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

Lesson 1.4Math is Explaining and Sharing

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.

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.

Suppose each large box is 8 inches long, 3 inches wide, and 10 inches tall. Its volume is 8 × 3 × 10 = 240 cubic inches, so three large boxes hold 240 × 3 = 720 cubic inches.

  1. Suppose each jumbo box is 10 inches long, 4 inches wide, and 10 inches tall. Its volume is 10 × 4 × 10 = 400 cubic inches, so two jumbo boxes hold 400 × 2 = 800 cubic inches.
  2. I recommend buying two jumbo boxes because 800 cubic inches is greater than 720 cubic inches — the total volume is greater, so there is more cereal for the same price.

Now you trySame steps, your turn

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

Not every good reason is an equation. Finish this argument: “I recommend buying two jumbo boxes because …”

Answer:

Say it and write itSentence starters

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

  • An argument using is stronger here because .
  • I recommend because .
  • A reason that is not about volume is .
  • Explaining helps because .

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 1.4Math is Explaining and Sharing

Version ASupported 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.

Part 1Apply itreal-world problems
  1. 1Circle the letter of the best answer. Show how you know.

    An egg muffin is about 60 calories. A plate holds 4 egg muffins. About how many calories are on the plate?

    1. AAbout 15
    2. BAbout 64
    3. CAbout 240
    4. DAbout 600

    Hint How many muffins, and how many calories in each one?

    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    A large cereal box is 8 in long, 3 in wide, and 10 in tall. What is its volume?

    1. A21 cubic inches
    2. B80 cubic inches
    3. C240 cubic inches
    4. D240 square inches

    Hint Volume of a box is length × width × height.

    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?
  3. 3Circle the letter of the best answer. Show how you know.

    Each jumbo box holds 400 cubic inches. How much do TWO jumbo boxes hold?

    1. A200 cubic inches
    2. B402 cubic inches
    3. C800 cubic inches
    4. D4,000 cubic inches

    Hint Two equal boxes — what operation combines them?

    Show your work
  4. 4Circle the letter of the best answer. Show how you know.

    Which unit should the garden group use when reporting how much soil fills the beds?

    1. AFeet
    2. BCubic feet
    3. CSquare feet
    4. DDegrees

    Hint Soil fills SPACE, not a line or a flat surface.

    Show your work
Part 2Explain and correctreasoning
  1. 5Answer in complete sentences.

    Yuzuki can buy three large boxes or two jumbo boxes for the same price. Give ONE reason in words (no equations) for either choice.

    Sentence starter I recommend ___ because ___ .
    A reason that is not about volume is ___ .
    Write your answer
  2. 6Answer in complete sentences.

    Why does it help to explain your thinking to others instead of just giving the answer?

    Sentence starter Explaining helps because ___ .
    When someone hears my reasons, they can ___ .
    Write your answer

Explain your thinkingOne of you sorted a card into 'Argument using equations' and the other into 'Argument using words.' Which argument would convince a skeptic faster, and what would it take to turn the other one into a counterexample?

Sentence starter An argument using ___ is stronger here because ___.

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 · Pre-UnitStandard 5.MD.C.5

Lesson 1.4Math is Explaining and Sharing

Version BCore 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.

Part 1Understand the ideamodels and meaning
  1. 1Circle the letter of the best answer. Show how you know.

    Which statement is a CONJECTURE?

    1. A“8 × 3 × 10 = 240.”
    2. B“I think the two jumbo boxes hold more cereal than the three large boxes.”
    3. C“Volume is measured in cubic units.”
    4. D“Yuzuki bought cereal.”
    Show your work
Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    Three large boxes hold 240 cubic inches each. Two jumbo boxes hold 400 cubic inches each. Which is the correct volume comparison?

    1. A240 cubic inches vs. 400 cubic inches — the jumbo option holds more
    2. B480 cubic inches vs. 800 cubic inches — the jumbo option holds more
    3. C720 cubic inches vs. 800 cubic inches — the jumbo option holds more
    4. D720 cubic inches vs. 800 cubic inches — the large option holds more
    Show your work
  2. 3Circle the letter of the best answer. Show how you know.

    One garden bed is 4 ft long, 3 ft wide, and 2 ft deep. A second bed is 6 ft long, 2 ft wide, and 2 ft deep. How much soil fills BOTH beds?

    1. A19 cubic feet
    2. B24 cubic feet
    3. C48 cubic feet
    4. D96 cubic feet
    Show your work
  3. 4Circle the letter of the best answer. Show how you know.

    The group found the volume by decomposing the garden into prisms and adding. Why would they compute it a SECOND, different way?

    1. ABecause the first way is always wrong
    2. BTo get a bigger number for the soil order
    3. CIf both ways give the same answer, the solution is accurate
    4. DBecause volume changes each time you measure it
    Show your work
Part 3Explain and correctreasoning
  1. 5Answer in complete sentences.

    A student recommends the three large boxes because the cereal stays fresher — each box is open for less time. Is this argument convincing? Explain.

    Write your answer
  2. 6Answer in complete sentences.

    Use precise vocabulary to explain how you would find the soil needed for a bed 5 ft long, 2 ft wide, and 2 ft deep. Include the answer with its unit.

    Write your answer

Explain your thinkingOne of you sorted a card into 'Argument using equations' and the other into 'Argument using words.' Which argument would convince a skeptic faster, and what would it take to turn the other one into a counterexample?

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 · Pre-UnitStandard 5.MD.C.5

Lesson 1.4Math is Explaining and Sharing

ChallengeExtension

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.

Part 1Understand the ideamodels and meaning
  1. 1Write the letter of the matching item on each line.

    Match each prism to a DIFFERENT prism with the SAME volume.

    1. 8 × 3 × 10
    2. 4 × 3 × 2
    3. 5 × 8 × 10
    4. 6 × 2 × 4
    • A6 × 4 × 10
    • B6 × 2 × 2
    • C20 × 10 × 2
    • D8 × 3 × 2
Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    A student claims: “Greater box volume ALWAYS means more cereal inside.” Which is the best counterexample?

    1. AA large box that costs more than a jumbo box
    2. BA jumbo box with more volume that is sold half-filled with air
    3. CTwo jumbo boxes that are easier to store than three large boxes
    4. DA box of a different cereal brand
    Show your work
  2. 3Circle the letter of the best answer. Show how you know.

    The garden needs 48 cubic feet of soil. One decomposition used two prisms of 24 cubic feet each. Which of these is ANOTHER decomposition of the same garden volume?

    1. AA 3 × 3 × 3 prism and a 3 × 3 × 2 prism
    2. BA 4 × 4 × 2 prism and a 4 × 2 × 2 prism
    3. CA 4 × 4 × 2 prism and a 4 × 4 × 2 prism
    4. DA 6 × 4 × 2 prism and a 2 × 2 × 2 prism
    Show your work
Part 3Explain and correctreasoning
  1. 4Answer in complete sentences.

    Another garden bed design is also being considered. What information would you need to compare the two designs, and how would you argue for the one you recommend?

    Write your answer
  2. 5Answer in complete sentences.

    Write TWO arguments for the same recommendation about Yuzuki's cereal — one using equations, one using only words. Then say which you think would convince a classmate more, and why.

    Write your answer

Explain your thinkingOne of you sorted a card into 'Argument using equations' and the other into 'Argument using words.' Which argument would convince a skeptic faster, and what would it take to turn the other one into a counterexample?

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