Curriculum Map–Algebra 1
Course Understandings / Essential Questions / Assessments / Course Knowledge/SkillsStandards/Eligible Content
First Quarter
Students will understand:
Analyze Graphs:
Read and analyze graphs; create box/whisker, stem/leaf, bar/line graphs and scatter plots; make predictions and generalizations from graphs; design and conduct an experiment using random sampling; find measures of central tendency; calculate and apply interquartile range; make predictions based on line of best fit. (Ch 1.6 4.1, 6.7, 3 days)
Probability and odds:
Calculate probability and odds from independent, dependent and compound events.(Ch 2.8, 3 days)
Numbers and their relationships:
Compare irrational numbers; evaluate numerical expressions including the four basic operations and include roots, reciprocals, opposites, and absolute values; scientific and exponential notation; solve expressions using the rules for signed numbers. (Ch 1, 2; 15 days)
Radicals:
Evaluate roots and find solutions using the Pythagorean Theorem. (Ch 2, 9 days)
Solving Equations:
Solve one and two step equations, include distribution and fractions. (Ch 3: 10 days) / How does the use of properties help to solve expressions?
How does the order of operations impact the process by which expressions and/or equations are solved?
How can absolute value situations occur in the real world?
Summarize the differences between finding the results of probability and odds.
How can data be illustrated differently? How can you create an algebraic equation from a word problem or a graph?
How are measures of central tendencies represented in data on different graphs?
How do you isolate a variable?
How does grouping like terms assist in solving an algebraic equation?
How can you predict the trend of data from a graph?
Compare/contrast domain vs range.
How can you use the distributive property to simplify an equation that has a fraction? / Diagnostic:
The students will be assessed at the start of the school year through a diagnostic pre-test to determine current academic levels.
Formative:
The students will be assessed using daily student questioning to check for understanding of section.
The students will be assessed with weekly quizzes on individual units, emphasizing new or more difficult curriculum areas.
The students will be assessed using unit blogs to gauge student comprehension of content and to facilitate open-ended writing skills.
Summative:
The students will be assessed by a quiz on properties and solving expressions with absolute value and order of operations.
The students will be assessed by a quiz number line.
The students will be assessed by a quiz on finding probability and odds of dependent/independent events.
The students will be assessed by a quiz and test on solving expressions using the rules for signed numbers, including absolute value expressions.
The students will be assessed by a quiz and tests for simplifying radical expressions and application problems using the Pythagorean Theorem.
The students will be assessed through a Common Assessment on Chapters 1-3.
Benchmark:
The students will be assessed through Study Island diagnostic tests that are aligned to the State Standards. / A1.1.1.1.1 Compare and/or order any real numbers
(rational and irrational)
A1.1.1.1.2Simplify square roots
A1.1.1.2.1 Find the Greatest Common Factor and or Least
Common Multiple for sets of monomials
A1.1.1.3.1 Simply /evaluate expressions involving properties/laws of exponents, roots and/or absolute value to solve problems
A1.1.1.1.4 Use estimation to solve problems.
A1.1.2.1.2 Use and/or identify an algebraic property to justify any step in an equation solving process (linear equations only)
A1.2.1.1.1 Analyze a set of data for the existence e of a pattern and represent the pattern algebraically and / or graphically
A1.2.1.1.1 Determine if a relation is a function given a set of points or a graph
A.1.2.1.1.3 Identify the domain or range of a relation (may be presented as ordered pairs, a graph, or a table)
A1.2.3.1.1: Calculate and/or interpret the range, quartiles and interquartile range of data.
A1.2.3.2.1: Estimate or calculate to make predictions based on a circle, line, bar graph, measures of central tendency, or other representations.
A1.2.3.2.2: Analyze data, make predictions, and/or answer questions based on displayed data (box-and-whisker plots, stem-and-leaf plots, scatter plots, measures of central tendency, or other representations).
