Grade 6 Mathematics · Pre-UnitStandard 5.OA.B.3

Lesson 1.51.5 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can find patterns and pattern rules, use them to make generalizations, and check my solutions with a table of values, explain why the method works, and use it on a problem I have not seen before.

Start hereWords for this lesson

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

WordWhat it meansExample
patternSpanish: patrón Something that repeats or changes in a predictable way. 1, 3, 7, 15, 31 — each tower's steps follow a predictable jump.
pattern ruleSpanish: regla del patrón The instruction that tells how to get from one number in a pattern to the next. 2, 4, 6, 8 … the rule is “+ 2 every time”.
generalizationSpanish: generalización A statement that is true for a whole pattern, made by noticing repeated calculations. 1 → 3, 2 → 5, 3 → 7 … so n → 2n + 1, for ANY n.
table of valuesSpanish: tabla de valores A table that lists each step of a pattern so you can check that a solution is reasonable. discs 1, 2, 3 beside steps 1, 3, 7 — one row per step.
reasonablenessSpanish: sensatez del resultado Whether an answer makes sense — checked as you work, with adjustments made when needed. 5/6 of 540 should land BELOW 540, so 650 fails the check.

How it worksWorked example

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

A jar has $53.50. It has 180 quarters, 70 dimes, and 20 nickels. The rest of the coins are pennies. How many pennies are in the jar?

  1. Find the value of the quarters: 180 × $0.25 = $45.00
  2. Find the value of the dimes and nickels: 70 × $0.10 = $7.00; 20 × $0.05 = $1.00
  3. Add the three values: $45.00 + $7.00 + $1.00 = $53.00
  4. Subtract from the total to find the pennies: $53.50 − $53.00 = $0.50 → 50 pennies
  5. There are 50 pennies in the jar.

Now you trySame steps, your turn

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

Try 200 quarters, 25 dimes, 15 nickels, and 25 pennies. Do they make exactly $53.50? Then explain the pennies.

Answer:

Say it and write itSentence starters

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

Word bank patternpattern rulegeneralizationtable of valuesreasonableness

Watch outA common mistake

Reporting only the points from the streak (20 or 30) and forgetting to add the points each player had before the streak began.

Grade 6 Mathematics · Pre-UnitStandard 5.OA.B.3

Lesson 1.51.5 Small Group · Group 2

Group 2Challenge practice

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

Learning target I can find patterns and pattern rules, use them to make generalizations, and check my solutions with a table of values, explain why the method works, and use it on a problem I have not seen before.

  1. 1Complete each step, then write the final answer.
    CoinNumberValue
    Quarters60$15.00
    Dimes40$4.00
    Nickels15$0.75
    Pennies??
    Total$20.75
    The pennies make up the rest of the $20.75.

    A jar has $20.75. It has 60 quarters, 40 dimes, and 15 nickels. The rest of the coins are pennies. How many pennies are in the jar?

    1. 1What are the quarters, dimes, and nickels worth?
    2. 2How much money is left for the pennies?
    3. 3How many pennies is that?
    Final answer:
  2. 2Complete each step, then write the final answer.
    CoinNumberValue
    Quarters30?
    Pennies15?
    Dimes??
    Total$9.65

    A jar has $9.65. It has 30 quarters and 15 pennies. The rest of the coins are dimes. How many dimes are in the jar?

    1. 1What are 30 quarters and 15 pennies worth?
    2. 2How much money is left for the dimes?
    3. 3How many dimes is that?
    4. 4Why must the pennies be a multiple of 5 in this jar?
    Final answer:
  3. 3Complete each step, then write the final answer.

    A jar has $4.50 in quarters and pennies. It has 17 quarters. How many pennies are in the jar?

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

    A jar has $41.30. It has 150 quarters, 30 dimes, and 6 nickels. The rest of the coins are pennies. How many pennies are in the jar?

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

    Lena saves only quarters and dimes. She has $12.00, and 36 of her coins are quarters. How many dimes does she have?

    Show your work
    Final answer:
  6. 6Circle the letter of the best answer. Show how you know.

    Omar says a jar of quarters, dimes, nickels, and pennies worth $25.35 has 32 pennies. Can he be right?

    1. ANo, because 32 is not a multiple of 5
    2. BYes, because any number of pennies can work
    3. CYes, because 32 is an even number
    Show your work

Explain your thinkingYou found a missing number of coins. How does a pattern help you check the answer before you trust it?

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