MPP.7 Lesson 10-5-group1 🟡 Group 1 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

10.5 Small Group · Group 1

Second Practice Form · Re-Teach, Homework or Retake · Same Standard, New Problems

repetition · pattern · Procedural Fluency · Reasoning & Critique

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — 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.
  • The first element of design is repetition: the same object or shape repeated multiple times. Because it involves one object, it has predictability. The second element is a pattern: a set of objects or shapes repeated and arranged in a regular order. We'll walk through a worked example, try one together, then you'll try a few with hints right there when you need them.
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.
3Mathematical 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.
4Watch 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

    What is rhythm in geometric design?

    1. AThe same objects or shapes with varying placement, size, or order of appearance
    2. BOne shape repeated exactly, over and over
    3. CShapes arranged in a strict, predictable order
    4. DA design with no shapes at all
    ✏️ Workspace & Solution Steps
  2. 2 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
  3. 3 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
  4. 4 MULTIPLE CHOICE

    How many COMPLETE pattern units appear in the first 18 shapes of the circle-square-triangle border?

    1. A6 units
    2. B15 units
    3. C9 units
    4. D3 units
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 OPEN RESPONSE

    How would you compare the visual appeal of a design with just repetition and a design with patterns?

    💬 Sentence Starter: A design with only repetition feels ___ .<br>A design with patterns feels ___ because ___ .
    ✏️ Mathematical Justification & Response
  2. 6 OPEN RESPONSE

    A painting shows circles whose colors, sizes, and thickness vary, along with the number of concentric circles inside each one. Describe how the painting demonstrates rhythm.

    💬 Sentence Starter: The painting uses the same object, but varies ___ .<br>It is rhythm and not a pattern because ___ .
    ✏️ 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
Starter: My mathematical claim is that the solution is...
E Evidence
Starter: The evidence from the model/table demonstrates that...
R Reasoning
Starter: This proves my answer because the standard mathematical definition of...
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It