🔢 9th grade Math

Units

1. Unit 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.

   Content standard: GDA.1 · rational and irrational numbers, including square roots

2. Unit 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.

   Content standard: GDA.4 · rearranging formulas to highlight a quantity of interest

3. Unit 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.

   Content standard: GDA.3; GDA.5 · where two lines meet, and the graph of a linear equation as the set of its solutions

4. 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.

   Content standard: GDA.15 · linear models of real situations, their rate of change and starting value

5. Unit 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.

   Content standard: GDA.18; GDA.32; GDA.33 · distance, midpoint and slope on the coordinate plane, and the slopes of parallel and perpendicular lines

6. Unit 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.

   Content standard: GDA.19; GDA.27; GDA.28 · dilations, scale factors and similar triangles

7. Unit 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.

   Content standard: GDA.19; GDA.36 · the Pythagorean Theorem in context, and how scaling changes lengths, areas and volumes

8. Unit 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.

   Content standard: GDA.35 · sine, cosine and tangent in right triangles and using them to find missing sides

9. Unit 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°.

   Content standard: GDA.37 · central and inscribed angles, chords, radii and tangents of circles

10. Unit 10

    🦋Line & Rotation Symmetry

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

    Content standard: GDA.22 · line and rotation symmetry: the reflections and turns that carry a figure onto itself

11. Unit 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.

    Content standard: GDA.17 · surface area of prisms, cylinders and composite solids

12. Unit 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.

    Content standard: GDA.2; GDA.17 · using units to solve problems, and volumes of cones, cylinders, pyramids and prisms

13. Unit 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.

    Content standard: GDA.9; GDA.12; GDA.13 · box plots and scatter plots, lines of fit and the strength of an association

14. Unit 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.

    Content standard: GDA.10; GDA.11 · comparing the center and spread of data sets and the effect of outliers

15. Unit 15

    🧮Two-Way Tables & Causation

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

    Content standard: GDA.14; AIP.35 · two-way tables, relative frequency, and correlation versus causation

16. Unit 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.

    Content standard: AIP.15; AIP.16 · functions as a mapping from domain to range, and function notation

17. Unit 17

    🔗Solving Systems

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

    Content standard: AIP.10; AIP.13 · solving systems of linear equations and representing constraints in context

18. Unit 18

    🧱Factoring & Quadratics

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

    Content standard: AIP.5; AIP.9 · factoring quadratic expressions and solving quadratic equations