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Quadrilateral Quest

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Lesson Plan

Quadrilateral Quest

Students will investigate patterns in the diagonals of quadrilaterals and the interior and exterior angles of polygons to make conjectures about these geometric relationships.

Understanding geometric patterns helps us predict and solve problems in design, engineering, and everyday life. This skill builds a strong foundation for advanced mathematics.

Audience

9th Grade Students

Time

30 minutes

Approach

Discovery-based learning through guided exploration.

Materials

Prep

Materials and Room Setup

10 minutes

  • Review the Quadrilateral Quest Slide Deck to ensure familiarity with content and flow.
  • Print copies of the Exploration Worksheet for each student.
  • Gather rulers, protractors, and pencils for each student or group.
  • Ensure the classroom is set up for collaborative work, if applicable, or individual exploration.

Step 1

Warm-Up: What Do You See?

5 minutes

  • Display a slide with various quadrilaterals (square, rectangle, rhombus, trapezoid, parallelogram, kite).
  • Ask students to silently observe and jot down any patterns or relationships they notice.
  • Facilitate a brief class discussion, encouraging students to share their observations. (Refer to Quadrilateral Quest Slide Deck for visual aids and discussion prompts.)

Step 2

Diagonals Deep Dive

10 minutes

  • Introduce the concept of diagonals in quadrilaterals.
  • Instruct students to use their rulers to draw diagonals in the quadrilaterals provided on the Exploration Worksheet.
  • Guide them to measure the lengths of the diagonals and the segments they create, and observe how they intersect.
  • Encourage students to make conjectures about the properties of diagonals in different quadrilaterals. (See Quadrilateral Quest Slide Deck for examples and guiding questions.)

Step 3

Angle Adventures

10 minutes

  • Shift focus to interior and exterior angles of polygons.
  • Provide polygons on the Exploration Worksheet for students to measure their interior and exterior angles using protractors.
  • Prompt students to look for patterns in the sum of interior angles and the sum of exterior angles for different polygons.
  • Guide them to formulate conjectures about these angle relationships. (The Quadrilateral Quest Slide Deck has visuals and prompts.)

Step 4

Conjecture Conclusion

5 minutes

  • Bring the class back together.
  • Have students share their most interesting conjectures from both the diagonal and angle investigations.
  • Briefly discuss how mathematicians use patterns to form theories.
  • Assign remaining parts of the Exploration Worksheet as homework or an extension activity, focusing on writing their conjectures clearly and providing evidence.
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Slide Deck

Quadrilateral Quest: Pattern Power!

Today, we're becoming geometry detectives!
We'll investigate patterns to make cool conjectures about shapes.
Ready to unleash your inner mathematician?

Welcome students and introduce the day's quest: discovering geometric patterns.

What Do You See?

Look closely at these shapes.

  • What do you notice?
  • What do you wonder?
  • Jot down any interesting features or relationships.

(Display images of a square, rectangle, rhombus, trapezoid, parallelogram, kite.)

Display various quadrilaterals. Give students 1-2 minutes to silently observe before discussing. Encourage them to look beyond just names.

Diagonals Deep Dive

Diagonals are lines connecting opposite corners.

  • How do they behave in different quadrilaterals?
  • Do they always bisect each other?
  • Are they ever equal in length?
  • Are they perpendicular?

Use your Exploration Worksheet to investigate!

Introduce diagonals. Guide students to draw and measure on their worksheets. Circulate and ask probing questions like 'What if the diagonals are equal?' or 'What if they bisect each other?'

Angle Adventures

Let's explore angles inside and outside polygons!

  • What's the sum of the interior angles in a triangle? A quadrilateral? A pentagon?
  • What about the exterior angles?
  • Can you find a pattern based on the number of sides?

Measure and make your own conjectures using your Exploration Worksheet!

Transition to angles. Ensure students understand interior vs. exterior. Prompt them to consider how the number of sides affects the sum of angles. Emphasize that a conjecture is an educated guess.

Conjecture Conclusion

Time to share your discoveries!

  • What's the most surprising pattern you found?
  • What conjecture are you most confident about?
  • How could you prove your conjecture?

Keep exploring, geometers!

Facilitate a sharing session. Encourage constructive feedback on conjectures. Remind them that mathematical conjectures need evidence.

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Worksheet

Quadrilateral Quest: Exploration Worksheet

Name: ____________________________

Date: ____________________________

Part 1: Diagonals Deep Dive

Instructions: For each quadrilateral below, draw both diagonals. Measure the length of each diagonal and the segments they form when they intersect. Observe their intersection points (do they bisect each other? are they perpendicular?). Record your observations and then write a conjecture.

1. Square

![Square outline]





Observations:





Conjecture:





2. Rectangle

![Rectangle outline]





Observations:





Conjecture:





3. Rhombus

![Rhombus outline]





Observations:





Conjecture:





4. Parallelogram

![Parallelogram outline]





Observations:





Conjecture:





Part 2: Angle Adventures

Instructions: For each polygon below, measure all interior angles and one exterior angle at each vertex. Calculate the sum of interior angles and the sum of exterior angles. Record your observations and then write a conjecture.

1. Triangle (3 sides)

![Triangle outline]





Sum of Interior Angles:


Sum of Exterior Angles:

Conjecture about Triangles:





2. Quadrilateral (4 sides)

![Quadrilateral outline]





Sum of Interior Angles:


Sum of Exterior Angles:

Conjecture about Quadrilaterals:





3. Pentagon (5 sides)

![Pentagon outline]





Sum of Interior Angles:


Sum of Exterior Angles:

Conjecture about Polygons (General):










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Quadrilateral Quest • Lenny Learning