Finding surface area
The purpose of this activity is to support students to calculate surface areas of cuboids in an efficient manner using multiplication and addition.
About this resource
New Zealand Curriculum: Level 3 to early Level 4
Learning Progression Frameworks: Measurement sense, Signpost 5 to Signpost 7
These activities are intended for students who understand how to use units of measure to find the length and area of rectangles. They should understand the following:
- Units relate to the attribute being measured (for example, area is measured with iterations of area).
- 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 common metric units of length, metres, centimetres, and possibly millimetres, though they may not be able to convert measures (e.g., 45 cm = 450 mm). Students should have a partial or full grasp of their basic multiplication facts and the division equivalents.
Finding surface area
Achievement objectives
GM4-3: Use side or edge lengths to find the perimeters and areas of rectangles, parallelograms, and triangles and the volumes of cuboids.
Required materials
- cardboard boxes with dimensions that are whole numbers of centimetres. You need at least one for every pair of students in your class
- rulers
- calculators
- cardboard or paper, glue sticks, scissors
1.
Presents students with one of the cardboard boxes.
- Suppose I want to paint the outside of this cuboid-shaped box. What amount of surface area would I cover with paint?
If needed, provide students with a definition of horahanga mata (surface area). For example, it is the area on the outside of a shape.
Let students discuss how they would calculate the surface area. Look for them to:
- recognise that the cuboid has six faces, arranged in three pairs of identical parallel faces
- use multiplication to calculate the area of each face.
2.
Model the process of finding the surface area using a diagram like this with the dimensions of the box you have:
Ask students to calculate the area of each rectangle and explain how they calculated it.
Reflect on the calculated areas.
- Did we need to calculate all of these amounts of area?
- Is there a way we could have been more efficient?
Look for students to recognise that the amounts of area are the same for the parallel faces: the top and bottom, the left and right faces, and the front and back faces.
3.
Work together to find the total surface area. Students might explore adding all of the surface area measurements together, or they might explore multiplying the parallel measurements by two and then adding these measurements together. Links could be made here to the order of operations.
4.
Open the box and lay it flat to form a net. Cut off the tabs.
- Does our calculation of surface area look right?
Write dimensions on the surfaces of the net to confirm the calculation.
5.
Organise students into pairs that will encourage peer scaffolding, and extension, and productive learning conversations. Provide each pair with a box and ask them to calculate and record the surface area of the box, then draw a diagram to prove their calculations. Roam and look for students to find the area of all six faces, efficiently and accurately combine the areas to form a total amount of surface area, and record the surface area using the correct unit of measurement, square centimetres (cm2). Calculators should be freely available. Support students by helping them draw a diagram or write measurements on the box, as required.
1.
Give students open-ended challenges like this:
- Design five cuboids that have a surface area of 600 cm2.
- Can you make one that is a cube?
Note that a 10 cm x 10 cm x 10 cm cube has a surface area of 600 cm2.
- What is the volume of that cuboid?
- Why is it significant? (1 Litre)
- Design different nets for a cuboid that is 8 cm x 7 cm x 6 cm.
- Which net is the most compact and will fit on the smallest sheet of cardboard?
Note that packaging is a major industry, and small savings in the area of one box can produce huge savings if large numbers of boxes are produced.
2.
Make links to meaningful, real-world situations in which calculating the total surface is useful.
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