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

Lesson 1.51.5 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can find patterns and pattern rules, use them to make generalizations, and check my solutions with a table of values — one step at a time, with support.

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 pennies, nickels, dimes, and quarters worth $53.50 in all. What is the value of 100 of each coin?

  1. Multiply the value of one penny by 100: 100 × $0.01 = $1.00
  2. Do the same for nickels and dimes: 100 × $0.05 = $5.00; 100 × $0.10 = $10.00
  3. Do the same for quarters: 100 × $0.25 = $25.00
  4. 100 pennies are worth $1.00, 100 nickels $5.00, 100 dimes $10.00, and 100 quarters $25.00.
  5. The coins in the jar are worth $53.50. Why must the number of pennies be a multiple of 5?
  6. Write the other coins' values in cents: nickel 5¢ · dime 10¢ · quarter 25¢
  7. Write the total in cents: $53.50 → 5,350¢
  8. Decide what the pennies must make.
  9. The number of pennies must be a multiple of 5: 0, 5, 10, 15, 20, 25, and so on.

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?

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 1

Group 1Supported practice

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

Learning target With my small group, I can find patterns and pattern rules, use them to make generalizations, and check my solutions with a table of values — one step at a time, with support.

  1. 1Complete each step, then write the final answer.
    CoinValue of 1Value of 40
    Nickel$0.05?
    Dime$0.10?
    Quarter$0.25?
    The value of 40 coins is 40 times the value of 1.

    What are 40 nickels, 40 dimes, and 40 quarters worth?

    1. 1What are 40 nickels worth? Find 40 × $0.05.
    2. 2What are 40 dimes worth?
    3. 3What are 40 quarters worth?
    Final answer:
  2. 2Complete each step, then write the final answer.
    CoinNumberValue
    Quarters100?
    Dimes30?
    Nickels8?
    Pennies10?
    Total?
    Find each value, then add.

    Do 100 quarters, 30 dimes, 8 nickels, and 10 pennies make exactly $28.50?

    1. 1What are 100 quarters and 30 dimes worth?
    2. 2What are 8 nickels and 10 pennies worth?
    3. 3What is the total?
    4. 4Is 10 pennies a multiple of 5?
    Final answer:
  3. 3Complete each step, then write the final answer.

    What are 30 dimes worth?

    Show your work

    Hint 10 dimes make $1.00.

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

    What are 150 quarters and 40 dimes worth together?

    Show your work

    Hint 4 quarters make $1.00. 10 dimes make $1.00.

    Final answer:
  5. 5Complete each step, then write the final answer.
    CoinNumberValue
    Quarters60?
    Dimes25?
    Pennies50?
    Total?

    A jar has 60 quarters, 25 dimes, and 50 pennies. What is the total value of the coins?

    Show your work

    Hint Find the value of each kind of coin. Then add.

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

    A jar of pennies, nickels, dimes, and quarters is worth $12.40. Jay says it has 43 pennies. Ana says it has 45 pennies. Who could be right?

    1. AAna, because 45 is a multiple of 5
    2. BJay, because 43 is close to 45
    3. CBoth could be right
    4. DNeither could be right

    Hint Nickels, dimes, and quarters make a multiple of 5 cents. What must the pennies make?

    Show your work

Explain your thinkingWhy must the pennies be a multiple of 5 when the jar is worth $12.40? How does that help you check?

Sentence starter The pennies must be a multiple of 5 because ___. · The pattern helps me check because ___.

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