NY-5.OA: Operations and Algebraic Thinking

1.1: Write and interpret numerical expressions.

NY-5.OA.1: Apply the order of operations to evaluate numerical expressions.

Order of Operations

1.2: Analyze patterns and relationships.

NY-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)
Function Machines 3 (Functions and Problem Solving)
Pattern Finder
Pattern Flip (Patterns)
Points, Lines, and Equations

NY-5.NBT: Number and Operations in Base Ten

2.1: Understand the place value system.

NY-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)
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

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

NY-5.NBT.3.a: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form.

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)

2.1.3.2: e.g., 47.392 = 4 × 10 + 7 × 1 + 3 × 1/10 + 9 × 1/100 + 2 × 1/1000; 47.392 = (4 × 10) + (7 × 1) + (3 × 1/10) + (9 × 1/100) + (2 × 1/1000); 47.392 = (4 × 10) + (7 × 1) + (3 × 0.1) + (9 × 0.01) + (2 × 0.001)

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)

NY-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 numbers and with decimals to hundredths.

NY-5.NBT.5: Fluently multiply multi-digit whole numbers using a standard algorithm.

Critter Count (Modeling Multiplication)

NY-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)

NY-5.NBT.7: Using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between operations: add and subtract decimals to hundredths; multiply and divide decimals to hundredths. Relate the strategy to a written method and explain the reasoning used.

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

NY-5.NF: Number and Operations—Fractions

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

NY-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.

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

NY-5.NF.2: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators. 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)

3.1.2.1: e.g., using visual fraction models or equations to represent the problem

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.

NY-5.NF.3: Interpret a fraction as division of the numerator by the denominator (a/b = a divided by b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.

Fraction Artist 1 (Area Models of Fractions)

3.2.1.2: e.g., using visual fraction models or equations to represent the problem

Fraction Artist 1 (Area Models of Fractions)

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

NY-5.NF.4.a: Interpret the product (??/??) × ?? as ?? parts of a partition of ?? into ?? equal parts; equivalently, as the result of a sequence of operations ?? × ?? ÷ ??.

Multiplying Fractions

NY-5.NF.4.b: Find the area of a rectangle with fractional side lengths by tiling it with rectangles 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

NY-5.NF.6: Solve real world problems involving multiplication of fractions and mixed numbers.

Multiplying Fractions

3.2.4.1: e.g., using visual fraction models or equations to represent the problem

Multiplying Fractions

NY-5.MD: Measurement and Data

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

NY-5.MD.1: Convert among different-sized standard measurement units within a given measurement system when the conversion factor is given. Use these conversions in solving multi-step, real world problems.

Cannonball Clowns (Number Line Estimation)

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

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

NY-5.MD.3.a: Recognize that 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)

NY-5.MD.3.b: Recognize that 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)

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

NY-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)
Prisms and Cylinders

NY-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)

NY-5.G: Geometry

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

NY-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.

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

5.1.1.1: e.g., ??-axis and ??-coordinate, ??-axis and ??-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

NY-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

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

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

Classifying Quadrilaterals

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

Classifying Quadrilaterals