Grade 6 Mathematics · Unit 5: Solve Area, Surface Area, and Volume ProblemsStandard 6.GR.2

Lesson 5.105.4–5.10 Catch-Up

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can show I am caught up on Lessons 5.4–5.10 by using each lesson's big idea in mixed practice.

Why This Matters Missed a lesson — or just want a refresher? This catch-up station reviews Lessons 5.4–5.10: 5.4 Apply Area Concepts to Solve Problems, 5.5 Determine the Volume of Rectangular Prisms, 5.6 Represent Three-Dimensional Figures in Two Dimensions, 5.7 Determine Surface Area of Prisms, 5.8 Determine Surface Area of Pyramids, 5.9 Area of Regular Polygons, 5.10 Volume of Rectangular Prisms. Work one example from each lesson, then prove you're caught up in the mixed practice.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
Composite FigureSpanish: Figura compuesta A shape made by putting two or more simple shapes together. An L-shaped room = a 12×8 rectangle joined to a 6×5 rectangle; total area = 96 + 30 = 126 sq ft
DecomposeSpanish: Descomponer To break a shape into smaller, simpler shapes. Draw a dashed line across the L-shape to split it into two rectangles — now you can find each area separately
AddSpanish: Sumar Add up the areas of the smaller shapes to get the total. T-shaped hallway: top rectangle = 30 sq ft, bottom rectangle = 28 sq ft → total = 30 + 28 = 58 sq ft
SubtractSpanish: Restar Take away the area of a missing piece from a bigger shape. A 14×10 pool with a 6×4 cutout: 140 − 24 = 116 sq ft of water surface
FormulaSpanish: Fórmula A math rule written with symbols. Rectangle: A = l × w; Triangle: A = ½ × b × h; use the right formula for each piece of a composite figure
VolumeSpanish: Volumen How much space is inside a solid shape. A box 3 × 2 × 4 holds 24 unit cubes, so V = 24 cubic units

How it worksWorked example

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

An L-shape is made of a 5 ft by 4 ft rectangle and a 3 ft by 2 ft rectangle. Find its area.

  1. Find the area of each rectangle: 5 × 4 = 20; 3 × 2 = 6
  2. Add the areas: 20 + 6 = 26
  3. The area is 26 square feet.
  4. A box is 5 units long, 2 units wide, and 2 units tall. Find its volume.
  5. Multiply the length by the width: 5 × 2 = 10
  6. Multiply by the height: 10 × 2 = 20
  7. The volume is 20 cubic units.
  8. A box is 4 in long, 3 in wide, and 2 in tall. Find its surface area.
  9. Find the area of each pair of faces: 2 × (4 × 3) = 24; 2 × (4 × 2) = 16; 2 × (3 × 2) = 12
  10. Add the three pairs: 24 + 16 + 12 = 52
  11. The surface area is 52 square inches.
  12. A rectangular prism is 5 cm long, 4 cm wide, and 3 cm tall. Find its surface area.
  13. Find the area of each pair of faces: 2 × (5 × 4) = 40; 2 × (5 × 3) = 30; 2 × (4 × 3) = 24
  14. Add the three pairs: 40 + 30 + 24 = 94
  15. The surface area is 94 square centimeters.
  16. A square pyramid has a base that is 4 in by 4 in. Its slant height is 5 in. Find its surface area.
  17. Find the area of the base: 4 × 4 = 16
  18. Find the area of the 4 triangle faces: 1/2 × 4 × 5 = 10; 4 × 10 = 40
  19. Add the base and the faces: 16 + 40 = 56
  20. The surface area is 56 square inches.
  21. A regular pentagon splits into 5 equal triangles. Each triangle has a base of 4 cm and a height of 3 cm. Estimate the area.
  22. Find the area of one triangle: 1/2 × 4 × 3 = 6
  23. Multiply by the number of sides: 5 × 6 = 30
  24. The area is about 30 square centimeters.
  25. A box is 4 units long, 2 units wide, and 0.5 units tall. Find its volume.
  26. Find the base area: B = 4 × 2 = 8
  27. Multiply the base area by the height: 8 × 0.5 = 4
  28. The volume is 4 cubic units.

Now you trySame steps, your turn

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

A shape is made of a 6 ft by 2 ft rectangle joined to a 3 ft by 3 ft square. Find its total area.

Answer:

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • Capsules A and B both have V = because × × = × × . I'd choose because .

Word bank Composite FigureDecomposeAddSubtractFormulaVolume3volumesamedifferentdimensionsshape

Watch out!A common mistake

A common mistake in Volume of Rectangular Prisms is rounding a fractional edge length to the nearest whole number before multiplying, instead of using the exact fraction or decimal. For a box that is 2 ft × 1.5 ft × 1 ft, a student might round 1.5 down to 1 and compute 2 × 1 × 1 = 2 ft³, but the correct volume uses the exact edge length: 2 × 1.5 × 1 = 3 ft³

Grade 6 Mathematics · Unit 5: Solve Area, Surface Area, and Volume ProblemsStandard 6.GR.2

Lesson 5.105.4–5.10 Catch-Up

Catch-UpSkill bridge

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can show I am caught up on Lessons 5.4–5.10 by using each lesson's big idea in mixed practice.

