1: Students will understand numerical concepts and mathematical operations.

1.A: Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

1.A.1: Compare and order rational numbers.

Comparing and Ordering Decimals
Comparing and Ordering Fractions
Comparing and Ordering Integers
Comparing and Ordering Rational Numbers
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1

1.A.2: Use equivalent representations for rational numbers (e.g., integers, decimals, fractions, percents, ratios, numbers with whole-number exponents).

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

1.A.5: Identify and represent on a number line decimals, fractions, mixed numbers, and positive and negative integers.

Comparing and Ordering Fractions
Comparing and Ordering Integers
Comparing and Ordering Rational Numbers
Real Number Line - Activity A

1.B: Understand the meaning of operations and how they relate to one another.

1.B.3: Demonstrate the relationship and equivalency among ratios and percents.

Estimating Population Size
Part:Part and Part:Whole Ratios
Percents and Proportions
Polling: Neighborhood

1.B.4: Use proportions to solve problems.

Estimating Population Size

1.B.5: Explain and perform:

1.B.5.b: addition, subtraction, multiplication, and division with decimals

Multiplying with Decimals
Sums and Differences with Decimals

1.B.5.c: addition and subtraction with integers

Adding Real Numbers
Adding and Subtracting Integers
Adding and Subtracting Integers with Chips
Order of Operations

1.B.5.d: addition, subtraction, and multiplication with fractions and mixed numerals

Fractions with Unlike Denominators
Multiplying Fractions
Multiplying Mixed Numbers

1.B.6: Determine the least common multiple and the greatest common divisor of whole numbers and use them to solve problems with fractions.

Dividing Fractions
Dividing Mixed Numbers
Fractions with Unlike Denominators
Multiplying Fractions
Multiplying Mixed Numbers

1.C: Compute fluently and make reasonable estimates.

1.C.3: Determine if a problem situation calls for an exact or approximate answer and perform the appropriate computation.

Adding Real Numbers

1.C.4: Compare and order positive and negative fractions, decimals, and mixed numbers and place them on a number line.

Comparing and Ordering Fractions

1.C.5: Convert fractions to decimals and percents and use these representations in estimations, computations, and applications.

Percents, Fractions and Decimals

1.C.6: Interpret and use ratios in different contexts.

Estimating Population Size
Part:Part and Part:Whole Ratios
Polling: Neighborhood

1.C.7: Compute and perform multiplication and division of fractions and decimals and apply these procedures to solving problems.

Dividing Fractions
Multiplying Fractions
Multiplying with Decimals

2: Students will understand algebraic concepts and applications.

2.A: Understand patterns, relations, and functions.

2.A.1: Solve problems involving proportional relationships.

Estimating Population Size

2.A.2: Graph ordered pairs in the coordinate plane.

Points in the Coordinate Plane - Activity A

2.A.3: Explain and use symbols to represent unknown quantities and variable relationships.

Using Algebraic Equations

2.A.4: Explain and use the relationships among ratios, proportions, and percents.

Estimating Population Size
Part:Part and Part:Whole Ratios
Polling: Neighborhood
Proportions and Common Multipliers

2.B: Represent and analyze mathematical situations and structures using algebraic symbols.

2.B.2: Use letters to represent an unknown in an equation.

Using Algebraic Equations

2.B.3: Solve one-step linear equations and inequalities in one variable with positive whole-number solutions.

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Solving Two-Step Equations

2.B.4: Demonstrate that a variable can represent a single quantity that changes.

Using Algebraic Equations

2.B.5: Demonstrate how changes in one variable affect other variables.

Using Algebraic Equations

2.C: Use mathematical models to represent and understand quantitative relationships.

2.C.2: Create, explain, and use mathematical models such as:

2.C.2.b: equations and inequalities to model numerical relationships

Using Algebraic Equations

2.D: Analyze changes in various contexts.

2.D.1: Represent and explain changes using one-step equations with one variable.

