They are used to create maps and other scale diagrams. When things are too big to draw on paper, scale factors are used to calculate smaller, proportional measurements.
Floor plans for house designs are drawn on a smaller scale. Answer: 2 Your child may be asked to solve a problem where they are only given part of the information and have to 'work backwards', for example: A triangle was increased by a scale factor of 3 resulting in this new shape: What were the measurements of the original triangle? Answer: 3cm by 5cm by 6cm. Learning about scale factor at home The concept of scale factor is closely linked to ratio , proportion and percentages , where various amounts must be multiplied or divided by the same number to increase or decrease a quantity.
Your child will need to understand the relationship between these concepts. Here are some example of activities they may have to carry out at school, related to scale factor; a lot of them are very useful in the everyday maths we depend on at home, too! Increasing all the ingredients in a recipe by multiplying each one by the same number in order to feed a larger group of people Increasing amounts by a certain percentage, or finding a percentage of an amount.
Working out ratios and proportions of different groups, using their knowledge of times tables. More like this. Now let's create Polygon Q, and remember, Polygon Q is a scaled copy of P using a scale factor of one half. So we're gonna scale it by one half. So instead of this side being four, it's going to be two and instead of this side over here being eight, the corresponding side in the scaled version is going to be four. So there you go, we've scaled it by one half, and now what is our area going to be?
Well our area, and this Polygon Q, and so our area is going to be two times four which is equal to eight. So notice that Polygon Q's area is one fourth of Polygon P's area and that makes sense because when you scale the dimensions of the Polygon by one half, the area is going to change by the square of that. One half squared is one fourth and so the area has been changed by a factor of one fourth or another way to answer this question, Polygon Q's area is what fraction of Polygon P's area?
Well it's going to be one fourth of Polygon P's area. And the big takeaway here is if you scale something, if you scale the sides of a figure by one half each, then the area is going to be the square of that and so one half squared is one over four.
If it was scaled by one third, then the area would be scaled, or the area would be one ninth. If it was scaled by a factor of two, then our area would have grown by a factor of four. Let's do another example. Here we're told, Rectangle N has an area of five square units. Let me do this in a different color. So Rectangle N has an area of five square units.
James drew a scaled version of Rectangle N and labeled it Rectangle P. So they have that right over here. To convert from a scale drawing to real life, measure a line in the drawing and multiply it by the scale factor to find the real length. To convert from real life to a scale drawing, divide the real life measurement by the scale factor. If a map is drawn using a scale factor where 2 cm represents 3.
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