Finding the areas of rectangles using side lengths
The purpose of this activity is to support students to find areas of rectangles by measuring and multiplying side lengths.
About this resource
New Zealand Curriculum: Level 4
Learning Progression Frameworks: Measurement sense, Signpost 5 to Signpost 7
These activities are intended for students who understand how to use metric units of measure to find lengths. When working with units, they should understand the following:
- Units relate to the attribute being measured (for example, length is measured with iterations of length).
- Identical units need to be used when measuring.
- Units should be tiled (or iterated) with no gaps or overlaps to create a measure.
- Units can be equally partitioned into smaller units when greater accuracy is needed.
Students should also know how to use a measurement scale, such as a ruler or tape measure. They should be familiar with the most common metric units of length, metres, centimetres, and possibly millimetres, though they may not be able to convert measures (e.g., 45cm = 450mm). Students should also have a partial or full grasp of their basic multiplication and division facts.
Finding the areas of rectangles using side lengths
Achievement objectives
GM3-2: Find areas of rectangles and volumes of cuboids by applying multiplication.
Required materials
- rectangles of various sizes with whole-number-of-centimetres dimensions. (See slide 3 of the Finding the areas of rectangles using side lengths)
- rulers
- unit place value blocks – 1 cm3 (optional) or Grid paper
- calculators
See Materials that come with this resource to download:
- Finding the areas of rectangles using side lengths (.pptx)
- Grid paper (.pdf)
1.
Show students slide 1 of the PowerPoint, Finding the areas of rectangles using side lengths.
- What is the area of this notebook?
- How will you work out the area?
Let students discuss a strategy to try. Roam and look to see that they:
- notice that the side lengths are measured in centimetres
- understand that area is the amount of flat space enclosed by the rectangle
- consider using square units that are 1cm x 1cm (these are called 1 square centimetre and written as 1 cm2)
- consider using multiplication, as in 14 x 10 = 140 cm2.
2.
Discuss the strategies students use. Animate slide 2 to show how an array of square centimetres might be visualised and the units counted. Alternatively, draw a rectangle that is 14 cm x 10 cm and fill it with unit place value (Dienes MAB) blocks.
Use place value knowledge to work out that 14 x 10 = 140 cm2. Draw attention to the meaning of the different numbers and symbols in the expression.
You might introduce relevant te reo Māori kupu such as roa (length), tapawhā hāngai (rectangle), and horahanga (area).
3.
Pose similar problems using the rectangles on slide 3. These could be photocopied for the students. Take care that the rectangles have whole numbers of centimetres as dimensions.
- Encourage students to measure the side lengths accurately. Look for them to begin measurements at zero and use whole numbers of centimetres when measuring. Allow the use of calculators if needed, and encourage students to use multiplication to find the areas. Fill each rectangle with place value cubes or place a 1cm2 grid over each rectangle to check the calculations.
1.
Pose problems where the students are given the side lengths in centimetres and asked to work out the areas. Choose several different-sized books from the reading corner or library.
Get one student to measure the side lengths. Draw a picture of the problem by tracing around the book and recording the dimensions.
Look to see that students:
- Interpret the rectangle as an array of unit squares, when asked. A good question is “Can you draw a single square centimetre in the bottom right corner?”
- Use multiplication, with support from a calculator if needed, to find the area.
- Express the area using equations and measures, e.g., 30 cm x 20 cm = 600 cm2.
2.
Pose problems about finding the areas of shapes that can be partitioned into rectangles. For example, find the area of this U-shaped house.
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