Sample+Tasks+to+Use

We highly recommend all of these tasks as a way to connect your students to the content.
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And for you realists out there, do not fear! We have already thought of your potential problems and solved the issues!

**TASK 1:** Geoboards and The Pythagorean Theorem from Mathematics: Applications and Connections

In order for students to be successful with this cooperative, investigative lesson, they will need the prior knowledge of "the relationship between the area of a square and the length of its side."

Objective of this Lesson: Explore the relationships in a right triangle to discover The Pythagorean Theorem

Materials: Geoboards (one per student) Rubberbands Worksheet

Directions: 1. Ask students to create a right triangle on their Geoboard. 2. Have students make a square using the longest side of the triangle. 3. Then, build squares on the two shorter sides. <span style="color: #137272; font-family: Georgia,serif; font-size: 120%;">4. Have students record their results on this worksheet: <span style="color: #137272; font-family: Georgia,serif; font-size: 120%;">

<span style="color: #137272; font-family: Georgia,serif; font-size: 120%;">5. Students need to try at least 3 examples of different size right triangles and record their findings. <span style="color: #137272; font-family: Georgia,serif; font-size: 120%;">6. Have students talk with their neighbor to find a relationship among all the triangles and their three squares. Have pairs write a mathematical statement that describes the relationship. <span style="color: #137272; font-family: Georgia,serif; font-size: 120%;">*After students have recorded their findings, they should notice that the two areas of the smaller squares (on the smaller legs of the triangle) add up to the area of the large square (on the hypotenuse). <span style="color: #137272; font-family: Georgia,serif; font-size: 120%;">7. Have class discussion about the activity (maybe students can present their statements in front of the class) and work out the true statement.

**<span style="color: #137272; font-family: Georgia,serif;">Main Ideas: ** <span style="color: #137272; font-family: Georgia,serif; font-size: 140%;">**This is a great activity because:** <span style="color: #137272; font-family: Georgia,serif; font-size: 120%;">1. it encourages student discovery to derive the formula <span style="color: #137272; font-family: Georgia,serif; font-size: 120%;">2. it requires students to verbally articulate their mathematical ideas <span style="color: #137272; font-family: Georgia,serif; font-size: 120%;">3. it shows students where the formula comes from so that it's not just a formula they memorize <span style="color: #137272; font-family: Georgia,serif; font-size: 120%;">4. it's HANDS ON <span style="color: #137272; font-family: Georgia,serif; font-size: 120%;">5. it utilizes the 4 Phase Lesson Plan

<span style="color: #137272; font-family: Georgia,serif; font-size: 21px;">**TASK 2:** <span style="color: #137272; font-family: Georgia,serif; font-size: 16px;">Worksheet for classtime <span style="color: #137272; font-family: Georgia,serif; font-size: 16px;">Courtesy, Anne Adams, Math Teacher

<span style="color: #137272; font-family: Georgia,serif; font-size: 16px;">This activity is intended for the second day of teaching because it requires some knowledge of The Pythagorean Theorem yet still encourages investigation for deeper understanding.

<span style="color: #137272; font-family: Georgia,serif; font-size: 16px;">Objective of this Lesson: Apply knowledge and deepen understanding of Pythagorean Theorem to Real Life Examples

<span style="color: #137272; font-family: Georgia,serif; font-size: 16px;">Materials: <span style="color: #137272; font-family: Georgia,serif; font-size: 16px;">Handout (Below)

<span style="color: #137272; font-family: Georgia,serif; font-size: 16px;"> <span style="color: #137272; font-family: Georgia,serif; font-size: 16px;">

<span style="color: #137272; display: block; font-family: Georgia,serif; font-size: 16px; text-align: center;">Main Ideas: <span style="color: #137272; display: block; font-family: Georgia,serif; font-size: 16px; text-align: center;">This worksheet can serve as a type of "notes" for the day. This handout allows very interactive participation between student and teacher as for most problems, students could discuss with a neighbor, the whole class, or work on their own. Students will be responsible to complete the entire handout and this will be a record of their work that day. <span style="color: #137272; font-family: Georgia,serif; font-size: 18px;">This is a great activity because: <span style="color: #137272; font-family: Georgia,serif; font-size: 16px;">1. it encourages discovery and investigative learning through the 4 Phase Lesson Plan <span style="color: #137272; font-family: Georgia,serif; font-size: 16px;">2. it could be used for the entire class period- some individual work, some small group work, and some whole class discussion about each section <span style="color: #137272; font-family: Georgia,serif; font-size: 16px;">3. it's a real world example! <span style="color: #137272; font-family: Georgia,serif; font-size: 16px;">4. it can be used as an assessment during the middle of the content unit

<span style="color: #137272; font-family: Georgia,serif; font-size: 160%;">**TASK 3:** <span style="color: #137272; font-family: Georgia,serif; font-size: 120%;">"Ticket Out the Door" <span style="color: #137272; font-family: Georgia,serif; font-size: 120%;">Courtesy, Anna Williford, Pre-service Teacher

<span style="color: #137272; font-family: Georgia,serif; font-size: 120%;">Objectives: To both formatively assess the student (and teacher) in the students' understanding of the content and the teacher's effectiveness.

<span style="color: #137272; font-family: Georgia,serif; font-size: 120%;">Materials: <span style="color: #137272; font-family: Georgia,serif; font-size: 120%;">Handout (below) <span style="color: #137272; display: block; font-family: Georgia,serif; font-size: 120%; text-align: center;">Students must complete these two problems and turn them in to the teacher as they leave the classroom. <span style="color: #137272; display: block; font-family: Georgia,serif; font-size: 120%; text-align: left;"> <span style="color: #137272; font-family: Georgia,serif; font-size: 18px;">This is a great activity because: <span style="color: #137272; font-family: Georgia,serif; font-size: 16px;">1. it can be used as a post-test for the day <span style="color: #137272; font-family: Georgia,serif; font-size: 16px;">2. students will be "thinking of math" even as they leave the classroom <span style="color: #137272; font-family: Georgia,serif; font-size: 16px;">3. it contains two problems- each with a different level of difficulty <span style="color: #137272; font-family: Georgia,serif; font-size: 16px;">4. while a good homework problem encourages further thought, this reinforces what students learned in class that day <span style="color: #137272; font-family: Georgia,serif; font-size: 16px;">5. it acts as a formative assessment for the teacher for this lesson <span style="color: #137272; font-family: Georgia,serif; font-size: 16px;">6. It shows the student (and teacher) where the student is in their understanding


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