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High school · Grade 9

Algebra 1

13 chapters112 lessons
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1

Real numbers, expressions and properties

8 lessons

Sets of numbers and the properties of the real numbers that justify every algebraic move, plus estimating with quantities.

Review first: Sorting a number into its sets Combining like terms The distributive property with variables
1.1Elements and membership
1.2Writing sets: roster, rule and the empty set
1.3Commutative, associative and distributive properties
1.4Identity and inverse elements
1.5Closure
1.6Interpreting the parts of an expression
1.7Units, quantities and a sensible level of accuracy
1.8Estimating a huge quantity from small facts
2

Linear inequalities in one and two variables

12 lessons

Solving multi-step and compound inequalities, writing their solution sets, and graphing inequalities and their overlaps in the plane.

Review first: Two-step inequalities Graphing a line from its equation
2.1Multi-step inequalities
2.2Union, intersection and complement
2.3Compound inequalities: and, or
2.4Interval and set-builder notation
2.5Graphing a linear inequality in two variables
2.6The overlap of two shaded regions
2.7Writing and interpreting constraints
2.8Multi-step equationsretaught
2.9Equations with variables on both sidesretaught
2.10Literal equations: solving for one variableretaught
2.11Solving systems by substitutionretaught
2.12Solving systems by eliminationretaught
3

Functions: notation, domain, range, graphs and linear models

13 lessons

Using function notation in context, reading domain, range and end behavior from graphs, measuring average rate of change, and linear functions as models.

Review first: Evaluating a function at a number Reading values off a graph
3.1Function notation in a real situation
3.2Evaluating a function at an expression
3.3The identity and constant functions
3.4Domain and range from a graph
3.5A reasonable domain for a real situation
3.6End behavior
3.7Average rate of change from a table or graph
3.8Average rate of change from a formula
3.9Linear functions in context
3.10Solving f(x) = g(x) with graphs and tables
3.11Point-slope form and the line through two pointsretaught
3.12Standard form of a lineretaught
3.13Modeling with linear relationshipsretaught
4

Piecewise and absolute value functions

8 lessons

Functions defined by pieces, the absolute value function, and solving absolute value equations and inequalities as distance.

Review first: Absolute value Compound inequalities: and, or
4.1Evaluating a piecewise function
4.2Graphing a piecewise function
4.3Writing a piecewise rule from a graph
4.4Step functions and the greatest integer function
4.5Piecewise functions in context
4.6The absolute value graph
4.7Absolute value equations
4.8Absolute value inequalities
5

Arithmetic and geometric sequences

6 lessons

Sequences as functions on the counting numbers, with explicit and recursive rules for adding and multiplying patterns.

5.1Sequences, terms and notation
5.2Arithmetic sequences and the explicit formula
5.3Geometric sequences and the explicit formula
5.4Recursive formulas
5.5Generating a sequence from a rule
5.6Closed form versus recursive form
6

Exponential functions and choosing a model

12 lessons

Exponential growth and decay, their graphs, and choosing, building and interpreting linear and exponential models.

Review first: Monomials and the exponent rules The multiplier for a percent change
6.1Growth and decay factors
6.2What an asymptote is
6.3Graphs of exponential functions
6.4Writing an exponential function from a table or graph
6.5Linear versus exponential growth
6.6Choosing a function family for data
6.7Interpreting the numbers in a model
6.8Building a model from a description
6.9Where a model holds: domain, interpolation and extrapolation
6.10Multiplying and dividing powers with the same baseretaught
6.11Powers of powers, products and quotientsretaught
6.12Zero and negative exponentsretaught
7

Polynomials and their operations

5 lessons

Polynomials as sums of monomials, and adding, subtracting and multiplying them, including the special products.

7.1Multiplying two binomials
7.2Degree, terms and standard form
7.3Adding and subtracting polynomials
7.4Multiplying polynomials
7.5Special products
8

Factoring

5 lessons

Undoing multiplication by factoring trinomials, grouping, special patterns, and choosing a strategy to factor completely.

Review first: Factoring out the greatest common factor Special products
8.1Factoring when the leading coefficient is one
8.2Factoring by grouping
8.3Factoring when the leading coefficient is not one
8.4Factoring special patterns
8.5Factoring completely and choosing a strategy
9

Quadratic functions and their graphs

10 lessons

The parabola, its vertex, axis and zeros, and the features of any graph read off a quadratic, with quadratics in context.

9.1What makes an expression quadratic
9.2The shape of a parabola
9.3The vertex and the axis of symmetry
9.4Graphing from standard form
9.5Roots, zeros and x-intercepts
9.6Intercepts and zeros of a function
9.7Increasing, decreasing, constant, positive and negative intervals
9.8Turning points, maximums and minimums
9.9Maximum, minimum and range of a quadratic function
9.10Quadratic functions in context
10

Radicals

3 lessons

Simplifying square roots and computing with radicals, ready for the radical answers of the quadratic formula.

Review first: Square roots Irrational numbers Closure
10.1Simplifying a square root
10.2Operations with radicals
10.3Rationalizing a denominator
11

Solving quadratic equations

12 lessons

Solving quadratics by factoring, square roots, completing the square and the quadratic formula, and choosing the method.

Review first: Factoring completely and choosing a strategy Simplifying a square root Solving systems by substitution
11.1Solving quadratics by factoring
11.2Solving quadratics with square roots
11.3Completing the square
11.4Completing the square, leading coefficient not one
11.5Vertex form: reading, converting and graphing
11.6Factored form
11.7Reading a quadratic in its three forms
11.8Deriving the quadratic formula
11.9Using the quadratic formula
11.10The discriminant and the number of real solutions
11.11Maximum, minimum and projectile problems
11.12Systems with a curve
12

One-variable statistics

7 lessons

Describing a distribution with percentiles, outliers and the standard deviation, and what rescaling data does to them.

Review first: Making and reading box plots Quartiles and the five number summary Outliers and the 1.5 IQR rule
12.1Relative frequency histograms
12.2Percentiles
12.3Box plots that show outliers
12.4Variance of a data set
12.5Computing a standard deviation, sample and population
12.6Interpreting a standard deviation
12.7Shifting and rescaling a data set
13

Two-variable statistics

11 lessons

Fitting and judging a line for paired data with residuals and correlation, and why correlation is not causation.

Review first: Interpreting the slope and intercept
13.1Fitting linear and exponential models with technology
13.2Predicting with a regression line, and extrapolation
13.3Interpreting a residual
13.4Making and reading residual plots
13.5The correlation coefficient
13.6Properties of the correlation coefficient
13.7Observational studies and experiments
13.8Correlation is not causation: lurking and confounding variables
13.9Describing a scatter plotretaught
13.10Line of best fitretaught
13.11Conditional relative frequenciesretaught