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.

4.1.6 A: Number Sense

4.1.6 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).

4.1.6 A.1.a: All integers

Integers, Opposites, and Absolute Values

4.1.6 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

Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)
Fraction Garden (Comparing Fractions)
Fractions Greater than One (Fraction Tiles)
Modeling Fractions (Area Models)
No Alien Left Behind (Division with Remainders)
Rational Numbers, Opposites, and Absolute Values
Toy Factory (Set Models of Fractions)

4.1.6 A.1.c: All decimals

Comparing and Ordering Decimals
Modeling Decimals (Area and Grid Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Percents, Fractions, and Decimals
Sums and Differences with Decimals
Treasure Hunter (Decimals on the Number Line)

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

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Part-to-part and Part-to-whole Ratios
Percents and Proportions
Proportions and Common Multipliers
Road Trip (Problem Solving)

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

Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals
Real-Time Histogram

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

Dividing Mixed Numbers
Estimating Sums and Differences
Fraction Garden (Comparing Fractions)
Improper Fractions and Mixed Numbers
Modeling Decimals (Area and Grid Models)
Modeling Fractions (Area Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals
Toy Factory (Set Models of Fractions)

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

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

Chocomatic (Multiplication, Arrays, and Area)
Factor Trees (Factoring Numbers)
Finding Factors with Area Models
Operations with Radical Expressions

4.1.6 A.7.b: Common multiples, common factors

Factor Trees (Factoring Numbers)
Finding Factors with Area Models
Operations with Radical Expressions

4.1.6 A.8: Compare and order numbers.

Comparing and Ordering Decimals
Fraction Garden (Comparing Fractions)
Rational Numbers, Opposites, and Absolute Values

4.1.6 B: Numerical Operations

4.1.6 B.1: Recognize the appropriate use of each arithmetic operation in problem situations.

Adding Whole Numbers and Decimals (Base-10 Blocks)
Cargo Captain (Multi-digit Subtraction)
Multiplying Decimals (Area Model)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)

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

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

Dividing Fractions
Dividing Mixed Numbers
Fractions Greater than One (Fraction Tiles)
Fractions with Unlike Denominators
Improper Fractions and Mixed Numbers
Modeling Fractions (Area Models)
Multiplying with Decimals
Sums and Differences with Decimals

4.1.6 B.2.b: Mental math

Adding Fractions (Fraction Tiles)
Adding Whole Numbers and Decimals (Base-10 Blocks)
Estimating Sums and Differences
Fractions Greater than One (Fraction Tiles)
Fractions with Unlike Denominators
Improper Fractions and Mixed Numbers
Multiplying Decimals (Area Model)
Multiplying Fractions
Multiplying Mixed Numbers
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Sums and Differences with Decimals

4.1.6 B.2.c: Calculator

Dividing Fractions
Dividing Mixed Numbers
Improper Fractions and Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals

4.1.6 B.3: Use an efficient and accurate pencil-and-paper procedure for division of a 3-digit number by a 2-digit number.

No Alien Left Behind (Division with Remainders)

4.1.6 B.5: Find squares and cubes of whole numbers.

Operations with Radical Expressions
Square Roots

4.1.6 B.6: Check the reasonableness of results of computations.

Estimating Sums and Differences

4.1.6 B.7: Understand and use the various relationships among operations and properties of operations.

Order of Operations

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

Order of Operations
Solving Algebraic Equations II

4.1.6 C: Estimation

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

Estimating Sums and Differences
Multiplying Decimals (Area Model)

4.1.6 C.2: Recognize when an estimate is appropriate, and understand the usefulness of an estimate as distinct from an exact answer.

Multiplying Decimals (Area Model)

4.1.6 C.3: Determine the reasonableness of an answer by estimating the result of operations.

Adding Whole Numbers and Decimals (Base-10 Blocks)
Estimating Sums and Differences
Subtracting Whole Numbers and Decimals (Base-10 Blocks)

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

4.2.6 A: Geometric Properties

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

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

Concurrent Lines, Medians, and Altitudes
Parallel, Intersecting, and Skew Lines

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

Polygon Angle Sum
Triangle Angle Sum

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

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

Classifying Triangles
Concurrent Lines, Medians, and Altitudes
Isosceles and Equilateral Triangles
Triangle Angle Sum
Triangle Inequalities

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

Area of Parallelograms
Perimeter and Area of Rectangles

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

Classifying Triangles

4.2.6 A.3: Identify similar figures.

Circles

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

Holiday Snowflake Designer
Quilting Bee (Symmetry)
Rock Art (Transformations)

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

Pyramids and Cones
Surface and Lateral Areas of Pyramids and Cones

4.2.6 A.6: Identify, describe, and draw the faces or shadows (projections) of three-dimensional geometric objects from different perspectives.

