General Information
Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.
Test Item Specifications
All triangles must be right triangles and on a coordinate grid. Numbers in items must be rational numbers. Functions must be linear.
Yes
Allowable
Sample Test Items (2)
Test Item # | Question | Difficulty | Type |
Sample Item 1 | Select all pairs of triangles that can be used to show the slope of a line is the same
anywhere along the line.
|
N/A | MS: Multiselect |
Sample Item 2 | Two collinear points are given in the table. Give a third point that is also on this line.
|
N/A | TI: Table Item |
Related Courses
Course Number1111 | Course Title222 |
1205050: | M/J Accelerated Mathematics Grade 7 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 - 2024, 2024 and beyond (current)) |
1205070: | M/J Grade 8 Pre-Algebra (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 and beyond (current)) |
1204000: | M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 and beyond (current)) |
7812030: | Access M/J Grade 8 Pre-Algebra (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current)) |
Related Resources
Formative Assessments
Name | Description |
Deriving Lines - 2 | Students are asked to derive the general equation of a line with a y-intercept of (0, b). |
Slope Triangles | Students are asked to use similar triangles to explain why the slope is the same regardless of the points used to calculate it. |
Deriving Lines - 1 | Students are asked to derive the general equation of a line containing the origin. |
Lesson Plans
Name | Description |
Slope Intercept - Lesson #3 | This is lesson 3 of 3 in the Slope Intercept unit. This lesson introduces similar triangles to explain why slope is the same between any two points on a non-vertical line. In this lesson students perform an activity to determine that slope is constant throughout a line and students will discover the slope for vertical and horizontal lines. |
Slope Intercept - Lesson #2 | This is lesson 2 of 3 in the Slope Intercept unit. This lesson introduces graphing non-proportional linear relationships. In this lesson students will perform an activity to collect data to derive y = mx + b and will use a Scratch program to plot the graph of the data, as well as check for proportional and/or linear relationships. |
Designing a Skateboard Kicker Ramp | In this lesson students will design a "Skateboard Kicker Ramp" to discover that slope of similar triangles is the same at any two distinct points. Students will model with mathematics the concept of slope by looking at the pattern set by similar triangles. |
Original Student Tutorial
Name | Description |
Hailey’s Treehouse: Similar Triangles & Slope | Learn how similar right triangles can show how the slope is the same between any two distinct points on a non-vertical line as you help Hailey build stairs to her tree house in this interactive tutorial. |
Problem-Solving Task
Name | Description |
Find the Change | This activity challenges students to recognize the relationship between slope and the difference in x- and y-values of a linear function. Help students solidify their understanding of linear functions and push them to be more fluent in their reasoning about slope and y-intercepts. This task has also produced a reasonable starting place for discussing point-slope form of a linear equation. |
Tutorials
Name | Description |
Finding the slope from two ordered pairs | This tutorial shows how to find the slope from two ordered pairs. Students will see what happens to the slope of a horizontal line. |
Using Similar Triangles to Prove that Slope is Constant for a Line | In this tutorial, you will use your knowledge about similar triangles, as well as parallel lines and transversals, to prove that the slope of any given line is constant. |
Finding the slope from two ordered pairs | This tutorial shows an example of finding the slope between two ordered pairs. Slope is presented as rise/run, the change in y divided by the change in x and also as m. |
Student Resources
Original Student Tutorial
Name | Description |
Hailey’s Treehouse: Similar Triangles & Slope: | Learn how similar right triangles can show how the slope is the same between any two distinct points on a non-vertical line as you help Hailey build stairs to her tree house in this interactive tutorial. |
Problem-Solving Task
Name | Description |
Find the Change: | This activity challenges students to recognize the relationship between slope and the difference in x- and y-values of a linear function. Help students solidify their understanding of linear functions and push them to be more fluent in their reasoning about slope and y-intercepts. This task has also produced a reasonable starting place for discussing point-slope form of a linear equation. |
Tutorials
Name | Description |
Finding the slope from two ordered pairs: | This tutorial shows how to find the slope from two ordered pairs. Students will see what happens to the slope of a horizontal line. |
Using Similar Triangles to Prove that Slope is Constant for a Line: | In this tutorial, you will use your knowledge about similar triangles, as well as parallel lines and transversals, to prove that the slope of any given line is constant. |
Finding the slope from two ordered pairs: | This tutorial shows an example of finding the slope between two ordered pairs. Slope is presented as rise/run, the change in y divided by the change in x and also as m. |
Parent Resources
Problem-Solving Task
Name | Description |
Find the Change: | This activity challenges students to recognize the relationship between slope and the difference in x- and y-values of a linear function. Help students solidify their understanding of linear functions and push them to be more fluent in their reasoning about slope and y-intercepts. This task has also produced a reasonable starting place for discussing point-slope form of a linear equation. |