Lesson 5.65.6 Small Group · Group 2
Start hereWords, worked example, and sentence starters
Learning target I can find the surface area of a solid by using its net, explain why the method works, and use it on a problem I have not seen before.
Why This Matters This is your challenge small group for Lesson 5.6. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| Surface areaSpanish: Área de superficie | The total area of all the flat sides of a solid. | A box 6 × 4 × 2: SA = 2(24) + 2(12) + 2(8) = 88 in² — like wrapping paper needed |
| NetSpanish: Plantilla (desarrollo plano) | A flat shape that folds up into a solid. | unfolded box |
| FaceSpanish: Cara | One flat side of a solid shape. | a cube has 6 faces |
| Two-dimensionalSpanish: Bidimensional | A flat shape with length and width, but no thickness. | a net on paper |
| EdgeSpanish: Arista | The line where two flat sides of a solid meet. | A cube has 12 edges — the lines where two flat faces connect |
| PyramidSpanish: Pirámide | A solid with one base and triangular sides that meet at a point. | square base + 4 triangles |
How it worksWorked example
These numbers are not on your problems. The steps are. Follow them with your own numbers.
Net for a box 5 cm × 3 cm × 2 cm.
- Bottom and top: 5 cm by 3 cm.
- Front and back: 5 cm by 2 cm.
- Two sides: 3 cm by 2 cm.
Answer: 6 rectangles, 3 matching pairs
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
A box is 4 in long, 3 in wide, and 2 in tall. Use its net to find its surface area.
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- This solid has faces shaped like .
- The net needs flat pieces because .
- I attached each to a side of the .
- When the net folds up, the meets the .
Word bank netfacefoldunfoldbasepyramidprismcubetrianglesquarerectangletwo-dimensionalthree-dimensional
Watch out!A common mistake
A common mistake in Surface Area Using Nets is finding the area of only one face from each of the 3 matching pairs and forgetting to double it, instead of counting all 6 faces. For a box that is 9 in × 4 in × 5 in, a student might add just one face from each pair: (9×4) + (9×5) + (4×5) = 36 + 45 + 20 = 101 in², but the net actually has two of each face, so the correct total is 2(36) + 2(45) + 2(20) = 72 + 90 + 40 = 202 in²
Lesson 5.65.6 Small Group · Group 2
Group 2Challenge practice
Learning target I can find the surface area of a solid by using its net, explain why the method works, and use it on a problem I have not seen before.
Why This Matters This is your challenge small group for Lesson 5.6. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.
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1Complete each step, then write the final answer.
A toy chest is 3 ft long, 2 ft wide, and 2.5 ft tall. Paint costs $3 for each square foot. What does it cost to paint every face of the chest?
Show your workFinal answer:
-
2Complete each step, then write the final answer.
6 congruent squares share the 150 square centimeters. A cube has a surface area of 150 square centimeters. How long is each edge?
- 1How many faces does a cube have? Are they the same size?
- 2What is the area of one face?
- 3Which edge length makes a square with area 25?
Final answer: -
3Complete each step, then write the final answer.
A box is 5 in long and 4 in wide. Its surface area is 112 square inches. How tall is the box?
- 1What is the area of the top and bottom together?
- 2How much area is left for the four side faces?
- 3The four sides unfold into one rectangle 18 in long. How tall is the box?
- 4Why is that long rectangle 18 in long?
Final answer: -
4Complete each step, then write the final answer.
A box is 4.5 cm long, 2 cm wide, and 3 cm tall. Find its surface area.
Show your workFinal answer: -
5Complete each step, then write the final answer.
A cube-shaped box needs 216 square inches of paper to cover it with no overlap. How long is each edge?
Show your workFinal answer: -
6Complete each step, then write the final answer.
Kim says boxes with the same volume need the same paper. Box A is 3 in × 3 in × 4 in. Box B is 9 in × 4 in × 1 in. Both hold 36 cubic inches. How much more paper does B need?
Show your workFinal answer: