1: Number, Number Sense and Operations

1.B: Compare, order and convert among fractions, decimals and percents.

1.B.2: Use various forms of "one" to demonstrate the equivalence of fractions; e.g., 8/24 = 9/12 x 2/2 = 3/4 x 6/6.

Equivalent Fractions (Fraction Tiles)
Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)
Fraction Garden (Comparing Fractions)

1.F: Apply number system properties when performing computations.

1.F.7: Use commutative, associative, distributive, identity and inverse properties to simplify and perform computations.

Chocomatic (Multiplication, Arrays, and Area)

1.F.8: Identify and use relationships between operations to solve problems.

Function Machines 3 (Functions and Problem Solving)

1.H: Use and analyze the steps in standard and non-standard algorithms for computing with fractions, decimals and integers.

1.H.10: Justify why fractions need common denominators to be added or subtracted.

Adding Fractions (Fraction Tiles)

1.H.11: Explain how place value is related to addition and subtraction of decimals; e.g., 0.2 + 0.14; the two tenths is added to the one tenth because they are both tenths.

Adding Decimals (Base-10 Blocks)
Subtracting Decimals (Base-10 Blocks)
Treasure Hunter (Decimals on the Number Line)

1.I: Use a variety of strategies, including proportional reasoning, to estimate, compute, solve and explain solutions to problems involving integers, fractions, decimals and percents.

1.I.4: Round decimals to a given place value and round fractions (including mixed numbers) to the nearest half.

Treasure Hunter (Decimals on the Number Line)

1.I.12: Use physical models, points of reference, and equivalent forms to add and subtract commonly used fractions with like and unlike denominators and decimals.

Adding Decimals (Base-10 Blocks)
Adding Fractions (Fraction Tiles)
Equivalent Fractions (Fraction Tiles)
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)
Subtracting Decimals (Base-10 Blocks)

1.I.13: Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies.

Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)
Treasure Hunter (Decimals on the Number Line)

2: Measurement

2.C: Identify appropriate tools and apply appropriate techniques for measuring angles, perimeter or circumference and area of triangles, quadrilaterals, circles and composite shapes, and surface area and volume of prisms and cylinders.

2.C.6: Use strategies to develop formulas for determining perimeter and area of triangles, rectangles and parallelograms, and volume of rectangular prisms.

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

2.C.7: Use benchmark angles (e.g.; 45°, 90°, 120°) to estimate the measure of angles, and use a tool to measure and draw angles.

Measuring Motion

2.F: Analyze and explain what happens to area and perimeter or surface area and volume when the dimensions of an object are changed.

2.F.3: Demonstrate and describe the differences between covering the faces (surface area) and filling the interior (volume) of three-dimensional objects.

Balancing Blocks (Volume)

2.G: Understand and demonstrate the independence of perimeter and area for two-dimensional shapes and of surface area and volume for three-dimensional shapes.

2.G.3: Demonstrate and describe the differences between covering the faces (surface area) and filling the interior (volume) of three-dimensional objects.

Balancing Blocks (Volume)

3: Geometry and Spatial Sense

3.B: Draw circles, and identify and determine the relationships among the radius, diameter, center and circumference.

3.B.1: Draw circles, and identify and determine relationships among the radius, diameter, center and circumference; e.g., radius is half the diameter, the ratio of the circumference of a circle to its diameter is an approximation of pi.

Measuring Trees

3.C: Specify locations and plot ordered pairs on a coordinate plane.

3.C.6: Extend understanding of coordinate system to include points whose x or y values may be negative numbers.

City Tour (Coordinates)

3.H: Predict and describe results (size, position, orientation) of transformations of two-dimensional figures.

Quilting Bee (Symmetry)
Rock Art (Transformations)

4: Patterns, Functions and Algebra

4.A: Describe, extend and determine the rule for patterns and relationships occurring in numeric patterns, computation, geometry, graphs and other applications.

4.A.1: Justify a general rule for a pattern or a function by using physical materials, visual representations, words, tables or graphs.

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Pattern Flip (Patterns)

4.A.2: Use calculators or computers to develop patterns, and generalize them using tables and graphs.

Pattern Flip (Patterns)

4.B: Represent, analyze and generalize a variety of patterns and functions with tables, graphs, words and symbolic rules.

4.B.3: Use variables as unknown quantities in general rules when describing patterns and other relationships.

Pattern Flip (Patterns)

4.C: Use variables to create and solve equations and inequalities representing problem situations.

