1: Number, Number Sense and Operations

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

1.B.1: Use models and visual representation to develop the concept of ratio as part-to-part and part-to-whole, and the concept of percent as part-to-whole.

Fraction, Decimal, Percent (Area and Grid Models)

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.

Adding Fractions (Fraction Tiles)
Equivalent Fractions (Fraction Tiles)
Factor Trees (Factoring Numbers)
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)
Toy Factory (Set Models of Fractions)

1.B.3: Identify and generate equivalent forms of fractions, decimals and percents.

Fraction, Decimal, Percent (Area and Grid Models)
Modeling Decimals (Area and Grid Models)

1.C: Develop meaning for percents, including percents greater than 100 and less than 1.

Fraction, Decimal, Percent (Area and Grid Models)

1.D: Use models and pictures to relate concepts of ratio, proportion and percent.

1.D.1: Use models and visual representation to develop the concept of ratio as part-to-part and part-to-whole, and the concept of percent as part-to-whole.

Fraction, Decimal, Percent (Area and Grid Models)

1.E: Use order of operations, including use of parenthesis and exponents to solve multi-step problems, and verify and interpret the results.

1.E.9: Use order of operations, including use of parentheses, to simplify numerical expressions.

Order of Operations

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)
Critter Count (Modeling Multiplication)
Order of Operations

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.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)

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.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 Fractions (Fraction Tiles)
Fraction Artist 2 (Area Models of Fractions)
Fractions Greater than One (Fraction Tiles)
Modeling Fractions (Area Models)

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

Cannonball Clowns (Number Line Estimation)
Multiplying Decimals (Area Model)

2: Measurement

2.B: Convert units of length, area, volume, mass and time within the same measurement system.

2.B.5: Make conversions within the same measurement system while performing computations.

Cannonball Clowns (Number Line Estimation)

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.

Area of Triangles
Balancing Blocks (Volume)

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.4: Demonstrate understanding of the differences among linear units, square units and cubic units.

Cannonball Clowns (Number Line Estimation)
Fido's Flower Bed (Perimeter and Area)

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.4: Demonstrate understanding of the differences among linear units, square units and cubic units.

Cannonball Clowns (Number Line Estimation)
Fido's Flower Bed (Perimeter and Area)

3: Geometry and Spatial Sense

3.A: Identify and label angle parts and the regions defined within the plane where the angle resides.

3.A.2: Use standard language to describe line, segment, ray, angle, skew, parallel and perpendicular.

Elevator Operator (Line Graphs)

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.

Points in the Coordinate Plane

3.D: Identify, describe and classify types of line pairs, angles, two-dimensional figures and three-dimensional objects using their properties.

3.D.2: Use standard language to describe line, segment, ray, angle, skew, parallel and perpendicular.

Elevator Operator (Line Graphs)

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

Rock Art (Transformations)

4: Patterns, Functions and Algebra

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.

Comparing and Ordering Decimals

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.

Reaction Time 1 (Graphs and Statistics)

4.J: Use formulas in problem-solving situations.

Area of Triangles

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.

Reaction Time 1 (Graphs and Statistics)

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.

Distance-Time Graphs
Elevator Operator (Line Graphs)
Graphing Skills
Mascot Election (Pictographs and Bar Graphs)
Prairie Ecosystem

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
Prairie Ecosystem
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.

Graphing Skills
Mascot Election (Pictographs and Bar Graphs)

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.

Graphing Skills
Mascot Election (Pictographs and Bar Graphs)
Movie Reviewer (Mean and Median)
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.H: Find all possible outcomes of simple experiments or problem situations, using methods such as lists, arrays and tree diagrams.

5.H.7: List and explain all possible outcomes in a given situation.

Spin the Big Wheel! (Probability)

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

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)

6: Mathematical Processes

6.H: Use representations to organize and communicate mathematical thinking and problem solutions.

Fraction, Decimal, Percent (Area and Grid Models)