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TACHS Math setup and checking

Teaching notes and examples for focused review. Use the family lessons and annual question bank to practice these methods.

Updated October 3, 2026

6 terms with examples.

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Term / patternMeaning / methodExample
Percent changeDivide change by the original amount.A price from $40 to $46 rises 6/40 = 15%.
Unit rateExpress both quantities on a common one-unit basis.180 miles in 3 hours gives 60 miles per hour.
Distributive lawMultiply each term inside parentheses.3(2x − 5) = 6x − 15.
ComplementCount everything except the unwanted event.If 3 of 10 equally likely outcomes fail, success probability is 7/10.
Area versus perimeterArea covers a surface; perimeter measures its boundary.A 3 by 8 rectangle has area 24 and perimeter 22.
Mean totalRecover a total by multiplying mean by count.Five values with mean 12 sum to 60.

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