9th grade Math
17 units matched to the Minnesota K-12 Academic Standards.
Focus areas
- Patterns and relationships: linear, exponential and quadratic functions, systems of equations, and polynomials
- Spatial reasoning, data and probability: modeling with data, and the Grades 9–11 benchmarks
- Mathematical practices: making sense of problems and explaining reasoning
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.
Benchmark: 9.3.6.8; 9.3.5.2 · the properties of exponents and radicals
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.
Benchmark: 9.3.6.1 · 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.
Benchmark: 9.3.5.7 · using the structure of an equation to solve it
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.
Benchmark: 9.3.7.7; 9.3.7.10 · the key features of a function's graph, and function values
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.
Benchmark: 9.1.1.9; 9.1.1.13 · comparing the center and spread of data sets
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.
Benchmark: 9.3.5.3 · the number systems from whole numbers to the real numbers
Unit 7
Expressions
Writing an expression for a pattern or a sentence, deciding which expressions are equivalent, expanding brackets, and collecting like terms.
Benchmark: 9.3.5.8; 9.3.5.7 · writing expressions in equivalent forms
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.
Benchmark: 9.3.7.3; 9.3.7.1 · how a graph moves when its equation changes, and where two graphs meet
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.
Benchmark: 9.1.1.10; 9.1.1.11 · scatter plots, box plots and lines 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.
Benchmark: 9.3.7.10; 9.3.7.6 · function notation, and the domain and range of a function
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.
Benchmark: 9.3.7.1 · representing situations with linear inequalities
Unit 12
Solving Systems
Solving systems of two linear equations by elimination and substitution, and writing a system from a word problem.
Benchmark: 9.3.7.1 · solving systems of linear equations in context
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.
Benchmark: 9.1.1.11; 9.3.7.2 · telling linear from exponential models
Unit 14
Factoring & Quadratics
Factoring quadratic expressions (common factors, trinomials, difference of squares) and solving quadratic equations by factoring and square roots.
Benchmark: 9.3.6.4; 9.3.6.5 · factoring quadratics and solving quadratic equations
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.
Benchmark: 9.3.5.7 · 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.
Benchmark: 9.1.2.5; 9.1.1.5 · two-way frequency tables, and correlation versus causation
Unit 17
Sequences
Arithmetic and geometric sequences as functions: finding any term, writing a rule, and using a recursive rule.
Benchmark: 9.3.7.4 · arithmetic and geometric sequences
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