Second Quarter
Students will understand:
Solving Equations:
Solve one, two step equations, equations with variables on both sides, and polynomials , proportions.
Lines and their graphs:
Rewrite equations so y is a function of x; plot points in a coordinate plane; graph linear equations using a table, x-y intercepts, and slope-intercept form; find the slope and y-intercept from graphs and equations; graph vertical and horizontal lines.
Lines and their equations:
Write equations of lines in slope-intercept and standard form, given slope and y-intercept, given point and slope, given two points; write lines that are parallel and /or perpendicular to given lines or their equations.
Systems of equations:
Solve a system of equations by graphing and by elimination.
Absolute value and Inequalities and their graphs:
Solve and graph absolute value and linear inequalities – include graphing linear inequalities in a coordinate plane. / How can you write a mathematical model to solve a practical or abstract real-life situation?
Why is it necessary to isolate the ‘y’ variable in order to find the slope of a line or its equation?
How can you graphically illustrate a line of an equation, and how does this model real-life situations?
What are real-life examples for the use of vertical and horizontal lines?
How do the graphs of parallel and/or perpendicular lines differ from the graph of their original equation?
What does it mean when you solve a pair of equations and find the coordinate pair?
How do the various methods for solving systems of equations relate to each other?
How can you predict if lines will be parallel by looking at a pair of equations or by solving the system?
How can you predict if an absolute value inequality will be graphed overlapping or will go in opposite directions?
How can you predict if an absolute value inequality will graph the entire number line or have no solution? / Diagnostic:
The students will be assessed at the start of the unit through a diagnostic pre-test to determine current academic levels.
Formative:
The students will be assessed using daily student questioning to check for understanding of section.
The students will be assessed with weekly quizzes on individual units, emphasizing new or more difficult curriculum areas.
The students will be assessed using unit blogs to gauge student comprehension of content and to facilitate open-ended writing skills.
Summative:
The students will be assessed by a quiz on solving multi-step equations.
The students will be assessed by a quiz on proportions.
The students will be assessed by a quiz on rewriting equations so y is a function of x.
The students will be assessed by a quiz or project on plotting points in a coordinate plane.
The students will be assessed by a quiz on graphing linear equations using a table, using the slope-intercept form, and by using x,y intercepts (to include graphing vertical and horizontal lines).
The students will be assessed by a quiz (or several) on writing equations of lines in slope-intercept form and standard form given the slope and y intercept, given two points, given one point and the slope.
The students will be assessed by a quiz on writing equations of lines parallel and/or perpendicular to given lines and/or given a point and a slope.
The students will be assessed by a quiz on estimating a line of best fit and writing its equation.
The students will be assessed by a quiz on solving systems of equations by graphing, elimination, and substitutions.
The students will be assessed by a quiz on solving/graphing inequalities and absolute value equations on a number line.
The students will be assessed by a quiz on graphing linear inequalities in a coordinate plane.
The students will be assessed through a Common Assessment on Chapters 4-6.
Benchmark:
The students will be assessed through Study Island diagnostic tests that are aligned to the State Standards. / A1.1.2.1.2Use and/or identify an algebraic property to justify any step in an equation solving process (linear equations only)
A1.1.1.5.3. Simplify/reduce a rational algebraic expression
A1.1.2.1.1. Write, solve, and/or apply a linear equation (including problem situations)
A1.1.2.1.3.. Interpret solutions to problems in the context of the problem situation
A1.2.2.1.1: Identify, describe and/or use constant rates of change.
A1.2.2.1.2: Apply the concept of linear rate of change (slope) to solve problems.
A1.2.2.1.3:Write or identify a linear equation when given the graph of the line 2 points on the line, or the slope and a point on a line, (Linear equation may be in point-slope, standard and/or slope-intercept form).
A1.2.2.1.4: Determine the slope and/or y-intercept represented by a linear equation or graph.
A1.2.2.2.1: Draw, find and/or write an equation for a line of best fit for a scatter plot.
