© DMTI (2017) | Resource Materials | www.dmtinstitute.com The Developing Mathematical Thinking Institute (DMTI) is dedicated to enhancing students’ learning of mathematics by supporting educators in the implementation of research-based instructional strategies through high-quality professional development. For more information contact Dr. Brendefur at jonathan@dmtinstitute.com © DMTI (2017) | Resource Materials | www.dmtinstitute.com

Linear Function Warm Ups Write a story (context) that matches this graph. Write an equation that matches your story and this graph. Have students write in their journals after they have a minute or two to discuss the tasks with a neighbor. There are no intervals given in order to prompt students’ thinking of appropriate scale intervals. Discuss the concept of intervals and scale as needed with students or the entire class. You might want to limit the contexts to height, distance, and money situations if students need more guidance on how to construct a context from a graph. © DMTI (2017) | Resource Materials | www.dmtinstitute.com

Linear Function Warm Ups Now, modify your story from the original line to the new line. What changed in your story? What stayed the same? What changed in your equation? Have students write in their journals after they have a minute or two to discuss the tasks with a neighbor. There are no intervals given in order to prompt students’ thinking of appropriate scale intervals. Discuss the concept of intervals and scale as needed with students or the entire class. You might want to limit the contexts to height, distance, and money situations if students need more guidance on how to construct a context from a graph. © DMTI (2017) | Resource Materials | www.dmtinstitute.com

Linear Function Warm Ups Now, modify your story from the original line to the new line. What changed in your story? What stayed the same? What changed in your equation? Have students write in their journals after they have a minute or two to discuss these with a neighbor. There are no numbers on purpose, so, watch for students who don’t use 1 interval scale if you want that discussion. You might want to limit the stories to height, distance, and money contexts if your students need to be more focused on the stories. © DMTI (2017) | Resource Materials | www.dmtinstitute.com

Linear Function Warm Ups Write a story (context) that matches this graph. Write an equation that matches your story and this graph. Have students write in their journals after they have a minute or two to discuss the tasks with a neighbor. There are no intervals given in order to prompt students’ thinking of appropriate scale intervals. Discuss the concept of intervals and scale as needed with students or the entire class. You might want to limit the contexts to height, distance, and money situations if students need more guidance on how to construct a context from a graph. © DMTI (2017) | Resource Materials | www.dmtinstitute.com

Linear Function Warm Ups Now, modify your story from the original line to the new line. Write an equation that matches your story and this graph. Have students write in their journals after they have a minute or two to discuss the tasks with a neighbor. There are no intervals given in order to prompt students’ thinking of appropriate scale intervals. Discuss the concept of intervals and scale as needed with students or the entire class. You might want to limit the contexts to height, distance, and money situations if students need more guidance on how to construct a context from a graph. © DMTI (2017) | Resource Materials | www.dmtinstitute.com

© DMTI (2017) | Resource Materials | www.dmtinstitute.com Now, write a story (context) for each graph. What does EACH number and variable mean in the story? Linear Number Sense Describe the following graphs with an equation. 1. 2. 3. Students’ don’t need to be exact, but should demonstrate a general understanding regarding the way in which the slope can be increasing to be greater than 1 or less than 1 as well as understanding of the y-intercept 𝑦= 1 2 𝑥 𝑦=𝑥 𝑦=2𝑥 © DMTI (2017) | Resource Materials | www.dmtinstitute.com

© DMTI (2017) | Resource Materials | www.dmtinstitute.com Now, write a story (context) for each graph. What does EACH number and variable mean in the story? Linear Number Sense Describe the following graphs with an equation. 4. 5. 6. 𝑦= 1 3 𝑥 −1 𝑦= 2 1 𝑥+2 𝑦=𝑥+1 © DMTI (2017) | Resource Materials | www.dmtinstitute.com

