1.1.1: knows, explains, and uses equivalent representations for rational numbers and simple algebraic expressions including integers, fractions, decimals, percents, and ratios; integer bases with whole number exponents; positive rational numbers written in scientific notation with positive integer exponents; time; and money, e.g., 253,000 is equivalent to 2.53 x 10 to the 5th power or x + 5x is equivalent to 6x.
1.1.2: compares and orders rational numbers and the irrational number pi.
1.1.3: explains the relative magnitude between rational numbers and between rational numbers and the irrational number pi.
1.1.4: knows and explains what happens to the product or quotient when:
1.1.4.a: a whole number is multiplied or divided by a rational number greater than zero and less than one,
1.1.4.b: a whole number is multiplied or divided by a rational number greater than one,
1.1.4.c: a rational number (excluding zero) is multiplied or divided by zero.
1.1.5: explains and determines the absolute value of rational numbers.
1.2.1: knows and explains the relationships between natural (counting) numbers, whole numbers, integers, and rational numbers using mathematical models, e.g., number lines or Venn diagrams.
1.2.2: classifies a given rational number as a member of various subsets of the rational number system, e.g., - 7 is a rational number and an integer.
1.2.3: names, uses, and describes these properties with the rational number system and demonstrates their meaning including the use of concrete objects:
1.2.3.a: commutative properties of addition and multiplication (changing the order of the numbers does not change the solution);
1.2.3.c: distributive property [distributing multiplication or division over addition or subtraction, e.g., 2(4 - 1) = 2(4) - 2(1) = 8 - 2 = 6];
1.2.4: uses and describes these properties with the rational number system and demonstrates their meaning including the use of concrete objects:
1.2.4.a: identity properties for addition and multiplication (additive identity - zero added to any number is equal to that number; multiplicative identity - one multiplied by any number is equal to that number);
1.2.4.c: zero property of multiplication (any number multiplied by zero is zero);
1.2.4.d: addition and multiplication properties of equality (adding/multiplying the same number to each side of an equation results in an equivalent equation);
1.3.2: uses various estimation strategies and explains how they were used to estimate rational number quantities and the irrational number pi.
1.3.4: determines the appropriateness of an estimation strategy used and whether the estimate is greater than (overestimate) or less than (underestimate) the exact answer and its potential impact on the result.
1.4.1: computes with efficiency and accuracy using various computational methods including mental math, paper and pencil, concrete objects, and appropriate technology.
1.4.2: performs and explains these computational procedures:
1.4.2.a: adds and subtracts decimals from ten millions place through hundred thousandths place;
1.4.2.b: multiplies and divides a four-digit number by a two-digit number using numbers from thousands place through thousandths place;
1.4.2.c: multiplies and divides using numbers from thousands place through thousandths place by 10; 100; 1,000;.1;.01;.001; or single-digit multiples of each; e.g., 54.2 ÷.002 or 54.3 x 300;
1.4.2.d: adds, subtracts, multiplies, and divides fractions and expresses answers in simplest form;
1.4.2.e: adds, subtracts, multiplies, and divides integers;
1.4.2.f: uses order of operations (evaluates within grouping symbols, evaluates powers to the second or third power, multiplies or divides in order from left to right, then adds or subtracts in order from left to right) using whole numbers;
1.4.2.g: simplifies positive rational numbers raised to positive whole number powers;
1.4.4: finds prime factors, greatest common factor, multiples, and the least common multiple.
1.4.5: finds percentages of rational numbers, e.g., 12.5% x $40.25 = n or 150% of 90 is what number? (For the purposes of assessment, percents will not be between 0 and 1.)
2.1.1: identifies, states, and continues a pattern presented in various formats including numeric (list or table), algebraic (symbolic notation), visual (picture, table, or graph), verbal (oral description), kinesthetic (action), and written using these attributes:
2.1.1.a: counting numbers including perfect squares, cubes, and factors and multiples (number theory);
2.1.1.b: positive rational numbers including arithmetic and geometric sequences (arithmetic: sequence of numbers in which the difference of two consecutive numbers is the same, geometric: a sequence of numbers in which each succeeding term is obtained by multiplying the preceding term by the same number), e.g., 2, 1/2, 1/8, 1/32, ...
2.1.1.c: geometric figures;
2.1.1.e: things related to daily life, e.g., tide, moon cycle, or temperature.
2.1.3: extends a pattern when given a rule of one or two simultaneous changes (addition, subtraction, multiplication, division) between consecutive terms, e.g., find the next three numbers in a pattern that starts with 3, where you double and add 1 to get the next number; the next three numbers are 7, 15, and 31.
2.2.3: shows and explains how changes in one variable affects other variables, e.g., changes in diameter affects circumference.
2.2.5.a: one-step linear equations in one variable with positive rational coefficients and solutions, e.g., 7x = 28 or x + 3/ = 7 or x/3 = 5;
2.2.5.b: two-step linear equations in one variable with counting number coefficients and constants and positive rational solutions;
2.2.5.c: one-step linear inequalities with counting numbers and one variable, e.g., 3x > 12.
2.2.7: knows the mathematical relationship between ratios, proportions, and percents and how to solve for a missing term in a proportion with positive rational number solutions and monomials, e.g., 5/6 = 2/x.
2.3.1: recognizes constant and linear relationships using various methods including mental math, paper and pencil, concrete objects, and graphing utilities or appropriate technology.
2.3.2: finds the values and determines the rule through two operations using a function table (input/output machine, T-table).
2.3.3: demonstrates mathematical relationships using ordered pairs in all four quadrants of a coordinate plane.
2.4.1: knows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships. Mathematical models include:
2.4.1.a: process models (concrete objects, pictures, diagrams, number lines, hundred charts, measurement tools, multiplication arrays, division sets, or coordinate grids) to model computational procedures, algebraic relationships, and mathematical relationships and to solve equations
2.4.1.c: fraction and mixed number models (fraction strips or pattern blocks) and decimal and money models (base ten blocks or coins) to compare, order, and represent numerical quantities;