A1.1.2.2.1 Write/and or solve a system of linear equations (including problem situations) using graphing, substitution and/or elimination (limit systems to 2 linear equations)
A1.1.2.2.2 Interpret solutions to problems in the context of the problem situation (systems of 2 linear equations only)
A1.1.3.1.1. Write or solve compound inequalities and / or graph their solution sets on a number line (may include absolute value inequalities)
A1.1.3.1.2 Identify or graph the solution set to a linear inequality of a number line
Third Quarter
Students will be able to understand:
Systems of equations
Solve systems of equations by elimination (include review of graphing systems).
Absolute value equations and inequalities:
Solve absolute value equations and inequalities and graph on the number line.
Inequalities and their graphs:
Solve multi-step and compound inequalities; graph linear inequalities in two variables.
Properties of Powers:
Simplify and evaluate expressions involving properties and laws of exponents to solve problems (include zero and negative powers
Polynomials:
Classify; add, subtract, multiply and simplify polynomial expressions
Foil (two binomials); multiply binomial/trinomial; square binomials; use sum and difference pattern to multiply binomials
GCF and factor trinomials when a=1. / How do the different methods for solving systems of equations relate to each other?
How can you graphically illustrate a system of linear inequalities and how does this model real-life situations?
How does the graph of a linear inequality differ from that of a system of linear equations, and how do their solutions compare?
How does a negative sign impact the term(s) in parenthesis that follow it?
How do powers impact their base?
How does a negative on the base impact a power?
How does a power that includes a negative impact the result?
How does a 0 power impact the result?
How does factoring a trinomial compare/contrast when a=1 vs a>1?
How do the patterns to multiply binomials help in foiling them? / Diagnostic:
The students will be assessed at the start of the unit through a diagnostic pre-test to determine current academic levels.
Formative:
The students will be assessed using daily student questioning to check for understanding of section.
The students will be assessed with weekly quizzes/test on individual units, emphasizing new or more difficult curriculum areas.
The students will be assessed using unit blogs to gauge student comprehension of content and to facilitate open-ended writing skills.
Students will be assessed through Study Island assignments that meet the current standards and curriculum, and are tied to Benchmarks.
Summative:
The students will be assessed by a quiz on solving/graphing inequalities and absolute value equations on a number line.
The students will be assessed by a quiz on solving/graphing compound inequalities.
The students will be assessed by a quiz on graphing linear inequalities in a coordinate plane.
The students will be tested on a unit of linear equations/inequalities.
The students will be assessed by a quiz on powers and their properties.
The students will be tested on a unit of powers and their properties.
The students will be assessed by a quiz on simplifying polynomial expressions.
The students will be tested on a unit of simplifying polynomials.
The students will be assessed on a quiz of foiling.
The students will be assessed on a quiz of factoring (including GCF).
The students will be tested on a unit of factoring.
The students will be assessed through a Common Assessment for the quarter curriculum.
Benchmark:
The students will be assessed through Study Island diagnostic tests that are aligned to the State Standards. / A1.1.1.5.3. Simplify/reduce a rational algebraic expression.
A1.1.2.2.1 Write and/or solve a system of linear equations using graphing, and elimination.
A1.1.2.1.3.. Interpret solutions to problems in the context of the problem situation.
A1.1.3.1.1. Write or solve compound inequalities and / or graph their solution sets on a number line.
A1.1.3.1.2 Identify or graph the solution set to a linear inequality of a number line.
A1.1.3.1.3 Interpret solutions to problems in the context of the problem situation (limit to linear inequalities).
A1.1.1.3.1: Simplify/evaluate expressions involving properties/laws of exponents, roots and/or absolute values to solve problems (exponents should be integers from -10 to 10).
A1.1.1.5.1: Add, subtract and/or multiply polynomial expressions (express answers in simplest form – nothing larger than a binomial multiplied by a trinomial).
