5.NS: Number Sense

5.NS.1: Use a number line to compare and order fractions, mixed numbers, and decimals to thousandths. Write the results using >, =, and < symbols.

Comparing and Ordering Decimals
Equivalent Fractions (Fraction Tiles)
Fraction Garden (Comparing Fractions)
Fraction, Decimal, Percent (Area and Grid Models)
Fractions Greater than One (Fraction Tiles)
Modeling Decimals (Area and Grid Models)
Modeling Fractions (Area Models)
Ordering Percents, Fractions, and Decimals Greater Than 1
Treasure Hunter (Decimals on the Number Line)

5.NS.2: Explain different interpretations of fractions, including: as parts of a whole, parts of a set, and division of whole numbers by whole numbers.

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)

5.NS.3: Recognize the relationship 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 inversely, a digit in one place represents 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)
Number Systems
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

5.NS.4: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

Comparing and Ordering Decimals
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Unit Conversions 2 - Scientific Notation and Significant Digits

5.NS.6: Understand, interpret, and model percents as part of a hundred (e.g. by using pictures, diagrams, and other visual models).

Fraction, Decimal, Percent (Area and Grid Models)
Ordering Percents, Fractions, and Decimals Greater Than 1
Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals

5.C: Computation

5.C.1: Multiply multi-digit whole numbers fluently using a standard algorithmic approach.

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

5.C.2: Find whole-number quotients and remainders 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. Describe the strategy and explain the reasoning used.

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

5.C.4: Add and subtract fractions with unlike denominators, including mixed numbers.

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

5.C.5: Use visual fraction models and numbers to multiply a fraction by a fraction or a whole number.

Multiplying Fractions

5.C.7: Use visual fraction models and numbers to divide a unit fraction by a non-zero whole number and to divide a whole number by a unit fraction.

Dividing Fractions

5.C.8: Add, subtract, multiply, and divide decimals to hundredths, using models or drawings and strategies based on place value or the properties of operations. Describe the strategy and explain the reasoning.

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.C.9: Evaluate expressions with parentheses or brackets involving whole numbers using the commutative properties of addition and multiplication, associative properties of addition and multiplication, and distributive property.

Chocomatic (Multiplication, Arrays, and Area)
Equivalent Algebraic Expressions I

5.AT: Algebraic Thinking

5.AT.1: Solve real-world problems involving multiplication and division of whole numbers (e.g. by using equations to represent the problem). In division problems that involve a remainder, explain how the remainder affects the solution to the problem.

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

5.AT.2: Solve real-world problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators (e.g., by using visual fraction models and equations to represent the problem). Use benchmark fractions and number sense of fractions to estimate mentally and assess whether the answer is reasonable.

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

5.AT.3: Solve real-world problems involving multiplication of fractions, including mixed numbers (e.g., by using visual fraction models and equations to represent the problem).

Multiplying Fractions

5.AT.4: Solve real-world problems involving division of unit fractions by non-zero whole numbers, and division of whole numbers by unit fractions (e.g., by using visual fraction models and equations to represent the problem).

Dividing Fractions

5.AT.5: Solve real-world problems involving addition, subtraction, multiplication, and division with decimals to hundredths, including problems that involve money in decimal notation (e.g. by using equations to represent the problem).

Adding Whole Numbers and Decimals (Base-10 Blocks)
Multiplying with Decimals
Subtracting Whole Numbers and Decimals (Base-10 Blocks)

5.AT.6: Graph points with whole number coordinates on a coordinate plane. Explain how the coordinates relate the point as the distance from the origin on each 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.AT.7: Represent real-world problems and equations by graphing ordered pairs 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

5.AT.8: Define and use up to two variables to write linear expressions that arise from real-world problems, and evaluate them for given values.

Function Machines 3 (Functions and Problem Solving)

5.G: Geometry

5.G.1: Identify, describe, and draw triangles (right, acute, obtuse) and circles using appropriate tools (e.g., ruler or straightedge, compass and technology). Understand the relationship between radius and diameter.

Circumference and Area of Circles
Classifying Triangles

5.G.2: Identify and classify polygons including quadrilaterals, pentagons, hexagons, and triangles (equilateral, isosceles, scalene, right, acute and obtuse) based on angle measures and sides. Classify polygons in a hierarchy based on properties.

Classifying Quadrilaterals
Classifying Triangles
Parallelogram Conditions
Special Parallelograms

5.M: Measurement

5.M.1: Convert among different-sized standard measurement units within a given measurement system, and use these conversions in solving multi-step real-world problems.

Cannonball Clowns (Number Line Estimation)
Unit Conversions

5.M.2: Find the area of a rectangle with fractional side lengths by modeling 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.M.3: Develop and use formulas for the area of triangles, parallelograms and trapezoids. Solve real-world and other mathematical problems that involve perimeter and area of triangles, parallelograms and trapezoids, using appropriate units for measures.

Area of Parallelograms
Area of Triangles
Fido's Flower Bed (Perimeter and Area)
Perimeter and Area of Rectangles

5.M.4: 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 or multiplying the height by the area of the base.

Balancing Blocks (Volume)
Prisms and Cylinders

5.M.6: Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real-world problems and other mathematical problems.

Balancing Blocks (Volume)

5.DS: Data Analysis and Statistics

5.DS.1: Formulate questions that can be addressed with data and make predictions about the data. Use observations, surveys, and experiments to collect, represent, and interpret the data using tables (including frequency tables), line plots, bar graphs, and line graphs. Recognize the differences in representing categorical and numerical data.

Describing Data Using Statistics
Elevator Operator (Line Graphs)
Mascot Election (Pictographs and Bar Graphs)
Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

5.DS.2: Understand and use measures of center (mean and median) and frequency (mode) to describe a data set.

Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)