### 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.

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: 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.

#### 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.

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: 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.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: 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.

2.2.1: 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: 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;

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: 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.

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: 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

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: Geometry

#### 3.1: The student recognizes geometric figures and compares their properties in a variety of situations.

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;

3.1.3.f: squares have angles of 90°, all sides congruent;

3.1.3.g: trapezoids have one pair of opposite sides parallel and the other pair of opposites sides are not parallel.

3.1.4: identifies and describes:

3.1.4.a: the altitude and base of a rectangular prism and triangular prism,

3.1.5: identifies corresponding parts of similar and congruent triangles and quadrilaterals.

3.1.10: describes the relationship between the diameter and the circumference of a circle.

#### 3.2: The student estimates, measures, and uses measurement formulas in a variety of situations.

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.

3.2.3: converts within the customary system and within the metric system.

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.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: The student recognizes and performs transformations on two- and three- dimensional geometric figures in a variety of situations.

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: The student relates geometric concepts to a number line and a coordinate plane in a variety of situations.

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: Data

#### 4.1: The student applies the concepts of probability to draw conclusions, generate convincing arguments, and make predictions and decisions including the use of concrete objects in a variety of situations.

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: The student collects, organizes, displays, and explains numerical (rational numbers) and non-numerical data sets in a variety of situations with a special emphasis on measures of central tendency.

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.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.

4.2.5: 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.

Correlation last revised: 5/11/2018

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.