It's a wrap
This is a level 4 measurement activity from the Figure It Out series. It is focused on investigating areas and perimeters of cuboids. A PDF of the student activity is included.
About this resource
Figure It Out is a series of 80 books published between 1999 and 2009 to support teaching and learning in New Zealand classrooms.
This resource provides the teachers’ notes and answers for one activity from the Figure It Out series. A printable PDF of the student activity can be downloaded from the materials that come with this resource.
Specific learning outcomes:
- Investigate areas and perimeters of cuboids.
It's a wrap
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
- Figure It Out, Levels 3–4, Measurement, "It's a wrap", page 22
- ruler, scissors, string or ribbon
- a newspaper
- different-sized cardboard boxes
- a classmate
See Materials that come with this resource to download:
- It's a wrap activity (.pdf)
Activity
Before the students begin question 1, they could wrap up a box with newspaper so they understand how the paper wraps around the box, especially around the ends, and how much paper is needed.
A common mistake is to assume that the width of the piece of paper is the length of the box plus two times the height of the box. If the students make this mistake, point out that the paper needs to cover the length of the box and then go only halfway up the height of the box.The other half of the box height will be covered when the paper wraps around the box and folds down. The students could model this to check.
Another potential source of confusion is that the long side of the box, or the length of the box, is used to work out the width of the piece of paper. This is because the length of the paper has to cover the width of the box twice and the height of the box twice. This will usually be longer than the box’s length.
In question 3, the students can express the rules in words or symbols or in any other way as long as the rule is equivalent to the answer shown. After they have a correct rule, you may wish to show them some efficient ways to use symbols to express their rules. For example, using P for paper and B for box: Pw = Bw + Bh + 2 cm and Pl = 2(Bh + Bw) + 2 cm.
Note that the paper length rule can be expressed as Pl = 2Bh + 2Bd + 2, which can be compressed as P1 = 2(Bh + Bd + 1), using the common factor rule.
1.
To get the width of the piece of paper, she took the width of the box, added the height, and then added 2 cm for overlap. To get the length of the piece of paper, she multiplied the depth by 2, added that to the height multiplied by 2, and added 2 cm overlap. For the tape length, she went: (2 x 30 cm) + (2 x 20 cm) + (4 x 15 cm) + 40 cm for tying.
2.
Answers will vary. Teacher to check.
3.
Rules could be expressed as:
- paper width = box width + box height + 2 cm
- paper length = (box depth x 2) + (box height x 2) + 2 cm
- tape length = (2 x box length) + (2 x box width) + (4 x box height) + 40 cm.
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