Why This Matters Missed a lesson — or just want a refresher? This catch-up station reviews Lessons 5.4–5.10: 5.4 Apply Area Concepts to Solve Problems, 5.5 Determine the Volume of Rectangular Prisms, 5.6 Represent Three-Dimensional Figures in Two Dimensions, 5.7 Determine Surface Area of Prisms, 5.8 Determine Surface Area of Pyramids, 5.9 Area of Regular Polygons, 5.10 Volume of Rectangular Prisms. Work one example from each lesson, then prove you're caught up in the mixed practice.

  1. 1Complete each step, then write the final answer.
    126 m3 m2 m5 m

    A shape is made of a 6 m by 3 m rectangle joined to a 2 m by 5 m rectangle. Find its total area.

    Show your work

    Hint Find each rectangle. They are joined, so add.

    Final answer:
  2. 2Complete each step, then write the final answer.

    A rectangle is 8 ft by 5 ft. A 2 ft by 2 ft square is cut out of it. Find the area that is left.

    Show your work

    Hint The square is cut out, so subtract it.

    Final answer:
  3. 3Complete each step, then write the final answer.
    2 units3 units2 units

    A box is 2 units long, 2 units wide, and 3 units tall. Find its volume.

    Show your work

    Hint Count the cubes in one layer. Then multiply by the layers.

    Final answer:
  4. 4Complete each step, then write the final answer.

    A box is 5 cm long, 4 cm wide, and 2 cm tall. Find its volume.

    Show your work

    Hint Multiply 5 × 4 first. Then multiply by 2.

    Final answer:
  5. 5Complete each step, then write the final answer.
    bottomfrontbacktopleftright3 in1 in3 in

    A box is 3 in long, 3 in wide, and 1 in tall. Find its surface area.

    Show your work

    Hint Find each pair of faces: top and bottom, front and back, left and right.

    Final answer:
  6. 6Complete each step, then write the final answer.

    A cube has edges of 2 cm. Find its surface area.

    Show your work

    Hint A cube has 6 faces, and they are all the same square.

    Final answer:
  7. 7Complete each step, then write the final answer.

    A rectangular prism is 6 in long, 2 in wide, and 1 in tall. Find its surface area.

    Show your work

    Hint Find each pair of matching faces. Then add.

    Final answer:
  8. 8Complete each step, then write the final answer.
    8 cm2 cm10 cm12 cm

    A triangular prism is 2 cm long. Each triangle end has a base of 12 cm and a height of 8 cm. The slanted sides are 10 cm. Find the surface area.

    Show your work

    Hint Find the 2 triangles. Then find the 3 rectangles. Add all 5 faces.

    Final answer:
  9. 9Complete each step, then write the final answer.
    base5 in2 in

    A square pyramid has a base that is 2 in by 2 in. Its slant height is 5 in. Find its surface area.

    Show your work

    Hint Find the base. Then find the 4 triangle faces. Add them.

    Final answer:
  10. 10Complete each step, then write the final answer.

    A square pyramid has a base that is 6 cm by 6 cm. Its slant height is 4 cm. Find its surface area.

    Show your work

    Hint One triangle face is half of 6 × 4.

    Final answer:
  11. 11Complete each step, then write the final answer.
    1 of 45 m10 m

    A square splits into 4 equal triangles from its center. Each triangle has a base of 10 m and a height of 5 m. Find the area.

    Show your work

    Hint Find one triangle: half of base × height. Then multiply by 4.

    Final answer:
  12. 12Complete each step, then write the final answer.

    A regular octagon splits into 8 equal triangles. Each triangle has a base of 2 in and a height of 2.4 in. Estimate the area.

    Show your work

    Hint Find one triangle. Then multiply by 8.

    Final answer:
  13. 13Complete each step, then write the final answer.
    3 in0.5 in2 in

    A box is 3 in long, 2 in wide, and 0.5 in tall. Find its volume.

    Show your work

    Hint Find the base area. Then take half of it, because the height is 0.5.

    Final answer:
  14. 14Complete each step, then write the final answer.

    A box is 4 ft long, 3 ft wide, and 1.5 ft tall. Find its volume.

    Show your work

    Hint Find the base area. Then multiply by 1.5.

    Final answer:

Explain your thinkingCapsules A and B have the same volume (3 ft³) but different dimensions. Why? Which design would you choose and why?

Sentence starter Capsules A and B both have V = ___ because ___ × ___ × ___ = ___ × ___ × ___. I'd choose ___ because ___.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help