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.
1.3.2: uses various estimation strategies and explains how they were used to estimate rational number quantities and the irrational number pi.
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.d: adds, subtracts, multiplies, and divides fractions and expresses answers in simplest form;
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;
1.4.4: 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.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.
2.2.1: knows and explains that a variable can represent a single quantity that changes, e.g., daily temperature.
2.2.2: knows, explains, and uses equivalent representations for the same simple algebraic expressions, e.g., x + y + 5x is the same as 6x + y.
2.2.4: explains the difference between an equation and an expression.
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;
2.2.6: explains and uses the equality and inequality symbols (=, not equal to, <, less than or equal to, >, greater than or equal to) and corresponding meanings (is equal to, is not equal to, is less than, is less than or equal to, is greater than, is greater than or equal to) to represent mathematical relationships with rational numbers.
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.b: place value models (place value mats, hundred charts, base ten blocks, or unifix cubes) to compare, order, and represent numerical quantities and to model computational procedures;
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;
2.4.1.e: equations and inequalities to model numerical relationships - 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;
2.4.1.f: function tables to model numerical and algebraic relationships; - factor trees to find least common multiple and greatest common factor and to model prime factorization;
2.4.1.g: coordinate planes to model relationships between ordered pairs and linear equations; - equations and inequalities to model numerical relationships
2.4.1.h: two- and three-dimensional geometric models (geoboards, dot paper, nets or solids) to model perimeter, area, volume, and surface area, and properties of two- and three-dimensional; - function tables to model numerical and algebraic relationships;
2.4.1.i: geometric models (spinners, targets, or number cubes), process models (coins, pictures, or diagrams), and tree diagrams to model probability; - coordinate planes to model relationships between ordered pairs and linear equations;
2.4.1.j: frequency tables, bar graphs, line graphs, circle graphs, Venn diagrams, charts, tables, single stem-and-leaf plots, scatter plots, and box-and-whisker plots to organize and display data; - two- and three-dimensional geometric models (geoboards, dot paper, nets or solids) to model perimeter, area, volume, and surface area, and properties of two- and three-dimensional;
3.1.1: recognizes and compares properties of two- and three-dimensional figures using concrete objects, constructions, drawings, appropriate terminology, and appropriate technology.
3.1.3: identifies angle and side properties of triangles and quadrilaterals:
3.1.3.a: sum of the interior angles of any triangle is 180°;
3.1.3.b: sum of the interior angles of any quadrilateral is 360°;
3.1.3.c: parallelograms have opposite sides that are parallel and congruent;
3.1.3.d: rectangles have angles of 90°, sides may or may not be equal;
3.1.3.e: rhombi have all sides equal in length, angles may or may not be equal;