Task Teacher Guide
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In This Task…
Students will compare the areas of squares off the sides of rectangles to see if a relationship exists with the areas and the type of triangle.
Intentionality…
In this task students will explore how the relationship between the area of squares off the sides of a triangle can be used to determine if a triangle is right, obtuse, or acute. [The converse of the Pythagorean Relationship].
Spark
Estimate
What Do You Notice? What Do You Wonder?
Show students the following video:
Consider pausing this video at various points to have students estimate the number of squares in the larger squares.
Then, ask students:
What do you notice?
What do you wonder?
Give students 60 seconds (or more) to do a rapid write on a piece of paper.
Replaying the video and/or leaving a screenshot from the video up can be helpful here.
Then, ask students to share with their neighbours for another 60 seconds.
Finally, allow students to share with the entire group. Be sure to write down these noticings and wonderings on the blackboard/whiteboard, chart paper, or some other means to ensure students know that their voice is acknowledged and appreciated.
Some of the noticing and wondering that may come up includes:
- I see three triangles with squares
- Some squares are full and some aren’t.
- I wonder why the figure’s squares fit and the others don’t.
- Why are we doing this?
- I notice three different types of triangles.
Prompt
After we have heard students and demonstrated that we value their voice, we can land on the first question we will challenge them with:
How does a triangle’s type affect the area of the squares off the sides of that triangle?
Allow students to make conjectures with their elbow partners in a think-pair share format.
Engage your students in a class discussion about classifying triangles by their angles (obtuse, acute, right) and/or by their lengths (scalene, equilateral, isosceles).
Ask students to brainstorm how they can reach conclusions to any conjectures they have.
Sense Making
Crafting A Productive Struggle: Investigation
Group your students (randomly is best) in partners or groups of 3.
Distribute each group a copy of BLM 2.1 TRIANGLES.
A downloadable PDF blackline master of this investigation can be downloaded and used with your students in your classroom here: [ OPEN | DOWNLOAD ]
Students are to cut out each triangle.
For each triangle:
- Measure the side lengths;
- Measure the angles;
- Classify the triangle;
- Draw the square off each side length (similar to the video) and determine its area.
Students may wish to record their measurements on BLM 2.2 RECORDING SHEET to keep organized. Other students may wish to record and share their thinking on whiteboards or other non permanent surfaces.
A downloadable PDF blackline master of this investigation can be downloaded and used with your students in your classroom here: [ OPEN | DOWNLOAD ]
During Moves
While Students Are Productively Struggling…
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Student Solution #1: Summary of acute triangles
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Student Solution #2: Summary of right triangles
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Next Moves
Consolidation: Making Connections
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Purposeful Practice
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Resources and Downloads
Lesson Tip Sheet
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Videos & Images
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Keynote Slides
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PowerPoint Slides
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Printable Handout
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Explore The Entire Unit of Study
This Make Math Moments Task was designed to spark curiosity for a multi-day unit of study with built in purposeful practice, and extensions to elicit and emerge mathematical models and strategies.
Click the links at the top of this task to head to the other related lessons created for this unit of study.
Crafting A Productive Struggle: Prompt
How does a triangle’s type affect the area of the squares off the sides of that triangle?
Instructions
For each triangle in BLM 2.1 TRIANGLES
Cut out the triangle;
Measure the side lengths;
Measure the angles;
Classify the triangle;
Draw the square off of each side length (similar to the video) and determine its area.
Explore the question: How does a triangle’s type affect the area of the squares off of the sides of that triangle? Record your results in BLM 2.2 RECORDING
Determine all side lengths of the triangle
Determine all side lengths of the triangle
Determine all side lengths of the triangle
Determine all side lengths of the triangle
Determine all side lengths of the triangle
Determine all side lengths of the triangle
Download Printable PDF Handout
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