5.MP: Mathematical Practices

(Framing Text): Students become mathematically proficient in engaging with mathematical content and concepts as they learn, experience, and apply these skills and attitudes.

5.MP.1: Make sense of problems and persevere in solving them.

Biconditional Statements
Conditional Statements
Estimating Population Size
Pattern Flip (Patterns)

5.MP.1.a: Explain the meaning of a problem, look for entry points to begin work on the problem, and plan and choose a solution pathway. When a solution pathway does not make sense, look for another pathway that does. Explain connections between various solution strategies and representations. Upon finding a solution, look back at the problem to determine whether the solution is reasonable and accurate, often checking answers to problems using a different method or approach.

Biconditional Statements
Fraction, Decimal, Percent (Area and Grid Models)
Improper Fractions and Mixed Numbers
Linear Inequalities in Two Variables
Modeling One-Step Equations
Multiplying with Decimals
Pattern Flip (Patterns)
Polling: City
Solving Equations on the Number Line
Using Algebraic Expressions

5.MP.2: Reason abstractly and quantitatively.

Conditional Statements
Estimating Population Size

5.MP.3: Construct viable arguments and critique the reasoning of others.

Biconditional Statements

5.MP.3.a: Use stated assumptions, definitions, and previously established results to construct arguments. Explain and justify the mathematical reasoning underlying a strategy, solution, or conjecture by using concrete referents such as objects, drawings, diagrams, and actions. Listen to or read the arguments of others, decide whether they make sense, ask useful questions to clarify or improve the arguments, and build on those arguments.

Biconditional Statements
Conditional Statements

5.MP.4: Model with mathematics.

Estimating Sums and Differences

5.MP.5: Use appropriate tools strategically.

Elapsed Time

5.MP.5.a: Consider the tools that are available when solving a mathematical problem, whether in a real-world or mathematical context. Choose tools that are relevant and useful to the problem at hand, such as drawings, diagrams, technologies, and physical objects and tools, as well as mathematical tools such as estimation or a particular strategy or algorithm.

Segment and Angle Bisectors

5.MP.6: Attend to precision.

Biconditional Statements
Fraction, Decimal, Percent (Area and Grid Models)
Using Algebraic Expressions

5.MP.6.a: Communicate precisely to others by crafting careful explanations that communicate mathematical reasoning by referring specifically to each important mathematical element, describing the relationships among them, and connecting their words clearly to representations. Calculate accurately and efficiently, and use clear and concise notation to record work.

Arithmetic Sequences
Finding Patterns
Fraction, Decimal, Percent (Area and Grid Models)
Function Machines 2 (Functions, Tables, and Graphs)
Geometric Sequences
Pattern Flip (Patterns)

5.MP.7: Look for and make use of structure.

Pattern Flip (Patterns)

5.MP.7.a: Recognize and apply the structures of mathematics such as patterns, place value, the properties of operations, or the flexibility of numbers. See complicated things as single objects or as being composed of several objects.

Arithmetic Sequences
Finding Patterns
Function Machines 2 (Functions, Tables, and Graphs)
Geometric Sequences
Pattern Flip (Patterns)

5.MP.8: Look for and express regularity in repeated reasoning.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences
Pattern Finder
Pattern Flip (Patterns)

5.MP.8.a: Notice repetitions in mathematics when solving multiple related problems. Use observations and reasoning to find shortcuts or generalizations. Evaluate the reasonableness of intermediate results.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

5.OA: Operations and Algebraic Thinking

(Framing Text): Write and interpret numerical expressions.

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

Order of Operations

(Framing Text): Write and interpret numerical expressions, and analyze patterns and relationships.

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

City Tour (Coordinates)
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Points, Lines, and Equations

5.NBT: Number and Operations in Base Ten

(Framing Text): 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.

Cannonball Clowns (Number Line Estimation)
Modeling Decimals (Area and Grid Models)
Treasure Hunter (Decimals on the Number Line)
Whole Numbers with Base-10 Blocks

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. For example, 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (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
Treasure Hunter (Decimals on the Number Line)

(Framing Text): Perform operations with multi-digit whole numbers and with decimals to hundredths.

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. Illustrate and explain the calculation 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)

5.NBT.7: Add, subtract, multiply, and divide 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; relate the strategy to a written method and explain the reasoning used. In this standard, dividing decimals is limited to a whole number dividend with a decimal divisor or a decimal dividend with a whole number divisor. Compare the value of the quotient on the basis of the values of the dividend and divisor.

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

(Framing Text): 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 of fractions with like denominators.

Fraction Artist 2 (Area Models of Fractions)
Fractions with Unlike Denominators

5.NF.2: Solve real-world problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators by, for example, using visual fraction models or equations to represent the problem. 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)

(Framing Text): 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 real-world problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, through the use of visual fraction models or equations to represent the problem.

Fraction Artist 1 (Area Models of Fractions)

5.NF.4: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

5.NF.4.a: Interpret the product (a/b) x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q ÷ b using a visual fraction model.

Multiplying Fractions

5.NF.4.b: 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. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

Multiplying Fractions

5.NF.6: Solve real-world problems involving multiplication of fractions and mixed numbers, for example, by using visual fraction models or equations to represent the problem.

Multiplying Fractions

5.MD: Measurement and Data

(Framing Text): Convert like measurement units within a given measurement system.

5.MD.1: Convert among different-sized standard measurement units within a given measurement system (for example, convert 5 cm to 0.05 m); use these conversions in solving multi-step, real-world problems.

Cannonball Clowns (Number Line Estimation)

(Framing Text): Understand concepts of geometric measurement and volume, as well as how multiplication and addition relate to volume.

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 one unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume.

Balancing Blocks (Volume)
Pyramids and Cones

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)
Pyramids and Cones

5.MD.4: Measure volumes by counting unit cubes, using cubic cm, cubic in., cubic ft., and improvised 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. Represent threefold whole-number products as volumes, for example, to represent the associative property of multiplication.

Balancing Blocks (Volume)
Prisms and Cylinders

5.MD.5.b: Apply the formulas V = l x w x h and V = b x h 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)
Prisms and Cylinders

5.G: Geometry

(Framing Text): Graph points on the coordinate plane to solve real-world and mathematical problems in quadrant one.

5.G.1: Compose and understand the coordinate plane.

5.G.1.a: 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 zero on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates.

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.1.b: Using quadrant one on the coordinate plane, understand that the first number in a coordinate pair indicates how far to travel from the origin in the direction of the horizontal axis, and the second number indicates how far to travel in the direction of the vertical axis, with the convention that the names of the two axes and the coordinates correspond (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)
Function Machines 2 (Functions, Tables, and Graphs)
Points in the Coordinate Plane
Points, Lines, and Equations

(Framing Text): Classify two-dimensional figures into categories based on their properties.

Classifying Quadrilaterals
Classifying Triangles
Parallelogram Conditions
Special Parallelograms

5.G.3: Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and all squares are rectangles, so all squares have four right angles.

Classifying Quadrilaterals

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

Classifying Quadrilaterals
Parallelogram Conditions
Special Parallelograms