MPP.7 Lesson 10-5-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

10.5 Small Group · Group 2

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

repetition · pattern · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — Repetition, pattern, and rhythm
1Math can be used to create beautiful designs. These designs often have repetition, patterns, and rhythm — and the pattern unit lets you predict what comes next — 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 use a pattern unit
  1. A border repeats: pink circle, purple square, blue triangle, pink circle, purple square, blue triangle, ...
  2. The pattern unit is 3 shapes long: circle, square, triangle.
  3. To predict shape number 12, I divide: 12 ÷ 3 = 4 with no remainder, so shape 12 ends a complete unit — it is the blue triangle.
  4. The next three shapes after any complete unit will be a pink circle, a purple square, and a blue triangle.
3Second Model — Try it together — then prove it
  1. The pattern unit is still 3 shapes long.
  2. 20 ÷ 3 = 6 complete units with a remainder of 2, because 6 × 3 = 18 and 20 − 18 = 2.
  3. A remainder of 2 means shape 20 is the second shape in the unit.
  4. The second shape is the purple square.
  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
  • repetition (repetición) — The same object, shape, or form repeated multiple times.
  • pattern (patrón) — A set of objects or shapes that are repeated and arranged in a regular order.
  • pattern unit (unidad del patrón) — The smallest chunk of a pattern that repeats.
  • rhythm (ritmo) — A design element created by varying the placement, size, orientation, or order of the same objects or shapes.
  • predictability (previsibilidad) — Being able to know what comes next because the design follows a rule.
5Watch out
  • Calling every repeated design a 'pattern.' One identical shape repeated is repetition; a pattern needs a unit of shapes repeating in a regular order; and rhythm varies the shapes' size and order, so it is neither.
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    The pattern unit circle-square-triangle repeats. What is shape number 12?

    1. AThe blue triangle
    2. BThe pink circle
    3. CThe purple square
    4. DIt cannot be determined
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Same pattern. What is shape number 20?

    1. AThe purple square
    2. BThe pink circle
    3. CThe blue triangle
    4. DThe 20th shape starts a new pattern
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 3 OPEN RESPONSE

    Create a design that has repetition, pattern, AND rhythm. Describe (or sketch) it, and label where each element appears.

    ✏️ Mathematical Justification & Response
  2. 4 OPEN RESPONSE

    Why do you think the lesson is called 'Math is Boundless'? Use repetition, pattern, and rhythm in your answer.

    ✏️ Mathematical Justification & Response
  3. 5 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:The pattern unit circle-square-triangle repeats. What is shape number 12?
    2. 2A classmate at our table answered:The pink circle

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

    ✏️ Corrected Mathematical Work & Explanation
  4. 6 OPEN RESPONSE

    The border repeats circle–square–triangle. A classmate says: 'Shape number 100 must be a triangle, because 100 is even.' Is the reasoning right, the answer right, both, or neither? Then write a rule that finds shape number n for ANY n, and use it on shape 100.

    ✏️ Mathematical Justification & Response
📐 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