School Rocks!

_{Standard I}
Students will acquire number sense and perform operations with rational numbers.

Objective 1  Represent whole numbers and decimals in a variety of ways.
     Change whole numbers with exponents to standard form (e.g., 2⁴ = 16) and recognize that 10⁰ = 1.

b.        Read and write numerals from thousandths to one billion.

c.        Write a whole number to 999,999 in expanded form using exponents (e.g., 876,539 = 8 x 10⁵ + 7 x 10⁴ + 6 x 10³ + 5 x 10² + 3 x 10¹ + 9 x 10⁰).

d.        Express numbers in scientific notation using positive powers of ten.

e.        Classify whole numbers to 100 as prime, composite, or neither.

f.         Determine the prime factorization for a whole number up to 50.

Objective 2  Identify relationships among whole numbers, fractions (rational numbers), decimals, and percents.

a.        Find the greatest common factor and least common multiple for two numbers using a variety of methods (e.g., list of multiples, prime factorization).

b.        Compare and order rational numbers, including mixed fractions, using a variety of methods and symbols.

c.        Locate positive rational numbers on a number line.

d.        Convert common fractions, decimals, and percents from one form to another (e.g., 3/4= 0.75 = 75%).

Objective 3  Model and illustrate meanings of operations and describe how they relate.

a.        Represent division of a multi-digit dividend by two-digit divisors, including decimals, using models, pictures, and symbols.

b.        Model addition, subtraction, multiplication, and division of fractions and decimals in a variety of ways (e.g., objects, a number line).

c.        Apply rules of divisibility.

d.        Select or write a number sentence that can be used to solve a multi-step problem and write a word problem when given a two-step expression or equation.

Objective 4  Use fractions and percents to communicate parts of the whole.

a.        Divide regions, sets of objects, and line segments into equal parts using a variety of models and illustrations.

b.        Name and write a fraction to represent a portion of a unit whole for halves, thirds, fourths, fifths, sixths, eighths, tenths, twelfths, and sixteenths.

c.        Write a fraction or ratio in simplest form.

d.        Name equivalent forms for fractions (halves, thirds, fourths, fifths, tenths), ratios, percents, and decimals, including repeating or terminating decimals.

e.        Relate percents less than 1% or greater than 100% to equivalent fractions, decimals, whole numbers, and mixed numbers.

Objective 5  Solve problems using the four operations with whole numbers, decimals, and fractions.

a.        Determine when it is appropriate to use estimation, mental math strategies, paper and pencil, or a calculator.

b.        Use estimation strategies to determine whether results obtained using a calculator are reasonable.

c.        Multiply up to a three-digit factor by a one- or two-digit factor including decimals.

d.        Divide up to a four-digit dividend by a one- or two-digit divisor including decimals.

e.        Add and subtract decimals to the thousandths place (e.g., 34.567+3.45; 65.3-5.987).

f.         Add, subtract, multiply, and divide fractions and mixed numbers.

g.        Solve problems using ratios and proportions.

h.        Simplify expressions, with exponents, using the order of operations.

Objective 6
Model, illustrate, and perform the operations of addition and subtraction of integers.

a.        Recognize that the sum of an integer and its opposite is zero.

b.        Model addition and subtraction of integers using manipulatives and a number line.

c.        Add and subtract integers.