Lesson 1.41.4 Small Group · Group 1
Start hereWords, worked example, and sentence starters
Learning target With my small group, I can construct an argument using equations, drawings, or words, and use volume to defend a recommendation — one step at a time, with support.
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| 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.
A large cereal box is 8 inches long, 3 inches wide, and 10 inches tall. What is the total volume of 3 large boxes?
- Multiply length × width × height for one box: 8 × 3 × 10 = 240
- Multiply by the number of boxes: 240 × 3 = 720
- 3 large boxes hold 720 cubic inches.
- A jumbo box is 10 inches long, 4 inches wide, and 10 inches tall. Should you buy 2 jumbo boxes or 3 large boxes (720 cubic inches)? Use volume to decide.
- Find the volume of one jumbo box: 10 × 4 × 10 = 400
- Multiply by 2 boxes: 400 × 2 = 800
- Compare the two totals: 800 > 720
- State your claim with the reason.
- I recommend 2 jumbo boxes, because 800 cubic inches is more than 720 cubic inches.
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 listen to the other side.
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- I recommend because .
- A reason that is not about volume is .
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.
Lesson 1.41.4 Small Group · Group 1
Group 1Supported practice
Learning target With my small group, I can construct an argument using equations, drawings, or words, and use volume to defend a recommendation — one step at a time, with support.
-
1Complete each step, then write the final answer.
One small box: 6 in by 2 in by 9 in. A small cereal box is 6 inches long, 2 inches wide, and 9 inches tall. What is the total volume of 4 small boxes?
- 1Find the volume of one box: 6 × 2 × 9.
- 2Multiply by the number of boxes.
Final answer: -
2Complete each step, then write the final answer.
One big box: 8 in by 4 in by 12 in. A big box is 8 inches long, 4 inches wide, and 12 inches tall. Should you buy 1 big box or the 4 small boxes (432 cubic inches)? Use volume to decide.
- 1Find the volume of the big box.
- 2Compare 384 and 432. Which choice holds more?
- 3State your claim with a reason.
Final answer: -
3Complete each step, then write the final answer.
A box is 3 inches long, 2 inches wide, and 5 inches tall. What is its volume?
Show your workHint Multiply length × width × height.
Final answer: -
4Complete each step, then write the final answer.
A box is 9 inches long, 3 inches wide, and 12 inches tall. What is the total volume of 2 of these boxes?
Show your workHint Find the volume of one box first. Then multiply by 2.
Final answer: -
5Complete each step, then write the final answer.
Pack A has 3 boxes. Each box holds 150 cubic inches. Pack B has 2 boxes. Each box holds 210 cubic inches. How many more cubic inches does the bigger pack hold?
Show your workHint Find the total for each pack. Then subtract.
Final answer: -
6Complete each step, then write the final answer.
Pack A has 4 boxes of 120 cubic inches. Pack B has 2 boxes of 200 cubic inches. Leo says Pack B holds more because its boxes are bigger. How many more cubic inches does Pack A hold?
Show your workHint Bigger boxes are not enough. Find the total volume of each pack.
Final answer:
Explain your thinkingLeo chose Pack B. Give one reason with numbers and one reason with words for the pack you recommend.
Sentence starter I recommend ___ because ___ cubic inches is more than ___ cubic inches. · Another reason, in words, is ___.