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: Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 6 pertain to these sets of numbers as well).

4.1.A.1.b: All fractions as part of a whole, as subset of a set, as a location on a number line, and as divisions of whole numbers

Comparing and Ordering Fractions

4.1.A.4: Explore the use of ratios and proportions in a variety of situations.

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Geometric Probability - Activity A
Part:Part and Part:Whole Ratios
Polling: Neighborhood
Proportions and Common Multipliers

4.1.A.5: Understand and use whole-number percents between 1 and 100 in a variety of situations.

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

4.1.A.6: Use whole numbers, fractions, and decimals to represent equivalent forms of the same number.

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

4.1.A.7: Develop and apply number theory concepts in problem solving situations.

4.1.A.7.a: Primes, factors, multiples

Finding Factors with Area Models

4.1.A.8: Compare and order numbers.

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.B: Numerical Operations

4.1.B.2: Construct, use, and explain procedures for performing calculations with fractions and decimals with:

4.1.B.2.a: Pencil-and-paper

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.2.b: Mental math

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.8: Understand and apply the standard algebraic order of operations for the four basic operations, including appropriate use of parentheses.

Order of Operations

4.1.C: Estimation

4.1.C.1: Use a variety of strategies for estimating both quantities and the results of computations.

Estimating Population Size
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.A: Geometric Properties

4.2.A.1: Understand and apply concepts involving lines and angles.

4.2.A.1.b: Properties of parallel, perpendicular, and intersecting lines

Construct Parallel and Perpendicular Lines

4.2.A.1.c: Sum of the measures of the interior angles of a triangle is 180°

Investigating Angle Theorems - Activity A
Polygon Angle Sum - Activity A
Triangle Angle Sum - Activity A

4.2.A.2: Identify, describe, compare, and classify polygons and circles.

4.2.A.2.a: Triangles by angles and sides

Classifying Triangles
Isosceles and Equilateral Triangles
Triangle Angle Sum - Activity A

4.2.A.2.b: Quadrilaterals, including squares, rectangles, parallelograms, trapezoids, rhombi

Area of Parallelograms - Activity A
Classifying Quadrilaterals - Activity A

4.2.A.2.c: Polygons by number of sides.

Classifying Triangles

4.2.A.2.d: Equilateral, equiangular, regular

Classifying Triangles
Isosceles and Equilateral Triangles

4.2.A.2.e: All points equidistant from a given point form a circle

Circles

4.2.A.4: Understand and apply the concepts of congruence and symmetry (line and rotational).

Holiday Snowflake Designer

4.2.A.5: Compare properties of cylinders, prisms, cones, pyramids, and spheres.

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

4.2.A.7: Identify a three-dimensional shape with given projections (top, front and side views).

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

4.2.A.8: Identify a three-dimensional shape with a given net (i.e., a flat pattern that folds into a 3D shape).

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: Use a translation, a reflection, or a rotation to map one figure onto another congruent figure.

Constructing Congruent Segments and Angles
Rotations, Reflections and Translations

4.2.B.2: Recognize, identify, and describe geometric relationships and properties as they exist in nature, art, and other real-world settings.

Classifying Triangles

4.2.C: Coordinate Geometry

4.2.C.1: Create geometric shapes with specified properties in the first quadrant on a coordinate grid.

Construct Parallel and Perpendicular Lines
Constructing Congruent Segments and Angles
Points in the Coordinate Plane - Activity A

4.2.E: Measuring Geometric Objects

4.2.E.2: Develop and apply strategies and formulas for finding perimeter and area.

4.2.E.2.a: Triangle, square, rectangle, parallelogram, and trapezoid

Area of Parallelograms - Activity A
Perimeter, Circumference, and Area - Activity B
Rectangle: Perimeter and Area

4.2.E.2.b: Circumference and area of a circle

Circle: Circumference and Area
Perimeter, Circumference, and Area - Activity B

4.2.E.3: Develop and apply strategies and formulas for finding the surface area and volume of rectangular prisms and cylinders.

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

4.2.E.4: Recognize that shapes with the same perimeter do not necessarily have the same area and vice versa.

Minimize Perimeter
Perimeter, Circumference, and Area - Activity B
Rectangle: Perimeter and Area

4.2.E.5: Develop informal ways of approximating the measures of familiar objects (e.g., use a grid to approximate the area of the bottom of one's foot).

Area of Parallelograms - Activity A
Rectangle: Perimeter and Area

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 and rational numbers.

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

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

4.3.A.1.b: Formal iterative formulas (e.g., NEXT = NOW * 3)

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

4.3.A.1.c: Recursive patterns, including Pascal’s Triangle (where each entry is the sum of the entries above it) and the Fibonacci Sequence: 1, 1, 2, 3, 5, 8, . . . (where NEXT = NOW + PREVIOUS)

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

4.3.B: Functions and Relationships

4.3.B.1: Describe the general behavior of functions given by formulas or verbal rules (e.g., graph to determine whether increasing or decreasing, linear or not).

Using Algebraic Equations
Using Algebraic Expressions
Using Tables, Rules and Graphs

4.3.C: Modeling

4.3.C.1: Use patterns, relations, and linear functions to model situations.

4.3.C.1.a: Using variables to represent unknown quantities

Using Algebraic Equations

4.3.C.1.b: Using concrete materials, tables, graphs, verbal rules, algebraic expressions/equations/inequalities

Using Algebraic Equations

4.3.C.2: Draw freehand sketches of graphs that model real phenomena and use such graphs to predict and interpret events.

4.3.C.2.a: Changes over time

Distance-Time Graphs

4.3.C.2.b: Relations between quantities

Introduction to Functions

4.3.C.2.c: Rates of change (e.g., when is plant growing slowly/rapidly, when is temperature dropping most rapidly/slowly)

Distance-Time Graphs

4.3.D: Procedures

4.3.D.1: Solve simple linear equations with manipulatives and informally.

4.3.D.1.a: Whole-number coefficients only, answers also whole numbers

Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Two-Step Equations

4.3.D.1.b: Variables on one or both sides of equation

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Two-Step Equations

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.2: Read, interpret, select, construct, analyze, generate questions about, and draw inferences from displays of data.

4.4.A.2.a: Bar graph, line graph, circle graph, table, histogram

Histograms
Populations and Samples

4.4.A.2.b: Range, median, and mean

Box-and-Whisker Plots
Describing Data Using Statistics
Line Plots
Mean, Median and Mode

4.4.B: Probability

4.4.B.3: Explore compound events.

Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events

4.4.B.4: Model situations involving probability using simulations (with spinners, dice) and theoretical models.

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.5: Recognize and understand the connections among the concepts of independent outcomes, picking at random, and fairness.

Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events
Polling: Neighborhood

4.4.C: Discrete Mathematics-Systematic Listing and Counting

4.4.C.1: Solve counting problems and justify that all possibilities have been enumerated without duplication.

4.4.C.1.a: Organized lists, charts, tree diagrams, tables

Box-and-Whisker Plots
Histograms
Line Plots
Permutations and Combinations
Scatter Plots - Activity A
Stem-and-Leaf Plots

4.4.C.2: Apply the multiplication principle of counting.

4.4.C.2.b: Number of ways a specified number of items can be arranged in order (concept of permutation)

Permutations and Combinations

4.4.C.3: List the possible combinations of two elements chosen from a given set (e.g., forming a committee of two from a group of 12 students, finding how many handshakes there will be among ten people if everyone shakes each other person’s hand once).

Permutations and Combinations