NO: Number and Operations

NO.1: Students shall understand numbers, ways of representing numbers, relationships among numbers and number systems.

NO.1.5.1: Use models and visual representations to develop the concepts of the following:

NO.1.5.1.a: Fractions:

NO.1.5.1.a.1: parts of unit wholes

Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)
Modeling Fractions (Area Models)

NO.1.5.1.a.2: parts of a collection

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)

NO.1.5.1.a.3: locations on number lines

Fraction Garden (Comparing Fractions)
Fractions Greater than One (Fraction Tiles)
Modeling Fractions (Area Models)

NO.1.5.1.c: Percents:

NO.1.5.1.c.1: part-to-100

Fraction, Decimal, Percent (Area and Grid Models)

NO.1.5.2: Develop understanding of decimal place value using models

Adding Whole Numbers and Decimals (Base-10 Blocks)
Comparing and Ordering Decimals
Modeling Decimals (Area and Grid Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Treasure Hunter (Decimals on the Number Line)

NO.1.5.3: Identify decimal and percent equivalents for benchmark fractions

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

NO.1.5.5: Use models of benchmark fractions and their equivalent forms:

NO.1.5.5.a: to analyze the size of fractions

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)

NO.1.5.5.b: to determine that simplification does not change the value of the fraction

Adding Fractions (Fraction Tiles)
Equivalent Fractions (Fraction Tiles)
Factor Trees (Factoring Numbers)
Fraction Artist 1 (Area Models of Fractions)
Fractions Greater than One (Fraction Tiles)
Modeling Fractions (Area Models)
Toy Factory (Set Models of Fractions)

NO.1.5.5.c: to convert between mixed numbers and improper fractions

Fractions Greater than One (Fraction Tiles)

NO.2: Students shall understand meanings of operations and how they relate to one another.

NO.2.5.1: Use divisibility rules to determine if a number is a factor of another number (2, 3, 5, 10)

Factor Trees (Factoring Numbers)

NO.2.5.3: Identify the distributive property by using physical models to solve computation and real world problems

Chocomatic (Multiplication, Arrays, and Area)

NO.2.5.4: Apply rules (conventions) for order of operations to whole numbers where the left to right computations are modified only by the use of parentheses

Order of Operations

NO.2.5.5: Model addition, subtraction, and multiplication of 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)

NO.3: Students shall compute fluently and make reasonable estimates.

NO.3.5.2: Develop and use algorithms:

NO.3.5.2.a: to add and subtract numbers containing decimals (up to thousandths place)

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

NO.3.5.2.b: to multiply decimals (hundredths x tenths)

Multiplying Decimals (Area Model)

NO.3.5.2.d: to add and subtract fractions with like denominators

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

NO.3.5.4: Develop and use strategies to Estimate the results of whole number computations and to judge the reasonableness of such results

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

NO.3.5.5: Use factors of numbers:

NO.3.5.5.c: to simplify fractions to the lowest terms

Factor Trees (Factoring Numbers)

A: Algebra

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)