Grade 6 Mathematics · Pre-UnitStandard 5.MD.C.5

Lesson 1.41.4 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can construct an argument using equations, drawings, or words, and use volume to defend a recommendation, explain what each part stands for, and build one for a situation I have not seen before.

Start hereWords for this lesson

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

WordWhat it meansExample
argumentSpanish: argumento A chain of reasons — equations, drawings, or words — used to defend your thinking. “Two jumbo boxes hold more, because 400 × 2 = 800 > 720.”
conjectureSpanish: conjetura A mathematical statement you believe is true but have not yet proven. “A bigger box ALWAYS holds more cereal” — believed, not yet proven.
counterexampleSpanish: contraejemplo A single example that shows a statement is not always true. One jumbo box sold half full of air breaks “bigger always holds more”.
volumeSpanish: volumen The amount of space a solid figure takes up, measured in cubic units. 8 in × 3 in × 10 in = 240 cubic inches of cereal space.
cubic unitSpanish: unidad cúbica A cube with edges 1 unit long — the unit used to measure volume. One cube, 1 unit on every edge — the block volume is counted in.

How it worksWorked example

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

Jo claims, “A taller box always holds more cereal.” Box A is 4 in long, 2 in wide, and 10 in tall. Box B is 5 in long, 4 in wide, and 8 in tall. Is Jo right?

  1. Find the volume of Box A: 4 × 2 × 10 = 80
  2. Find the volume of Box B: 5 × 4 × 8 = 160
  3. Compare the taller box to the shorter box: 80 < 160
  4. Decide if the claim is true.
  5. No. Box A is taller but holds 80 cubic inches. Box B holds 160 cubic inches. This counterexample shows the claim is false.

Now you trySame steps, your turn

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

Finish this argument: “I recommend buying two jumbo boxes because …” Then judge the argument for the three large boxes.

Answer:

Say it and write itSentence starters

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

Word bank argumentconjecturecounterexamplevolumecubic unit

Watch outA common mistake

Reporting volume without cubic units — saying the garden needs '48 feet' of soil, which is a length, or '48 square feet', which is an area.

Grade 6 Mathematics · Pre-UnitStandard 5.MD.C.5

Lesson 1.41.4 Small Group · Group 2

Group 2Challenge practice

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

Learning target I can construct an argument using equations, drawings, or words, and use volume to defend a recommendation, explain what each part stands for, and build one for a situation I have not seen before.

  1. 1Complete each step, then write the final answer.
    BoxLengthWidthHeightVolume
    A12 in2 in5 in?
    B6 in5 in5 in?
    Box A is longer. Find which box holds more.

    Ana claims, “A longer box always holds more.” Box A is 12 in long, 2 in wide, and 5 in tall. Box B is 6 in long, 5 in wide, and 5 in tall. Is Ana right?

    1. 1Find the volume of Box A.
    2. 2Find the volume of Box B.
    3. 3Box A is longer. Does it hold more?
    Final answer:
  2. 2Complete each step, then write the final answer.
    3 in5 in4 in
    The box before you double its height.

    Ben claims, “If you double the height of a box, the volume doubles.” Test it with a box that is 3 in by 4 in by 5 in.

    1. 1Find the volume of the box.
    2. 2Double the height to 10 in. Find the new volume.
    3. 3Is 120 double 60?
    4. 4One example worked. Why does that not prove “always”?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Box C is 2 in by 3 in by 7 in. Box D is 3 in by 3 in by 5 in. How many more cubic inches does Box D hold?

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

    Pack A has 3 boxes, each 10 in by 2 in by 9 in. Pack B has 2 boxes, each 9 in by 4 in by 8 in. How many more cubic inches does Pack B hold?

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.

    Mia claims, “A bigger bottom always means more volume.” Box E: 6 in by 6 in bottom, 3 in tall. Box F: 4 in by 5 in bottom, 10 in tall. How many more cubic inches does Box F hold?

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

    Zoe claims, “Two boxes always hold more than one box.” One big box is 10 in by 6 in by 10 in. Two small boxes are each 5 in by 4 in by 10 in. How many more cubic inches does the big box hold?

    Show your work
    Final answer:

Explain your thinkingWhy can one counterexample prove a claim false, but one example cannot prove it true? Use Zoe's claim.

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

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