9th grade Math
22 units matched to the New York State Learning Standards.
Focus areas
- Algebra I: expressions, polynomials, and linear and quadratic equations and inequalities
- Functions: linear, exponential and quadratic functions, their graphs and their key features
- Statistics: describing data, two-way tables, scatter plots and lines of best fit
Units
Unit 1
Exponents & Powers
Evaluating powers, using the product, quotient and power laws, working with powers of products and fractions, and order of operations with exponents.
Learning standard: AI-A.SSE.3; AI-A.SSE.2 · using the properties of exponents to rewrite expressions
Unit 2
Polynomials
Naming polynomials by terms and degree, combining like terms, subtracting polynomials, multiplying and dividing by a constant, and substituting values for x.
Learning standard: AI-A.APR.1 · adding, subtracting and multiplying polynomials
Unit 3
Multi-Step Equations
Solving linear equations with brackets, fractions and variables on both sides, checking solutions, and turning word problems into equations.
Learning standard: AI-A.REI.1; AI-A.REI.3 · solving multi-step linear equations and explaining each step
Unit 4
Linear Relations
Finding slope from points and graphs, reading y = mx + b, finding intercepts, deciding whether a point is on a line, spotting parallel lines, and using rates of change in stories.
Learning standard: AI-F.IF.6; AI-F.IF.7; AI-F.LE.2 · rate of change and key features of linear functions
Unit 5
Statistics in Society
Telling a population from a sample, spotting bias in who is asked and how, predicting from a sample, noticing misleading graphs, and why correlation is not causation.
Learning standard: AI-S.ID.2; AI-S.ID.3 · comparing the center and spread of data sets and the effect of outliers
Unit 6
Number Sets
Natural numbers, whole numbers, integers, rational and irrational numbers, how they fit inside each other, and why there are always more numbers between any two rational numbers.
Learning standard: AI-N.RN.3 · rational and irrational numbers and their different forms
Unit 7
Expressions
Writing an expression for a pattern or a sentence, deciding which expressions are equivalent, expanding brackets, and collecting like terms.
Learning standard: AI-A.SSE.1 · building and interpreting expressions in context
Unit 8
Lines & Intersections
Finding where two lines meet and what it means in a story, graphing x = k, y = k and ax + by = k, regions of an inequality, and translating, reflecting and rotating lines through the origin.
Learning standard: AI-A.REI.11; AI-F.BF.3 · where two graphs meet, and how a graph moves when its equation changes
Unit 9
Data & Scatter Plots
Finding the median and quartiles of a data set, reading a box plot, telling positive, negative and no correlation apart, and using a line of best fit to make predictions. Correlation does not prove one thing causes another.
Learning standard: AI-S.ID.1; AI-S.ID.6; AI-S.ID.7 · box plots, scatter plots and the slope and intercept of a line of best fit
Unit 10
Function Notation
Evaluating and solving with function notation, and naming the domain and range of a function, including a sensible domain in a real situation.
Learning standard: AI-F.IF.1; AI-F.IF.2; AI-F.IF.5 · functions, function notation, and the domain of a function in context
Unit 11
Linear Inequalities
Solving linear inequalities (flipping the sign when dividing by a negative), checking a solution, and writing inequalities from budgets and limits.
Learning standard: AI-A.REI.3; AI-A.CED.1 · creating and solving linear inequalities in context
Unit 12
Solving Systems
Solving systems of two linear equations by elimination and substitution, and writing a system from a word problem.
Learning standard: AI-A.REI.6; AI-A.CED.3 · solving systems of linear equations and representing constraints with equations
Unit 13
Linear or Exponential?
Telling linear growth (add the same amount) from exponential growth (multiply by the same factor), writing exponential functions, and reading growth and decay rates.
Learning standard: AI-F.LE.1; AI-F.LE.2; AI-F.LE.5 · telling linear from exponential situations and comparing their growth
Unit 14
Factoring & Quadratics
Factoring quadratic expressions (common factors, trinomials, difference of squares) and solving quadratic equations by factoring and square roots.
Learning standard: AI-A.REI.4; AI-A.SSE.3; AI-A.APR.3 · factoring quadratic expressions, finding zeros, and solving quadratic equations by factoring and square roots
Unit 15
Rearranging Formulas
Rearranging a formula to solve for one quantity (d = rt for t, P = 2l + 2w for l) and using it, plus justifying each step in solving an equation.
Learning standard: AI-A.CED.4; AI-A.REI.1 · rearranging formulas to highlight a quantity
Unit 16
Two-Way Tables & Causation
Reading two-way frequency tables, finding conditional relative frequencies, spotting associations, and knowing that correlation does not prove causation.
Learning standard: AI-S.ID.5; AI-S.ID.9 · two-way tables, relative frequency, and correlation versus causation
Unit 17
Sequences
Arithmetic and geometric sequences as functions: finding any term, writing a rule, and using a recursive rule.
Learning standard: AI-F.IF.3; AI-F.BF.1 · sequences as functions, and telling patterns that add from patterns that multiply
Unit 18
Graphs of Equations & Inequalities
Writing equations and inequalities in two variables from real situations, knowing that a graph is every point that makes the equation true, and graphing inequalities as shaded half-planes with solid or dashed lines.
Learning standard: AI-A.CED.2; AI-A.REI.10; AI-A.REI.12 · creating equations and inequalities in two variables, understanding a graph as the set of all solutions, and graphing linear inequalities and systems of them as half-planes
Unit 19
Comparing Functions
Reading key features of a function from a formula, a table or a graph (highest point, when it rises, intercepts), comparing two functions shown in different ways, and seeing that exponential growth eventually passes linear and quadratic growth.
Learning standard: AI-F.IF.4; AI-F.IF.9; AI-F.LE.3 · interpreting key features of functions in context, comparing functions shown in different ways, and seeing that exponential growth eventually exceeds linear and quadratic growth
Unit 20
Parabolas & Lines
Rewriting a quadratic in factored form to show its zeros and in vertex form to show its vertex, and solving a system of a line and a parabola by setting them equal and factoring.
Learning standard: AI-F.IF.8; AI-A.REI.7 · writing quadratic functions in equivalent forms to show zeros and the vertex, and solving a system of a linear and a quadratic equation
Unit 21
Units & Accuracy
Using units to set up and check multi-step problems (gallons per minute times minutes), choosing sensible scales for graphs, and reporting answers to an accuracy that fits the measurements.
Learning standard: AI-N.Q.1; AI-N.Q.3 · using units to guide multi-step problems, formulas and graph scales, and choosing a level of accuracy that fits the measurements
Unit 22
The Correlation Coefficient
Reading the correlation coefficient r that technology gives for a line of best fit: its sign shows direction, its closeness to 1 or −1 shows strength, and it never shows cause on its own.
Learning standard: AI-S.ID.8 · calculating the correlation coefficient of a linear fit with technology and interpreting it
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