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 to the hundredths place 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: Generalize place value understanding for multi-digit whole numbers.

1.1.a.i: Explain that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.

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)
Rounding Whole Numbers (Number Line)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Target Sum Card Game (Multi-digit Addition)
Whole Numbers with Base-10 Blocks

1.1.a.ii: Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form.

Cannonball Clowns (Number Line Estimation)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Whole Numbers with Base-10 Blocks

1.1.a.iii: Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

Cannonball Clowns (Number Line Estimation)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Whole Numbers with Base-10 Blocks

1.1.a.iv: Use place value understanding to round multi-digit whole numbers to any place.

Rounding Whole Numbers (Number Line)

1.1.b: Students can: Use decimal notation to express fractions, and compare decimal fractions.

1.1.b.ii: Use decimal notation for fractions with denominators 10 or 100.

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

1.1.b.iii: Compare two decimals to hundredths by reasoning about their size.

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

1.2: Understand that equivalence is a foundation of mathematics represented in numbers, shapes, measures, expressions, and equations

1.2: Different models and representations can be used to compare fractional parts

1.2.a: Students can: Use ideas of fraction equivalence and ordering to:

1.2.a.i: Explain equivalence of fractions using drawings and models.

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)

1.2.a.ii: Use the principle of fraction equivalence to recognize and generate equivalent 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)

1.2.a.iii: Compare two fractions with different numerators and different denominators, and justify the conclusions.

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)

1.2.b: Students can: Build fractions from unit fractions by applying understandings of operations on whole numbers.

1.2.b.i: Apply previous understandings of addition and subtraction to add and subtract fractions.

Adding Fractions (Fraction Tiles)
Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)
Fractions Greater than One (Fraction Tiles)
Modeling Fractions (Area Models)

1.2.b.i.1: Compose and decompose fractions as sums and differences of fractions with the same denominator in more than one way and justify with visual models.

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)

1.2.b.i.2: Add and subtract mixed numbers with like denominators.

Fractions Greater than One (Fraction Tiles)

1.2.b.i.3: Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators.

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

1.2.b.ii: Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

1.2.b.ii.1: Express a fraction a/b as a multiple of 1/b.

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

1.2.b.ii.2: Use a visual fraction model to express a/b as a multiple of 1/b, and apply to multiplication of whole number by a fraction.

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

1.3: Are fluent with basic numerical, 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

1.3: Formulate, represent, and use algorithms to compute with flexibility, accuracy, and efficiency

1.3.a: Students can: Use place value understanding and properties of operations to perform multi-digit arithmetic.

1.3.a.i: Fluently add and subtract multi-digit whole numbers using the standard algorithm.

Adding Whole Numbers and Decimals (Base-10 Blocks)
Cargo Captain (Multi-digit Subtraction)
Number Line Frog Hop (Addition and Subtraction)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Target Sum Card Game (Multi-digit Addition)
Whole Numbers with Base-10 Blocks

1.3.a.ii: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations.

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

1.3.a.iii: Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division.

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

1.3.a.iv: Illustrate and explain multiplication and division calculation by using equations, rectangular arrays, and/or area models.

Chocomatic (Multiplication, Arrays, and Area)
Critter Count (Modeling Multiplication)
Multiplying Decimals (Area Model)
No Alien Left Behind (Division with Remainders)
Pattern Flip (Patterns)

1.3.b: Students can: Use the four operations with whole numbers to solve problems.

1.3.b.i: Interpret a multiplication equation as a comparison.

Chocomatic (Multiplication, Arrays, and Area)
Critter Count (Modeling Multiplication)
Factor Trees (Factoring Numbers)
Multiplying Decimals (Area Model)

1.3.b.ii: Represent verbal statements of multiplicative comparisons as multiplication equations.

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

1.3.b.iii: Multiply or divide to solve word problems involving multiplicative comparison.

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

1.3.b.iv: Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted.

Cannonball Clowns (Number Line Estimation)
Cargo Captain (Multi-digit Subtraction)
No Alien Left Behind (Division with Remainders)
Number Line Frog Hop (Addition and Subtraction)

1.3.b.v: Represent multistep word problems with equations using a variable to represent the unknown quantity.

Cannonball Clowns (Number Line Estimation)
Cargo Captain (Multi-digit Subtraction)
No Alien Left Behind (Division with Remainders)
Number Line Frog Hop (Addition and Subtraction)

1.3.b.vi: Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Cannonball Clowns (Number Line Estimation)
Cargo Captain (Multi-digit Subtraction)
No Alien Left Behind (Division with Remainders)
Number Line Frog Hop (Addition and Subtraction)

1.3.b.vii: Using the four operations analyze the relationship between choice and opportunity cost.

Road Trip (Problem Solving)

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

Function Machines 1 (Functions and Tables)
Pattern Finder
Pattern Flip (Patterns)

2.2: 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

2.1: Number patterns and relationships can be represented by symbols

2.1.a: Students can: Generate and analyze patterns and identify apparent features of the pattern that were not explicit in the rule itself.

Finding Patterns
Function Machines 1 (Functions and Tables)
Pattern Flip (Patterns)

2.1.a.iii: Complete input/output tables.

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)

2.1.b: Students can: Apply concepts of squares, primes, composites, factors, and multiples to solve problems.

2.1.b.i: Find all factor pairs for a whole number in the range 1–100.

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

2.1.b.ii: Recognize that a whole number is a multiple of each of its factors.

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

2.1.b.iii: Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number.

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

2.1.b.iv: Determine whether a given whole number in the range 1–100 is prime or composite.

Chocomatic (Multiplication, Arrays, and Area)
Factor Trees (Factoring Numbers)
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: Appropriate measurement tools, units, and systems are used to measure different attributes of objects and time

4.1.a: Students can: Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

4.1.a.i: Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec.

Cannonball Clowns (Number Line Estimation)

4.1.a.ii: Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.

Cannonball Clowns (Number Line Estimation)

4.1.a.iii: Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit.

Elapsed Time
Road Trip (Problem Solving)

4.1.a.iv: Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

Elapsed Time
Road Trip (Problem Solving)

4.1.a.v: Apply the area and perimeter formulas for rectangles in real world and mathematical problems.

Chocomatic (Multiplication, Arrays, and Area)

4.1.b: Students can: Use concepts of angle and measure angles.

4.1.b.iii: Demonstrate that angle measure as additive.

Polygon Angle Sum

4.1.b.iv: Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems.

Polygon Angle Sum

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 in the plane and in space are described and analyzed by their attributes

4.2.a: Students can: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines.

City Tour (Coordinates)
Classifying Quadrilaterals
Elevator Operator (Line Graphs)

4.2.b: Students can: Identify points, line segments, angles, and perpendicular and parallel lines in two-dimensional figures.

City Tour (Coordinates)
Classifying Quadrilaterals
Elevator Operator (Line Graphs)

4.2.c: Students can: Classify and identify two-dimensional figures according to attributes of line relationships or angle size.

Classifying Quadrilaterals
Classifying Triangles
Elevator Operator (Line Graphs)
Parallelogram Conditions

4.2.d: Students can: Identify a line of symmetry for a two-dimensional figure.

Quilting Bee (Symmetry)