1: Numeric Reasoning: Students will develop Numeric Reasoning and an understanding of Number and Operations by solving problems in which there is a need to represent and model real numbers verbally, physically, and symbolically; to explain the relationship between numbers; to determine the relative magnitude of real numbers; to use operations with understanding; and to select appropriate methods of calculations from among mental math, paper-and-pencil, calculators, or computers.

1.1: Number sense

1.1.1: Demonstrate an understanding that our number system is based on combinations of 1s, 10s, and 100s-place value

Adding Whole Numbers and Decimals (Base-10 Blocks)
Cannonball Clowns (Number Line Estimation)
Cargo Captain (Multi-digit Subtraction)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)

1.1.3: Connect skip counting to multiplication

Chocomatic (Multiplication, Arrays, and Area)
Critter Count (Modeling Multiplication)

1.1.4: Develop understanding of fractions as parts of unit wholes

Equivalent Fractions (Fraction Tiles)
Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)
Fraction Garden (Comparing Fractions)
Fraction, Decimal, Percent (Area and Grid Models)
Modeling Fractions (Area Models)
Toy Factory (Set Models of Fractions)

1.1.5: Compare the size of common fractions using models

Equivalent Fractions (Fraction Tiles)
Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)
Fraction Garden (Comparing Fractions)
Modeling Fractions (Area Models)
Toy Factory (Set Models of Fractions)

1.2: Operations

1.2.3: Develop and use strategies to estimate the results of addition and subtraction operations on whole numbers

Adding Whole Numbers and Decimals (Base-10 Blocks)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)

1.2.5: Develop the concept of multiplication by using models to represent and count the number of groups and the number of elements in each group (e.g., repeated addition, arrays, skip counting)

Chocomatic (Multiplication, Arrays, and Area)
Critter Count (Modeling Multiplication)
Multiplying Decimals (Area Model)

1.2.6: Select and use appropriate methods and tools for computing (e.g., mental computation, estimation, calculators, paper and pencil) depending on the context and nature of the computation

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

2: Algebraic Reasoning: Students will develop Algebraic Reasoning and an understanding of Patterns and Functions by solving problems in which there is a need to recognize and extend a variety of patterns; to progress from the concrete to the abstract using physical models, equations, and graphs; to describe, represent, and analyze relationships among variable quantities; and to analyze, represent, model, and describe real-world functional relationships.

2.1: Patterns and change

2.1.2: Describe the patterns that result when skip counting

Pattern Flip (Patterns)

2.2: Representations

2.2.1: Model situations that involve the addition, subtraction, and multiplication of whole numbers using objects, pictures, symbols, and geometric models

Adding Whole Numbers and Decimals (Base-10 Blocks)
Critter Count (Modeling Multiplication)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)

3: Geometric Reasoning: Students will develop Geometric Reasoning and an understanding of Geometry and Measurement by solving problems in which there is a need to recognize, construct, transform, analyze properties of, and discover relationships among geometric figures; and to measure to a required degree pf accuracy by selecting appropriate tools and units.

3.2: Location and transformation

3.2.1: Describe a flip or slide of a given shape that demonstrates that the two shapes are congruent

Rock Art (Transformations)

3.3: Measurement

3.3.2: Find objects that match a standard unit (e.g., one inch, one foot, one centimeter, one meter)

Cannonball Clowns (Number Line Estimation)

3.3.5: Make number lines and break each unit into smaller units (e.g., 1/2 units, 1/3 units, 1/4 units)

Fraction Garden (Comparing Fractions)
Fractions Greater than One (Fraction Tiles)
Modeling Fractions (Area Models)
Treasure Hunter (Decimals on the Number Line)

3.3.6: Find the area of a design by counting the number of units used to cover or fill it (e.g., pattern blocks, color tiles)

Balancing Blocks (Volume)
Chocomatic (Multiplication, Arrays, and Area)
Fido's Flower Bed (Perimeter and Area)

4: Quantitative Reasoning: Students will develop Quantitative Reasoning and an understanding of Data Analysis and Probability by solving problems in which there is a need to collect, appropriately represent, and interpret data; to make inferences or predictions and to present convincing arguments; and to model mathematical situations to determine the probability.

