Cooperative Learning – Knurek

Team-Building Lesson: “If You Build It…”

Gumdrop and Toothpick Bridges


  • 8.F.4: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.


  • Students will be able to work cooperatively with group members to achieve a common goal.
  • Students will be able to share ideas with their group members.
  • Students will be able to write algebraic expressions to model real-world situations.


  • Bag of gumdrops (they can get more from the teacher if they need it)
  • Bag of toothpicks (they can get more from the teacher if they need it)
  • Two solo cups (placed upside down, exactly 12 inches apart

Task #1: Students are to create a bridge from one top of the cup to the other out of the toothpicks and gumdrops. (See image above) They can use any method of construction that they’d like. However, the bridge must only consist of toothpicks and gumdrops.

Class Discussion #1: As groups are starting to complete the bridges, the teacher will bring the class into a discussion on strategies that are being used around the room. Groups will share their ‘methods’ for constructing their bridges. This conversation can take place before any groups have finished. This will allow teams to re-think their construction methods if necessary.

Task #2: Once groups are finished, they will count the number of toothpicks and the number of gumdrops that they used. Now students will be tasked with building a new bridge that uses less material. Teams will compete to build a bridge using the fewest materials.

Task #3: Once teams have finished the previous task, they will be challenged with writing algebraic expressions to represent the following pictures (there will be more than just the pictures shown below). The teacher will circulate the room and guide teams that are struggling to make the connection.



Class Discussion #2: The teacher will lead a full-class discussion over the algebraic expressions that teams came up with to represent the pictures above.



Cooperative Learning Lesson: Guided Reciprocal Peer Questioning (modified with a Chalk Talk)

Pythagorean Theorem “5 W’s”

This lesson would take place after 2 or 3 days of working with the Pythagorean Theorem in class. By the time this lesson roles around, students know how to use the Pythagorean Theorem. Now, they will explore the value of the Pythagorean Theorem using both guided reciprocal peer questioning techniques and a chalk talk.

This lesson will be centered around these ‘Generic Question Stems’, that follow a ‘Who, What, When, Where, Why progression:

  • Who uses the Pythagorean Theorem?”
  • What can we do with the Pythagorean Theorem?”
  • When is the Pythagorean Theorem useful?”
  • Where can we see the Pythagorean Theorem in the world around us?”
  • Why are we learning about the Pythagorean Theorem?”


  • 8.G.6: Explain a proof of the Pythagorean Theorem and its converse.
  • 8.G.7: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
  • 8.G.8: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.


  • Students can identify parts of a right triangle.
  • Students can use the Pythagorean Theorem to find missing sides of a right triangle.
  • Students can use the inverse of the Pythagorean Theorem to prove whether or not a triangle is a right triangle.

Chalk Talk (Stations): The teacher will write these 5 Generic Question Stems around the room on the boards. The teacher will them announce to the class that they will doing a chalk talk in groups (collaboratively, so people are allowed to talk!

At each ‘question’, students will write ideas and thoughts stemming off of the generic question stem. Then, they will come up with some further questions that can be discussed and analyzed at a later time. Each group will have a certain amount of time at the question before rotating. Students are encouraged to create stems off of other students stems.

Class Discussion: The teacher will lead a full-class discussion over 5 questions. Students will spend the majority of time looking at the 5 completed chalk talks and discussing what is shown.


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162 Responses to Cooperative Learning – Knurek

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  144. frydrycr says:

    Bobby – I love the bridge activity! I especially like that you’ve tied in a math component at the end… my students are always annoyed with me when we do something fun, then there is a surprise math side of the activity. The joy of being a teacher 🙂 Ditto to what Grady said about the Pythagorean Theorem activity! Your students deeper interaction with it will hopefully turn into deeper understanding!

    • knurekrm says:

      Thanks for the reply Courtney! I’m hoping the students won’t give me too much push-back on the math portion of this lesson after having spent time working on their bridges.

  145. peterskl says:

    Great lessons! I love teaching the Pythagorean Theorem to my advanced 7th graders. Here is a cool water video I found to show the Pythagorean Theorem.

  146. Grady says:


    Great job on your two lessons. I am sure that all of your students will enjoy the bridge activity. I look forward to using the 5 w’s activity dealing with Pythagorean Theorem will be fun to use in my classes as it really helps the student develop a deeper understanding of the concept.


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