#### 4.1: All students will develop number sense and will perform standard numerical operations and estimations on all types of numbers in a variety of ways.

4.1.A: Number Sense

4.1.A.1: Extend understanding of the number system by constructing meanings for the following (unless otherwise noted, all indicators for grade 7 pertain to these sets of numbers as well):

4.1.A.1.b: Percents

4.1.A.3: Understand and use ratios, proportions, and percents (including percents greater than 100 and less than 1) in a variety of situations.

4.1.A.4: Compare and order numbers of all named types.

4.1.A.5: Use whole numbers, fractions, decimals, and percents to represent equivalent forms of the same number.

4.1.B: Numerical Operations

4.1.B.1: Use and explain procedures for performing calculations with integers and all number types named above with:

4.1.B.1.a: Pencil-and-paper

4.1.B.1.b: Mental math

4.1.B.1.c: Calculator

4.1.B.3: Understand and apply the standard algebraic order of operations, including appropriate use of parentheses.

4.1.C: Estimation

4.1.C.1: Use equivalent representations of numbers such as fractions, decimals, and percents to facilitate estimation.

#### 4.2: All students will develop spatial sense and the ability to use geometric properties, relationships, and measurement to model, describe and analyze phenomena.

4.2.A: Geometric Properties

4.2.A.1: Understand and apply properties of polygons.

4.2.A.1.a: Quadrilaterals, including squares, rectangles, parallelograms, trapezoids, rhombi

4.2.A.2: Understand and apply the concept of similarity.

4.2.A.2.a: Using proportions to find missing measures

4.2.A.2.c: Models of 3D objects

4.2.B: Transforming Shapes

4.2.B.1: Understand and apply transformations.

4.2.B.1.a: Finding the image, given the pre-image, and vice-versa

4.2.B.1.b: Sequence of transformations needed to map one figure onto another

4.2.B.1.c: Reflections, rotations, and translations result in images congruent to the pre-image

4.2.B.1.d: Dilations (stretching/shrinking) result in images similar to the pre-image

4.2.C: Coordinate Geometry

4.2.C.1: Use coordinates in four quadrants to represent geometric concepts.

4.2.C.2: Use a coordinate grid to model and quantify transformations (e.g., translate right 4 units).

4.2.D: Units of Measurement

4.2.D.2: Select and use appropriate units and tools to measure quantities to the degree of precision needed in a particular problem-solving situation.

4.2.E: Measuring Geometric Objects

4.2.E.1: Develop and apply strategies for finding perimeter and area.

4.2.E.1.b: Estimation of area using grids of various sizes

4.2.E.2: Recognize that the volume of a pyramid or cone is one-third of the volume of the prism or cylinder with the same base and height (e.g., use rice to compare volumes of figures with same base and height).

#### 4.3: All students will represent and analyze relationships among variable quantities and solve problems involving patterns, functions, and algebraic concepts and processes.

4.3.A: Patterns

4.3.A.1: Recognize, describe, extend, and create patterns involving whole numbers, rational numbers, and integers.

4.3.A.1.a: Descriptions using tables, verbal and symbolic rules, graphs, simple equations or expressions

4.3.A.1.b: Finite and infinite sequences

4.3.A.1.c: Generating sequences by using calculators to repeatedly apply a formula

4.3.B: Functions and Relationships

4.3.B.1: Graph functions, and understand and describe their general behavior.

4.3.B.1.a: Equations involving two variables

4.3.C: Modeling

4.3.C.1: Analyze functional relationships to explain how a change in one quantity can result in a change in another, using pictures, graphs, charts, and equations.

4.3.C.2: Use patterns, relations, symbolic algebra, and linear functions to model situations.

4.3.C.2.a: Using manipulatives, tables, graphs, verbal rules, algebraic expressions/equations/inequalities

4.3.C.2.b: Growth situations, such as population growth and compound interest, using recursive (e.g., NOW-NEXT) formulas (cf. science standard 5.5 and social studies standard 6.6)

4.3.D: Procedures

4.3.D.1: Use graphing techniques on a number line.

4.3.D.1.a: Absolute value

4.3.D.2: Solve simple linear equations informally and graphically.

4.3.D.2.a: Multi-step, integer coefficients only (although answers may not be integers)

4.3.D.2.b: Using paper-and-pencil, calculators, graphing calculators, spreadsheets, and other technology

4.3.D.3: Create, evaluate, and simplify algebraic expressions involving variables.

4.3.D.3.a: Order of operations, including appropriate use of parentheses

#### 4.4: All students will develop an understanding of the concepts and techniques of data analysis, probability, and discrete mathematics, and will use them to model situations, solve problems, and analyze and draw appropriate inferences from data.

4.4.A: Data Analysis

4.4.A.1: Select and use appropriate representations for sets of data, and measures of central tendency (mean, median, and mode).

4.4.A.1.a: Type of display most appropriate for given data

4.4.A.1.b: Box-and-whisker plot, upper quartile, lower quartile

4.4.A.1.c: Scatter plot

4.4.B: Probability

4.4.B.1: Interpret probabilities as ratios, percents, and decimals.

4.4.B.2: Model situations involving probability with simulations (using spinners, dice, calculators and computers) and theoretical models.

4.4.B.2.a: Frequency, relative frequency

4.4.B.3: Estimate probabilities and make predictions based on experimental and theoretical probabilities.

4.4.C: Discrete Mathematics-Systematic Listing and Counting

4.4.C.1: Apply the multiplication principle of counting.

4.4.C.1.a: Permutations: ordered situations with replacement (e.g., number of possible license plates) vs. ordered situations without replacement (e.g., number of possible slates of 3 class officers from a 23 student class)

Correlation last revised: 11/13/2008

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