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;
2.4.1.d: factor trees to find least common multiple and greatest common factor and to model prime factorization; - 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.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;
2.4.1.k: Venn diagrams to sort data and show relationships. - geometric models (spinners, targets, or number cubes), process models (coins, pictures, or diagrams), and tree diagrams to model probability;
3.1.1: recognizes and compares properties of two- and three-dimensional figures using concrete objects, constructions, drawings, appropriate terminology, and appropriate technology.
3.1.2: classifies regular and irregular polygons having through ten sides as convex or concave.
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.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;
3.1.4: identifies and describes:
3.1.4.a: the altitude and base of a rectangular prism and triangular prism,
3.1.4.b: the radius and diameter of a cylinder.
3.1.5: identifies corresponding parts of similar and congruent triangles and quadrilaterals.
3.1.6: uses symbols for right angle within a figure, parallel, perpendicular, and triangle to describe geometric figures.
3.1.7: classifies triangles as:
3.1.7.a: scalene, isosceles, or equilateral;
3.1.7.b: right, acute, obtuse, or equiangular.
3.1.9: generates a pattern for the sum of angles for 3-, 4-, 5-, ... n-sides polygons.
3.1.10: describes the relationship between the diameter and the circumference of a circle.
3.2.1: determines and uses rational number approximations (estimations) for length, width, weight, volume, temperature, time, perimeter, and area using standard and nonstandard units of measure.
3.2.2: selects and uses measurement tools, units of measure, and level of precision appropriate for a given situation to find accurate rational number representations for length, weight, volume, temperature, time, perimeter, area, and angle measurements.
3.2.4: knows and uses perimeter and area formulas for circles, squares, rectangles, triangles, and parallelograms;
3.2.5: finds perimeter and area of two-dimensional composite figures of circles, squares, rectangles, and triangles;
3.2.7: finds surface area of rectangular prisms using concrete objects;
3.2.7.a: surface area of cubes,
3.2.7.b: volume of rectangular prisms.
3.2.8: uses appropriate units to describe rate as a unit of measure, e.g., miles per hour.
3.2.9: finds missing angle measurements in triangles and quadrilaterals.
3.3.1: identifies, describes, and performs single and multiple transformations [reflection, rotation, translation, reduction (contraction/shrinking), enlargement (magnification/growing)] on a two-dimensional figure.
3.4.1: finds the distance between the points on a number line by computing the absolute value of their difference.
3.4.2: uses all four quadrants of a coordinate plane to:
3.4.2.a: identify in which quadrant or on which axis a point lies when given the coordinates of a point,
3.4.2.b: plot points,
3.4.2.c: identify points,
3.4.2.d: list through five ordered pairs of a given line.
3.4.3: uses a given linear equation with whole number coefficients and constants and a whole number solution to find the ordered pairs, organize the ordered pairs using a T-table, and plot the ordered pairs on the coordinate plane.
4.1.1: finds the probability of a compound event composed of two independent events in an experiment or simulation.
4.1.2: explains and gives examples of simple or compound events in an experiment or simulation having probability of zero or one.
4.1.3: uses a fraction, decimal, and percent to represent the probability of:
4.1.3.a: a simple event in an experiment or simulation;
4.1.3.b: a compound event composed of two independent events in an experiment or simulation.
4.1.4: finds the probability of a simple event in an experiment or simulation using geometric models, e.g., Using spinners or dartboards, what is the probability of landing on 2? The answer is ¼,.25, or 25%.
4.2.1: organizes, displays, and reads quantitative (numerical) and qualitative (non-numerical) data in a clear, organized, and accurate manner including a title, labels, categories, and rational number intervals using these data displays :
4.2.1.a: frequency tables;
4.2.1.b: bar, line, and circle graphs;
4.2.1.c: Venn diagrams or other pictorial displays;
4.2.1.d: charts and tables;
4.2.1.e: stem-and-leaf plots (single);
4.2.1.f: scatter plots;
4.2.1.g: box-and-whiskers plots.
4.2.2: selects and justifies the choice of data collection techniques (observations, surveys, or interviews) and sampling techniques (random sampling, samples of convenience, or purposeful sampling) in a given situation.
4.2.3: conducts experiments with sampling and describes the results.
4.2.4: determines the measures of central tendency (mode, median, mean) for a rational number data set.
4.2.5: identifies and determines the range and the quartiles of a rational number data set.
4.2.6: identifies potential outliers within a set of data by inspection rather than formal calculation, e.g., consider the data set (1, 100, 101, 120, 140, 170); the outlier is 1.
Content correlation last revised: 12/8/2008