Grade 7 · Level 68 · Transition to abstraction
MATH 68
Proportionality in five costumes.
Meridian Note
Proportionality is the single organizing idea, pushed to KS-6–7 across every strand at once — percents, scale drawings, unit rates, probability. A student who meets proportionality in five costumes and recognizes it each time is doing early KS-8 analysis whether he knows the word or not.
The Fix Registry
Skills of This Course
Every skill is pinned to the meridian by fix notation — where along the scale, and at what depth. The highlighted state is this course's target: the state an honest instrument must certify before the skill counts as covered here.
| Skill | Fixes | Target at Level 68 |
|---|---|---|
| Ratio & proportional reasoning | 60-KS768-KS888-KS9 | KS-8Analyzed |
| One-variable equations | 60-KS468-KS781-KS8 | KS-7Applied |
| Rational number operations | 68-KS681-KS8 | KS-6Understood |
| Percent increase & decrease | 68-KS781-KS8 | KS-7Applied |
| Probability | 68-KS688-KS8 | KS-6Understood |
Course of Instruction
Units
Unit 1.Rational Numbers: The Full Number Line
7 practice itemsThis year the number line doubles in size. Until now, most of your math has lived to the right of zero. Grade 7 hands you the other half: negative numbers, and the rules for adding, subtracting, multiplying, and dividing with them. Here is the secret most textbooks skip: none of these rules were invented to annoy you. Each one is forced on us — it is the only rule that lets the arithmetic you already trust keep working. This unit shows you why.
MatchingMultiple choiceFill in the blankMultiple choice (misconception distractors)Short answer
Unit 2.Proportional Relationships and Unit Rates
9 practice itemsOne idea runs through this entire year, and this unit hands it to you plainly: two quantities are **proportional** when one is always the same multiple of the other. That single sentence will show up wearing five different costumes — unit rates, percents, scale drawings, probability, and more. Learn to recognize the idea underneath the costume and half of Grade 7 becomes one skill instead of five.
Multiple choiceFill in the blankMultiple choice (misconception distractors)Problem solvingTransfer problem
Unit 3.Percent Change: Proportionality in Disguise
7 practice itemsPercent problems are proportion problems wearing their most popular costume. "Percent" literally means "per hundred" — a percent is a ratio whose second number is always 100. Once you see that, sales, tips, taxes, discounts, and population growth all become the same move: multiply by the right constant. This unit teaches you to find that constant in one step, and to avoid the traps that catch most adults.
Multiple choiceFill in the blankMultiple choice (misconception distractors)Problem solvingFind the flaw
Unit 4.Scale Drawings: Proportionality You Can See
9 practice itemsA map of El Paso fits in your pocket; the city does not. A blueprint fits on a table; the house does not. Scale drawings work because of one promise: every length in the drawing is the same fraction of its real length. That promise is proportionality made visible — costume number three. This unit teaches you to use the scale in both directions, and shows you the one place almost everyone gets fooled: area.
Multiple choiceFill in the blankMultiple choice (misconception distractors)Problem solvingTransfer problem
Unit 5.Probability: Measuring Chance
8 practice itemsSome questions have no fixed answer — will it rain, will the coin land heads, will you draw a red marble? Probability is how mathematicians measure that uncertainty with an exact number. And here is proportionality's fourth costume: a probability is just a ratio, the part of the time an event happens out of all the times it could. Same idea, new stage.
Multiple choiceFill in the blankMultiple choice (misconception distractors)Problem solvingShort answer
Unit 6.Multi-Step Equations: Undoing in the Right Order
7 practice itemsLast year you met equations like x + 5 = 12, where one move finishes the job. This year the equations grow layers: 3x + 7 = 25, variables on both sides, parentheses. The good news: it is still the same game with the same single rule — keep the two sides balanced. The new skill is choosing the *order* of your moves, and there is a logic to it you already use every morning when you get dressed.
Multiple choiceFill in the blankMultiple choice (misconception distractors)Problem solvingFind the flaw