Subject: Algebra 1
Subject: Algebra 1
Grade Level: 7th
Unit Title: What’s my line? |Timeframe Needed for Completion:
Grading Period: 2nd nine weeks | |
|Big Idea/Theme: Coordinate plane, functions, linear equations in standard, slope intercept and point slope form, developing regression lines, all areas involving linear inequalities, and solving systems of |
|equations and inequalities, using graphing, substitution and elimination. |
|7th grade topics: Histograms, Box and whisker plots, Central Tendencies |
|Understandings: Graphing linear equations and inequalities, solving systems of equations and inequalities, determing correlation and best-fit lines |
|Essential Questions: |Curriculum Goals/Objectives (to be assessed at the end of the unit/quarter) |
|How can scatterplots be used to predict information? |Find the lengths and midpoints of segments to solve problems (2.01) |
|In the equation y = 4x, what is the constant of variation |Use formulas and algebraic expressions to model and solve problems (1.02) |
|What are the advantages and disadvantages of using graphs, using equations, and using tables? |Model and solve problems using direct variation (1.03) |
|Describe situations where compound inequalities are used in life. |Create linear models for sets of data to solve problems: interpret constants and coefficients in the |
|List examples where parallel and perpendicular lines are found in everyday items. |context of the data, and check the model for best fit and use the model, where appropriate, to draw |
|Describe situations where systems of equations are applicable to real life situations. |conclusions or make predictions (3.03). |
|Describe some real life examples using direct variation |Use linear functions or inequalities to model and solve problems: a) solve using tables, graphs and |
| |algebraic properties, and b) interpret constants and coefficients in the context of the problem (4.01) |
| |Use systems of linear equations or inequalities in two variables to model or solve problems. Solve |
| |using tables, graphs and algebraic properties (4.03) |
| |Use the parallelism or perpendicularity of lines and segments to solve problems (2.02). |
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|Essential Skills/Vocabulary: |Assessment Tasks: |
|Vocabulary: arithmetic sequence, axes, best-fit line, boundary, common difference, compound inequality,| |
|constant of variation, coordinate plane, direct variation, elimination, function, function notation, |Quick writes |
|graph, half-plane, intersection, inverse, linear equation, linear extrapolation, linear interpolation, |Teacher made tests and quizzes |
|line of fit, mapping, negative correlation, origin, parallel lines, perpendicular lines, point-slope |Find the error |
|form, positive correlation, quadrant, rate of change, scatter plot, sequence, slope, slope-intercept |Foldables |
|form, standard form, substitution, system of equations, system of inequalities, terms, union, vertical |Cornell notes |
|line test, x-axis, x-coordinate, x-intercept, y-axis, y-coordinate, y-intercept |Groupwork |
| |Projects |
| |Graphic organizers |
|Essential skills: |Venn Diagrams |
|construct scatterplots from data |Anticipation/prediction guides |
|determine best fit lines | |
|use the best fit line to predict both inside and outside the data | |
|find the midpoint of a line segment | |
|find the endpoint of a line segment given the midpoint and one endpoint | |
|write, graph and solve problems involving direct variation. | |
|determine if a relation is a function, including using the vertical line test | |
|find the slope given two points, from a table, from a graph | |
|graph linear equations and inequalities from a table, from data contained in a problem | |
|write equations in point slope, slope-intercept and standard forms | |
|graph equations from point-slope, slope-intercept and standard forms | |
|solve compound inequalities (and/or) | |
|solve absolute value inequalities | |
|solve systems of equations using graphing, and elimination | |
|solve systems of inequalities, graph the solution | |
|understand parallelism and perpendicularity of lines | |
|find the distance between points on the coordinate plane | |
|find a point a given distance from another point in a plane | |
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|Guiding questions: | |
|What is a scatterplot and how is it helpful when making | |
|predictions. | |
|What is meant by a best fit line? | |
|How is a best fit line used to make predictions? | |
|How is a best fit line used to draw conclusions? | |
|How can the results of statistical investigations be used to support an argument? | |
|Why is the distance formula a direct variation? | |
|Given two points on a line, how do you find the slope? | |
|What is slope intercept form of a line and how can it be used to draw the line it represents? | |
|How can I write a linear equation with standard and slope intercept forms of equations? | |
|How can you tell if a given equation passes through a given point? | |
|How can I write an equation that models given data? | |
|How do you determine the y-intercept of an equation in slope-intercept form? In standard form? What do | |
|we know about lines that are parallel? Perpendicular? | |
|What is the relationship between the domain and range of a function? | |
|What is a linear equation? | |
|What is the vertical line test for a function? | |
|What are two examples of non-linear equations? | |
|Given a set of ordered pairs, a graph, or a table, how would you determine if these relations are | |
|functions? | |
|How can compound inequalities help describe real world situations? | |
|How are graphing equations similar, and different, from graphing inequalities? | |
|How can I solve and graph inequalities using the properties of inequality? | |
|How are patterns of change represented in functions? | |
|What methods can be used to solve systems of equations? | |
|How are systems of equations and inequalities useful? | |
|Materials Suggestions: |
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