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Slope from Similar Triangles Guided Notes w/ Doodles | Slope Intercept Form
$4.25
Overview
- Standard: CCSS 8.EE.B.6
- Unit: 8th Grade → Unit 4: Functions
- Grade: 8th Grade
Get the Lesson Materials
Slope from Similar Triangles Guided Notes w/ Doodles | Slope Intercept Form
$4.25
Learning Objectives
After this lesson, students will be able to:
- Apply the principles of similar triangles to find the slope of a line
- Calculate the slope from a graph on a coordinate plane
- Determine the slope of a line using two given points
- Write linear equations in slope-intercept form (y=mx and y = mx + b)
Prerequisites
Before this lesson, students should be familiar with:
- Identifying points on a coordinate plane and graphing ordered pairs
- Understanding the concept of similar triangles and how their sides are proportional
Materials
- Pencils
- Colored pencils or markers
- Slope from Similar Triangles Guided Notes w/ Doodles | Slope Intercept Form
Key Vocabulary
- Slope
- Similar triangles
- Rate of change
- Slope Intercept Form
Procedure
Introduction
As a hook, ask students why understanding slope is important in real-life scenarios such as determining the steepness of a hill for construction or designing a ramp for accessibility.
Use the first page of the guided notes to introduce the concept of slope and how it is calculated using principles of similar triangles. Walk through the key points of identifying rise over run and explaining how slope relates to the steepness of a line.
Continue using the subsequent pages of the guided notes to dive deeper into understanding slope, including identifying positive, negative, zero and undefined slope. Provide examples and guide students through calculating slope from graphs and given points. Refer back to the real-life application of slope to reinforce the relevance of this mathematical concept.
Using the next page of the guided notes (pg. 3), teach students how to calculate slope using two ordered points and then write equations in y=mx and y=mx + b forms.
Based on student responses and engagement levels, reteach concepts that students need extra help with regarding slope calculations and the relationship with similar triangles. If your class has varying proficiency levels, consider pulling out students for targeted reteaching while allowing more advanced students to work on the practice exercises provided.
Practice
Walk around the classroom to address any questions students may have while they work on the practice worksheet (pg. 2-3) and the maze activity (pg. 4 of guided notes).
Fast finishers can move on to the color by number activity (pg. 5 of guided notes) included in the resource for extra practice. You can also assign it as homework for the remaining class time.
Real-Life Application
Using the last page of the guided notes (pg. 6), bring the class back together, and introduce the concept of calculating slope in real-world scenarios. Students read about real life applications of slope and discuss how understanding slope is essential in fields like architecture, where builders need to determine the slope of roofs to ensure proper drainage, or in sports like skiing, where the slope of a hill impacts the speed at which skiers travel. Refer to the FAQ for more ideas on how to teach real-life applications of slope!
Extensions
Additional Self-Checking Digital Practice
If you’re looking for digital practice for adding and subtracting numbers in scientific notation, try my Pixel Art activities in Google Sheets. Every answer is automatically checked, and correct answers unlock parts of a mystery picture. It’s incredibly fun, and a powerful tool for differentiation.
Here are some activities to explore:
- Calculating Slope (Points, Graphs, Equations) Pixel Art
- Constructing Linear Functions Pixel Art
- Slope Intercept Form Linear Functions Pixel Art
Additional Print Practice
A fun, no-prep way to practice adding and subtracting numbers in scientific notation is Doodle Math — they’re a fresh take on color by number or color by code. It includes multiple levels levels of practice, perfect for a review day or sub plan.
Here are some activities to try:
Another engaging method for practicing slope is through the Slope Sketches Math Project. In this project, students enhance their skills by calculating the slope of various lines within a character drawing inspired by Alex from Minecraft. This makes for an ideal project-based learning activity, unit review, exam preparation, or substitute plan to conclude your unit with!
This activity is NOT AN OFFICIAL MINECRAFT PRODUCT. NOT APPROVED BY OR ASSOCIATED WITH MOJANG.
FAQs
Slope is a measure of the steepness of a line. It represents how much a line rises or falls for every unit it moves to the right.
- Slope is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on a line.
To calculate slope from similar triangles, you need to compare the rise and run of the line to the corresponding sides of a similar triangle.
- Identify the rise and run on the line and compare them to the corresponding sides of the similar triangle.
- Use the proportions of corresponding sides to find the slope of the line.
Slope intercept form is a way to write the equation of a line in the form y = mx + b, where m represents the slope of the line and b represents the y-intercept.
- The slope intercept form makes it easy to identify the slope and y-intercept of a line from its equation.
To graph a line using the slope intercept form, start by plotting the y-intercept (where x=0), then use the slope to find another point on the line.
- Plot the y-intercept first at the point (0, b).
- Use the slope to find a second point by moving vertically (for the rise) and horizontally (for the run) from the y-intercept.
- Connect the two points to draw the line.
The slope of a line directly correlates to its steepness.
- A larger slope value indicates a steeper line, while a smaller slope value represents a flatter line.
- A positive slope indicates an upward slope, while a negative slope represents a downward slope.
Understanding slope helps in various real-life scenarios, such as calculating rates of change, gradients, and determining the direction of change.
- In engineering and architecture, slope helps in designing ramps, roads, and roofs.
- In economics, slope helps in analyzing trends in graphs and predicting future outcomes.
Writing equations in slope intercept form (y = mx + b) makes it easier to interpret the equation visually and extract critical information about the line.
- The form directly shows the slope (m) and y-intercept (b) of the line, providing valuable information for graphing and analysis.
Similar triangles provide a geometric way to understand the concept of slope visually.
- By comparing the sides of similar triangles with the rise and run of a line, you can grasp the relationship between the angles of inclination and the slope.