5.OA: Operations and Algebraic Thinking

1.1: Write and interpret numerical expressions.

5.OA.1: Use and explain parentheses, in numerical expressions, and evaluate expressions with these symbols.

Order of Operations

1.2: Analyze patterns and relationships.

5.OA.3: Generate two numerical patterns using two given rules. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. Identify the relationship between the two 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

5.NBT: Number and Operation in Base Ten

2.1: Understand the place value system.

5.NBT.1: Recognize 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)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Treasure Hunter (Decimals on the Number Line)

5.NBT.3: Read, write, and compare decimals to thousandths.

5.NBT.3.a: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).

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)

5.NBT.3.b: 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)

2.2: Perform operations with multi-digit whole number and with decimals to hundredths.

5.NBT.5: Fluently multiply multi-digit whole numbers using an algorithm, including but not limited to the standard algorithm.

Critter Count (Modeling Multiplication)

5.NBT.6: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Explain the calculation by using equations, rectangular arrays, illustrations, area models, or other representations based on place value.

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

5.NBT.7: Use the four operations with decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; justify the reasoning used with a written explanation.

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

5.NBT.7.a: Add and subtract decimals.

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

5.NBT.7.b: Multiply and divide decimals.

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

5.NF: Number and Operations—Fractions

3.1: Use equivalent fractions as a strategy to add and subtract fractions.

5.NF.1: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference with a like denominator. It is not necessary at this grade level to simplify the sum or difference.

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

5.NF.2: Solve word problems involving addition and subtraction of fractions.

5.NF.2.a: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem.

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

5.NF.2.b: 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)

3.2: Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

5.NF.3: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

Fraction Artist 1 (Area Models of Fractions)

5.MD: Measurement and Data

4.1: Convert like measurement units within a given measurement system.

5.MD.1: Convert customary and metric measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m). Use these conversions in solving multi-step, real world problems involving distances, intervals of time, liquid volumes, masses of objects, and money (including problems involving simple fractions or decimals).

Cannonball Clowns (Number Line Estimation)

4.3: Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

5.MD.3: Recognize volume as an attribute of solid figures and understand concepts of volume measurement.

5.MD.3.a: A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume.

Balancing Blocks (Volume)

5.MD.3.b: A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.

Balancing Blocks (Volume)

5.MD.5: Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

5.MD.5.a: Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and 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)

5.MD.5.c: Apply the formulas V = l × w × h and V = B × h (where B is the area of the base) for rectangular prisms to find volumes of right rectangular prisms with whole number edge lengths in the context of solving real world and mathematical problems.

Balancing Blocks (Volume)

5.G: Geometry

5.1: Graph points on the coordinate plane to solve real-world and mathematical problems.

5.G.1: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).

City Tour (Coordinates)
Elevator Operator (Line Graphs)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Points in the Coordinate Plane
Points, Lines, and Equations

5.G.2: 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)
Points in the Coordinate Plane
Points, Lines, and Equations

5.2: Classify two-dimensional figures into categories based on their properties.

5.G.3: Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.

Classifying Quadrilaterals

5.G.4: Classify two-dimensional figures in a hierarchy based on properties.

Classifying Quadrilaterals