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: Decompose and recompose whole numbers up to 10,000 using a variety of one, two- and three-digit combinations

Number Line Frog Hop (Addition and Subtraction)

1.1.2: Determine factor pairs that make up a given number

Chocomatic (Multiplication, Arrays, and Area)
Factor Trees (Factoring Numbers)

1.1.3: Develop an understanding of fractions as parts of unit wholes and division of whole numbers

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)

1.1.4: Demonstrate equivalent forms of common fractions using physical models, pictures, and number lines

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)

1.1.5: Compare and order fractions using physical models, pictures, and number lines

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)
Modeling Fractions (Area Models)
Number Line Frog Hop (Addition and Subtraction)
Toy Factory (Set Models of Fractions)
Treasure Hunter (Decimals on the Number Line)

1.2: Operations

1.2.2: Add and subtract larger numbers (e.g., three digits + two digits) and explain how the operation works

Adding Whole Numbers and Decimals (Base-10 Blocks)
Number Line Frog Hop (Addition and Subtraction)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)

1.2.3: Demonstrate mastery of mental math strategies for multiplying numbers (e.g., 25 * 8)

Multiplying Decimals (Area Model)

1.2.4: Show how multiplication and division facts up to 50 are related, using arrays, skip counting, and area models

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

1.2.5: Master multiplication facts and the related division facts up to the 10s tables

Critter Count (Modeling Multiplication)

1.2.7: Develop and use strategies to estimate the results of operations on whole numbers

Critter Count (Modeling Multiplication)
Multiplying Decimals (Area Model)

1.2.8: Use physical models and pictures to add and subtract benchmark fractions

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

1.2.9: Find 1/3, 1/4, and 1/5 of a given set or area using models

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

1.2.11: 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

2.1.3: Interpret tables, graphs and real-world events based on how they change over time

Graphing Skills

2.2: Representations

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

Critter Count (Modeling Multiplication)
No Alien Left Behind (Division with Remainders)

2.3: Symbols

2.3.2: Develop an understanding of the Commutative and Associative Properties of whole number multiplication as a tool to solve problems (e.g., is 4 × 5 always the same as 5 × 4?)

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

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.

3.1: Classification

3.1.1: Identify and classify two-dimensional and three-dimensional shapes according to their properties

Classifying Quadrilaterals

3.2: Location and transformation

3.2.1: Identify line and rotational symmetry in two-dimensional shapes

Quilting Bee (Symmetry)

3.3: Measurement

3.3.4: Find the distance around a geometric figure to the nearest whole number (perimeter)

Fido's Flower Bed (Perimeter and Area)

3.3.5: Find the number of square units it takes to cover a rectangle (area)

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

3.3.6: Count the number of cubes it takes to fill a three-dimensional figure (volume)

Balancing Blocks (Volume)

3.3.8: Estimate and then measure the mass of an object to the nearest whole unit

Cannonball Clowns (Number Line Estimation)

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: Pose questions that can be answered with data; systematically collect and organize both categorical and numerical data

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

4.2: Represent

4.2.1: Construct and use data displays (e.g., tables, scaled pictographs, bar graphs, line plots) in order to answer a question

Forest Ecosystem
Graphing Skills
Mascot Election (Pictographs and Bar Graphs)
Prairie Ecosystem
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

4.3: Analyze

4.3.1: Describe a set of data as a whole, noting important features such as concentration of values, spread of the values, and extreme values

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

4.3.2: Find and use measures of center (mode and median) to summarize and interpret data

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

4.4: Probability

4.4.1: Describe the outcomes of an experiment or event (e.g., possible/impossible, certain/uncertain, less likely/equally likely/more likely)

Spin the Big Wheel! (Probability)

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)