I: Students will expand number sense to include integers and perform operations with whole numbers, simple fractions, and decimals.

I.1: Represent whole numbers and decimals from thousandths to one billion, fractions, percents, and integers.

I.1.a: Read and write numbers in standard and expanded form.

Cannonball Clowns (Number Line Estimation)

I.1.b: Demonstrate multiple ways to represent whole numbers, decimals, fractions, percents, and integers using models and symbolic representations (e.g., 108 = 2 x 50 + 8; 108 = 102 + 8; 90% = 90 out of 100 squares on a hundred chart).

Comparing and Ordering Decimals
Fraction Artist 1 (Area Models of Fractions)
Fraction, Decimal, Percent (Area and Grid Models)
Modeling Decimals (Area and Grid Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Multiplying Decimals (Area Model)
Treasure Hunter (Decimals on the Number Line)

I.1.c: Identify, read, and locate fractions, mixed numbers, decimals, and integers on the number line.

Comparing and Ordering Decimals
Fraction Garden (Comparing Fractions)
Fraction, Decimal, Percent (Area and Grid Models)
Fractions Greater than One (Fraction Tiles)
Modeling Decimals (Area and Grid Models)
Modeling Fractions (Area Models)
Treasure Hunter (Decimals on the Number Line)

I.2: Explain relationships and equivalencies among integers, fractions, decimals, and percents.

I.2.a: Compare fractions by finding a common denominator.

Adding Fractions (Fraction Tiles)
Equivalent Fractions (Fraction Tiles)
Factor Trees (Factoring Numbers)
Fraction Artist 2 (Area Models of Fractions)
Modeling Fractions (Area Models)

I.2.b: Order integers, fractions (including mixed numbers), and decimals using a variety of methods, including the number line.

Comparing and Ordering Decimals
Fraction Garden (Comparing Fractions)
Modeling Decimals (Area and Grid Models)
Modeling Fractions (Area Models)
Treasure Hunter (Decimals on the Number Line)

I.2.d: Represent commonly used fractions as decimals and percents in a variety of ways (e.g., models, fraction strips, pictures, calculators, algorithms).

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

I.2.e: Model and calculate equivalent forms of a fraction (including simplest form).

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)

I.3: Use number theory concepts to develop and use divisibility tests; classify whole numbers to 50 as prime, composite, or neither; and find common multiples and factors.

I.3.b: Use strategies for classifying whole numbers to 50 as prime, composite, or neither.

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

I.3.c: Rewrite a composite number between 2 and 50 as a product of only prime numbers.

Factor Trees (Factoring Numbers)

I.3.d: Find common multiples and factors and apply to adding and subtracting fractions.

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

I.4: Model and illustrate meanings of multiplication and division.

I.4.a: Represent division-with-remainder using whole numbers, decimals, or fractions.

No Alien Left Behind (Division with Remainders)
Pattern Flip (Patterns)

I.4.c: Model multiplication of fractions and decimals (e.g., tenths multiplied by tenths, a whole number multiplied by tenths, or a whole number with tenths multiplied by tenths) in a variety of ways (e.g., manipulatives, number line and area models, patterns).

Multiplying Decimals (Area Model)

I.5: Solve problems involving one or two operations.

I.5.a: Determine when it is appropriate to use estimation, mental math strategies, paper and pencil, and algorithms.

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

I.5.d: Interpret division-with-remainder problems as they apply to the environment (e.g., If there are 53 people, how many vans are needed if each van holds 8 people?).

Pattern Flip (Patterns)

I.6: Demonstrate proficiency with multiplication and division of whole numbers and compute problems involving addition, subtraction, and multiplication of decimals and fractions.

I.6.b: Divide multi-digit dividends by a one-digit divisor with fluency, using efficient procedures.

No Alien Left Behind (Division with Remainders)

I.6.c: Add and subtract decimals with fluency, using efficient procedures.

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

I.6.d: Add and subtract fractions with fluency.

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

II: Students will use patterns and relations to represent and analyze mathematical problems and number relationships using algebraic symbols.

II.2: Use algebraic expressions, inequalities, or equations to represent and solve simple real-world problems.

II.2.a: Use properties and the order of operations involving addition, subtraction, multiplication, division, and the use of parentheses to compute with whole numbers, decimals, and fractions.

Adding Fractions (Fraction Tiles)
Adding Whole Numbers and Decimals (Base-10 Blocks)
Cargo Captain (Multi-digit Subtraction)
Critter Count (Modeling Multiplication)
Fractions Greater than One (Fraction Tiles)
Multiplying Decimals (Area Model)
Number Line Frog Hop (Addition and Subtraction)
Order of Operations
Pattern Flip (Patterns)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)

III: Students will use spatial reasoning to recognize, describe, and analyze geometric shapes and principles.

III.1: Describe relationships between two- and three-dimensional shapes and analyze attributes and properties of geometric shapes.

III.1.a: Draw, label, and describe line segments, rays, lines, parallel lines, and perpendicular lines.

Elevator Operator (Line Graphs)

III.1.c: Classify triangles and quadrilaterals and analyze the relationships among the shapes in each classification (e.g., a square is a rectangle).

Classifying Quadrilaterals

III.2: Specify locations in a coordinate plane.

III.2.a: Locate points defined by ordered pairs of integers.

City Tour (Coordinates)
Elevator Operator (Line Graphs)
Points in the Coordinate Plane
Points, Lines, and Equations

III.2.b: Write an ordered pair for a point in a coordinate plane with integer coordinates.

City Tour (Coordinates)
Elevator Operator (Line Graphs)
Points in the Coordinate Plane
Points, Lines, and Equations

III.2.c: Specify possible paths between locations on a coordinate plane and compare distances of the various paths.

City Tour (Coordinates)

IV: Students will determine area of polygons and surface area and volume of three-dimensional shapes.

IV.2: Recognize, describe, and determine surface area and volume of three-dimensional shapes.

IV.2.c: Derive and use the formula to determine the volume of a right prism with a triangular or rectangular base.

Balancing Blocks (Volume)

V: Students will construct, analyze, and construct reasonable conclusions from data and apply basic concepts of probability.

V.1: Formulate and answer questions using statistical methods to compare data, and propose and justify inferences based on data.

V.1.a: Construct, analyze, and display data using an appropriate format (e.g., line plots, bar graphs, line graphs).

Distance-Time Graphs
Elevator Operator (Line Graphs)
Graphing Skills
Mascot Election (Pictographs and Bar Graphs)
Prairie Ecosystem
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

V.1.d: Identify and calculate the mean, median, mode, and range.

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

V.2: Apply basic concepts of probability.

V.2.a: Describe the results of experiments involving random outcomes using a variety of notations (e.g., 4 out of 9, 4/9).

Spin the Big Wheel! (Probability)

V.2.b: Recognize that probability is always a value between 0 and 1 (inclusively).

Spin the Big Wheel! (Probability)