1: The student will demonstrate an understanding of numbers, operations, and quantitative reasoning.

1.6.1: The student represents and uses rational numbers in a variety of equivalent forms.

1.6.1.A: compare and order non-negative rational numbers;

Comparing and Ordering Decimals
Comparing and Ordering Fractions
Comparing and Ordering Integers
Comparing and Ordering Rational Numbers
Fraction Garden (Comparing Fractions)
Modeling Fractions (Area Models)
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions, and Decimals Greater Than 1

1.6.1.B: generate equivalent forms of rational numbers including whole numbers, fractions, and decimals;

Improper Fractions and Mixed Numbers
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions, and Decimals Greater Than 1
Percents, Fractions, and Decimals

1.6.1.D: write prime factorizations using exponents;

Factor Trees (Factoring Numbers)
Finding Factors with Area Models

1.6.1.E: identify factors of a positive integer, common factors, and the greatest common factor of a set of positive integers; and

Factor Trees (Factoring Numbers)
Finding Factors with Area Models

1.6.2: The student adds, subtracts, multiplies, and divides to solve problems and justify solutions.

1.6.2.A: model addition and subtraction situations involving fractions with [objects,] pictures, words, and numbers;

Adding Decimals (Base-10 Blocks)
Adding Fractions (Fraction Tiles)
Fractions with Unlike Denominators
Subtracting Decimals (Base-10 Blocks)

1.6.2.B: use addition and subtraction to solve problems involving fractions and decimals;

Adding Decimals (Base-10 Blocks)
Adding Fractions (Fraction Tiles)
Fractions with Unlike Denominators
Subtracting Decimals (Base-10 Blocks)
Sums and Differences with Decimals

1.6.2.C: use multiplication and division of whole numbers to solve problems including situations involving equivalent ratios and rates;

Part-to-part and Part-to-whole Ratios
Polling: Neighborhood

1.6.2.E: use order of operations to simplify whole number expressions (without exponents) in problem solving situations.

Order of Operations

2: The student will demonstrate an understanding of patterns, relationships, and algebraic reasoning.

2.6.3: The student solves problems involving direct proportional relationships.

2.6.3.A: use ratios to describe proportional situations;

Beam to Moon (Ratios and Proportions)
Part-to-part and Part-to-whole Ratios
Polling: Neighborhood
Proportions and Common Multipliers

2.6.3.B: represent ratios and percents with [concrete] models, fractions, and decimals; and

Part-to-part and Part-to-whole Ratios
Polling: Neighborhood
Toy Factory (Set Models of Fractions)

2.6.3.C: use ratios to make predictions in proportional situations.

Beam to Moon (Ratios and Proportions)
Part-to-part and Part-to-whole Ratios
Polling: Neighborhood
Proportions and Common Multipliers

2.6.4: The student uses letters as variables in mathematical expressions to describe how one quantity changes when a related quantity changes.

2.6.4.A: use tables and symbols to represent and describe proportional and other relationships such as those involving conversions, arithmetic sequences (with a constant rate of change), perimeter and area; and

Area of Parallelograms - Activity B
Arithmetic Sequences
Arithmetic and Geometric Sequences
Elevator Operator (Line Graphs)
Unit Conversions

2.6.4.B: use tables of data to generate formulas representing relationships involving perimeter, area, volume of a rectangular prism, etc.

Area of Parallelograms - Activity B
Balancing Blocks (Volume)
Points, Lines, and Equations
Prisms and Cylinders - Activity A
Rectangle: Perimeter and Area

3: The student will demonstrate an understanding of geometry and spatial reasoning.

3.6.6: The student uses geometric vocabulary to describe angles, polygons, and circles.

3.6.6.A: use angle measurements to classify angles as acute, obtuse, or right;

Classifying Triangles

3.6.6.B: identify relationships involving angles in triangles and quadrilaterals; and

Isosceles and Equilateral Triangles

3.6.6.C: describe the relationship between radius, diameter, and circumference of a circle.

Circles: Circumference and Area

3.6.7: The student uses coordinate geometry to identify location in two dimensions.

3.6.7.A: locate and name points on a coordinate plane using ordered pairs of non-negative rational numbers.

City Tour (Coordinates)
Points in the Coordinate Plane - Activity A

4: The student will demonstrate an understanding of the concepts and uses of measurement.

4.6.8: The student solves application problems involving estimation and measurement of length, area, time, temperature, volume, weight, and angles.

4.6.8.A: estimate measurements (including circumference) and evaluate reasonableness of results;

Area of Parallelograms - Activity B
Balancing Blocks (Volume)
Circles: Circumference and Area
Prisms and Cylinders - Activity A

4.6.8.B: select and use appropriate units, tools, or formulas to measure and to solve problems involving length (including perimeter), area, time, temperature, volume, and weight;

Area of Parallelograms - Activity B
Circles: Circumference and Area
Fido's Flower Bed (Perimeter and Area)
Measuring Trees
Minimize Perimeter
Perimeter, Circumference, and Area - Activity B
Rectangle: Perimeter and Area

4.6.8.D: convert measures within the same measurement system (customary and metric) based on relationships between units.

Unit Conversions

5: The student will demonstrate an understanding of probability and statistics.

5.6.9: The student uses experimental and theoretical probability to make predictions.

5.6.9.A: construct sample spaces using lists and tree diagrams; and

Permutations and Combinations

5.6.9.B: find the probabilities of a simple event and its complement and describe the relationship between the two.

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

5.6.10: The student uses statistical representations to analyze data.

5.6.10.A: select and use an appropriate representation for presenting and displaying different graphical representations of the same data including line plot, line graph, bar graph, and stem and leaf plot;

Describing Data Using Statistics
Elevator Operator (Line Graphs)
Line Plots
Mascot Election (Pictographs and Bar Graphs)
Mean, Median and Mode
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Stem-and-Leaf Plots

5.6.10.B: identify mean (using [concrete objects and] pictorial models), median, mode, and range of a set of data;

Box-and-Whisker Plots
Describing Data Using Statistics
Line Plots
Mean, Median and Mode
Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

5.6.10.C: sketch circle graphs to display data; and

Box-and-Whisker Plots
Describing Data Using Statistics
Graphing Skills
Histograms
Line Plots
Mascot Election (Pictographs and Bar Graphs)
Scatter Plots - Activity A
Stem-and-Leaf Plots

5.6.10.D: solve problems by collecting, organizing, displaying, and interpreting data.

Box-and-Whisker Plots
Describing Data Using Statistics
Estimating Population Size
Graphing Skills
Histograms
Line Plots
Mascot Election (Pictographs and Bar Graphs)
Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Scatter Plots - Activity A
Stem-and-Leaf Plots

6: These skills will not be listed under a separate recording category. Instead, they will be incorporated into at least 75% of the test questions in reporting categories 1?5 and will be identified along with content standards.

6.6.11: The student applies Grade 6 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school.

6.6.11.A: identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics;

Estimating Population Size

6.6.11.C: select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem; and

Estimating Population Size

6.6.12: The student communicates about Grade 6 mathematics through informal and mathematical language, representations, and models.

6.6.12.A: communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models.

Elevator Operator (Line Graphs)
No Alien Left Behind (Division with Remainders)