power_point_MATHEMATICS 7-WEEK 2_lesson_plan

lesson about mathematics for week 7

1. O U R W E E K ! July 28-31, 2025

2. I. Classify polygons according to the number of sides, whether they are regular or irregular, and whether they are convex or non-convex.

3. How to classify polygons based on: 1. Number of sides 2. Regular vs. Irregular 3. Convex vs. Non-convex

4. Polygon Name Number of Sides Example Triangle 3 sides Traffic sign (Yield sign) Quadrilateral 4 sides Square, rectangle Pentagon 5 sides Home plate (baseball field) Hexagon 6 sides Beehive cell Heptagon 7 sides Rare architecture shapes Octagon 8 sides Stop sign Nonagon 9 sides Tile pattern Decagon 10 sides Complex board game tokens

5. Regular vs. Irregular Polygons Regular Polygon : All sides and angles are equal ✅ Example: Regular hexagon, equilateral triangle, square Irregular Polygon : Sides or angles are not equal ✅ Example: Scalene triangle, rectangle, irregular pentagon

6. Convex vs. Non-convex (Concave) Polygons Convex Polygon : All interior angles are less than 180°, and no sides curve inward ✅ Example: Square, regular pentagon, rectangle Non-convex (Concave) Polygon : At least one angle is more than 180°, and part of the shape caves in ✅ Example: Star-shaped polygon, arrow-shaped figure

7. Classification Category Examples By sides Triangle, Hexagon Road signs, honeycomb Regular Square, Equilateral Triangle Tiles, dice faces Irregular Rectangle, scalene triangle Tools, furniture Convex Pentagon, Octagon Coins, frames Non-convex Star, Arrow polygon Logos, decorations

8. Activity 1: Polygon Walk and Sort (G) Instructions: The learners will walk around the classroom where polygon shapes made from recycled paper are posted. Each group will collect and sketch five different polygons and sort them on their group paper based on the number of sides, regularity, and convexity. Groups will share their sorting criteria with the class. From this activity, students may use recycled paper, pencil, and rulers. Activity 2: Partner Polygon Classifier (P) Instructions: The learners will work in pairs using recycled paper with hand-drawn polygons. They will classify each based on number of sides, regularity, and convexity, writing their answers in a chart. After classifying, each pair will briefly explain one example to the class. From this activity, students may use recycled paper, pencil, and rulers. Activity 3: My Polygon Chart (I) Instructions: The learner will draw ten different polygons on recycled paper. For each, the learner will label the number of sides, identify if it is regular or irregular, and state if it is convex or non-convex. The learner will also write one short explanation for each classification type. From this activity, students may use recycled paper, pencil, and rulers.

9. Why This Is Important for Grade 7 Helps in identifying and describing shapes in math and daily life Prepares students for angle measurement and area/perimeter calculations Connects geometry to real-world objects (e.g., buildings, tiles, logos) Encourages visual learning and pattern recognition

10. II. Describe and explain the relationships between angle pairs based on their measures.

11. What are angle pairs? Angle pairs are two angles that have a special relationship based on their position or the sum of their measures. These relationships help us solve for unknown angles and understand geometric figures better.

12. 1. Complementary Angles Definition: Two angles whose measures add up to 90° Example: If one angle is 60°, the other is 30°, because 60° + 30° = 90° Important Fact: They don't have to be adjacent (side-by-side), but often are.

13. 2. Supplementary Angles Definition: Two angles whose measures add up to 180° Example: If one angle is 110°, the other is 70°, because 110° + 70° = 180° Important Fact: Supplementary angles often form a straight line .

14. 3. Adjacent Angles Definition: Two angles that share a common side and a common vertex , but do not overlap Example: The two angles on a corner of a square (e.g., 40° and 50°) can be adjacent if they meet at the same corner.

15. 4. Vertical Angles (Opposite Angles) Definition: Angles formed by two intersecting lines . They are opposite each other and always equal . Example: When two lines cross and one angle is 120°, the opposite angle is also 120°.

16. 5. Linear Pair Definition: A pair of adjacent angles that form a straight line (180°) Example: If one angle is 70°, the other is 110° (because 70° + 110° = 180°)

17. Angle Pair Definition Sum Example Complementary Angles Angles that add up to 90° 90° 45° + 45° Supplementary Angles Angles that add up to 180° 180° 130° + 50° Adjacent Angles Share a side and vertex, don’t overlap — 40° next to 60° Vertical Angles Opposite angles from intersecting lines Equal 115° and 115° Linear Pair Adjacent angles forming a straight line 180° 90° + 90°

18. Activity 1: Angle Pair Match-Up (G) Instructions: The learners will work in groups to match angle pair cards (e.g., vertical, supplementary, complementary, adjacent) with diagrams that represent them. After matching, the group will discuss the relationships shown in the matched pairs. From this activity, students may use angle pair cards, diagram sheets, tape, pencil   Activity 2: Angle Pair Roleplay (P) Instructions: The learners will work in pairs. One learner will describe an angle relationship (e.g., “two angles that add up to 90°”), while the other identifies the correct term and draws a simple representation. They will switch roles afterward. From this activity, students may use whiteboard, marker, angle reference sheet     Activity 3: Angle Relationship Analysis (I) Instructions: The learner will individually answer a worksheet with diagrams of intersecting lines. The learner will identify and describe the relationships of angle pairs in each figure and compute missing angle measures. From this activity, students may use worksheet, pencil, protractor