3D and Orthographic Views

4.2.6 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 Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

4.2.6 B: Transforming Shapes

4.2.6 B.1: Use a translation, a reflection, or a rotation to map one figure onto another congruent figure.

Rock Art (Transformations)
Rotations, Reflections, and Translations

4.2.6 C: Coordinate Geometry

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

Points in the Coordinate Plane

4.2.6 D: Units of Measurement

4.2.6 D.1: Select and use appropriate units to measure angles, area, surface area, and volume.

Area of Triangles
Balancing Blocks (Volume)
Fido's Flower Bed (Perimeter and Area)
Surface and Lateral Areas of Prisms and Cylinders

4.2.6 D.2: Use a scale to find a distance on a map or a length on a scale drawing.

Points in the Coordinate Plane

4.2.6 D.3: Convert measurement units within a system (e.g., 3 feet = ___ inches).

Unit Conversions

4.2.6 D.4: Know approximate equivalents between the standard and metric systems (e.g., one kilometer is approximately 6/10 of a mile).

Unit Conversions

4.2.6 E: Measuring Geometric Objects

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

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

Fido's Flower Bed (Perimeter and Area)
Perimeter and Area of Rectangles

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

Circumference and Area of Circles

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

Prisms and Cylinders
Surface and Lateral Areas of Prisms and Cylinders

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

Circumference and Area of Circles
Fido's Flower Bed (Perimeter and Area)
Perimeter and Area of Rectangles

4.2.6 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
Fido's Flower Bed (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.

4.3.6 A: Patterns

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

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

Arithmetic Sequences
Geometric Sequences

4.3.6 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

4.3.6 B: Functions and Relationships

4.3.6 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).

Arithmetic Sequences
Compound Interest
Function Machines 1 (Functions and Tables)
Function Machines 3 (Functions and Problem Solving)
Points, Lines, and Equations
Slope-Intercept Form of a Line

4.3.6 C: Modeling

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

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

Using Algebraic Expressions

4.3.6 C.1.b: Using concrete materials, 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

4.3.6 D: Procedures

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

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

Modeling and Solving Two-Step Equations

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

Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations on the Number Line

4.3.6 D.2: Understand and apply the properties of operations and numbers.

4.3.6 D.2.a: Distributive property

Chocomatic (Multiplication, Arrays, and Area)
Equivalent Algebraic Expressions II
Square Roots

4.3.6 D.3: Evaluate numerical expressions.

Order of Operations
Solving Equations by Graphing Each Side
Solving Equations on the Number Line

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.

4.4.6 A: Data Analysis

4.4.6 A.1: Collect, generate, organize, and display data.

4.4.6 A.1.a: Data generated from surveys

Describing Data Using Statistics
Graphing Skills
Mascot Election (Pictographs and Bar Graphs)
Movie Reviewer (Mean and Median)
Polling: City
Polling: Neighborhood
Reaction Time 2 (Graphs and Statistics)
Stem-and-Leaf Plots

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

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

Graphing Skills
Histograms
Mascot Election (Pictographs and Bar Graphs)
Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram

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

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Polling: City
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram
Sight vs. Sound Reactions
Stem-and-Leaf Plots

4.4.6 B: Probability

4.4.6 B.1: Determine probabilities of events.

4.4.6 B.1.b: Multiplication rule for probabilities

Independent and Dependent Events

4.4.6 B.1.c: Probability of certain event is 1 and of impossible event is 0

Spin the Big Wheel! (Probability)

4.4.6 B.1.d: Probabilities of event and complementary event add up to 1

Geometric Probability
Theoretical and Experimental Probability

4.4.6 B.2: Determine probability using intuitive, experimental, and theoretical methods (e.g., using model of picking items of different colors from a bag).

4.4.6 B.2.a: Given numbers of various types of items in a bag, what is the probability that an item of one type will be picked

Independent and Dependent Events
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

4.4.6 B.2.b: Given data obtained experimentally, what is the likely distribution of items in the bag

Geometric Probability
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

4.4.6 B.3: Explore compound events.

Independent and Dependent Events

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

Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

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

Polling: Neighborhood
Probability Simulations

4.4.6 C: Discrete Mathematics-Systematic Listing and Counting

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

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

Permutations and Combinations

4.4.6 C.1.b: Venn diagrams

Compound Inequalities

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

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

Permutations and Combinations

4.4.6 C.2.c: Number of ways of selecting a slate of officers from a class (e.g., if there are 23 students and 3 officers, the number is 23 x 22 x 21)

Permutations and Combinations

4.4.6 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