Modeling One-Step Equations - Activity A
Using Algebraic Equations

2.D.2: Solve problems that involve change using proportional relationships.

Estimating Population Size
Polling: Neighborhood

2.D.4: Use tables and symbols to represent and describe proportional and other relationships involving conversions, sequences, and perimeter.

Using Tables, Rules and Graphs

3: Students will understand geometric concepts and applications.

3.A: Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematics arguments about geometric relationships.

3.A.1: Identify, describe, and classify the properties of, and the relationships between, plane and solid geometric figures:

3.A.1.a: measure, identify, and draw angles, perpendicular and parallel lines, rectangles, and triangles by using appropriate tools (e.g., straightedge, ruler, compass, protractor, drawing software)

Construct Parallel and Perpendicular Lines
Constructing Congruent Segments and Angles

3.A.1.b: understand that the sum of angles of any triangle is 180 degrees and the sum of the angles of any quadrilateral is 360 degrees and use this information to solve problems

Classifying Quadrilaterals - Activity A
Triangle Angle Sum - Activity A

3.A.1.c: visualize and draw two-dimensional views of three-dimensional objects made from rectangular solids

3D and Orthographic Views - Activity A
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

3.A.2: Classify angles as right, obtuse, or straight.

Classifying Triangles
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

3.A.3: Describe the properties of geometric figures that include regular polygons, circles, ellipses, cylinders, cones, spheres, and cubes.

Classifying Triangles
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Surface and Lateral Area of Pyramids and Cones

3.A.4: Classify polygons as regular or irregular.

Classifying Triangles
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

3.A.5: Classify triangles as scalene, isosceles, or equilateral and by angles (i.e., right, acute, and obtuse).

Classifying Triangles
Isosceles and Equilateral Triangles
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Triangle Angle Sum - Activity A

3.A.7: Describe the relationship between radius, diameter, and circumference of a circle.

Circle: Circumference and Area

3.B: Specify locations and describe spatial relationships using coordinate geometry and other representational systems.

3.B.1: Use coordinate geometry to describe location on a plane.

Points in the Coordinate Plane - Activity A

3.B.2: Recognize skewed lines in space.

Investigating Parallel Lines and Planes

3.C: Apply transformations and use symmetry to analyze mathematical situations.

3.C.1: Identify line of symmetry with rotation and scaling.

Holiday Snowflake Designer
Rotations, Reflections and Translations

3.D: Use visualization, spatial reasoning, and geometric modeling to solve problems.

3.D.1: Use appropriate technology, manipulatives, constructions, or drawings to recognize or compare geometric figures.

Classifying Quadrilaterals - Activity A
Construct Parallel and Perpendicular Lines
Constructing Congruent Segments and Angles

4: Students will understand measurement systems and applications.

4.A: Understand measurable attributes of objects and the units, systems, and processes of measurement.

4.A.3: Select and use units of appropriate size and type to measure angles (e.g., degrees, radians), perimeter, area, and capacity in both U.S. customary and metric systems.

Perimeter, Circumference, and Area - Activity B

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

4.B.1: Apply various measurement techniques and tools, units of measure, and degrees of accuracy to find accurate rational number representations for length, liquid, weight, perimeter, temperature, and time.

Perimeter, Circumference, and Area - Activity B

4.B.2: Select and use formulas for perimeters of squares and rectangles.

Perimeter, Circumference, and Area - Activity B
Rectangle: Perimeter and Area

4.B.4: Select and justify the selection of measurement tools, units of measure, and degrees of accuracy appropriate to the given situation.

Triple Beam Balance

5: Students will understand how to formulate questions, analyze data, and determine probabilities.

5.A: Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.

5.A.2: Draw and compare different graphical representations of the same data.

Box-and-Whisker Plots
Histograms
Line Plots
Populations and Samples
Scatter Plots - Activity A
Stem-and-Leaf Plots

5.A.3: Use mean, median, mode, and range to describe data.

