5.OA.B.3 Lesson 1-5-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

1.5 Small Group · Group 2

Second Challenge Form · Non-Routine Extension · Same Standard, New Problems

pattern · pattern rule · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — When we do math, we look for patterns and relationships
1We use the patterns and relationships we notice to solve problems, make generalizations, and check that our solutions are reasonable — and you can say why it is true, and where it would stop being true.
  • You already can do this. So we go up a level, not up a number: find what is always true, show it a second way, and be ready to defend it with a reason instead of an answer.
2Worked Example — Watch me find the coin patterns
  1. A change jar is full of pennies, nickels, dimes, and quarters worth $53.50 in total. How many of each coin could there be?
  2. Each penny has a value of $0.01, so 100 pennies have a value of $1.00.
  3. Each nickel has a value of $0.05, so 100 nickels have a value of $5.00. Each dime has a value of $0.10, so 100 dimes have a value of $10. Each quarter has a value of $0.25, so 100 quarters have a value of $25.
  4. I multiply the number of each coin by its value. And I notice a generalization: because the jar's total, $53.50, ends in 0, the number of pennies can only be a multiple of 5.
3Second Model — Try it together — then prove it
  1. Try 200 quarters: 200 × $0.25 = $50.00.
  2. Add 25 dimes: 25 × $0.10 = $2.50, bringing the total to $52.50.
  3. Add 15 nickels: 15 × $0.05 = $0.75, and 25 pennies: 25 × $0.01 = $0.25.
  4. $50.00 + $2.50 + $0.75 + $0.25 = $53.50. It works — and 25 pennies is a multiple of 5, just as the pattern predicted. Now use the patterns to find a different combination.
  5. Now prove it: say why that move had to work at all — not just that it did.
  6. Sentence frame — convince a skeptic: "My method works because ___ . It would stop working if ___ ."
4Mathematical Word Bank
  • pattern (patrón) — Something that repeats or changes in a predictable way.
  • pattern rule (regla del patrón) — The instruction that tells how to get from one number in a pattern to the next.
  • generalization (generalización) — A statement that is true for a whole pattern, made by noticing repeated calculations.
  • table of values (tabla de valores) — A table that lists each step of a pattern so you can check that a solution is reasonable.
  • reasonableness (sensatez del resultado) — Whether an answer makes sense — checked as you work, with adjustments made when needed.
5Watch out
  • Reporting only the points from the streak (20 or 30) and forgetting to add the points each player had before the streak began.
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    Player A had 18 points before making 10 two-pointers in a row. How many points does Player A have after the streak?

    1. A38
    2. B28
    3. C20
    4. D48
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Akela's jar totals $53.50. Why can the number of pennies only be a multiple of 5?

    1. ABecause the total's cents end in 0, and only pennies make amounts that aren't multiples of 5 cents
    2. BBecause pennies always come in rolls of 5
    3. CBecause there are exactly 5 kinds of coins in the jar
    4. DBecause $53.50 is divisible by 5
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    Which combination of coins totals exactly $53.50?

    1. A200 quarters, 25 dimes, 15 nickels, 25 pennies
    2. B200 quarters, 25 dimes, 15 nickels, 20 pennies
    3. C200 quarters, 30 dimes, 15 nickels, 25 pennies
    4. D100 quarters, 25 dimes, 15 nickels, 25 pennies
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 OPEN RESPONSE

    Write a generalization about ANY player who makes n shots in a row worth p points each, starting from s points. Then test it on Player A.

    ✏️ Mathematical Justification & Response
  2. 5 OPEN RESPONSE

    The lesson says we 'evaluate the reasonableness of solutions as we work and make adjustments.' Describe a moment solving the coin-jar problem where you would stop and adjust.

    ✏️ Mathematical Justification & Response
  3. 6 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:Akela's jar totals $53.50. Why can the number of pennies only be a multiple of 5?
    2. 2A classmate at our table answered:Because $53.50 is divisible by 5

    Which step contains the error? Explain the mathematical misconception and write the correct calculation below.

    ✏️ Corrected Mathematical Work & Explanation
📐 CER MATHEMATICAL PROOF MATRIX (CER 2.0) SMP.3 / Proof & Justification

Writing Task: Justify why your mathematical solution is accurate and complete.

C Claim
State your direct mathematical answer/claim with units.
E Evidence
Cite exact numbers, calculations, dimensions, or graph data.
R Reasoning
Explain the mathematical theorem, property, or definition connecting evidence to claim.
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It