1: Number and Computation

1.1: The student demonstrates number sense for rational numbers, the irrational number pi, and simple algebraic expressions in one variable in a variety of situations.

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.

 Improper Fractions and Mixed Numbers
 Ordering Percents, Fractions and Decimals
 Ordering Percents, Fractions and Decimals Greater Than 1
 Percents, Fractions and Decimals
 Polling: Neighborhood

1.1.2: compares and orders rational numbers and the irrational number pi.

 Comparing and Ordering Decimals
 Comparing and Ordering Fractions
 Comparing and Ordering Integers
 Comparing and Ordering Rational Numbers
 Fraction Garden (Comparing Fractions)
 Ordering Percents, Fractions and Decimals
 Ordering Percents, Fractions and Decimals Greater Than 1

1.1.3: explains the relative magnitude between rational numbers and between rational numbers and the irrational number pi.

 Comparing and Ordering Decimals
 Comparing and Ordering Fractions
 Comparing and Ordering Integers
 Comparing and Ordering Rational Numbers
 Fraction Garden (Comparing Fractions)
 Ordering Percents, Fractions and Decimals
 Ordering Percents, Fractions and Decimals Greater Than 1

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,

 Dividing Fractions
 Dividing Mixed Numbers
 Multiplying Fractions
 Multiplying Mixed Numbers
 Multiplying with Decimals

1.1.4.b: a whole number is multiplied or divided by a rational number greater than one,

 Dividing Fractions
 Dividing Mixed Numbers
 Multiplying Fractions
 Multiplying Mixed Numbers
 Multiplying with Decimals

1.1.4.c: a rational number (excluding zero) is multiplied or divided by zero.

 Chocomatic (Multiplication, Arrays, and Area)

1.1.5: explains and determines the absolute value of rational numbers.

 Comparing and Ordering Integers
 Real Number Line - Activity A

1.2: The student demonstrates an understanding of the rational number system and the irrational number pi; recognizes, uses, and describes their properties; and extends these properties to algebraic expressions in one variable.

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.

 Comparing and Ordering Integers
 Improper Fractions and Mixed Numbers

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.

 Improper Fractions and Mixed Numbers
 Ordering Percents, Fractions and Decimals
 Ordering Percents, Fractions and Decimals Greater Than 1
 Percents, Fractions and Decimals

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);

 Chocomatic (Multiplication, Arrays, and Area)

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];

 Chocomatic (Multiplication, Arrays, and Area)

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);

 Chocomatic (Multiplication, Arrays, and Area)

1.2.4.c: zero property of multiplication (any number multiplied by zero is zero);

 Chocomatic (Multiplication, Arrays, and Area)

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);

 Modeling One-Step Equations - Activity A
 Modeling and Solving Two-Step Equations
 Solving Formulas for any Variable
 Solving Two-Step Equations

1.3: The student uses computational estimation with rational numbers and the irrational number pi in a variety of situations.

1.3.2: uses various estimation strategies and explains how they were used to estimate rational number quantities and the irrational number pi.

 Estimating Sums and Differences

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.

 Estimating Sums and Differences

1.4: The student models, performs, and explains computation with rational numbers, the irrational number pi, and first-degree algebraic expressions in one variable in a variety of situations.

1.4.1: computes with efficiency and accuracy using various computational methods including mental math, paper and pencil, concrete objects, and appropriate technology.

 Adding Real Numbers
 Dividing Fractions
 Dividing Mixed Numbers
 Fractions with Unlike Denominators
 Multiplying Fractions
 Multiplying Mixed Numbers
 Multiplying with Decimals
 Sums and Differences with Decimals

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;

 Sums and Differences with Decimals

1.4.2.b: multiplies and divides a four-digit number by a two-digit number using numbers from thousands place through thousandths place;

 Multiplying with Decimals

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 รท.002 or 54.3 x 300;

 Multiplying with Decimals

1.4.2.d: adds, subtracts, multiplies, and divides fractions and expresses answers in simplest form;

 Adding Fractions (Fraction Tiles)
 Dividing Fractions
 Dividing Mixed Numbers
 Fractions with Unlike Denominators
 Multiplying Fractions
 Multiplying Mixed Numbers

1.4.2.e: adds, subtracts, multiplies, and divides integers;

 Adding Real Numbers
 Adding and Subtracting Integers
 Adding and Subtracting Integers with Chips

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;

 Order of Operations

1.4.2.g: simplifies positive rational numbers raised to positive whole number powers;

 Exponents and Power Rules

1.4.4: finds prime factors, greatest common factor, multiples, and the least common multiple.

 Finding Factors with Area Models

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.)

 Percent of Change
 Percents and Proportions
 Polling: Neighborhood

2: Algebra

2.1: The student recognizes, describes, extends, develops, and explains the general rule of a pattern in a variety of situations.

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);

 Arithmetic Sequences
 Arithmetic and Geometric Sequences
 Finding Patterns
 Geometric Sequences

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, ...

 Arithmetic Sequences
 Arithmetic and Geometric Sequences
 Finding Patterns
 Geometric Sequences

2.1.1.c: geometric figures;

 Arithmetic and Geometric Sequences
 Finding Patterns
 Geometric Sequences

2.1.1.d: measurements;

 Arithmetic and Geometric Sequences
 Finding Patterns
 Geometric Sequences

2.1.1.e: things related to daily life, e.g., tide, moon cycle, or temperature.

 Finding Patterns

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.

 Arithmetic Sequences
 Arithmetic and Geometric Sequences
 Finding Patterns
 Geometric Sequences

2.2: The student uses variables, symbols, rational numbers, and simple algebraic expressions in one variable to solve linear equations and inequalities in a variety of situations.

2.2.3: shows and explains how changes in one variable affects other variables, e.g., changes in diameter affects circumference.

 Circle: Circumference and Area
 Measuring Trees

2.2.5: solves:

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;

 Modeling One-Step Equations - Activity A

2.2.5.b: two-step linear equations in one variable with counting number coefficients and constants and positive rational solutions;

 Modeling and Solving Two-Step Equations
 Solving Two-Step Equations

2.2.5.c: one-step linear inequalities with counting numbers and one variable, e.g., 3x > 12.

 Solving Linear Inequalities using Addition and Subtraction
 Solving Linear Inequalities using Multiplication and Division

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.

 Beam to Moon (Ratios and Proportions)
 Estimating Population Size
 Part:Part and Part:Whole Ratios
 Polling: Neighborhood
 Proportions and Common Multipliers

2.3: The student recognizes, describes, and analyzes constant and linear relationships in a variety of situations.

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.

 Arithmetic Sequences
 Arithmetic and Geometric Sequences
 Function Machines 2 (Functions, Tables, and Graphs)
 Linear Functions
 Point-Slope Form of a Line - Activity A
 Using Tables, Rules and Graphs

2.3.2: finds the values and determines the rule through two operations using a function table (input/output machine, T-table).

 Function Machines 1 (Functions and Tables)
 Function Machines 2 (Functions, Tables, and Graphs)
 Function Machines 3 (Functions and Problem Solving)
 Introduction to Functions
 Linear Functions
 Using Tables, Rules and Graphs

2.3.3: demonstrates mathematical relationships using ordered pairs in all four quadrants of a coordinate plane.

 Points in the Coordinate Plane - Activity A

2.4: The student generates and uses mathematical models to represent and justify mathematical relationships found in a variety of situations.

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

 City Tour (Coordinates)
 Modeling and Solving Two-Step Equations
 Real Number Line - Activity A

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;

 Content correlation last revised: 12/8/2008

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below to go to the Gizmo Details page.