High School Math Guide

Connecting Algebra and Geometry

Unit 8

MATH CORE STANDARDS I.G.GPE.7 : Use coordinates to compute perimeters of polygons and areas of triangles and rectangles; connect with the Pythagorean Theorem and the distance formula. I.G.GPE.5 : Prove the slope criteria for parallel and perpendicular lines; use them to solve geometric problems. I.G.GPE.4 : Use coordinates to prove simple geometric theorems algebraically I.F.BF.3 : Identify the effect on the graph of replacing f(x) by f(x) + k , for specific values of k (both positive and negative); find the value of k given the graphs. Relate the vertical translation of a linear function to its y- intercept. I.F.BF.1 : Write a function that describes a relationship between two quantities. I.F.IF.9 : Compare properties of two functions, each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Critical Background Knowledge • Solve real-world and mathematical problems involved perimeters of polygons (3.G.8)

• Compose and understand the coordinate plane (5.G.1) and solve problems by graphing points in all four quadrants of the coordinate plane and use coordinates to find distance between points with same x-coordinate or same y-coordinate (6.NS.8) • Find and position pairs of integers and other rational numbers on a coordinate plane (6.NS.6c) • Draw polygons in the coordinate plane given coordinates for the vertices (6.G.3) • Solve real-world problems involving area (7.G.6) • Interpret the equation y = mx +b as defining a linear function, whose graph is a straight line (8.F.3,4) • Use similar triangles to explain why the slope m is the same between any two district points (8.EE.6) • Apply the Pythagorean Theorem to find the distance between two points (8.G.8) • Create equations in tow or more variable to represent relationships between quantities; graph equations on coordinate axes with labels and scales (I.A.CED.2) • Graphing linear (8.F.3) and exponential (I.F.IF.7) functions. • Definition of function (8.F.3) • Construct linear functions (8.F.4) • Simplifying expressions (7.EE.2) • Apply integer exponent properties (8.EE.1) • Describe relationships between quantities (8.F.5) • Compare properties of two functions (linear to linear), each represented in a different way (8.F.2) • Interpret the equation of y = mx + b as defining a linear function (8.F.3) • Construct a function, determine and interpret a rate of change and initial value of a linear function (8.F.4) • Analyze graphs (increasing, decreasing, linear or nonlinear) (8.F.5)