Learning Challenge:
To calculate the perimeter and
area of compound shapes.
Which vocabulary are you already familiar with and can
define?
Are there any words in today’s learning challenge that
you are unsure of?
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Calculating Perimeter and Area of Compound Shapes: Vocabulary and Strategies, Study notes of Reasoning
A learning challenge for calculating the perimeter and area of compound shapes. It includes definitions, conversions, strategies for calculation, and problem-solving activities. Students are encouraged to explain their reasoning and workings out.
What you will learn
- How can you calculate the perimeter of a rectangle?
- What is the definition of area?
- How can you calculate the perimeter and area of compound shapes with missing lengths?
- What is the definition of perimeter?
- How can you calculate the area of a rectangle?
Typology: Study notes
2021/2022
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Learning Challenge:
To calculate the perimeter and
area of compound shapes.
Which vocabulary are you already familiar with and can define? Are there any words in today’s learning challenge that you are unsure of?
Steps to success:
- I can explain what is meant by perimeter
- I can explain what is meant by area
- I know the formula for calculating the perimeter of rectangles
- I know the formula for calculating the area of rectangles
- I can calculate missing lengths from compound shapes
- I can calculate perimeters and areas of compound shapes
- I can explain my workings out (reasoning)
- I can show my workings out clearly
Definitions Challenge!
Mathematical Language Definition Perimeter Area Formula Quadrilateral Compound Shape
Rediscover – Converting measurements 10cm =? m 20cm =? m ? M = 50cm 100cm =? m ? M = 105cm 97.6cm =? m 2.00m =? cm 2.1m =? cm 2.15m =? cm ? km = 1000m 1500m =? km 1750m = ?km Apply your learning from last week to convert these metric units of measurement. You will find these conversions on your sheet. Go through as a class and self-mark in green pen!
Possible strategies…
- Add all the sides together
- a + b + c + d
- Double the length, double the width and add them together - 2l + 2w
- Add the length and width and double it
- 2(l+w) Class discussion 10cm 5cm
Find the Perimeter of this shape…
25cm 10cm Which strategy is the most efficient? Which strategy do you prefer? Why?
Find the Perimeter of this shape…
50.5cm 10.25cm Which strategy is the most efficient? Which strategy do you prefer? Why? Does the inclusion of a decimal change your thinking? Can you make any connections between these examples?
3cm 5cm 7cm 3cm 4cm 3cm Perimeter = 18cm Perimeter = 22cm Perimeter = 28cm
Find the Perimeter of these
polygons.
How does your strategy differ? Can you make any generalisations? (E.g. To find the perimeter of a regular hexagon…)
How can we calculate the perimeter when
there are missing lengths?
10cm 10cm 5cm 18cm Let’s calculate the perimeter of this further example. Explain how you can find a numerical value of the missing lengths.
Calculate the perimeter of this shape?
5cm 5cm 3cm 3cm Which strategy is the most efficient? Which strategy do you prefer? Why?
How can we calculate the area of a shape?
Area is the measure of how much space a shape takes up. We measure it in squares such as square centimetres or metres. 10cm 5cm How can you calculate the area of a rectangle? Which strategy would you use?
Area = b x h
Calculate the area of these rectangles. Which unit will we need to express our answers in? 6 cm 1.5 cm 9 cm 2 10 mm 18 mm 180 mm 2 7 m 49 m 7 m 2
12 cm 6 cm 5 cm 7 cm 3 cm
How can we calculate the area for this
compound shape?
We can divide the shape into two quadrilaterals. Is there anything else that we would then need to find? How can we use this information to help us calculate? Can you think of more than one strategy that we can use?
6 cm 5 cm 7 cm 3 cm
5 × 6 = 30 cm
2
7 × 3 = 21 cm
2
How can we calculate the area for this
compound shape?
Calculate the area of both quadrilaterals. How can we use this information to help us calculate? What would we need to do with this information?
30cm
2
+ 21cm
2
= 51 cm
2