Mathematics

Grade 7 Math: scope and sequence

A traditional sequence: number systems and exponents, then algebra, measurement and geometry, finishing with data, Pythagoras and functions.

There is no fixed calendar for this course. The units are written to be taken in order, and most families spend one to two weeks on each.

The units, in order

#	Unit and what it covers	Lessons
1	Exponents & Scientific Notation An exponent counts how many times you multiply, not what you multiply by. That one idea explains every rule.	5
2	Problem Solving A hard problem is rarely beaten by cleverness. It is beaten by a method: understand it, pick a strategy, carry it out, then check.	6
3	Squares & Square Roots Squaring and taking a square root undo each other. A root asks: what number, times itself, gives this?	5
4	Real Numbers Every number you meet this year is either rational — a fraction — or irrational. Knowing which tells you how it behaves.	5
5	GCF and LCM Prime factorisation answers both questions at once: shared factors give the GCF, and everything needed gives the LCM.	5
6	Positive & Negative Rational Number Operations Negative numbers are directions, not just "less than nothing". Subtraction is adding the opposite, and sign rules come from patterns you can see.	5
7	Representing Other Algebraic Relationships Not everything is proportional. Learn to read a pattern, name the rule, and write it as an expression you can trust.	5
8	Solving Equations Undo what was done, in reverse order, doing the same thing to both sides every time.	5
9	Measurement Every conversion is a multiplication by one. Write the unit you want on top, the unit you have on the bottom, and the wrong units cancel themselves.	5
10	Circles Every circle has the same ratio of circumference to diameter. That ratio is $\pi$, and it drives both formulas.	5
11	Volume & Surface Area of 3-D Figures Volume fills the inside — base area times height. Surface area wraps the outside — add up every face.	5
12	Proportional Reasoning with Rates A rate compares two different kinds of quantity. Turn it into a unit rate and you can compare anything.	4
13	Proportional Relationships A proportional relationship is $y = kx$: a straight line through the origin, with one constant ratio running through every pair.	5
14	Reading Graphs & Estimation A graph is an argument. Read the scale before the shape, or you will believe whatever it wants you to believe.	5
15	Sampling, Inferences & Comparing Populations You cannot measure everyone, so you measure some. A random sample lets a small group speak honestly for a large one.	5
16	Probability of Simple Events Probability is a fraction: what you want over everything that could happen — as long as every outcome is equally likely.	5
17	Probability of Compound Events Two or more things happening: multiply along a path, add across paths, and watch whether the first event changes the second.	5
18	Pythagorean Theorem In any right triangle, the two legs squared add to the hypotenuse squared. It turns a right angle into arithmetic.	6
19	Functions A function is a machine: one input goes in, exactly one output comes out. The rule is the machine.	5

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