Middle school math, i.e. 6th 7th and 8th grade math are generally the same math concepts repeated at a slightly greater difficulty each year. It basically prepares students for algebra. If middle school students do, very well with middle school math they can start Algebra in 8th grade.
Here are the concepts your middle school student must master (at 90% accuracy) before moving on to Algebra.
Place Value: Students should be able to name place value up to a billion
Decimals: Estimating, rounding, adding, subtracting, multiplying, dividing and conversion to fractions
Percent: Students should be able to calculate a percentage of a number to the nearest hundredths.
Exponents: Students must be able to calculate exponents, which tell the number of times to multiply a base number by itself.
Square roots: Students must be able to find the square root of a number.
Signed integers: addition, subtraction, multiplication, division, and properties
Fractions: reducing, addition, subtraction, multiplication, and division
Ratios: A student should be able to determine a ratio from a math problem and to multiply or both parts of the ration to find an equal ration.
Proportions: A student should be able to solve for X to determine equal proportions by cross-multiplying.
Distance, rates, time: Students must be able to use a distance formula (D=RT) or a proportions formula (d1/t1=d2/t2) to find the missing number in a word problem about distance, rate, and time.
Similar figures: Students must be able to do basic geometry such as comparing similar figures and to determine the length of a side in a similar figure.
Factors and multiples: Students much know the difference between factors and multiples. They must also be able to calculate greatest common factor and least common multiple.
Mixed numbers: Addition, subtraction, multiplication, division and conversion to improper fractions
All of these topics, plus a few minor topics can be found in any middle school math and pre-algebra book.
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