Grade 6 Mathematics · Unit 5: Solve Area, Surface Area, and Volume ProblemsStandard 6.GR.4

Lesson 5.6Represent Three-Dimensional Figures in Two Dimensions

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can find the surface area of a solid by using its net.

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 exampledrawing a net from a solid's attributes

These numbers are not on your problems. The steps are. Follow them with your own numbers.

A triangular prism has 2 triangle bases and 3 rectangular side faces. Draw and describe its net.

List the attributes. bases: 2 triangles side faces: 3 rectangles
Draw the 3 rectangles in a row — these wrap around the outside.
Attach 1 triangle to the top edge of the row and 1 to the bottom edge.
Check: five flat pieces, and every folding edge has a partner.

Answer: The net is a row of 3 rectangles with a triangle on the top edge and one on the bottom.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

A square pyramid has a square base and 4 triangular faces that meet at one point. Draw its net.

List the attributes. base: square side faces: triangles
Draw the base shape first, near the middle of your page.
Attach one triangular face to each side of the base, folding outward.
Check: total flat pieces Any overlaps?

Answer:sketch and description of the net

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 outA 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 — exactly double. Before you submit, ask: 'Did I count both matching faces in each pair, or only one from each pair?'

Grade 6 Mathematics · Unit 5: Solve Area, Surface Area, and Volume ProblemsStandard 6.GR.4

Lesson 5.6Represent Three-Dimensional Figures in Two Dimensions

Version ASupported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

Name Date Period

Learning target I can find the surface area of a solid by using its net.

Part 1Understand the ideamodels and meaning

1Write the letter of the matching item on each line.
Match each concept about rectangular prisms.
1. Top & Bottom faces
2. Front & Back faces
3. Left & Right faces
4. Surface area formula
5. Volume formula
6. Number of faces
- Al × w (two of them)
- Bl × h (two of them)
- Cw × h (two of them)
- DSA = 2lw + 2lh + 2wh
- EV = l × w × h
- F6 faces total
Hint Each face pair uses two of the three dimensions: top/bottom skips height, front/back skips width, left/right skips length.
2Write the name of the correct group on each line.
Put these steps in order for finding the surface area of a 5 × 3 × 2 box.

Groups:
- Identify the three face pairs: 5×3, 5×2, 3×2
- Find area of each: 15, 10, 6
- Multiply each by 2: 30, 20, 12
- Add all pairs: 30 + 20 + 12
- SA = 62 in²
Hint Read the cards: one identifies face pairs, one finds areas, one doubles, one adds, one states the answer.

Part 2Apply itreal-world problems

3Circle the letter of the best answer. Show how you know.
A rectangular prism has l = 6 in, w = 4 in, h = 2 in. What is its surface area?
1. A44 in²
2. B48 in²
3. C88 in²
4. D88 in³
Hint Surface area covers all 6 faces of the 6 × 4 × 2 box — it's not the same as the space inside.
Formula

Put the numbers in

Work it out

Answer with its unit
1. 1Name itWhich measure is asked?
2. 2Write the formulaBefore any numbers.
3. 3SubstituteMatch each letter.
4. 4Unitunits, sq units, or cubic?
4Circle the letter of the best answer. Show how you know.
How many faces does a rectangular prism have?
1. A4
2. B6
3. C8
4. D12
Hint Picture a cereal box in your hands. Turn it: there's a front, a back, two sides, a top, and a bottom.
Show your work
5Circle the letter of the best answer. Show how you know.
Surface area is measured in which type of unit?
1. ACubic units (in³, cm³, ft³)
2. BSquare units (in², cm², ft²)
3. CLinear units (in, cm, ft)
4. DNo units needed
Hint Surface area measures the flat covering on the outside of a solid — like wrapping paper.
Show your work

Part 3Explain and correctreasoning

6Find the mistake. Explain it, then show the correct work.
Spot the Mistake — A Counted Face Was Skipped
1. 1ReadA time capsule box from the net is l = 6 in, w = 4 in, h = 2 in. Find the surface area.
2. 2Label the facesTop/Bottom: 6×4 = 24, Front/Back: 6×2 = 12, Left/Right: 4×2 = 8
3. 3Add the facesSA = 24 + 24 + 12 + 8 + 8 = 76 in² (only one front/back face counted)
Which step has the mistake? Explain what went wrong, then show the correct work.

