1: Number Sense, Properties, and Operations

1.1: Understand the structure and properties of our number system. At their most basic level numbers are abstract symbols that represent real-world quantities

1.1: The decimal number system describes place value patterns and relationships that are repeated in large and small numbers and forms the foundation for efficient algorithms

1.1.a: Students can: Explain that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

Adding Whole Numbers and Decimals (Base-10 Blocks)
Cannonball Clowns (Number Line Estimation)
Cargo Captain (Multi-digit Subtraction)
Comparing and Ordering Decimals
Modeling Decimals (Area and Grid Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Rounding Whole Numbers (Number Line)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Target Sum Card Game (Multi-digit Addition)
Treasure Hunter (Decimals on the Number Line)
Whole Numbers with Base-10 Blocks

1.1.b: Students can: Read, write, and compare decimals to thousandths.

1.1.b.i: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form.

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

1.1.b.ii: Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

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

1.1.d: Students can: Convert like measurement units within a given measurement system.

1.1.d.i: Convert among different-sized standard measurement units within a given measurement system.

Cannonball Clowns (Number Line Estimation)

1.1.d.ii: Use measurement conversions in solving multi-step, real world problems.

Cannonball Clowns (Number Line Estimation)

1.2: Are fluent with basic numerical and symbolic facts and algorithms, and are able to select and use appropriate (mental math, paper and pencil, and technology) methods based on an understanding of their efficiency, precision, and transparency

1.2: Formulate, represent, and use algorithms with multi-digit whole numbers and decimals with flexibility, accuracy, and efficiency

1.2.a: Students can: Fluently multiply multi-digit whole numbers using standard algorithms.

Critter Count (Modeling Multiplication)

1.2.b: Students can: Find whole-number quotients of whole numbers.

Critter Count (Modeling Multiplication)
Factor Trees (Factoring Numbers)
No Alien Left Behind (Division with Remainders)
Pattern Flip (Patterns)

1.2.b.i: Use strategies based on place value, the properties of operations, and/or the relationship between multiplication and division.

Critter Count (Modeling Multiplication)
Factor Trees (Factoring Numbers)
No Alien Left Behind (Division with Remainders)
Pattern Flip (Patterns)

1.2.b.ii: Illustrate and explain calculations by using equations, rectangular arrays, and/or area models.

Critter Count (Modeling Multiplication)
Factor Trees (Factoring Numbers)
No Alien Left Behind (Division with Remainders)
Pattern Flip (Patterns)

1.2.c: Students can: Add, subtract, multiply, and divide decimals to hundredths.

Adding Whole Numbers and Decimals (Base-10 Blocks)
Multiplying Decimals (Area Model)
Multiplying with Decimals
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Sums and Differences with Decimals

1.2.c.i: Use concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

Adding Whole Numbers and Decimals (Base-10 Blocks)
Multiplying Decimals (Area Model)
Multiplying with Decimals
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Sums and Differences with Decimals

1.2.c.ii: Relate strategies to a written method and explain the reasoning used.

Adding Whole Numbers and Decimals (Base-10 Blocks)
Multiplying Decimals (Area Model)
Multiplying with Decimals
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Sums and Differences with Decimals

1.2.d: Students can: Write and interpret numerical expressions.

1.2.d.i: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

Order of Operations

1.3: Formulate, represent, and use algorithms to add and subtract fractions with flexibility, accuracy, and efficiency

1.3.a: Students can: Use equivalent fractions as a strategy to add and subtract fractions.

1.3.a.i: Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.

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

1.3.a.ii: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions with like denominators.

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

1.3.a.iii: Solve word problems involving addition and subtraction of fractions referring to the same whole.

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

1.3: Understand the structure and properties of our number system. At their most basic level numbers are abstract symbols that represent real-world quantities

1.4: The concepts of multiplication and division can be applied to multiply and divide fractions

1.4.a: Students can: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b).