4.1: Collect

4.1.1: Collect categorical and numerical data to answer a question posed by the teacher or students

Reaction Time 2 (Graphs and Statistics)

4.2: Represent

4.2.1: Demonstrate a variety of informal and conventional techniques for representing and organizing categorical and numerical data (e.g., tallies, tables, pictographs, bar graphs)

Forest Ecosystem
Graphing Skills
Mascot Election (Pictographs and Bar Graphs)
Reaction Time 1 (Graphs and Statistics)

4.3: Analyze

4.3.2: Find and use the mode to describe and interpret data

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

A.6: Students shall develop and apply mathematical models to represent and understand quantitative relationships.

A.6.5.1: Draw conclusions and make predictions, with and without appropriate technology, from models, tables and line graphs

Graphing Skills

G: Geometry

G.8: Students shall analyze characteristics and properties of 2 and 3 dimensional geometric shapes and develop mathematical arguments about geometric relationships.

G.8.5.1: Identify and model regular and irregular polygons including decagon

Classifying Quadrilaterals

G.9: Students shall apply transformations and the use of symmetry to analyze mathematical situations.

G.9.5.1: Predict and describe the results of translation (slide), reflection (flip), rotation (turn), showing that the transformed shape remains unchanged

Rock Art (Transformations)

G.10: Students shall specify locations and describe spatial relationships using coordinate geometry and other representational systems.

G.10.5.1: Use geometric vocabulary (horizontal/x-axis, vertical/ y-axis, ordered pairs) to describe the location and plot points in Quadrant I

Points in the Coordinate Plane

M: Measurement

M.12: Students shall use attributes of measurement to describe and compare mathematical and real-world objects.

M.12.5.5: Model the differences between covering the faces (surface area/nets) and filling the interior (volume of cubes)

Balancing Blocks (Volume)

M.13: Students shall identify and use units, systems and processes of measurement.

M.13.5.1: Solve real world problems involving one elapsed time, counting forward (calendar and clock)

Elapsed Time

M.13.5.3: Draw and measure distance to the nearest cm and ¼ inch accurately

Cannonball Clowns (Number Line Estimation)

M.13.5.4: Develop and use strategies to solve real world problems involving perimeter and area of rectangles

Fido's Flower Bed (Perimeter and Area)

DAP: Data Analysis and Probability

DAP.14: Students shall formulate questions that can be addressed with data and collect, organize and display relevant data to answer them.

DAP.14.5.1: Develop appropriate questions for surveys

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

DAP.14.5.2: Collect numerical and categorical data using surveys, observations and experiments that would result in bar graphs, line graphs, line plots and stem-and-leaf plots

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

DAP.14.5.3: Construct and interpret frequency tables, charts, line plots, stem-and-leaf plots and bar graphs

Graphing Skills
Mascot Election (Pictographs and Bar Graphs)
Prairie Ecosystem
Reaction Time 1 (Graphs and Statistics)

DAP.15: Students shall select and use appropriate statistical methods to analyze data.

DAP.15.5.1: Interpret graphs such as line graphs, double bar graphs, and circle graphs

Elevator Operator (Line Graphs)
Graphing Skills
Prairie Ecosystem
Reaction Time 1 (Graphs and Statistics)

DAP.15.5.2: Determine, with and without appropriate technology, the range, mean, median and mode (whole number data sets) and explain what each indicates about the set of data

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

DAP.17: Students shall understand and apply basic concepts of probability.

DAP.17.5.2: List and explain all possible outcomes in a given situation

Spin the Big Wheel! (Probability)

M.13.4.9: Use strategies for finding the perimeter of a rectangle

Fido's Flower Bed (Perimeter and Area)

M.13.4.10: Use strategies for finding the area of a rectangle

Chocomatic (Multiplication, Arrays, and Area)
Fido's Flower Bed (Perimeter and Area)

M.13.4.11: Use strategies to find the volume (cubic units) of rectangular prisms and cubes

Balancing Blocks (Volume)

DAP.14.4.1: Create a data collection plan after being given a topic and collect, organize, display, describe and interpret simple data using frequency tables or line plots, pictographs and bar graphs

Graphing Skills

DAP.15.4.1: Represent and interpret data using pictographs, bar graphs and line graphs in which symbols or intervals are greater than one

Elevator Operator (Line Graphs)
Forest Ecosystem
Graphing Skills
Prairie Ecosystem
Reaction Time 1 (Graphs and Statistics)

DAP.15.4.2: Match a set of data with a graphical representation of the data

Graphing Skills
Mascot Election (Pictographs and Bar Graphs)

DAP.17.4.2: Conduct simple probability experiments, record the data and draw conclusions about the likelihood of possible outcome (roll number cubes, pull tiles from a bag, spin spinner, or determine the fairness of the game)

Spin the Big Wheel! (Probability)