4.C.4: Create and interpret the meaning of equations and inequalities representing problem situations.

Road Trip (Problem Solving)

4.E: Use rules and variables to describe patterns, functions and other relationships.

4.E.3: Use variables as unknown quantities in general rules when describing patterns and other relationships.

Pattern Flip (Patterns)

4.F: Use representations, such as tables, graphs and equations, to model situations and to solve problems, especially those that involve linear relationships.

4.F.5: Model problems with physical materials and visual representations, and use models, graphs and tables to draw conclusions and make predictions.

No Alien Left Behind (Division with Remainders)

4.G: Write, simplify and evaluate algebraic expressions.

4.G.3: Use variables as unknown quantities in general rules when describing patterns and other relationships.

Pattern Flip (Patterns)

4.H: Solve linear equations and inequalities symbolically, graphically and numerically.

Function Machines 2 (Functions, Tables, and Graphs)
Road Trip (Problem Solving)

4.I: Explain how inverse operations are used to solve linear equations.

Function Machines 3 (Functions and Problem Solving)
Road Trip (Problem Solving)

4.K: Graph linear equations and inequalities.

4.K.5: Model problems with physical materials and visual representations, and use models, graphs and tables to draw conclusions and make predictions.

No Alien Left Behind (Division with Remainders)

4.L: Analyze functional relationships, and explain how a change in one quantity results in a change in the other.

4.L.6: Describe how the quantitative change in a variable affects the value of a related variable; e.g., describe how the rate of growth varies over time, based upon data in a table or graph.

Elevator Operator (Line Graphs)

4.M: Approximate and interpret rates of change from graphical and numerical data.

Elevator Operator (Line Graphs)

5: Data Analysis and Probability

5.A: Read, create and use line graphs, histograms, circle graphs, box-and-whisker plots, stem-and-leaf plots, and other representations when appropriate.

5.A.1: Read, construct and interpret frequency tables, circle graphs and line graphs.

Elevator Operator (Line Graphs)
Graphing Skills
Mascot Election (Pictographs and Bar Graphs)

5.B: Interpret data by looking for patterns and relationships, draw and justify conclusions, and answer related questions.

Reaction Time 2 (Graphs and Statistics)

5.C: Evaluate interpretations and conclusions as additional data are collected, modify conclusions and predictions, and justify new findings.

5.C.5: Modify initial conclusions, propose and justify new interpretations and predictions as additional data are collected.

Reaction Time 2 (Graphs and Statistics)

5.D: Compare increasingly complex displays of data, such as multiple sets of data on the same graph.

5.D.3: Read and interpret increasingly complex displays of data, such as double bar graphs.

Graphing Skills
Mascot Election (Pictographs and Bar Graphs)
Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

5.E: Collect, organize, display and interpret data for a specific purpose or need.

5.E.2: Select and use a graph that is appropriate for the type of data to be displayed; e.g., numerical vs. categorical data, discrete vs. continuous data.

Mascot Election (Pictographs and Bar Graphs)
Reaction Time 1 (Graphs and Statistics)

5.E.4: Determine appropriate data to be collected to answer questions posed by students or teacher, collect and display data, and clearly communicate findings.

Mascot Election (Pictographs and Bar Graphs)
Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

5.F: Determine and use the range, mean, median and mode to analyze and compare data, and explain what each indicates about the data.

5.F.6: Determine and use the range, mean, median and mode, and explain what each does and does not indicate about the set of data.

Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

5.G: Evaluate conjectures and predictions based upon data presented in tables and graphs, and identify misuses of statistical data and displays.

Graphing Skills
Mascot Election (Pictographs and Bar Graphs)
Reaction Time 2 (Graphs and Statistics)

5.I: Describe the probability of an event using ratios, including fractional notation.

5.I.8: Identify the probability of events within a simple experiment, such as three chances out of eight.

Spin the Big Wheel! (Probability)

5.I.9: Use 0,1 and ratios between 0 and 1 to represent the probability of outcomes for an event, and associate the ratio with the likelihood of the outcome.

Spin the Big Wheel! (Probability)

5.J: Compare experimental and theoretical results for a variety of simple experiments.

5.J.10: Compare what should happen (theoretical/expected results) with what did happen (experimental/actual results) in a simple experiment.

Spin the Big Wheel! (Probability)

5.K: Make and justify predictions based on experimental and theoretical probabilities.

5.K.11: Make predictions based on experimental and theoretical probabilities.

Spin the Big Wheel! (Probability)