Grade 6 Mathematics · Pre-UnitStandard 5.NF.B.4

Lesson 1.21.2 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can make sense of a problem, plan a strategy, and use fractions of a whole number to compare quantities, explain how I can tell, and judge a case I have not seen before.

Start hereWords for this lesson

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

WordWhat it meansExample
quantitySpanish: cantidad An amount in a problem — a number with a meaning attached, like 540 meters. 540 meters — the number 540 AND what it measures.
relationshipSpanish: relación How two quantities compare or connect to each other. 1 hour → 48 km, 2 hours → 96 km: as one grows, so does the other.
strategySpanish: estrategia A plan for how to solve a problem before you start computing. “I will draw a tape diagram first, then divide” — chosen before computing.
reasonableSpanish: razonable A solution that makes sense in the context of the problem. 5/6 of 540 must be under 540, so 450 is reasonable and 650 is not.
persevereSpanish: perseverar To keep working on a problem, checking your progress and adjusting your plan when you get stuck. Stuck on the tram problem → try a tape diagram instead → keep going.

How it worksWorked example

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

Maya reads 1/2 of a 36-page story. Leo reads 3/4 of a 20-page story. Leo says, “3/4 is more than 1/2, so I read more pages.” Is Leo right?

  1. Find 1/2 of 36: 36 ÷ 2 = 18
  2. Find 3/4 of 20: 20 ÷ 4 = 5; 5 × 3 = 15
  3. Compare the pages, not the fractions: 18 > 15
  4. No. Maya read 18 pages and Leo read 15 pages. Leo's fraction is bigger, but his story is shorter.

Now you trySame steps, your turn

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

Decompose 105.76 in five ways. Then explain why a multiplication can name the same number.

Answer:

Say it and write itSentence starters

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

Word bank quantityrelationshipstrategyreasonablepersevere

Watch outA common mistake

Expecting a fraction of a number to be bigger than the number — 5/6 × 540 must be LESS than 540 because 5/6 is less than 1; only a fraction greater than 1, like 6/5, makes the product bigger.

Grade 6 Mathematics · Pre-UnitStandard 5.NF.B.4

Lesson 1.21.2 Small Group · Group 2

Group 2Challenge practice

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

Learning target I can make sense of a problem, plan a strategy, and use fractions of a whole number to compare quantities, explain how I can tell, and judge a case I have not seen before.

  1. 1Complete each step, then write the final answer.
    Kim??40 pagesRay???27 pages
    Different wholes, so compare pages, not fractions.

    Kim reads 1/2 of a 40-page story. Ray reads 2/3 of a 27-page story. Ray says, “2/3 is more than 1/2, so I read more pages.” Is Ray right?

    1. 1Find 1/2 of 40.
    2. 2Find 2/3 of 27.
    3. 3Compare the pages. Who read more?
    Final answer:
  2. 2Complete each step, then write the final answer.
    Ana444416 blocksBen?????? blocks
    Both shaded parts are the same distance.

    Ana walks 3/4 of a 16-block route. Ben walks 2/5 of his route. They walk the same number of blocks. How long is Ben's route?

    1. 1Find 3/4 of 16.
    2. 2Ben's 2/5 is 12 blocks. How many blocks is 1/5 of his route?
    3. 3How long is Ben's whole route?
    4. 4Why does Ben need a longer route to walk the same distance?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Sam has 1/4 of 32 stickers. Tia has 1/2 of 14 stickers. How many more stickers does Sam have?

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

    A tower is 540 meters tall. A new tower will be 7/9 as tall. How tall will the new tower be?

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

    Jo cuts 2/3 of a 45-meter rope. Max cuts 3/5 of a 60-meter rope. How many more meters does Max cut?

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

    Eva says 3/4 of 12 is more than 1/2 of 22, because 3/4 > 1/2. How many more is 1/2 of 22 than 3/4 of 12?

    Show your work
    Final answer:

Explain your thinkingWhen can a smaller fraction give the bigger amount? Use the two ropes to explain.

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