Fraction Artist 1 (Area Models of Fractions)

1.4.b: Students can: Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.

Fraction Artist 1 (Area Models of Fractions)

1.4.c: Students can: Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. In general, (a/b) × (c/d) = ac/bd.

Multiplying Fractions

1.4.d: Students can: Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths.

Multiplying Fractions

1.4.d.i: Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

Multiplying Fractions

1.4.f: Students can: Solve real world problems involving multiplication of fractions and mixed numbers.

Multiplying Fractions

2: Patterns, Functions, and Algebraic Structures

2.1: Make sound predictions and generalizations based on patterns and relationships that arise from numbers, shapes, symbols, and data

2.1: Number patterns are based on operations and relationships

2.1.a: Students can: Generate two numerical patterns using given rules.

City Tour (Coordinates)
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Pattern Finder
Pattern Flip (Patterns)
Points, Lines, and Equations

2.1.b: Students can: Identify apparent relationships between corresponding terms.

City Tour (Coordinates)
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Pattern Finder
Pattern Flip (Patterns)
Points, Lines, and Equations

2.1.c: Students can: Form ordered pairs consisting of corresponding terms from the two patterns, and graphs the ordered pairs on a coordinate plane.

City Tour (Coordinates)
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Pattern Finder
Pattern Flip (Patterns)
Points, Lines, and Equations

2.1.d: Students can: Explain informally relationships between corresponding terms in the patterns.

City Tour (Coordinates)
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Pattern Finder
Pattern Flip (Patterns)
Points, Lines, and Equations

2.1.f: Students can: Explain, extend, and use patterns and relationships in solving problems, including those involving saving and checking accounts such as understanding that spending more means saving less.

Pattern Finder
Pattern Flip (Patterns)

4: Shape, Dimension, and Geometric Relationships

4.1: Understand quantity through estimation, precision, order of magnitude, and comparison. The reasonableness of answers relies on the ability to judge appropriateness, compare, estimate, and analyze error

4.1: Properties of multiplication and addition provide the foundation for volume an attribute of solids.

4.1.a: Students can: Model and justify the formula for volume of rectangular prisms.

4.1.a.i: Model the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes.

Balancing Blocks (Volume)
Prisms and Cylinders

4.1.a.ii: Show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base.

Balancing Blocks (Volume)
Prisms and Cylinders

4.1.a.iii: Represent threefold whole-number products as volumes to represent the associative property of multiplication.

Balancing Blocks (Volume)
Prisms and Cylinders

4.1.b: Students can: Find volume of rectangular prisms using a variety of methods and use these techniques to solve real world and mathematical problems.

Balancing Blocks (Volume)
Prisms and Cylinders

4.1.b.i: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

Balancing Blocks (Volume)

4.1.b.ii: Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths.

Balancing Blocks (Volume)
Prisms and Cylinders

4.2: Make claims about relationships among numbers, shapes, symbols, and data and defend those claims by relying on the properties that are the structure of mathematics

4.2: Geometric figures can be described by their attributes and specific locations in the plane

4.2.a: Students can: Graph points on the coordinate plane to solve real-world and mathematical problems.

City Tour (Coordinates)
Elevator Operator (Line Graphs)
Function Machines 2 (Functions, Tables, and Graphs)
Points in the Coordinate Plane
Points, Lines, and Equations

4.2.b: Students can: Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

City Tour (Coordinates)
Elevator Operator (Line Graphs)
Function Machines 2 (Functions, Tables, and Graphs)
Points in the Coordinate Plane
Points, Lines, and Equations

4.2.c: Students can: Classify two-dimensional figures into categories based on their properties.

4.2.c.i: Explain that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.

Classifying Quadrilaterals

4.2.c.ii: Classify two-dimensional figures in a hierarchy based on properties.

Classifying Quadrilaterals
Classifying Triangles
Parallelogram Conditions
Special Parallelograms