M6:1: Demonstrates conceptual understanding of rational numbers with respect to

M6:1.1: ratios (comparison of two whole numbers by division a/b, a:b, and a / b , where b is not equal to 0); and rates (e.g., a out of b, 25%) using models, explanations, or other representations.

Beam to Moon (Ratios and Proportions)
Part-to-part and Part-to-whole Ratios

M6:1.2: Demonstrates conceptual understanding of proportional reasoning, and fluently moves between equivalent representations of commonly used fractions and decimals.

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Modeling Decimals (Area and Grid Models)
Part-to-part and Part-to-whole Ratios
Percents and Proportions
Percents, Fractions, and Decimals
Proportions and Common Multipliers

M6:2: Demonstrates understanding of the relative magnitude of numbers by ordering or comparing numbers with whole-number bases and whole-number exponents (e.g., 33 , 43), integers, or rational numbers within and across number formats (fractions, decimals, or whole-number percents from 1 to 100) using number lines or equality and inequality symbols.

Comparing and Ordering Decimals
Fraction Garden (Comparing Fractions)
Integers, Opposites, and Absolute Values
Modeling Decimals (Area and Grid Models)
Modeling Fractions (Area Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Rational Numbers, Opposites, and Absolute Values
Treasure Hunter (Decimals on the Number Line)

M6:3: Demonstrates understanding of mathematical operations by describing or illustrating the meaning of a power by representing the relationship between the base (whole number) and the exponent (whole number) (e.g., 33 , 43); and the effect on the magnitude of a whole number when multiplying or dividing it by a whole number, decimal, or fraction.

Multiplying Decimals (Area Model)

M6:4: Accurately solves problems involving single or multiple operations on fractions (proper, improper, and mixed), or decimals; and addition or subtraction of integers; percent of a whole; or problems involving greatest common factor or least common multiple.

Adding Fractions (Fraction Tiles)
Adding Whole Numbers and Decimals (Base-10 Blocks)
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

M6:7: Estimates and evaluates the reasonableness of solutions appropriate to grade level.

Estimating Sums and Differences
Multiplying Decimals (Area Model)

M6:8: Applies properties of numbers (factor, multiple, prime, composite, greatest common factor [GCF], least common multiple [LCM], composition/decomposition), divisibility, remainders), and commutative and associative properties of operations to solve problems and to simplify computations.

Adding and Subtracting Integers
Chocomatic (Multiplication, Arrays, and Area)
Factor Trees (Factoring Numbers)
Finding Factors with Area Models
Operations with Radical Expressions
Using Algebraic Equations

M6:9: Uses properties or attributes of angles (right, acute, or obtuse) or sides (number of congruent sides, parallelism, or perpendicularity) to identify, describe, classify, or distinguish among different types of triangles (right, acute, obtuse, equiangular, scalene, isosceles, or equilateral) or quadrilaterals (rectangles, squares, rhombi, trapezoids, or parallelograms).

Classifying Triangles

M6:11: Uses properties or attributes (shape of bases, number of lateral faces, number of bases, number of edges, or number of vertices) to identify, compare, or describe three-dimensional shapes (rectangular prisms, triangular prisms, cylinders, spheres, pyramids, or cones).

Pyramids and Cones

M6:12: Demonstrates congruency using the results of combining and subdividing shapes (e.g., rectangle into two triangles), by using transformations (fl ips, slides, and turns), and by using the properties of angles, and length of segments.

Holiday Snowflake Designer
Rock Art (Transformations)
Rotations, Reflections, and Translations

M6:13: Demonstrates conceptual understanding of similarity by describing the proportional effect on the linear dimensions of polygons or circles when scaling up or down while preserving the angles of polygons, or by solving related problems (including applying scales on maps). Describes effects using models orsc explanations. And applies concepts of similarity using constant of proportionality/scale factor to make larger and smaller scale drawings.

Circles
Similarity in Right Triangles

M6:14: Demonstrates conceptual understanding of perimeter of polygons, the area of quadrilaterals or triangles, and the volume of rectangular prisms by using models, formulas, or by solving problems; and demonstrates understanding of the relationships of circle measures (radius to diameter and diameter to circumference) by solving related problems. Expresses all measures using appropriate units.

Area of Triangles
Balancing Blocks (Volume)
Fido's Flower Bed (Perimeter and Area)

M6:15: Measures and uses units of measures appropriately and consistently, and makes conversions within systems when solving problems across the content strands.

Unit Conversions

M6:18: Solves problems using the Cartesian coordinate system (all quadrants) to locate coordinates and to represent data from tables.

Points, Lines, and Equations
Slope

M6:19: Identifies and extends to specific cases a variety of patterns (linear and nonlinear) represented in models, tables, sequences, graphs, or in problem situations; or writes a rule in words or symbols for finding specific cases of a linear relationship; or writes a rule in words or symbols for finding specific cases of a nonlinear relationship; and writes an expression or equation using words or symbols to express the generalization of a linear relationship (e.g., twice the term number plus 1 or 2n + 1).

Function Machines 1 (Functions and Tables)

M6:21: Demonstrates conceptual understanding of algebraic expressions by using letters to represent unknown quantities to write linear algebraic expressions involving two or more of the four operations and consistent with order of operations expected at this grade level; or by evaluating linear algebraic expressions (including those with more than one variable); or by evaluating an expression within an equation (e.g., determine the value of y when x = 4 given y = 3 x – 2).

Compound Interest
Order of Operations
Simplifying Algebraic Expressions II
Solving Equations by Graphing Each Side
Solving Equations on the Number Line

M6:23: Interprets a given representation (circle graphs, line graphs, or stem-and-leaf plots) to answer questions related to the data, to analyze the data to formulate or justify conclusions, to make predictions, or to solve problems. And (frequency charts, line graphs, Venn diagrams, pictographs, line plots, histograms).

Describing Data Using Statistics
Elevator Operator (Line Graphs)
Forest Ecosystem
Graphing Skills
Histograms
Mean, Median, and Mode
Polling: City
Prairie Ecosystem
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram
Sight vs. Sound Reactions
Stem-and-Leaf Plots

M6:24: Analyzes patterns, trends or distributions in data in a variety of contexts by determining or using measures of central tendency (mean, median, or mode) or dispersion (range) to analyze situations, or to solve problems.

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)
Real-Time Histogram

M6:25: Organizes and displays data using bar graphs, tables, frequency tables, line plots, circle graphs, and stem-and-leaf plots to answer question related to the data, to analyze the data to formulate or justify conclusions, or to make predictions.

Describing Data Using Statistics
Graphing Skills
Histograms
Mean, Median, and Mode
Polling: City
Prairie Ecosystem
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram
Stem-and-Leaf Plots

M6:26: Uses counting techniques to solve problems in context involving combinations or simple permutations using a variety of strategies (e.g., organized lists, tables, tree diagrams, models, Fundamental Counting Principle, orsc others).

Permutations and Combinations

M6:27: For a probability event in which the sample space may or may not contain equally likely outcomes, determines the experimental or theoretical probability of an event in a problem-solving situation.

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

M6:28: In response to a teacher- or student-generated question, makes a hypothesis, collects appropriate data, organizes the data, appropriately displays/represents numerical and/or categorical data, analyzes the data to draw conclusions about the questions or hypothesis being tested, and when appropriate makes predictions, asks new questions, or makes connection to real-world situations.

Graphing Skills

M6:29: Uses experimental probability to make and test conjectures or design fair games. Represent probabilities using fractions, decimals, or percents.

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