SQUARES TO TRIANGLES [DAY 4]
PYTHAGOREAN THEOREM
Dive into our problem based unit where we explore the Pythagorean relationship through area of squares & triangles. Â
Intentionality
Spark Curiosity
Fuel Sensemaking
During Moves
Student Approaches
Next Moves
Consolidation
Reflect and Consolidation Prompts
Resources & Downloads
Educator Discussion Area
Intentionality & Unit Overview
Length of Unit: 5 Days
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Students will determine the length of a string that stretches from corner to opposite corner in a classroom.
Intentionality…
In this task, students will observe an individual running a string from one corner of a classroom to the opposite corner. The purpose of the day 4 task is allow students to apply their understanding of the Pythagorean relationship in various ways.
Spark Curiosity
What Do You Notice? What Do You Wonder?
Show students the following video:
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.
![Squares To Triangles [Day 4] - SPARK IMAGE](https://learn.makemathmoments.com/wp-content/uploads/2021/06/Squares-To-Triangles-Day-4-SPARK-IMAGE.png)
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:
- There is a long string.
- Whose classroom is that?
- How long is the string?
- What’s he standing on?
- How many desks are there?
- What kind of string is that?
Estimation: 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:
Show students the image below.
Then, ask students:
How long is the string that stretches from corner to corner?
We can now ask students to make an estimate (not a guess) as we want them to be as strategic as they can possibly be. This will force them to estimate dimensions and use their knowledge of area.
Encourage students to share their estimates, however avoid sharing their justification just yet. We do not want to rob other students of their thinking.
Fuel Sense-making
Crafting A Productive Struggle: Prompt
Prompt students by asking:
If you were to have more information to help narrow your prediction/make your prediction more accurate what extra information would you want?
Engage your class in Think-Pair-Share where they Think independently on what they would like to have to update their prediction, Pair and share their thinking with a partner, finally share their thinking with the class.
Show the More Information images one at time pausing and prompting your students to share their strategies.
Image 1:
![Squares To Triangles [Day 4] - classroom-height](https://learn.makemathmoments.com/wp-content/uploads/2021/06/Squares-To-Triangles-Day-4-classroom-height-scaled.jpg)
Image 2:
![Squares To Triangles [Day 4] - Classroomlength](https://learn.makemathmoments.com/wp-content/uploads/2021/06/Squares-To-Triangles-Day-4-Classroomlength-scaled.jpg)
Image 3:
![Squares To Triangles [Day 4]- ClassroomWidth](https://learn.makemathmoments.com/wp-content/uploads/2021/06/Squares-To-Triangles-Day-4-ClassroomWidth-scaled.jpg)
With this information and ask students to update their prediction.
During Moves
While Students Are Productively Struggling…
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Student Approaches
Student Approach #1: Diagrams of Two Triangles Utilizing the Pythagorean Theorem
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Next Moves
Reveal
Consider sharing the following reveal video with your students:
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Consolidation
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Reflect and Consolidation Prompts
Engage students in a discussion on the accuracy of the answer revealed in the video and their calculated answer.
Consolidation Prompt #1:
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Consolidation Prompt #2:
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Resources & Downloads
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Educator Discussion Area
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