19. III. Identify and explain the relationships between complementary, supplementary, adjacent, and vertical angles.

20. Angle Pair Formed by Add to Equal Angles? Position Complementary Right angle division 90° Not always May be adjacent Supplementary Straight line division 180° Not always May form linear pair Adjacent Common side + vertex Varies Not always Always touching Vertical Intersecting lines Varies Always equal Opposite each other

21. Examples in Real Life Complementary : Corners of door frames or books standing up Supplementary : Straight road signs or bridges forming straight lines Adjacent : Two angles of a triangle at one vertex Vertical : Traffic lights poles where two streets cross

22. Activity 1: Angle Pair Sorting Challenge (G) Instructions: The learners will work in groups to sort a set of labeled angle diagrams into four categories: complementary, supplementary, adjacent, and vertical angles. The group will justify their classifications before sharing with the class. From this activity, students may use angle diagram cards, sorting sheet, pencil   Activity 2: Angle Relationship Quiz Show (P) Instructions: The learners will work in pairs to answer questions in a quiz format where they identify angle relationships based on descriptions or diagrams. Pairs will take turns answering and keeping score. From this activity, students may use quiz cards, whiteboard, marker Activity 3: Angle Identification Worksheet (I) Instructions: The learner will individually answer a worksheet by identifying the type of angle relationship shown in each diagram and providing a short explanation for each answer. From this activity, students may use worksheet, pencil, protractor

23. IV. Apply all learned skills to classify polygons, determine angle measures, and explain angle relationships.

24. 1. Classifying Polygons 🔺 Review: Polygons are flat, closed shapes made of straight lines.

25. Name Sides Example Triangle 3 Road signs, sails Quadrilateral 4 Windows, books Pentagon 5 Government buildings Hexagon 6 Beehive cells Octagon 8 Stop signs

26. ✅ Classify by other properties: Regular polygon – all sides and angles are equal Example: Square, regular hexagon Irregular polygon – sides and angles are not equal Example: Rectangle, scalene triangle Convex polygon – all angles < 180°, no sides bend inward Example: Pentagon, octagon Concave (non-convex) – at least one angle > 180° Example: Star-shaped polygon

27. Determining Angle Measures You can find unknown angle measures using: Sum of angles in polygons Angle relationships like complementary, supplementary, vertical, and adjacent angles ✅ Interior angle sum of a polygon : Use the formula: 🔸 (n – 2) × 180° Where n is the number of sides 🧮 Example: Find the sum of interior angles of a hexagon (6 sides) → (6 – 2) × 180 = 720° To find each angle in a regular hexagon : → 720 ÷ 6 = 120° per angle

28. Explaining Angle Relationships ✅ Complementary Angles → Two angles = 90° Example: 40° and 50° ✅ Supplementary Angles → Two angles = 180° Example: 120° and 60° ✅ Adjacent Angles → Side-by-side, share a vertex and side Example: Two corner angles in a square

29. ✅ Vertical Angles → Formed by intersecting lines, always equal Example: Opposite angles when two roads cross ✅ Linear Pair → Two adjacent angles forming a straight line (180°) Example: 110° and 70° on a line 🧮 Problem Example: Two angles form a linear pair. One angle is 65°. What is the other? → 180 – 65 = 115°

30. Integrated Example 🔸 Problem: A regular pentagon is drawn. One angle inside it is unknown. Find the measure of one interior angle. 👉 Step 1: Sum of interior angles = (5 – 2) × 180 = 540° 👉 Step 2: Each angle in a regular pentagon = 540 ÷ 5 = 108° ✅ Final Answer: Each interior angle = 108°

31. Important Lessons for Math 7 Geometry skills are connected : knowing sides, angles, and relationships helps solve more complex shapes. Recognizing angle relationships lets us solve unknown angles using basic math. These concepts apply to engineering, construction, art, and design . Mastering this topic builds strong reasoning and problem-solving skills for higher math.

32. Activity 1: Polygon and Angle Relay (G) Instructions: The learners will work in groups to complete a relay game where each member classifies a polygon, determines missing interior or exterior angle measures, or identifies an angle relationship before passing it to the next member. The group with the most correct answers wins. From this activity, students may use task cards, timer, answer sheets, pencil Activity 2: Diagram Discussion (P) Instructions: The learners will work in pairs to analyze composite diagrams containing polygons with marked angles. They will discuss and write down the polygon classification, calculate missing angles, and describe any angle relationships they observe. From this activity, students may use diagram sheet, ruler, pencil, protractor Activity 3: Integrated Math Task (I) Instructions: The learner will individually answer an assessment sheet requiring the classification of polygons, computation of interior/exterior angles, and explanation of angle relationships in given figures. From this activity, students may use assessment sheet, pencil, protractor

33. Assignment 2 and Quiz 2