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Algebra 1 Honors 7th grade or 8th grade
In Volusia County, courses are structured by Common Core State Standards (CCSS) even though you will be tested this year accoring to Florida's Next Generation Sunshine State Standards and associated benchmarks. You are hearing a lot about the Common Core Standards which will replace the NGSSS. This does not have a huge impact on your exam but it will change the topics we cover and the order we cover them.
The Real Number System- Review
Essential Question(s): How does knowledge of integers help when working with rational and irrational numbers?
| MACC.912.N-RN.2.3. Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. |
• classify real numbers as rational or irrational according to their definitions. • add, subtract, multiply and divide real numbers. • explain why the sum of two rational numbers is rational. • explain why the product of two rational numbers is rational. • explain why the sum of a rational and irrational is irrational. |
Unit 1-Solving Equations and Inequalities
Essential Question(s):
How can algebra describe the relationship between sets of numbers?
In what ways can the problem be solved, and why should one method be chosen over another?
| MACC.912A-CED.1.1. Create equations and inequalities in one variable and use them to solve problems. |
• identify the variables and quantities represented in a real world problem. • write the equation or inequality that best models the problem. • solve linear equations and inequalities. • interpret the solution in the context of the problem. |
| MACC.912A.REI.1.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. |
• explain a process to solve equations. • apply the distributive property when necessary to solve equations. • construct a viable argument to justify a solution method. |
| NGSS MA.912.A.5.4 | • solve algebraic proportions |
| MACC.912A.CED.1.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. |
• identify the variable and quantities represented in a real-world problem. • determine the best models for a real-world problem. • write inequalities that best models a problem. |
| MACC.912A.CED.1.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. |
• solve a formula for a given variable. • solve problems involving literal equations. |
| MACC.912A.REI.2.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. |
• solve linear equations and inequalities in one variable. |
Unit 2 - Linear Equations and Their Graphs
Essential Question(s):
In what ways can the problem be solved, and why should one method be chosen over another?
| MACC. 912.F-IF.1.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, the f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y=f(x). |
• define relation, domain and range. • define a function as a relation in which each input (domain) has exactly one output (range). • determine if a graph, table or set of ordered pairs represent a function. • determine if stated rules (both numeric and non-numeric) produce ordered pairs that form a function. • explain that when ‘x’ is an element of the input of a function f(x) represents the corresponding output. • explain that the graph of ‘f’ is the graph of the equation y=f(x). |
| MACC. 912.F-IF.1.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. |
• decode function notation and explain how the output of a function is matched to its input. • convert a table, graph, set of ordered pairs or description into function notation by identifying the rule used to turn inputs into outputs and writing the rule. • use order of operations to evaluate a function for a given domain value. • identify the numbers that are not in the domain of a function. • choose and analyze inputs (and outputs) that make sense based on the problem. • explain how the domain of a function is represented in its graph. • state, defend and explain the appropriate domain of a function that represents a problem situation. |
| MACC. 912.F-IF.2.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. |
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| MACC. 912.F-IF.2.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. |
• locate the information that explains what each quantity represents. • interpret the meaning of an ordered pair. • determine if negative inputs and/or outputs make sense in the problem. • identify and explain the x and y intercept • define intervals of increasing and decreasing of a table or graph. • identify and explain relative maximums and minimums. • identify reflective and rotational symmetries in a table or graph. • explain why the function has symmetry in the context of the problem. • identify and explain positive and negative end behavior of a function. • define and identify a periodic function from a table or graph. • explain why a function is periodic. |
| MACC. 912.F-IF.2.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. |
• define and explain interval, rate of change and average rate of change. • calculate the average rate of change of a function, represented either by function notation, a graph or a table over a specific interval. • compare the rates of change of two or more functions. • interpret the meaning of the average rate of change in the context of the problem. |
| MACC.912.A-CED.1.2 Create equation in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales |
• set up coordinate axes using an appropriate scale and label the axes. • write equations of lines in various forms. • graph equations on coordinate axes with appropriate labels and scales. |
| MACC.912.G.1.4 Use coordinate geometry to find slopes, parallel lines, perpendicular lines, and equations of lines. |
• write equations of parallel and perpendicular lines. |
| MACC.912.A-REI.4.10. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). |
• explain that every ordered pair on the graph of an equation represents values that make the equation true. • verify that any point on a graph will result in a true equation when their coordinates are substituted into the equation. |
| MACC.912.F-IF.3.7a Graph linear functions by hand and show intercepts, maxima, and minima. |
• identify that the parent function for lines is the line f(x) = x. • identify and graph a line in the point-slope form: y-y1=m(x-x1). • identify and graph a line in slope-intercept form: f(x)=mx+b. • identify the standard form of a linear function as Ax + By = C. • use the definitions of x and y intercepts to find the intercepts of a line in standard form and then graph the line. • relate the constants A, B, and C to the values of the x and y intercepts and slope. |
| MACC.912.F-LE.2.5 Interpret the parameters in a linear function in terms of a context. |
• identify the names and definitions of the parameters ‘m’ and ‘b’ in a linear function f(x)=mx+b. • explain the meaning (using appropriate units) of the slope, y-intercept and other points on the line when then line models a real-world relationship. • compose an original problem situations and construct a linear function to model it. |
We divide the courses by Essential Questions. The Essential Questions are then divided by Measurement Topics which are then outlined with learning targets.
Here are essential questions for algebra:
Measurement Topic |
Learning Target |
NGSSS |
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show the relationships between subsets of real numbers using Venn Diagrams |
MA.912.D.7.2 |
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perform set operations such as union and intersection, complement, and cross product |
MA.912.D.7.2 |
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Equations |
solve linear equations |
MA.912.A.3.1 |
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write and solve multi-step equations to represent real world situations |
MA.912.A.3.5 |
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solve literal equation for a specified variable |
MA.912.A.5.1 |
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solve algebraic proportions |
MA.912.A.5.2 |
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Inequalities |
identify and apply properties of real numbers and properties of inequalities |
MA.912.A.3.4 |
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solve and graph compound linear inequalities |
MA.912.A.3.4 |
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write and solve multi-step inequalities to represent real world situations |
MA.912.A.3.5 |
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solve and graph the solutions of absolute value equations and inequalities with one variable |
MA.9.12.A.3.6* |
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Proportionality |
determine the slope using the given information (two points, graph) |
MA.912.A.3.9 |
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determine the slope and y-intercept using an equation, a graph or two points |
MA.912.A.3.9 |
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Linear Equations |
write an equation from two points, a graph |
MA.912.A.3.10 |
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graph an equation using slope and y-intercept |
MA.912.A.3.8 |
1st Grading period review 3rd grading period review
Please note that there is now a state end-of-course exam for algebra 1 courses in Florida. This exam is taken in May. You must pass this exam in order to graduate from high school. I have placed prep material on this site(click here.)
You can read more at http://www.floridastandards.org/Courses/PublicPreviewCourse1.aspx
links on this siteExponential notation Percent converting fractions and decimals
pre algebra sample questions rates and proportions
greatest common factor least common multiple prime factorization
Introduction to rules for using exponents
links off-site
7th grade FCAT sample test (2.0)
8th grade FCAT sample test (2.0)webmath.com aaamath.com www.mathway.com/ math.com/students/homeworkhelp.html