# Slippery Slopes!

How does the slope of a ski path affect the swiftness of the skier?

Curriculum Topics: Slope of a Line, Graphing Linear Equations

### Standards

Idea Sheets are cross-referenced to subjects listed in the Common Core, Next Generation Science Standards, and California Content Standards.

Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 6||Mathematical Practices|||Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 7||Mathematical Practices|||7.EE.1. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.||Common Core Mathematics||Grade 7||Expressions And Equations||Use Properties Of Operations To Generate Equivalent Expressions|||Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 8||Mathematical Practices|||8.EE.5. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.||Common Core Mathematics||Grade 8||Expressions And Equations||Understand The Connections Between Proportional Relationships, Lines, And Linear Equations|||8.EE.6. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.||Common Core Mathematics||Grade 8||Expressions And Equations||Understand The Connections Between Proportional Relationships, Lines, And Linear Equations|||8.EE.7. Solve linear equations in one variable.||Common Core Mathematics||Grade 8||Expressions And Equations||Analyze And Solve Linear Equations And Pairs Of Simultaneous Linear Equations|||8.F.3. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.||Common Core Mathematics||Grade 8||Functions||Define, Evaluate, And Compare Functions|||Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||High School||Mathematical Practices

3.3 Graph linear functions, noting that the vertical change (change in y-value) per unit horizontal change (change in x-value) is always the same and know that the ratio (“rise over run”) is called the slope of a graph.||CA Mathematics||Grade 7||02. Algebra and Functions||3.0 Students graph and interpret linear and some nonlinear functions.|||4.0 Students solve simple linear equations and inequalities over the rational numbers.||CA Mathematics||Grade 7||02. Algebra and Functions|||4.1 Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results.||CA Mathematics||Grade 7||02. Algebra and Functions||4.0 Students solve simple linear equations and inequalities over the rational numbers.|||07.0 Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using the point-slope formula.||CA Mathematics||Grade 8 – 12||01. Algebra I

Categories include: