Circle Theorems Foldables | INB | SpEd Geometry HSG.C.A.2

Make circle theorems **CLICK** for your struggling learners. This **70-page, 7-foldable unit** uses color-coded diagrams, sentence frames, IEP-aligned exit tickets, and a consistent 4-step problem-solving protocol to make circle geometry more visible, tangible, and memorable.

Designed for **Geometry students with IEPs, English Learners, and other learners who benefit from additional visual and structured support**, this unit focuses on both understanding what the mathematics means and giving students consistent ways to show their understanding.

✨ **WHAT'S INSIDE — 70 PAGES, 7 FOLDABLES**

### **Foldable 1 — Parts of a Circle Vocabulary Flip Book**

8-tab cut-and-fold flip book + 8 Frayer-model vocabulary cards covering **center, radius, diameter, chord, secant, tangent, arc, and sector**.

Includes a **Ferris wheel real-world anchor**, sentence-frame practice, an IEP-aligned exit ticket, and reflection journal.

### **Foldable 2 — Inscribed Angles Theorem Accordion**

A discovery activity where students **measure inscribed and central angles and conjecture the theorem** before being given the rule.

Includes an accordion foldable template, **3 fully worked examples** using the 4-step protocol, and a clock-face real-world anchor.

### **Foldable 3 — Chord Properties 4-Tab Foldable**

Covers:

Perpendicular bisector theorem Equidistant chords Intersecting chords: **a × b = c × d** Chord length formula: **2√(r² − d²)**

Includes a pizza real-world anchor, cut-and-fold 4-tab template, mixed practice, and exit ticket.

### **Foldable 4 — Tangent Properties Tri-Fold**

Covers:

Radius perpendicular to tangent Common tangents (external & internal) Tangent segments from an external point

Includes geometrically correct diagrams with right-angle markers, a bicycle-wheel real-world anchor, a tri-fold template, and practice.

### **Foldable 5 — Inscribed Quadrilaterals Discovery**

A hands-on discovery activity where students measure opposite angles and identify that they sum to **180°**.

Includes the theorem with proof sketch, a 4-panel foldable template, and practice with algebraic extension problems.

### **Foldable 6 — Angle-Arc Relationships Pocket Sort**

Includes **16 sorting cards**—4 each for central, inscribed, interior, and exterior angle relationships—with clean mini-diagrams and formulas.

Includes a printable pocket template, recording sheet, and mixed practice.

### **Foldable 7 — Circle Theorems Cheat-Sheet One-Pager**

A **3-page reference** covering all 8 theorems with color-coded diagrams and a problem-solving decision tree:

**“Given a circle problem, which theorem do I use?”**

Students can keep this at the front of their notebook for reference.

### **PLUS**

**5-section Cumulative Reflection Journal** with metacognitive prompts

**4-section Teacher Answer Key** with 4-step worked solutions

**Teacher Notes** with a 14-day pacing guide, IEP goal alignment, and SpEd assembly tips

🎯 **WHY IT WORKS**

**Color-Coding:** Red = central angle, blue = inscribed angle, green = arc, purple = chord, orange = tangent. The system is used consistently across the resource.

**Spatial Organization:** Foldables provide a structured way for students to organize circle-theorem information visually.

**Discovery Before Telling:** Two of the seven foldables begin with hands-on discovery activities in which students measure, record data, and conjecture a theorem before learning the formal rule.

**4-Step Protocol:** Every practice problem uses the same routine:

**Identify → Label → Apply → Solve**

**Sentence Frames:** Universal sentence frames support mathematical explanations and discussion, including: “I know the angle is ___ because ___.” “The arc measures ___ because ___.” “The theorem that applies is ___ because ___.”

📋 **HOW TO USE**

**Pacing:** 14 class periods (~3 weeks of 50-minute periods). Each foldable is designed for 2 days: Day 1 for assembly, discovery, and direct instruction; Day 2 for practice and exit ticket.

**Materials:** Scissors, glue sticks, colored pencils (red/blue/green/purple/orange), protractors, and composition notebooks.

**SpEd Motor Scaffolds:** Pre-cut templates can be used for students with significant motor challenges. Cut lines can be highlighted in yellow before photocopying, and fold lines can be scored with a ballpoint pen.

**Differentiation:** Use Foldable 7 as a review tool before a circle assessment and the reflection journal as a unit-closing activity.

📐 **STANDARDS ALIGNMENT**

**CCSS.MATH.CONTENT.HSG.C.A.2** — Identify and describe relationships among inscribed angles, radii, and chords, including relationships among central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; and the radius is perpendicular to the tangent where they intersect.

**CCSS.MATH.CONTENT.HSG.C.A.3** — Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

**Grade Band:** 9–10 (Geometry) Also appropriate for Grade 11–12 Pre-Calculus review and Grade 8 advanced.

❤️ **WHY TEACHERS LOVE THIS RESOURCE**

“Finally — a circle theorems unit my IEP students can actually access. The color-coding is a game-changer.”

“The discovery activities are gold. My students figured out the inscribed angle theorem themselves and were SO proud.”

“The 4-step protocol has transferred to other units. My students now use Identify-Label-Apply-Solve on their own.”

📦 **FILE FORMAT**

**70-page PDF** — print-ready, vector quality, all fonts embedded

Single-side printing is recommended for foldable templates on cardstock.

**Answer key included** — 4 sections, with solutions using the same 4-step protocol students learn.

**TPT Preview:** 14-page sample showing every foldable type.