High School Mathematics Algebra I Part II Unit 5
Subject: Mathematics
Course: Algebra I Part II
Timeline: 12-24 Days
Unit 5 Title: Graphing Two-Variable Linear Equations and Inequalities
Unit Overview:
This unit formalizes the connections between both the parts of a linear equation and the different forms of linear equations. Recognizing slope as the steepness of the line in a graph, the constant rate of change in a problem context, the constant difference between output values when given the same change in the input values in a table, and the coefficient of the independent variable in an equation is emphasized. Similarly, students will recognize the y-intercept as where the line crosses the y-axis, the starting value in a problem context, the output value when the input is 0 in a table, and the constant term in an equation. Students are required to write different forms of linear equations and fluently translate between one form and another. Students will investigate the slopes of parallel and perpendicular lines and use patterns to draw conclusions. Finally, students will draw lines of best fit and write their equations when given a scatter plot. Graphing calculators are used extensively throughout this unit to graph linear equations when given an equation, points on the line, and/ or a table.
Unit Objectives:
By the end of Unit 5, all students will be able to:
- identify, define, and use rate of change;
- compare and contrast multiple representations of rate of change;
- apply the concept of slope to parallel and perpendicular lines;
- write or identify a linear equation in different forms (standard, slope-intercept, and point-slope);
- write or identify a linear equation when given different information (graph, two points, and the slope and a point on a line);
- determine the slope and y-intercept when given either a linear equation or graph;
- draw or identify the line of best fit given a scatter plot:
- fluently use the GRAPH and TABLE functions on a graphing calculator to graph linear equations given an equation, points on the line, and/ or a table.
Focus Standards:
PA.CCSS.Math.Eligible Content.A1.2.2.1.1 Identify, describe, and/ or use constant rates of change.
PA.CCSS.Math.Eligible Content.A1.2.2.1.2 Apply the concept of linear rate of change (slope) to solve problems.
PA.CCSS.Math.Eligible Content.A1.2.2.1.3 Write or identify a linear equation when given the graph of the line, two points on the line, or the slope and a point on the line.
PA.CCSS.Math.Eligible Content.A1.2.2.1.4 Determine the slope and/ or y-intercept represented by a linear equation or graph.
PA.CCSS.Math.Eligible Content.A1.2.2.2.1 Draw, identify, find, and/ or write an equation for a line of best fit for a scatter plot.
Mathematical Practice Standards:
#3 Construct viable arguments and critique the reasoning of others.
#5 Model with mathematics.
#7 Look for and make use of structure.
Assessments:
- Quiz 5.1-5.4
- Unit 5 Assessment
Differentiation:
This unit has accommodation suggestions included throughout.