Download Integrated Algebra January

January Topic: Linear Functions & Statistics
Grade: Algebra 1
Big Idea:
Students will learn how to solve a system of equations graphically and approximately from real-world and mathematical
problems. Students will also learn how to identify the solution set of a system of inequalities graphically and
algebraically. Students will apply their knowledge of linear functions to investigate patterns of association in bivariate
data.
Essential Information:
I- Review of Comparing Linear Functions
 Comparing rates of change, initial value, domain, range, etc. in terms of the context the function models on
specific intervals.
II – Graphing Linear Systems
 Understand that the intersection of two equations in two variables is the solution.
 Create a system of equations from a word problem and solve graphically.
 Estimate the solution of a system of equations graphically.
 Understand that if a system of equations has no solution the lines are parallel.
 Understand that if a system of equations has infinite solutions the lines are coincident.
II – Systems of Inequalities
 Understand that the solution set of a system of linear inequalities is the intersection of their corresponding half
planes.
 Create and solve a linear system of inequalities graphically from a word problem
 Create and solve a linear system of inequalities algebraically from a word problem
III – Statistics
 Know the different types of data and how to distinguish between them
o Univariate vs. bivariate
o Qualitative vs. quantitative
 Construct and interpret scatter plots to display data
o Positive, negative, or no correlation
o Outliers?
o Linear or nonlinear relationship
 Drawing a line of best fit in a scatter plot to show the relationship between the data and determining its linear
equation (using the graph and/or by using technology).
 Interpolate and extrapolate information from the scatter plot and line of best fit about the data.
 Understand if the data forms a causal relationship based on the scatter plot or by the data displayed in a chart
IV – Volume
 Know the formulas for volume of a cylinder, sphere, and cone.
 Apply the formulas for volume to solve real-world and mathematical problems.
o Including problems that require the formula to be rearranged when solving for a missing value, such as
the height.
January Topic: Linear Functions & Statistics
Grade: Algebra 1
Common Core State Standards:
8.EE.8a
8.EE.8c
A-REI.12
A-CED.3
8.SP.1
8.SP.2
8.SP.3
8.SP.4
8.G.9
Vocabulary:
Materials:
System of Equations
Pencil
Parallel
Paper
Coincident
Calculator
Half-Plane
Graph Paper
Solution Set
Ruler
Scatter Plot
Univariate Data
Bivariate Data
Qualitative Data
Quantitative Data
Correlation
Outlier
Linear Regression
Line of Best Fit
Interpolate
Extrapolate
Causal
“Solve for” _ “in terms of” _
Learning Objectives:
Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of
their graphs.
Understanding how to solve real-world and mathematical problems leading to two linear equations in two variables.
Understanding how to graph the solutions to a system of linear inequalities as the intersection of the corresponding half
planes.
Understanding how to represent constraints by a system of inequalities and interpret solutions as viable or non-viable
options in a modeling context.
Understanding how to construct and interpret scatter plots for bivariate data to investigate patterns of association
between two quantities.
Understanding how to draw a line of best fit to model relationships between two quantitative variables and to
informally assess the model fit by judging the closeness of the data points in the line.
Understanding how to interpolate and extrapolate information from the equation of a line of best fit to solve problems.
Understanding how to determine whether or not bivariate data has a causal relationship, and constructing and
interpreting tables summarizing data collected from subjects.
Apply the formulas for volumes of cones and cylinders to solve mathematical problems.
Apply the formulas for volume of spheres to solve mathematical problems.
January Topic: Linear Functions & Statistics
Grade: Algebra 1
Apply the formulas for volumes of cones, cylinders, and spheres to solve real-world and mathematical problems.
Assessments:
Systems of Equations Test
Systems of Inequalities Test
Statistics Test
Volume Quiz
Project