Box-and-Whisker Plots
Describing Data Using Statistics
Line Plots
Mean, Median and Mode

5.A.5: Solve problems by collecting, organizing, displaying and interpreting data.

Box-and-Whisker Plots
Describing Data Using Statistics
Histograms
Line Plots
Scatter Plots - Activity A
Stem-and-Leaf Plots

5.A.7: Conduct and explain sampling techniques such as observations, surveys, and random sampling for gathering data.

Polling: Neighborhood

5.A.8: Determine the median for a rational number data set containing an odd number of data points.

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

5.A.9: Calculate and explain the median for a whole number data set containing an even number of data points.

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

5.A.10: Explain advantages and disadvantages of using various display formats for a specific data set.

Box-and-Whisker Plots
Histograms
Line Plots
Scatter Plots - Activity A
Stem-and-Leaf Plots

5.A.11: Formulate and solve problems by collecting, organizing, displaying, and interpreting data.

Box-and-Whisker Plots
Describing Data Using Statistics
Histograms
Line Plots
Scatter Plots - Activity A
Stem-and-Leaf Plots

5.B: Select and use appropriate statistical methods to analyze data.

5.B.1: Choose an appropriate graphical format to organize and represent data.

Box-and-Whisker Plots
Histograms
Line Plots
Scatter Plots - Activity A
Stem-and-Leaf Plots

5.B.3: Compute and analyze statistical measurements for data sets:

5.B.3.a: understand how additional data added to data sets may affect the computations of central tendency

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

5.B.3.b: understand how the inclusion or exclusion of outliers affects measures of central tendency

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

5.B.3.c: know why a specific measure of central tendency provides the most useful information in a given context

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

5.B.5: Identify different ways of selecting a sample (e.g., convenience sampling, responses to a survey, random sampling) and which method makes a sample more representative for a population.

Polling: Neighborhood

5.B.7: Identify data that represent sampling errors and explain why the sample and the display might be biased.

Polling: Neighborhood

5.C: Develop and evaluate inferences and predictions that are based on data.

5.C.2: Conduct observations, surveys, experiments and/or simulations, record the results in charts, tables, or graphs, and use the results to draw conclusions and make predictions.

Histograms
Probability Simulations

5.C.3: Find all possible combinations in a given set (e.g., the number of ways a set of books can be arranged on a shelf).

Permutations and Combinations

5.C.4: Compare expected results with actual results in a simple experiment.

Populations and Samples

5.D: Understand and apply basic concepts of probability.

5.D.1: List all possible outcomes for a compound event composed of two independent events and recognize whether an outcome is certain, impossible, likely, or unlikely.

Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events

5.D.2: Determine and compare experimental (empirical) and mathematical (theoretical) probabilities (e.g., flipping two color counters).

Compound Independent Events
Compound Independent and Dependent Events
Geometric Probability - Activity A
Independent and Dependent Events
Polling: City
Probability Simulations
Theoretical and Experimental Probability

5.D.3: Determine theoretical and experimental probabilities and use them to make predictions about events.

Compound Independent Events
Compound Independent and Dependent Events
Geometric Probability - Activity A
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

5.D.4: Represent all possible outcomes for compound events in an organized way (e.g., tables, grids, tree diagrams) and express the theoretical probability of each outcome.

Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events
Permutations and Combinations
Probability Simulations
Theoretical and Experimental Probability

5.D.5: Use data to estimate the probability of future events (e.g., batting averages).

Mean, Median and Mode

5.D.6: Represent probabilities as ratios, proportions, decimals between 0 and 1, and percentages between 0 and 100 and verify that the probabilities computed are reasonable; know that if P is the probability of an event, 1- P is the probability of the event not occurring.

Compound Independent Events
Compound Independent and Dependent Events
Geometric Probability - Activity A
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

5.D.7: Describe the difference between independent and dependent events and identify situations involving independent or dependent events.

Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events