Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.NOS.3

Lesson 2.72.7 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can divide with decimals by making the divisor a whole number first, explain why the method works, and use it on a problem I have not seen before.

Why This Matters This is your challenge small group for Lesson 2.7. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.

Start hereWords for this lesson

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

WordWhat it meansExample
DividendSpanish: Dividendo The total number being divided into equal groups (the number inside the division bracket). In 84.6 ÷ 6, it is 84.6
DivisorSpanish: Divisor The number of equal groups you are dividing into (the number outside the division bracket). In 84.6 ÷ 6, it is 6
QuotientSpanish: Cociente The answer when you divide. 84.6 ÷ 6 = 14.1
Decimal Division AlgorithmSpanish: Algoritmo de división decimal The steps for dividing decimals: slide the divisor's decimal point right until the divisor is a whole number, slide the dividend's point right the same number of places, then divide. 8.4 ÷ 2.1 → move the point in both → 84 ÷ 21 → divide, multiply, subtract, bring down → 4
Equivalent divisionSpanish: División equivalente Multiplying both numbers by 10 or 100 gives the same answer. 7.56 ÷ 0.12 = 756 ÷ 12 = 63 (both multiplied by 100)
Annex a zeroSpanish: Agregar un cero Write a zero after the last decimal digit without changing the value. 7.2 → 7.20

How it worksWorked example

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

A rope 25.2 meters long is cut into 6 equal pieces. How long is each piece?

  1. Write 25.2 ÷ 6. Put the quotient’s point above the point in 25.2.
  2. 6 goes into 25 four times, 1 left over. Bring down the 2 to make 12.
  3. 12 ÷ 6 = 2. Check: 4.2 × 6 = 25.2.

Answer: 4.2 meters for each piece

Now you trySame steps, your turn

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

Find 8.4 ÷ 2.1.

Answer:

Say it and write itSentence starters

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

  • The dividend is and the divisor is .
  • I placed the decimal point because .
  • When a remainder appeared I .
  • I checked my quotient by .

Word bank dividenddivisorquotientdecimal pointalgorithmannexbring downplace valueestimatecheckmultiplysubtract

Watch out!A common mistake

A common mistake in Divide Decimals is moving the decimal point in the divisor but forgetting to move it the same number of places in the dividend. For example, in 6.4 ÷ 0.8 a student changes 0.8 to 8 but leaves the dividend as 6.4, then divides 6.4 ÷ 8 = 0.8 instead of moving both points to get 64 ÷ 8 = 8. A second version of this mistake happens when the divisor has two decimal places, like 0.12: students move both points only 1 place instead of 2, turning 9.6 ÷ 0.12 into 96 ÷ 1.2 instead of the correct 960 ÷ 12. Count the divisor's decimal places first, then move BOTH points that same number of places.

Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.NOS.3

Lesson 2.72.7 Small Group · Group 2

Group 2Challenge practice

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

Learning target I can divide with decimals by making the divisor a whole number first, explain why the method works, and use it on a problem I have not seen before.

Why This Matters This is your challenge small group for Lesson 2.7. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.

Part 1Practice the skillshow every step
  1. 1Complete each step, then write the final answer.
    845360360−0
    The new problem has a whole-number divisor.

    Find 3.6 ÷ 0.45.

    1. 1How many places must both points move?
    2. 23.6 has only 1 decimal place. Write a zero. What does 3.6 become?
    3. 3How many 45s fit into 360?
    Final answer:
  2. 2Complete each step, then write the final answer.
    31.25775.75−2525−0
    The divisor is whole. The dividend still has a decimal.

    Find 7.75 ÷ 2.5.

    1. 1Move both points to make the divisor whole. What is the new problem?
    2. 2Put the answer's point over the dividend's point. Divide. What is the quotient?
    3. 3Why is it fine that 77.5 still has a decimal point?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Find 0.84 ÷ 0.07.

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

    Find 5.4 ÷ 0.36.

    Show your work
    Final answer:
Part 2Apply itreal-world problems
  1. 5Complete each step, then write the final answer.
    Hours1.51Miles9.75?÷ ?÷ ?

    Evelyn runs 9.75 miles in 1.5 hours. She runs at the same speed the whole time. How many miles does she run each hour?

    Show your work
    Final answer:
  2. 6Complete each step, then write the final answer.

    Ana says 6.3 ÷ 0.07 is 9. She changed the problem to 63 ÷ 7. What is the correct quotient?

    Show your work
    Final answer:

Explain your thinkingKim says moving the points changes the problem. Is 5.4 ÷ 0.36 really the same as 540 ÷ 36? Defend your answer.

ChallengeWrite your own problem

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

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