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

Correlation last revised: 4/4/2018

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