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

Monday

Unfold the box
// Unfold a box, add up its faces
⏱ about 20 min

Monday: Unfold the Box

Rocket sets a small cardboard box on the Blueprint Table. "The clubhouse is a box. How much cardboard covers it?"

"Measure every face," Raven says. "But faces are hard to measure when they stand up."

Rocket cuts along four edges with the scissors and presses the box flat. Six rectangles spread out like a cross.

"A net," Raven says. "What do you notice about the rectangles?"

"They come in pairs," Rocket says. "Top and bottom match. Front and back match. The two ends match."

Nova hovers above the flattened box, her light landing on each pair in turn. "Three pairs," she says. "Three multiplications. Then double each."

"Four by two, four by three, two by three," Rocket says, already writing. "Eight, twelve, six. Doubled, fifty-two."

Rocket and Raven lay an unfolded box net and a pyramid net on the Blueprint Table while Nova hovers above.

A net is a solid laid flat

A box 4 cm long, 2 cm wide and 3 cm tall
The net of a box 4 by 2 by 3 cm: six rectangles laid flat

Cut a box along some of its edges and unfold it. The flat shape is its net. Every face of the box is one rectangle of the net.

A box is a rectangular prism. It has six faces in three matching pairs: top and bottom, front and back, the two ends.

Fold the net back up along its creases and the box returns. The net and the box are the same cardboard.

Surface area is the area of the net

This box is 4 cm long, 2 cm wide and 3 cm tall. Top and bottom: 4 × 2 = 8 each. Front and back: 4 × 3 = 12 each.

The two ends: 2 × 3 = 6 each. Add all six faces: 2 × 8 + 2 × 12 + 2 × 6 = 52 square centimeters.

That total is the surface area: all the cardboard it takes to cover the box. It is an area, so the unit is square centimeters.

FACES OF THE BOX
  • Read the question.
  • Tap your answer.
The box is 4 by 2 by 3 cm. What is the area of its top face, in square centimeters?
The box is 4 by 2 by 3 cm. What is the area of its front face, in square centimeters?
The box is 4 by 2 by 3 cm. What is the area of its end face, in square centimeters?
The net of a box 4 by 2 by 3 cm: six rectangles laid flatWhat is the surface area in square centimeters?
SURFACE AREA OF A BOX
  • Read the question.
  • Tap your answer.
The net of a box 5 by 3 by 2 cm: six rectangles laid flatWhat is the surface area in square centimeters?
The net of a box 6 by 4 by 1 cm: six rectangles laid flatWhat is the surface area in square centimeters?
The net of a box 3 by 3 by 5 cm: six rectangles laid flatWhat is the surface area in square centimeters?
StatementTrue or false?
A net is a solid shape unfolded flat.?
A box has eight faces.?
The faces of a box come in three matching pairs.?
2 × 8 + 2 × 12 + 2 × 6 = 52?
WHY THIS EXERCISESix faces in three pairs is the shape of every box, so three multiplications and a doubling always give its surface area.
How many faces does a box have? Type the number.
WHY THIS EXERCISEKnowing there are six faces in three pairs keeps you from missing one when you add.
Try it
Find a small empty box. Cut along edges with scissors until it lies flat, keeping all six faces joined.
Trace around the net on paper. Count the faces and mark the matching pairs with the same letter.
Safety first
Scissors only, never a craft blade, with a grown-up nearby. A grown-up cuts any thick cardboard.
Cut away from your fingers, and put scissors down closed between cuts.
Draw the net of a box 4 by 2 by 3. Label each rectangle with its two edge lengths and its area.

Six faces, three pairs, one total. Tomorrow a pyramid unfolds into a square and four triangles.