© DMTI (2017) | Resource Materials | www.dmtinstitute.com Now, write a story (context) for each graph. What does EACH number and variable mean in the story? Linear Number Sense Describe the following graphs with an equation. 7. 8. 9. 𝑦=−2𝑥−1 𝑦=− 1 3 𝑥+1 𝑦=−𝑥 © DMTI (2017) | Resource Materials | www.dmtinstitute.com

© DMTI (2017) | Resource Materials | www.dmtinstitute.com Now, write a story (context) for each graph. What does EACH number and variable mean in the story? Linear Number Sense Describe the following equations with a graph. 10. 𝑦=− 1 2 𝑥+1 12. 𝑦=𝑥 𝑦=3𝑥−2 11. © DMTI (2017) | Resource Materials | www.dmtinstitute.com

© DMTI (2017) | Resource Materials | www.dmtinstitute.com Now, write a story (context) for each graph. What does EACH number and variable mean in the story? Linear Number Sense Describe the following equations with a graph. 𝑦=− 3 2 𝑥+1 13. 15. 𝑦=−𝑥−3 𝑦= 2 3 𝑥+1 14. © DMTI (2017) | Resource Materials | www.dmtinstitute.com

© DMTI (2017) | Resource Materials | www.dmtinstitute.com Linear Number Sense Use Worksheets 9.1 to 9.3 to match the correct graph with the correct table with the correct equation. © DMTI (2017) | Resource Materials | www.dmtinstitute.com

© DMTI (2017) | Resource Materials | www.dmtinstitute.com Worksheet 9.1a Cut these out and shuffle them before matching. © DMTI (2017) | Resource Materials | www.dmtinstitute.com

© DMTI (2017) | Resource Materials | www.dmtinstitute.com Worksheet 9.1b Cut these out and shuffle them before matching. © DMTI (2017) | Resource Materials | www.dmtinstitute.com

© DMTI (2017) | Resource Materials | www.dmtinstitute.com Worksheet 9.2 𝒚=−𝒙+𝟎 𝒚= 𝟏 𝟏 𝒙 𝒚=− 𝟏 𝟑 𝒙+𝟎 𝒚=−𝟐𝒙 𝒚=𝟐𝒙 𝒚= 𝟑 𝟏 𝒙 𝒚=−𝒙+ 𝟏 𝟐 𝒚=𝒙 −𝟑 𝒚=− 𝟏 𝟑 𝒙+2 𝒚=− 𝟐 𝟏 𝒙−𝟑 𝒚= 𝟏 𝟐 𝒙−𝟑 𝒚=𝟑𝒙−𝟐 © DMTI (2017) | Resource Materials | www.dmtinstitute.com

© DMTI (2017) | Resource Materials | www.dmtinstitute.com Worksheet 9.3 X Y 𝟏 𝟐 𝟑 X Y 𝟎 𝟏 −𝟏 𝟐 −𝟐 X Y 𝟑 −𝟏 𝟔 −𝟐 𝟗 −𝟑 X Y 𝟎 2 3 1 6 X Y 𝟎 𝟐 𝟒 𝟖 X Y −𝟐 −𝟔 −𝟏 −𝟑 𝟎 X Y 𝟎 −𝟑 𝟐 −𝟏 𝟒 𝟏 X Y 𝟎 𝟏 𝟐 𝟏 − 𝟏 𝟐 𝟐 − 𝟑 𝟐 X Y 𝟏 −𝟐 𝟏 𝟐 𝟐 −𝟑 𝟑 −𝟏 𝟏 𝟐 X Y −𝟐 𝟏 −𝟏 𝟎 −𝟑 X Y −𝟐 −𝟖 −𝟏 −𝟓 𝟎 X Y 𝟎 𝟏 −𝟐 𝟐 −𝟒 © DMTI (2017) | Resource Materials | www.dmtinstitute.com

© DMTI (2017) | Resource Materials | www.dmtinstitute.com Brendefur and Strother (2017). DMTI Inc. www.dmtinstitute.com © DMTI (2017) | Resource Materials | www.dmtinstitute.com