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Geometry and Measurement 6-8 / Week 03 / Friday
5/6
Week 03 · Nets and Surface Area

Friday

Nets all around
// Unfold a box, add up its faces
⏱ about 20 min

Friday: Nets All Around

Rocket turns a shoebox over in his hands. "Thirty by eighteen by twelve. Six faces. I can see the net without cutting."

"What about wrapping a present?" Raven asks. "What do you notice about the paper?"

"It covers every face," Rocket says. "Surface area, plus a bit for the folds."

Nova hovers over the Blueprint Table. "A tent," she says. "A tissue box. A dice cube. All nets."

"And next week we fill the box instead of covering it," Raven says. "Volume."

Rocket is already stacking small cubes inside the shoebox. "How many fit? I have to know." Nova hums. "Monday."

Everyday nets

ThingIts netSurface area
A shoebox6 rectangles in 3 pairs2 × (top + front + end)
A tissue box shaped like a cube6 equal squares6 × side × side
A roof on a square tower4 triangles, no base4 × half × base × height
A gift box with a lidthe net of the box plus the lid facesadd every face you cover
A cardboard modelonly the faces you cutleave out faces already there

Wrapping paper, paint, cardboard and fabric all cover faces. Whenever you cover a solid, you are using its surface area.

Picture the net before you cut or wrap. Count the faces, match the pairs, and add.

How to find any surface area

  1. Picture or draw the net. Count the faces and match the ones that are the same.
  2. Find each different face area with base × height, or half of that for a triangle.
  3. Multiply by how many of each face there are, and add.
  4. Leave out any face that is not covered, and write the units in square units.
EVERYDAY SURFACE AREA
  • Read the question.
  • Tap your answer.
The net of a box 30 by 18 by 12 cm: six rectangles laid flatA shoebox is 30 by 18 by 12 cm. How much paper covers all six faces, in square centimeters?
The net of a box 12 by 12 by 12 cm: six rectangles laid flatA tissue box is a cube 12 cm on each edge. What is its surface area in square centimeters?
A tower roof is a pyramid with a 10 cm base and 12 cm triangles. What is the area of its four triangles?
An open storage bin is 20 by 10 by 8 cm with no lid. What is the area of its four sides, without top or bottom?
WEEK REVIEW
  • Read the question.
  • Tap your answer.
The net of a box 7 by 3 by 2 cm: six rectangles laid flatWhat is the surface area in square centimeters?
The net of a square pyramid: a 5 cm square with four triangles of height 4 cmWhat is the surface area in square centimeters?
The net of a box 4 by 4 by 4 cm: six rectangles laid flatWhat is the surface area in square centimeters?
The shoebox is 30 by 18 by 12 cm. What is the area of one end face?
Week reviewTrue or false?
Surface area is the area of the net.?
A box net has six rectangles in three matching pairs.?
A square pyramid net is a square and three triangles.?
Surface area is measured in cubic centimeters.?
When a face is not covered, leave it out of the surface area.?
WHY THIS EXERCISEThese are the week's rules: unfold, count and match the faces, add, and name square units.
OUR WEEK, IN ORDER
  • ?We unfolded a pyramid into a square and four triangles.
  • ?We unfolded a box into a net of six rectangles and added the three pairs.
  • ?We counted the cardboard sheets for the clubhouse walls and roof.
  • ?We ran Build Lab and measured every face of a real box against the prediction.
WHY THIS EXERCISEEach day built on the one before: one net, a second net, a real check, then a whole plan.
Try it
Find a box at home. Without cutting, sketch its net and label the three different faces.
Measure the edges and work out its surface area. Write it in your Blueprint Book.
Draw the net of a cube with each square labeled 1 to 6, the way a dice is numbered.

A week of unfolding. Tomorrow is Build Day: measure a real box with your family and work out its net.

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