- The learning objectives for the activity and their connection to the goals of the unit
- The mathematical practices that will be developed during the activity
- How the technology corresponds with the learning objectives
- The connection between the technology and the learning objectives
LESSON ONE
8.G.6 Explain a proof of the Pythagorean Theorem and its converse.
The objective for this lesson is to understand the relationship among the side lengths of a right triangle. Students will do this through an exploration of the relationship between the squares formed on the side lengths of any right triangle. This is designed as a partner activity to promote understanding and critiquing the work of others.The following are a list of the standards of mathematical practice that apply to this lesson:
CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively.
CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others.
CCSS.MATH.PRACTICE.MP4 Model with mathematics.
CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically.
CCSS.MATH.PRACTICE.MP7 Look for and make use of structure.
The technology used in this lesson allows the students a forum for collaboration through padlet, enhances the students ability to make conjectures by allowing them to perform explorations with the GeoGebra applets, and gives them the context to make connections through the closing video.
The objective for this lesson is to understand the relationship among the side lengths of a right triangle. Students will do this through an exploration of the relationship between the squares formed on the side lengths of any right triangle. This is designed as a partner activity to promote understanding and critiquing the work of others.The following are a list of the standards of mathematical practice that apply to this lesson:
CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively.
CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others.
CCSS.MATH.PRACTICE.MP4 Model with mathematics.
CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically.
CCSS.MATH.PRACTICE.MP7 Look for and make use of structure.
The technology used in this lesson allows the students a forum for collaboration through padlet, enhances the students ability to make conjectures by allowing them to perform explorations with the GeoGebra applets, and gives them the context to make connections through the closing video.
Lesson TWO
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.
The objectives for this lesson is to combine prior knowledge of square numbers and square roots with the proof of the Pythagorean Theorem to determine the measure of a missing side length of a right triangle through exploration and discovery. This can either be done by oneself or with a partner.
The following are a list of the standards of mathematical practice that apply to this lesson:
CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively.
CCSS.MATH.PRACTICE.MP4 Model with mathematics.
CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically.
CCSS.MATH.PRACTICE.MP6 Attend to precision.
CCSS.MATH.PRACTICE.MP7 Look for and make use of structure.
The technology used in this lesson enhances the students ability to learn by allowing them to perform explorations with the GeoGebra applet, work at their own pace and solve problems with the Shodor, and see a visual representation of the Pythagorean Theorem with the Google presentation.
The objectives for this lesson is to combine prior knowledge of square numbers and square roots with the proof of the Pythagorean Theorem to determine the measure of a missing side length of a right triangle through exploration and discovery. This can either be done by oneself or with a partner.
The following are a list of the standards of mathematical practice that apply to this lesson:
CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively.
CCSS.MATH.PRACTICE.MP4 Model with mathematics.
CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically.
CCSS.MATH.PRACTICE.MP6 Attend to precision.
CCSS.MATH.PRACTICE.MP7 Look for and make use of structure.
The technology used in this lesson enhances the students ability to learn by allowing them to perform explorations with the GeoGebra applet, work at their own pace and solve problems with the Shodor, and see a visual representation of the Pythagorean Theorem with the Google presentation.
Lesson THREE
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.
The objective for this lesson is to use what they learned about the Pythagorean Theorem in the previous two lessons and apply to solving real-world problems through a flipped classroom setting. The students are expected to watch the video at home that reviews how to solve a multi-step word problem and then apply that knowledge to a self-directed mini-project.
The following are a list of the standards of mathematical practice that apply to this lesson:
CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively.CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others.CCSS.MATH.PRACTICE.MP4 Model with mathematics.
CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically.
CCSS.MATH.PRACTICE.MP6 Attend to precision.
CCSS.MATH.PRACTICE.MP7 Look for and make use of structure.
Although there is not a great deal of technology in this lesson as compared to others the use of the flipped classroom provides students with an opportunity to own their learning for this period. They will have the use of calculators, but not for anything other than arithmetic calculations.
The objective for this lesson is to use what they learned about the Pythagorean Theorem in the previous two lessons and apply to solving real-world problems through a flipped classroom setting. The students are expected to watch the video at home that reviews how to solve a multi-step word problem and then apply that knowledge to a self-directed mini-project.
The following are a list of the standards of mathematical practice that apply to this lesson:
CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively.CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others.CCSS.MATH.PRACTICE.MP4 Model with mathematics.
CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically.
CCSS.MATH.PRACTICE.MP6 Attend to precision.
CCSS.MATH.PRACTICE.MP7 Look for and make use of structure.
Although there is not a great deal of technology in this lesson as compared to others the use of the flipped classroom provides students with an opportunity to own their learning for this period. They will have the use of calculators, but not for anything other than arithmetic calculations.
LESSON FOUR
8.G.6 Explain a proof of the Pythagorean Theorem and its converse.
The objective for this lesson is to understand that the Pythagorean Theorem only holds true for right triangles.
The following are a list of the standards of mathematical practice that apply to this lesson:
CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively.
CCSS.MATH.PRACTICE.MP4 Model with mathematics.
CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically.
CCSS.MATH.PRACTICE.MP7 Look for and make use of structure.
The technology used in this lesson allows the students to focus on the goal of the lesson when using the interactive worksheet since the calculations are performed for them, enhances the students ability to work through multiple scenarios efficiently through explorations with the GeoGebra applet, and allows them choice in their practice activity. The ticket out the door formative Google Form is an easy way for teachers to collect data. Features of Google Forms allow feedback emails to be sent directly to students that may include further practice or extensions, based on the student.
The objective for this lesson is to understand that the Pythagorean Theorem only holds true for right triangles.
The following are a list of the standards of mathematical practice that apply to this lesson:
CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively.
CCSS.MATH.PRACTICE.MP4 Model with mathematics.
CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically.
CCSS.MATH.PRACTICE.MP7 Look for and make use of structure.
The technology used in this lesson allows the students to focus on the goal of the lesson when using the interactive worksheet since the calculations are performed for them, enhances the students ability to work through multiple scenarios efficiently through explorations with the GeoGebra applet, and allows them choice in their practice activity. The ticket out the door formative Google Form is an easy way for teachers to collect data. Features of Google Forms allow feedback emails to be sent directly to students that may include further practice or extensions, based on the student.