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

Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Percents and Proportions

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.

Beam to Moon (Ratios and Proportions)
Compound Independent Events
Compound Independent and Dependent Events
Estimating Population Size
Geometric Probability - Activity A
Independent and Dependent Events
Part:Part and Part:Whole Ratios
Percents and Proportions
Polling: Neighborhood
Probability Simulations
Proportions and Common Multipliers
Similar Figures - Activity A
Theoretical and Experimental Probability

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

Comparing and Ordering Decimals
Comparing and Ordering Fractions
Comparing and Ordering Integers
Comparing and Ordering Rational Numbers
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1

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

Improper Fractions and Mixed Numbers
Percents, Fractions and Decimals

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

Adding and Subtracting Integers with Chips
Dividing Fractions
Dividing Mixed Numbers
Fractions with Unlike Denominators
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals

4.1.B.1.b: Mental math

Adding and Subtracting Integers with Chips
Dividing Fractions
Dividing Mixed Numbers
Fractions with Unlike Denominators
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals

4.1.B.1.c: Calculator

Adding and Subtracting Integers with Chips
Dividing Fractions
Dividing Mixed Numbers
Fractions with Unlike Denominators
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals

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

Order of Operations

4.1.C: Estimation

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

Percents, Fractions and Decimals

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

Area of Parallelograms - Activity A
Classifying Quadrilaterals - Activity A
Special Quadrilaterals

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

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

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Polling: Neighborhood
Proportions and Common Multipliers
Similar Figures - Activity A

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

3D and Orthographic Views - Activity A
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

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

Dilations
Reflections
Rotations, Reflections and Translations

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

Dilations
Reflections
Rotations, Reflections and Translations

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

Reflections
Rotations, Reflections and Translations

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

Dilations

4.2.C: Coordinate Geometry

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

Points in the Coordinate Plane - Activity A

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

Dilations
Parabolas - Activity A
Rotations, Reflections and Translations

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.

Triple Beam Balance

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

Area of Parallelograms - Activity A
Rectangle: Perimeter and Area

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).

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

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

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences
Introduction to Functions
Linear Functions
Using Algebraic Equations
Using Algebraic Expressions
Using Tables, Rules and Graphs

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

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

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

Arithmetic Sequences
Arithmetic and Geometric Sequences

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

Defining a Line with Two Points
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Standard Form of a Line

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.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs

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

Using Algebraic Equations

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)

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences
Simple and Compound Interest

4.3.D: Procedures

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

4.3.D.1.a: Absolute value

Comparing and Ordering Integers
Real Number Line - Activity A

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)

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

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

Modeling Linear Systems - Activity A

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

Order of Operations

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

Box-and-Whisker Plots
Describing Data Using Statistics
Histograms
Line Plots
Scatter Plots - Activity A
Stem-and-Leaf Plots

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

Box-and-Whisker Plots

4.4.A.1.c: Scatter plot

Correlation
Scatter Plots - Activity A
Solving Using Trend Lines

4.4.B: Probability

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

Compound Independent Events
Compound Independent and Dependent Events
Geometric Probability - Activity A
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

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

Populations and Samples

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

Compound Independent Events
Compound Independent and Dependent Events
Geometric Probability - Activity A
Independent and Dependent Events
Polling: City
Probability Simulations
Theoretical and Experimental Probability

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)

Permutations and Combinations