Algebra 1
Year Long Standards
Unit 1 – Connections to Algebra
Unit 2 – Solving Linear Equations
Unit 3 – Functions and Graphing
Unit 5- Systems of Linear Equations
Unit 6- Exponential Notation
Unit 7- Solving Quadratics
Unit 8- Quadratic Functions and Graphing
Unit 10- Displaying Data
Year Long Standards
- Students will make connections to real world applications.
- Students will use appropriate units of measure
- Students will evaluate answers for reasonableness.
- Students will create mathematical models to represent real world situations.
- Students will estimate the parameters and constraints of problems.
- Students will appropriately use technology.
- Students will understand and correctly use algebra terminology.
Unit 1 – Connections to Algebra
- Students will accurately evaluate mathematical expressions by applying the correct order of operations.
- Positive and negative numbers review – Add, subtract, multiply and divide real numbers.
- Evaluate, expand and contract exponents (non-variable)
- Students will understand and correctly use algebra terminology.
- Coefficient, variables, exponent, expression versus equations versus inequalities, like terms, solution, reciprocal.
- Students will simplify variable expressions.
- Identify terms of an expression
- Combine like terms of an expression
- Add, subtract, multiply and divide variable terms
- Correctly use distributive property
- Students will accurately round numbers to given place values.
- Place value names
- Students will translate written words into algebraic expressions.
- Students will evaluate expressions using an input/output table.
- Students will determine if given values are solutions of equations or inequalities (understanding what a solution means for an equation or inequality)
- Students will order decimals, fractions, positives, negatives, and whole numbers.
Unit 2 – Solving Linear Equations
- Students will be able to solve single variable equations.
- One step equations; undoing addition, subtraction, multiplication and division.
- Solving multi-step equations with variable on one side, no distributive property.
- Solving multi-step equations with variables on one side including like terms and distributive property.
- Solving multi-step equations with variables on both sides.
- Solving equations containing fractions and decimals, including techniques for eliminating them first.
- Approximating solutions by rounding decimals and recognizing the check will not be exact, but appropriate.
- Solving proportions.
- Probability (CC Probability requirement)
- Experimental
- Theoretical
- Frequency tables
- Odds
- Percentages
Unit 3 – Functions and Graphing
- Students will be able to manipulate a multi-variable equation or formula in order to isolate one variable.
- Terminology: coordinate plane, x and y axis, coordinate (x,y), quadrants, origin, ordered pair.
- Students will be able to describe locations in a plane and be able to plot locations given an ordered pair.
- Students will be able to graphically represent the solutions of linear functions.
- Understand functions have infinite solutions consisting of pairs of numbers.
- Graph a linear equation using a t-chart.
- Discuss the concept of intercepts
- Discuss equations that have only one intercept, eg. vertical and horizontal lines,
- Slope.
- Rate of change.
- What does slope mean.
- Positive/negative/zero/undefined slopes
- Calculate using various methods
- Graphing equations in y = mx + b
- Given m and b.
- Given a point and a slope.
- Given two points.
- Students will be able to write equations of lines in slope intercept form.
- Give m and b.
- Given a point and a slope.
- Given two points.
- Given a graph.
- Write the equations of lines parallel or perpendicular to a given line.
- Students will be able to calculate the equation of the line of best fit. (CC statistics requirement)
- Correlation coefficient.
- Students will be able to solve and graphically represent the solutions of single variable inequalities.
- Solve one step linear inequalities
- Solve multistep linear inequalities
- Know when to “flip” the inequality sign
- Write, solve and graph compound inequalities
- Students will be able to solve and graphically represent the solutions of a linear inequality in two variables.
- Solve and graphically represent the solutions of a system of linear inequalities.
Unit 5- Systems of Linear Equations
- Students will solve a system of linear equations/functions
- By graphing
- By substitution
- By linear combination
- Choose the best method for solving a system of linear equations
- Identify linear systems as having one solution, no solutions, or infinitely many solutions.
Unit 6- Exponential Notation
- Students will use properties of exponents to simplify or expand expressions with exponents.
- Simplify expressions using exponents. (ex. 5*5*5*5=54)
- Expand exponential notation. (ex. x3=x*x*x)
- Discover properties of exponents.
- (x2)3= x6
- x2*x3=x5
- =x3
- Explain why (x+1)2≠x2+12 (choose a value for x and check)
- Kay will check with Science Dept. about scientific notation
Unit 7- Solving Quadratics
- Identify or describe a polynomial/monomial, term, and coefficient.
- Students will be able to add and subtract polynomials.
- Students will be able to multiply polynomials.
- By FOIL method.
- By distributive property.
- Students will factor various quadratic expressions in the form ax2+bx+c, where a, b, and c are whole number coefficients.
- Factor a quadratic expression of the form x2+bx+c
- Factor a quadratic expressions of the form ax2+bx+c
- Use distributive property to factor a polynomial. (factor by grouping)
- Students will be able to solve a variety of quadratic equations.
- By finding square roots
- By factoring
- By using the quadratic formula (with real solutions)
Unit 8- Quadratic Functions and Graphing
- Students will be able to solve and graphically display the solutions to quadratic functions.
- Sketch a graph using the vertex and a table of values.
- Verify graphs using technology (e.g. desmos.com)
- Students will be able to solve a quadratic equation graphically.
- By finding the zeros/roots
- Compare solutions graphically to solutions found algebraically
- Use the discriminant to verify the number of solutions.
- Students will understand the relationship between the distance formula and the Pythagorean Theorem.
- Calculate the distance in a coordinate plane between two points.
- Students will use the Pythagorean Theorem and trigonometry to solve right triangles.
Unit 10- Displaying Data
- Students will interpret data and choose the best method to graphically display data.
- Histrogram
- Bar Graph
- Scatter plot
- Box plot
- Line Graph
- Circle Graph
- Students will calculate measures of central tendency for sets of data.
- Mean
- Median
- Mode
- Outliers
- Calculate quartiles