M6.A: Numbers and Operations

M6.A.1: Demonstrate an understanding of numbers, ways of representing numbers, relationships among numbers, and number systems.

M6.A.1.1: Express numbers in equivalent forms.

M6.A.1.1.1: Represent common percents as fractions and/or decimals (e.g., 25% = ¼ =.25) - common percents are 1%, 10%, 25%, 50%, 75%, 100%.

Percents, Fractions, and Decimals

M6.A.1.1.2: Convert between fractions and decimals and/or differentiate between a terminating decimal and a repeating decimal.

Modeling Decimals (Area and Grid Models)
Percents, Fractions, and Decimals

M6.A.1.2: Compare quantities and/or magnitudes of numbers.

M6.A.1.2.1: Compare and/or order whole numbers, mixed numbers, fractions and/or decimals (do not mix fractions and decimals - decimals through thousandths).

Adding Fractions (Fraction Tiles)
Adding Whole Numbers and Decimals (Base-10 Blocks)
Comparing and Ordering Decimals
Fraction Artist 2 (Area Models of Fractions)
Fraction Garden (Comparing Fractions)
Modeling Decimals (Area and Grid Models)
Modeling Fractions (Area Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Rational Numbers, Opposites, and Absolute Values
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Toy Factory (Set Models of Fractions)
Treasure Hunter (Decimals on the Number Line)

M6.A.1.3: Apply number theory concepts (i.e., factors, multiples).

M6.A.1.3.2: Find the Least Common Multiple (LCM) of two numbers (through 50) and/or use the LCM to find the common denominator of two fractions.

Adding Fractions (Fraction Tiles)

M6.A.1.3.3: Use divisibility rules for 2, 3, 5 and/or 10 to draw conclusions and/or solve problems.

Factor Trees (Factoring Numbers)

M6.A.1.4: Use or develop models to represent percents.

M6.A.1.4.1: Model percents (through 100%) using drawings, graphs and/or sets (e.g., circle graph, base ten blocks, etc)

Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals

M6.A.2: Understand the meanings of operations, use operations and understand how they relate to each other.

M6.A.2.1: Select and/or use operations to simplify or solve problems.

M6.A.2.1.1: Complete equations by using the following properties: associative, commutative, distributive and identity.

Solving Algebraic Equations II

M6.A.3: Compute accurately and fluently and make reasonable estimates.

M6.A.3.2: Solve problems with and without the use of a calculator.

M6.A.3.2.1: Solve problems involving operations (+, -, x, ÷) with whole numbers, decimals (through thousandths) and fractions (avoid complicated LCDs) - straight computation or word problems.

Adding Fractions (Fraction Tiles)
Adding Whole Numbers and Decimals (Base-10 Blocks)
Cargo Captain (Multi-digit Subtraction)
Dividing Fractions
Dividing Mixed Numbers
Estimating Sums and Differences
Fractions Greater than One (Fraction Tiles)
Fractions with Unlike Denominators
Improper Fractions and Mixed Numbers
Modeling Fractions (Area Models)
Multiplying Decimals (Area Model)
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Sums and Differences with Decimals

M6.B: Measurement

M6.B.1: Demonstrate an understanding of measurable attributes of objects and figures, and the units, systems and processes of measurement.

M6.B.1.1: Compare and/or determine elapsed time.

M6.B.1.1.1: Determine and/or compare elapsed time to the minute (time may cross AM to PM or more than one day).

Elapsed Time

M6.B.2: Apply appropriate techniques, tools and formulas to determine measurements.

M6.B.2.2: Solve problems involving length, perimeter, area and/or volume of geometric figures.

M6.B.2.2.1: Find the perimeter of any polygon (may include regular polygons where only the measure of one side is given - same units throughout).

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

M6.C: Geometry

M6.C.1: Analyze characteristics and properties of two- and three- dimensional geometric shapes and demonstrate understanding of geometric relationships.

M6.C.1.1: Define and/or use basic properties of triangles, quadrilaterals, pentagons, hexagons, heptagons, octagons, nonagons, decagons and circles.

M6.C.1.1.1: Identify, classify and/or compare polygons (up to ten sides.)

Classifying Triangles

M6.C.1.1.2: Identify and/or describe properties of all types of triangles (scalene, equilateral, isosceles, right, acute, obtuse).

Classifying Triangles

M6.C.1.1.3: Identify and/or determine the measure of the diameter and/or radius of a circle (when one or the other is given).

Circles

M6.C.1.2: Represent and/or use concepts and relationships of lines and line segments.

M6.C.1.2.2: Identify, draw and/or label points, planes, lines, line segments, rays, angles and vertices.

City Tour (Coordinates)
Elevator Operator (Line Graphs)
Points in the Coordinate Plane

M6.C.3: Locate points or describe relationships using the coordinate plane.

M6.C.3.1: Identify, plot or match points given an ordered pair.

M6.C.3.1.1: Plot, locate or identify points in Quadrant I and/or on the x and y axes with intervals of 1, 2, 5 or 10 units - up to a 200 by 200 grid. Points may be in-between lines.

Elevator Operator (Line Graphs)
Points in the Coordinate Plane

M6.D: Algebraic Concepts

M6.D.2: Represent and/or analyze mathematical situations and structures using algebraic symbols, words, tables, and graphs.

M6.D.2.1: Select and/or use appropriate strategies to solve number sentences.

M6.D.2.1.1: Identify the inverse operation needed to solve a one-step equation.

Modeling One-Step Equations

M6.D.2.2: Create and/or interpret expressions or equations that model problem situations.

M6.D.2.2.1: Match an equation or expression involving one variable, to a verbal math situation (one operation only).

Solving Equations on the Number Line
Using Algebraic Equations
Using Algebraic Expressions

M6.E: Data Analysis and Probability

M6.E.1: Formulate questions that can be addressed with data and/or collect, organize, display, and analyze data.

M6.E.1.1: Interpret data shown in frequency tables, histograms, circle, bar or double bar graphs, line or double line graphs or line plots.

M6.E.1.1.1: Analyze data and/or answer questions pertaining to data represented in frequency tables, circle graphs, double bar graphs, double line graphs or line plots (for circle graphs, no computation with percents).

Elevator Operator (Line Graphs)
Graphing Skills
Histograms
Mean, Median, and Mode
Reaction Time 1 (Graphs and Statistics)

M6.E.1.1.2: Choose the appropriate representation for a specific set of data (choices should be the same type of graph).

Box-and-Whisker Plots
Graphing Skills
Reaction Time 2 (Graphs and Statistics)

M6.E.1.1.3: Display data in frequency tables, circle graphs, double-bar graphs, double line graphs or line plots using a title, appropriate scale, labels and a key when needed. Circle graphs for open-ended items must show a center point and tic marks.

Distance-Time Graphs
Elevator Operator (Line Graphs)
Graphing Skills
Histograms
Mascot Election (Pictographs and Bar Graphs)
Mean, Median, and Mode
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Stem-and-Leaf Plots

M6.E.2: Select and use appropriate statistical methods to analyze data.

M6.E.2.1: Describe data sets using mean, median, mode and/or range.

M6.E.2.1.1: Determine/calculate the mean, median, mode and/or range of displayed data (data can be displayed in a table or line plot - use whole numbers only up to 2 digits).

Describing Data Using Statistics
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

M6.E.3: Understand and apply basic concepts of probability.

M6.E.3.1: Determine all possible combinations, outcomes and/or calculate the probability of a simple event.

M6.E.3.1.2: Determine/show all possible combinations involving no more than 20 total arrangements (e.g., tree diagram, table, grid).

Permutations and Combinations