By the end of grade seven, students are adept at manipulating numbers and equations and understand the general principles at work. Students understand and use factoring of numerators and denominators and properties of exponents. They know the Pythagorean theorem and solve problems in which they compute the length of an unknown side. Students know how to compute the surface area and volume of basic three-dimensional objects and understand how area and volume change with a change in scale. Students make conversions between different units of measurement. They know and use different representations of fractional numbers (fractions, decimals, and percents) and are proficient at changing from one to another. They increase their facility with ratio and proportion, compute percents of increase and decrease, and compute simple and compound interest. They graph linear functions and understand the idea of slope and its relation to ratio.

• 1.0 Students know the properties of, and compute with, rational numbers expressed in a variety of forms:

  1.1 Read, write, and compare rational numbers in scientific notation (positive and negative powers of 10) with approximate numbers using scientific notation.

  1.2 Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers.

  1.3 Convert fractions to decimals and percents and use these representations in estimations, computations, and applications.

  1.4 Differentiate between rational and irrational numbers.

  1.5 Know that every rational number is either a terminating or repeating decimal and be able to convert terminating decimals into reduced fractions.

  1.6 Calculate the percentage of increases and decreases of a quantity.

  1.7 Solve problems that involve discounts, markups, commissions, and profit and compute simple and compound interest.

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• 2.0 Students use exponents, powers, and roots and use exponents in working with fractions:

  2.1 Understand negative whole-number exponents. Multiply and divide expressions involving exponents with a common base.

  2.2 Add and subtract fractions by using factoring to find common denominators.

  2.3 Multiply, divide, and simplify rational numbers by using exponent rules.

  2.4 Use the inverse relationship between raising to a power and extracting the root of a perfect square integer; for an integer that is not square, determine without a calculator the two integers between which its square root lies and explain why.

  2.5 Understand the meaning of the absolute value of a number; interpret the absolute value as the distance of the number from zero on a number line; and determine the absolute value of real numbers.

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