🔢 9th grade Math: how to help at home

What each unit covers

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.

2. 🧩Polynomials

   Naming polynomials by terms and degree, combining like terms, subtracting polynomials, multiplying and dividing by a constant, and substituting values for x.

3. ⚖️Multi-Step Equations

   Solving linear equations with brackets, fractions and variables on both sides, checking solutions, and turning word problems into equations.

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.

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.

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.

7. ✏️Expressions

   Writing an expression for a pattern or a sentence, deciding which expressions are equivalent, expanding brackets, and collecting like terms.

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.

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.

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.

11. ⚖️Linear Inequalities

    Solving linear inequalities (flipping the sign when dividing by a negative), checking a solution, and writing inequalities from budgets and limits.

12. 🔗Solving Systems

    Solving systems of two linear equations by elimination and substitution, and writing a system from a word problem.

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.

14. 🧱Factoring & Quadratics

    Factoring quadratic expressions (common factors, trinomials, difference of squares) and solving quadratic equations by factoring and square roots.

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.

16. 🧮Two-Way Tables & Causation

    Reading two-way frequency tables, finding conditional relative frequencies, spotting associations, and knowing that correlation does not prove causation.

17. 🔢Sequences

    Arithmetic and geometric sequences as functions: finding any term, writing a rule, and using a recursive rule.

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.

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.

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.

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.

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.