🔢 9th grade Math: how to help at home

What each unit covers

1. 🔢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.

2. 🔧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.

3. 📉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.

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. 🧭Coordinate Geometry

   Finding the distance between two points with the Pythagorean Theorem, the midpoint of a segment, slopes of segments, telling parallel and perpendicular lines apart, and using slopes to check for a right angle.

6. 🔭Similarity & Scale

   Using scale factors to find missing sides, solving shadow and scale-drawing problems, and seeing how enlarging a shape changes its area and volume.

7. 📐Right Triangles & Scaling

   Using the Pythagorean relationship for ladders, ramps, roofs and diagonals, deciding whether a triangle is right-angled, and seeing how doubling or tripling dimensions changes perimeter, area and volume.

8. 📐Right-Triangle Trig

   The three trig ratios in a right triangle (SOH CAH TOA), choosing the right ratio for the sides you know, finding a missing side, and seeing why sin A = cos B for the two acute angles.

9. ⭕Circle Properties

   Using the rules of circle geometry: a perpendicular from the center bisects a chord, a central angle is twice an inscribed angle on the same arc, inscribed angles on the same arc are equal, and a tangent meets the radius at 90°.

10. 🦋Line & Rotation Symmetry

    Practices lines of symmetry and rotation symmetry (order and angle of rotation) in polygons, letters and designs.

11. 📦Surface Area of Objects

    Finding the surface area of a rectangular prism, of two solids joined together (taking away the faces that are hidden), and of a cylinder written in terms of π.

12. 🧊Volume & Units

    A pyramid holds a third of the matching prism and a cone a third of the matching cylinder, plus converting between metric units and between metric and imperial units.

13. 📊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.

14. 📊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.

15. 🧮Two-Way Tables & Causation

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

16. 🔣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.

17. 🔗Solving Systems

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

18. 🧱Factoring & Quadratics

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