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

10.5 Small Group · Group 1

Tier 2 Intervention · Concrete-Representational-Abstract (CRA) · Dual-Language Anchors

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 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 DRAG SORT

    Sort each shape: can it tessellate by itself?

    Target Categories: Tessellates by itself Cannot tessellate alone
    • Squares
    • Equilateral triangles
    • Regular hexagons
    • Circles
    • Regular pentagons
    • Regular octagons
  2. 2 FILL TABLE

    The border pattern repeats circle, square, triangle. Name the shape at each position.

    Position numberThinking with the unit of 3Shape
    7
    12
    20
    ✏️ Scratchpad / Reasoning
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 MULTIPLE CHOICE

    In geometric design, what is repetition?

    1. AThe same object or shape repeated multiple times
    2. BA set of different shapes arranged randomly
    3. CShapes that vary in size and order of appearance
    4. DAny drawing that uses color
    ✏️ Workspace & Solution Steps
  2. 4 MULTIPLE CHOICE

    A border shows: pink circle, purple square, blue triangle, pink circle, purple square, blue triangle. What are the next three shapes?

    1. APink circle, purple square, blue triangle
    2. BBlue triangle, purple square, pink circle
    3. CPink circle, blue triangle, purple square
    4. DIt is impossible to predict
    ✏️ Workspace & Solution Steps
  3. 5 MULTIPLE CHOICE

    In the circle-square-triangle border, how many shapes long is the pattern unit?

    1. A3 shapes
    2. B6 shapes
    3. C2 shapes
    4. D1 shape
    ✏️ Workspace & Solution Steps
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 6 OPEN RESPONSE

    Where have you seen geometric patterns decorating a building, clothing, or artwork? Describe the design.

    💬 Sentence Starter: I have seen a geometric pattern on ___ .<br>Its pattern unit is ___ .
    ✏️ Mathematical Justification & Response
✍️ The Writing Revolution (TWR) · Sentence Expansion Because · But · So

Complete each sentence stem to demonstrate precise mathematical reasoning:

BECAUSE The mathematical model proves the solution because each step preserves quantitative equivalence.
BUT An estimate provides a quick benchmark, but an exact proof is required for precision.
SO The quantities follow the standard rule, so the final result is verified with certainty.
📐 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