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.

4.1.7 A: Number Sense

4.1.7 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):

4.1.7 A.1.a: Rational numbers

Rational Numbers, Opposites, and Absolute Values

4.1.7 A.1.b: Percents

Percent of Change
Percents, Fractions, and Decimals

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

Beam to Moon (Ratios and Proportions)
Direct and Inverse Variation
Estimating Population Size
Independent and Dependent Events
Part-to-part and Part-to-whole Ratios
Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals
Proportions and Common Multipliers

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

Comparing and Ordering Decimals
Fraction Garden (Comparing Fractions)
Fractions Greater than One (Fraction Tiles)
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

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

Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals

4.1.7 B: Numerical Operations

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

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

Fraction Garden (Comparing Fractions)
Multiplying with Decimals
Percents, Fractions, and Decimals
Sums and Differences with Decimals
Toy Factory (Set Models of Fractions)

4.1.7 B.1.b: Mental math

Estimating Sums and Differences
Percents, Fractions, and Decimals
Sums and Differences with Decimals

4.1.7 B.1.c: Calculator

Fraction Garden (Comparing Fractions)
Multiplying with Decimals
Percents, Fractions, and Decimals
Sums and Differences with Decimals
Toy Factory (Set Models of Fractions)

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

Order of Operations

4.1.7 C: Estimation

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

Estimating Sums and Differences

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

4.2.7 A: Geometric Properties

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

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

Classifying Quadrilaterals
Perimeter and Area of Rectangles
Special Parallelograms

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

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

Beam to Moon (Ratios and Proportions)
Proportions and Common Multipliers

4.2.7 B: Transforming Shapes

4.2.7 B.1: Understand and apply transformations.

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

Dilations
Reflections
Rock Art (Transformations)

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

Dilations
Reflections
Rock Art (Transformations)

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

Dilations
Reflections
Rock Art (Transformations)
Rotations, Reflections, and Translations

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

Dilations
Similar Figures

4.2.7 C: Coordinate Geometry

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

City Tour (Coordinates)
Function Machines 2 (Functions, Tables, and Graphs)
Linear Functions
Points in the Coordinate Plane
Points, Lines, and Equations
Slope

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

Dilations
Rotations, Reflections, and Translations

4.2.7 D: Units of Measurement

4.2.7 D.1: Solve problems requiring calculations that involve different units of measurement within a measurement system (e.g., 4'3" plus 7'10" equals 12'1").

Unit Conversions

4.2.7 E: Measuring Geometric Objects

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

4.2.7 E.1.a: Geometric figures made by combining triangles, rectangles and circles or parts of circles

Area of Parallelograms
Area of Triangles
Polygon Angle Sum

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

Fido's Flower Bed (Perimeter and Area)

4.2.7 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).

Pyramids and Cones

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

4.3.7 A: Patterns

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

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

Arithmetic Sequences
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Geometric Sequences

4.3.7 B: Functions and Relationships

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

4.3.7 B.1.a: Equations involving two variables

Absolute Value with Linear Functions
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Point-Slope Form of a Line
Slope-Intercept Form of a Line
Standard Form of a Line

4.3.7 C: Modeling

4.3.7 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.

Translating and Scaling Functions

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

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

Compound Interest
Multiplying with Decimals
Solving Equations on the Number Line
Using Algebraic Equations
Using Algebraic Expressions

4.3.7 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)

Arithmetic Sequences
Compound Interest
Geometric Sequences

4.3.7 D: Procedures

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

4.3.7 D.1.a: Absolute value

Absolute Value Equations and Inequalities
Compound Inequalities
Rational Numbers, Opposites, and Absolute Values

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

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

Point-Slope Form of a Line
Solving Algebraic Equations II
Solving Equations by Graphing Each Side
Solving Two-Step Equations
Standard Form of a Line

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

Solving Equations by Graphing Each Side
Solving Two-Step Equations

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

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

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Order of Operations
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

4.3.7 D.3.b: Substitution of a number for a variable

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II

4.3.7 D.4: Understand and apply the properties of operations, numbers, equations, and inequalities.

4.3.7 D.4.a: Additive inverse

Adding and Subtracting Integers
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values
Simplifying Algebraic Expressions I
Solving Algebraic Equations I

4.3.7 D.4.b: Multiplicative inverse

Solving Algebraic Equations I

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.

4.4.7 A: Data Analysis

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

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

Box-and-Whisker Plots
Describing Data Using Statistics
Graphing Skills
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Stem-and-Leaf Plots

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

Box-and-Whisker Plots

4.4.7 A.1.c: Scatter plot

Graphing Skills

4.4.7 A.2: Make inferences and formulate and evaluate arguments based on displays and analysis of data.

Box-and-Whisker Plots
Graphing Skills
Polling: City
Real-Time Histogram

4.4.7 B: Probability

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

Estimating Population Size
Independent and Dependent Events

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

Independent and Dependent Events

4.4.7 B.4: Play and analyze probability-based games, and discuss the concepts of fairness and expected value.

Probability Simulations
Theoretical and Experimental Probability

4.4.7 C: Discrete Mathematics-Systematic Listing and Counting

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

4.4.7 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)

Permutations and Combinations