Hint Count the faces on the net — a box should have 6, not 5.
Correct work
Correct answer:

Explain your thinkingThe total surface area is 158 in². Which face pair contributes the most area? Why does that make sense when you look at the dimensions?

Sentence starter The ___ faces contribute the most area (___ in²) because their dimensions ___ × ___ = ___ are the largest. The total SA is ___ + ___ + ___ = ___ in².

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help

Grade 6 Mathematics · Unit 5: Solve Area, Surface Area, and Volume ProblemsStandard 6.GR.4

Lesson 5.6Represent Three-Dimensional Figures in Two Dimensions

Version BCore practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

Name Date Period

Learning target I can find the surface area of a solid by using its net.

Part 1Understand the ideamodels and meaning

1Complete the table. Show how you found each value.

Find the surface area of each time capsule box using its net.

Box Length Width Height Surface Area
Box A 10 in 6 in 4 in
Box B 7 cm 7 cm 3 cm
Box C 12 ft 5 ft 2 ft

Show your work
2Use the model to solve. Show your work.

What is the combined area of the left and right faces?
Show your work
Answer:
3Write the name of the correct group on each line.
Sort these rectangular prisms from LEAST surface area to GREATEST surface area.

Groups:
- 2 × 2 × 2
- 3 × 3 × 3
- 5 × 4 × 3
- 6 × 4 × 2
- 10 × 1 × 1

Box	Length	Width	Height
Box A	10 in	6 in	4 in
Box B	7 cm	7 cm	3 cm
Box C	12 ft	5 ft	2 ft

Part 2Apply itreal-world problems

4Circle the letter of the best answer. Show how you know.
A cube has edges of 5 cm. What is its surface area?
1. A30 cm²
2. B125 cm²
3. C150 cm²
4. D150 cm³
Formula

Put the numbers in

Work it out

Answer with its unit

Part 3Explain and correctreasoning

5Find the mistake. Explain it, then show the correct work.
Spot the Mistake — One Pair Was Not Doubled
1. 1ReadA time capsule box from the net is l = 7 in, w = 5 in, h = 4 in. Find the surface area.
2. 2Find each face pairTop/Bottom: 7×5 = 35, Front/Back: 7×4 = 28, Left/Right: 5×4 = 20
3. 3Apply the formulaSA = 2(35) + 2(28) + 20 = 70 + 56 + 20 = 146 in² (left/right pair not doubled)
4. 4AnswerSurface Area = 146 in²
Which step has the mistake? Explain what went wrong, then show the correct work.

Correct work
Correct answer:

Explain your thinkingThe total surface area is 158 in². Which face pair contributes the most area? Why does that make sense when you look at the dimensions?

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help

Grade 6 Mathematics · Unit 5: Solve Area, Surface Area, and Volume ProblemsStandard 6.GR.4

Lesson 5.6Represent Three-Dimensional Figures in Two Dimensions

ChallengeExtension

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

Name Date Period

Learning target I can find the surface area of a solid by using its net.

Part 1Understand the ideamodels and meaning

1Complete the table. Show how you found each value.

Compare volume and surface area. Which measurement is bigger for each prism?

Prism Volume (cubic units) Surface Area (square units) Which is numerically larger?
2 × 2 × 2
5 × 5 × 5
10 × 10 × 10

Show your work

Part 2Explain and correctreasoning

2Find the mistake. Explain it, then show the correct work.
Find the Surface Area Error
1. 1Dimensionsl = 10 in, w = 4 in, h = 3 in
2. 2FormulaSA = 2lw + 2lh + 2wh
3. 3CalculateSA = 2(10×4) + 2(10×3) + (4×3) = 80 + 60 + 12 = 152 in²
4. 4AnswerSurface Area = 152 in²
Which step has the mistake? Explain what went wrong, then show the correct work.

Correct work
Correct answer:
3Answer in complete sentences.

Two boxes have the same volume of 60 in³. Box A is 5 × 4 × 3. Box B is 10 × 6 × 1. Which box uses less wrapping paper (has less surface area)? Show your calculations and explain why a more cube-like shape might use less material.
Write your answer

Explain your thinkingThe total surface area is 158 in². Which face pair contributes the most area? Why does that make sense when you look at the dimensions?

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help

Prism	Volume (cubic units)	Surface Area (square units)	Which is numerically larger?
2 × 2 × 2
5 × 5 × 5
10 × 10 × 10