Mathematics

Grade 7 Accelerated: scope and sequence

Ratio and proportion, rational numbers, statistics and probability, equations and inequalities, then geometry.

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	Proportional Reasoning with Rates A rate compares two different kinds of quantity. Turn it into a unit rate and you can compare anything.	4
2	Proportional Reasoning with Percents A percent is a rate out of 100. Turn it into a multiplier and every percent problem becomes one multiplication.	5
3	Positive Rational Number Operations Fractions, decimals and percents are three costumes for the same number. Choose whichever makes the arithmetic easiest.	5
4	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
5	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
6	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
7	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
8	Proportional Relationships A proportional relationship is $y = kx$: a straight line through the origin, with one constant ratio running through every pair.	5
9	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
10	Reasoning with Equations & Inequalities Before you solve anything, translate. Most of the difficulty in a word problem is turning English into algebra.	5
11	Solving Equations Undo what was done, in reverse order, doing the same thing to both sides every time.	5
12	Solving Inequalities Solve them exactly like equations — with one extra rule that catches almost everyone.	5
13	Proportional Reasoning with Scale Drawings Scaling changes every length by the same factor $k$ — which multiplies area by $k^2$ and volume by $k^3$.	5
14	Length and Area in 2-D Figures Every area formula is a rectangle in disguise. Know where each one comes from and you will never mix them up.	5
15	Plane Sections of 3-D Figures Slice a solid with a flat plane and a flat shape appears. The angle of the cut decides which shape you get.	5
16	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
17	Geometric Construction With only a compass and a straightedge you can copy, bisect and build exactly — and the angle facts tell you when a figure is even possible.	5

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