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 whole number system describes place value relationships and forms the foundation for efficient algorithms

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

1.1.a.i: Use place value understanding to round whole numbers to the nearest 10 or 100.

Rounding Whole Numbers (Number Line)

1.1.a.ii: Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

Adding Fractions (Fraction Tiles)
Adding Whole Numbers and Decimals (Base-10 Blocks)
Cargo Captain (Multi-digit Subtraction)
Fractions Greater than One (Fraction Tiles)
Number Line Frog Hop (Addition and Subtraction)
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

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

1.2: Parts of a whole can be modeled and represented in different ways

1.2.a: Students can: Develop understanding of fractions as numbers.

1.2.a.i: Describe a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; describe a fraction a/b as the quantity formed by a parts of size 1/b.

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)

1.2.a.ii: Describe a fraction as a number on the number line; represent fractions on a number line diagram.

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

1.2.a.iii: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

1.2.a.iii.1: Identify two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

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.2: Identify and generate simple equivalent fractions. Explain why the fractions are equivalent.

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.3: Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.

Equivalent Fractions (Fraction Tiles)

1.2.a.iii.4: Compare two fractions with the same numerator or the same denominator by reasoning about their size.

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)
Fractions Greater than One (Fraction Tiles)
Modeling Fractions (Area Models)
Toy Factory (Set Models of Fractions)

1.2.a.iii.5: Explain why comparisons are valid only when the two fractions refer to the same whole.

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)
Fractions Greater than One (Fraction Tiles)
Modeling Fractions (Area Models)
Toy Factory (Set Models of Fractions)

1.2.a.iii.6: Record the results of comparisons with the symbols >, =, or <, and justify the conclusions.

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)
Fractions Greater than One (Fraction Tiles)
Modeling Fractions (Area Models)
Toy Factory (Set Models of Fractions)

1.3: 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

1.3: Multiplication and division are inverse operations and can be modeled in a variety of ways

1.3.a: Students can: Represent and solve problems involving multiplication and division.

1.3.a.i: Interpret products of whole numbers.

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

1.3.a.ii: Interpret whole-number quotients of whole numbers.

No Alien Left Behind (Division with Remainders)

1.3.a.iii: Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities.

Chocomatic (Multiplication, Arrays, and Area)
Critter Count (Modeling Multiplication)
No Alien Left Behind (Division with Remainders)

1.3.a.iv: Determine the unknown whole number in a multiplication or division equation relating three whole numbers.

Factor Trees (Factoring Numbers)

1.3.a.v: Model strategies to achieve a personal financial goal using arithmetic operations.

Road Trip (Problem Solving)

1.3.b: Students can: Apply properties of multiplication and the relationship between multiplication and division.

1.3.b.i: Apply properties of operations as strategies to multiply and divide.

Chocomatic (Multiplication, Arrays, and Area)
Critter Count (Modeling Multiplication)
Multiplying Decimals (Area Model)
Pattern Flip (Patterns)

1.3.b.ii: Interpret division as an unknown-factor problem.

Factor Trees (Factoring Numbers)

1.3.c: Students can: Multiply and divide within 100.

1.3.c.i: Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations.

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

1.3.c.ii: Recall from memory all products of two one-digit numbers.

Critter Count (Modeling Multiplication)
Factor Trees (Factoring Numbers)
Multiplying Decimals (Area Model)
Pattern Flip (Patterns)

1.3.d: Students can: Solve problems involving the four operations, and identify and explain patterns in arithmetic.

1.3.d.i: Solve two-step word problems using the four operations.

Cargo Captain (Multi-digit Subtraction)
Critter Count (Modeling Multiplication)
No Alien Left Behind (Division with Remainders)
Number Line Frog Hop (Addition and Subtraction)
Using Algebraic Equations
Using Algebraic Expressions

1.3.d.ii: Represent two-step word problems using equations with a letter standing for the unknown quantity.

Cargo Captain (Multi-digit Subtraction)
Critter Count (Modeling Multiplication)
No Alien Left Behind (Division with Remainders)
Number Line Frog Hop (Addition and Subtraction)
Using Algebraic Equations
Using Algebraic Expressions

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

Cargo Captain (Multi-digit Subtraction)
Critter Count (Modeling Multiplication)
No Alien Left Behind (Division with Remainders)
Number Line Frog Hop (Addition and Subtraction)
Using Algebraic Equations
Using Algebraic Expressions

1.3.d.iv: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.

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

3: Data Analysis, Statistics, and Probability

2.1: Solve problems and make decisions that depend on understanding, explaining, and quantifying the variability in data

3.1: Visual displays are used to describe data

3.1.a: Students can: Represent and interpret data.

3.1.a.i: Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories.

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

3.1.a.ii: Solve one- and two-step 'how many more' and 'how many less' problems using information presented in scaled bar graphs.

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

3.1.a.iii: Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters.

Reaction Time 2 (Graphs and Statistics)

4: Shape, Dimension, and Geometric Relationships

3.1: 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

4.1: Geometric figures are described by their attributes

4.1.a: Students can: Reason with shapes and their attributes.

4.1.a.i: Explain that shapes in different categories may share attributes and that the shared attributes can define a larger category.

Classifying Quadrilaterals

4.1.a.i.1: Identify rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

Classifying Quadrilaterals

4.1.a.ii: Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.

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

3.2: 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

4.2: Linear and area measurement are fundamentally different and require different units of measure

4.2.a: Students can: Use concepts of area and relate area to multiplication and to addition.

4.2.a.ii: Find area of rectangles with whole number side lengths using a variety of methods.

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

4.2.a.iii: Relate area to the operations of multiplication and addition and recognize area as additive.

Chocomatic (Multiplication, Arrays, and Area)

4.2.b: Students can: Describe perimeter as an attribute of plane figures and distinguish between linear and area measures.

Fido's Flower Bed (Perimeter and Area)

4.2.c: Students can: Solve real world and mathematical problems involving perimeters of polygons.

Fido's Flower Bed (Perimeter and Area)

4.2.c.i: Find the perimeter given the side lengths.

Fido's Flower Bed (Perimeter and Area)

4.2.c.ii: Find an unknown side length given the perimeter.

Fido's Flower Bed (Perimeter and Area)

4.2.c.iii: Find rectangles with the same perimeter and different areas or with the same area and different perimeters.

Fido's Flower Bed (Perimeter and Area)

4.3: Time and attributes of objects can be measured with appropriate tools

4.3.a: Students can: Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

4.3.a.i: Tell and write time to the nearest minute.

Elapsed Time

4.3.a.ii: Measure time intervals in minutes.

Elapsed Time

4.3.a.iii: Solve word problems involving addition and subtraction of time intervals in minutes using a number line diagram.

Elapsed Time

4.3.a.iv: Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).

Cannonball Clowns (Number Line Estimation)

4.3.a.v: Use models to add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units.

Cannonball Clowns (Number Line Estimation)