Maths in pictures: Scale and ratio
19 January 2009
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Show children that maths exists in the real world using images and a little imagination
This article aims to place scale and ratio problems in real-life contexts by using real-life images and creative ideas to inspire and challenge children. It is important to show children that maths exists all around them in their everyday lives. Children often see scale models, or scales on maps, without appreciating that this is the same concept that we talk about in maths lessons.
Begin the lesson by using one of the images on the Interactive resource, ‘Maths in pictures – scale and ratio’ to start a discussion on ratio problems, before moving on to one of the following activities. You can then return to one of the more difficult image problems on the PowerPoint® presentation to assess learning during the plenary.
All readers can access the Interactive resource, ‘Maths in pictures – scale and ratio’ – a PowerPoint® presentation of real-life images to stimulate maths thinking skills. ‘Measurement’ activities and an interactive resource are also available.
1. Using maps
Hand out local street maps to the children, drawing their attention to the scale (1:10,000 is a good one to start with – 1cm is equivalent to 100m). Ask the children to discuss together what they think this means. Ask: What would 1cm on the map be in real life? Challenge the children to find out how far it is from their house to the school. This should start discussions about the best way to measure the route. Should it be measured in a straight line? Or by following the roads that are actually travelled down to reach school? When a consensus has been reached, these distances can be measured and then, using the appropriate ratio, converted into a real-life distance. Extend this task by comparing the distance of the travelled route with the distance ‘as the crow flies’. Can the children find a shorter way to travel to school?
2. A dinosaur in the classroom
Toy models of dinosaurs that are made to a 1:40 scale, for example, are a fantastic resource for this activity. It is best to have one model for each group of children, and it would be even better if they are all different. Display the ratio on the board and discuss what this means. Present the children with their challenge: Would your dinosaur have fitted into our classroom? The children will need to measure the height, length and breadth of their dinosaur before using the ratio to calculate the real-life measurements. They could then measure the breadth and length of the classroom, or to save time you could have these already displayed for them. Discuss as a class whether any of the dinosaurs would fit into the classroom, or if they might have fitted elsewhere in the school.
3. Footprint mystery
Prepare a large footprint (three times the size of a child’s foot) and a small footprint (a tenth of the size of a child’s foot). Tell the children that the footprints belong to a giant and a pixie. Set the children the challenge to find out approximately how tall these creatures are. They will need to find out how much bigger or smaller these footprints are compared to their own. This can be done by seeing how many of the small footprints fit into the length of their own shoe, and how many of their own shoes fit into the length of the giant’s footprint. When this has been discovered, write up the relevant ratios, for example 3:1 and 1:10, on the board. Ask: How can we use these to help us find the answer? The children should then be able to use their own heights to find the giant and pixie’s approximate heights.
An interesting talking point could be: Why do we have different heights for the giant and pixie? It is worth the children noting that although they may have the same shoe size as their friend, they may not be the same height. Extend this task be asking the children to work out how long the giant’s arm might be, how long the pixie’s leg might be, how big their ears might be, and so on.