much easier to measure how far something has travelled than to measure its speed, and so this provided a great opportunity to collect some data.
The children were very invested in their ramp play and in the questions they had posed and were exploring. They decided to take the work a step further by making measurements. They were given the freedom to explore measurement, supported by simple resources and thoughtful, gentle questioning that encouraged curiosity and independence.
One girl chose to measure the distance her object had travelled in footsteps. When another girl (with different shoes!) tried to join in, she told her “I am the measurer ‘cos it’s my shoes, not yours. Your shoes are different.” This exchange showed a strong grasp of what a unit of measurement is – the number of footsteps doesn’t mean the same thing if the shoes aren’t the same size!
As well as thinking of ways to measure, the children also found a range of ways to record the measurements. One popular approach was to draw around the object where it stopped (long pieces of paper had been placed along the ground to enable this). This created a sort of ‘visual dataset’. Some children who were more confident with numbers decided to record their stopping distances in a table.
Either way, the children were able to interpret and discuss their data, and to make observations about which ramp setups seemed, in general, to send their objects a long way.
Did they think of all these approaches on their own? Not exactly. But all that was needed was a few questions: “Can you think of a way to record the distance so you can compare how far the ball went to how far the cylinder went?”
Final thoughts
All in all, the children amazed us by their mathematical thinking. There are doubtless other activities that could spark just as much math (indeed, many other activities have come up in the Young Minds Big Maths project), but ramps are so simple and versatile that they seemed a good focus.
Here are some final thoughts
You don’t need numbers to think about math
At this age (3-4 years) some children might not yet be very confident with numbers, especially large numbers. But so much of math is about comparisons, relationships between different variables and looking at what happens when you change something.
Children can ask their own questions
Math can often feel like something that is done to us, or where there are ‘correct’ questions we should think about. By following the children’s own curiosity, we treat them as mathematicians, and they are likely to have a more engaged and joyful experience of math.
It’s OK not to know the answer
One thing that might make an open exploration of math through ramp play quite daunting is that all sorts of questions might come up, and you might not know the answer. That’s fine – you can investigate together!
Something we (the mathematicians) struggled to figure out was whether a heavier object would roll further than a light one. It has more momentum, but it’s also slowed down more by friction. Maybe it depends on the ground surface? We weren’t sure! But you could think about which variables might be important, and work out together how to test your ideas.
Getting started
Why not leave a ramp and some objects somewhere for your children to find? Let them play with it for a while and see what they do. Do they repeat the same actions lots of times, or do they start varying things? Do they seem keen to make things go faster (or slower!)? Do they want to know how far or fast objects are going?
In our ramp play booklet (download for free), we have lots more examples of children’s ramp play, more reflections from ECEs and mathematicians, and many more suggestions for getting started.