A1.1.1.2.1 Find the Greatest Common factor (GCF) and/or the Least Common Multiple (LCM) for sets of monomials.
A1.1.1.5.2. Factor algebraic expressions, including difference of squares and trinomials .
A1.1.1.5.3 Simplify/reduce a rational algebraic expression.
A1.1.3.2.1 Write and/or solve a system of linear inequalities using graphing (limit system to 2 linear inequalities).
A1.1.3.2.2. Interpret solutions to problems in the context of the problem situation (systems of 2 linear inequalities only).
Fourth Quarter
Students will be able to understand:
Properties of Powers:
Simplify and evaluate expressions involving properties and laws of exponents to solve problems (include zero and negative powers)
Write, solve and/or apply linear or exponential growth or decay
Polynomials:
Classify; add, subtract, multiply and simplify polynomial expressions
Foil (two binomials); multiply binomial/trinomial; square binomials; use sum and difference pattern to multiply binomials
GCF and factor trinomial when a2=1.
GCF and factor trinomials when a2 > 1 / How do powers impact their base?
How does a negative on the base impact a power?
How does a 0 power impact the result?
How can you use addition to multiply exponential expressions?
How can you use multiplication to raise an exponential expression to a power?
How is finding the product of two powers of the same base different from finding a power of a power of the same base?
Explain why y = 3x is an exponential function and
y = x3 is not.
Identify the following models as linear or exponential:
y = 8(2)x
vs
y =8 + 2x
How does doubling impact growth rate?
Given an exponential model y = 80(b)t, how can you tell if the model represents growth or decay?
How does factoring help you to find the solutions of a quadratic functions?
How do the solutions of a quadratic function relate to its graph?
How does factoring a trinomial compare/contrast when a2=1 vs a2>1?
How do the patterns to multiply binomials help in foiling them? / Diagnostic:
The students will be assessed at the start of the unit through a diagnostic pre-test to determine current academic levels.
Formative:
The students will be assessed using daily student questioning to check for understanding of section.
The students will be assessed with weekly quizzes/test on individual units, emphasizing new or more difficult curriculum areas.
The students will be assessed using unit blogs to gauge student comprehension of content and to facilitate open-ended writing skills.
Students will be assessed through Study Island assignments that meet the current standards and curriculum, and are tied to Benchmarks.
Summative:
The students will be assessed by a quiz on properties of powers/simplify variable expressions with powers.
The students will be assessed by a quiz on exponential growth/decay and their graphs.
The students will be assessed by a quiz on the GCF of expressions and in terms of rational simplification.
The students will be assessed by a quiz on adding, subtracting, multiplying and simplifying polynomial expressions.
The students will be assessed by a quiz on terms/definitions and the graphs of quadratic equations.
The students will be assessed by a quiz on factoring difference of squares.
The students will be assessed by a quiz on factoring trinomials into binomials when a2 = 1
The students will be assessed by a quiz on factoring trinomials into binomials when a2 > 1
The students will be tested on a unit of polynomials.
The students will be assessed through a Common Assessment for the quarter curriculum.
Benchmark:
The students will be assessed through Study Island diagnostic tests that are aligned to the State Standards. / A1.1.1.5.3. Simplify/reduce a rational algebraic expression.
A1.1.2.1.3.. Interpret solutions to problems in the context of the problem situation.
A1.1.1.5.1: Add, subtract and/or multiply polynomial expressions (express answers in simplest form – nothing larger than a binomial multiplied by a trinomial).
A1.1.1.2.1 Find the Greatest Common factor (GCF) and/or the Least Common Multiple (LCM) for sets of monomials.
A1.1.1.5.2. Factor algebraic expressions, including difference of squares and trinomials .
A2.1.3.1.4 Write, solve and/or apply linear or exponential growth or decay (include problem situations)
A2.1.3.2.1 Determine how a change in one variable relates to a change in a second variable
A 2.1.3.1.1 Write and/or solve quadratic equations (include factoring and using the Quadratic Formula)