Mathematics – United States – Common Core State Standards
5.OA – Operations & Algebraic Thinking
Mathematics
5.OA.1 – Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

8 learning outcomes – click to view
Samples: Brackets in number operations. Brackets in number operations  Two Step. Balancing equations.

Brackets in number operations
 Activities: 1 course, 0 extra

Brackets in number operations  Two Step
 Activities: 1 course, 0 extra

Balancing equations  Equivalent number sentences
 Activities: 4 course, 2 extra

Balancing equations  Equivalent number sentences
 Activities: 5 course, 10 extra

Challenge puzzle  balancing equations
 Activities: 1 course, 0 extra

Order of operations : Multiply before adding
 Activities: 3 course, 0 extra

Order of operations  Multiply before subtracting
 Activities: 2 course, 0 extra

Order of operations  mixed
 Activities: 4 course, 2 extra


8 learning outcomes – click to view
5.OA.2 – Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.

5 learning outcomes – click to view
Samples: Continue number patterns. Rules defining number patterns. Applying rules to number tables. Order of Operations.

Continuing number patterns
 Activities: 2 course, 0 extra

Rules defining number patterns
 Activities: 1 course, 0 extra

Applying rules to number tables
 Activities: 1 course, 0 extra

Order of Operations
 Activities: 1 course, 0 extra

Numbers
 Activities: 1 course, 5 extra


5 learning outcomes – click to view
Mathematics
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. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

7 learning outcomes – click to view
Samples: Identifying expressions. Continuing number sequences including fractions and decimals.

Identifying expressions
 Activities: 1 course, 2 extra

Continuing number sequences
 Activities: 1 course, 4 extra

Substituting numbers for letters
 Activities: 1 course, 0 extra

Substituting Numerals
 Activities: 1 course, 4 extra

Subtraction of Like Terms
 Activities: 0 course, 1 extra

Patterns and Algebra
 Activities: 0 course, 2 extra

Equations Involving Subtraction
 Activities: 1 course, 0 extra


7 learning outcomes – click to view
5.NBT – Number & Operations in Base Ten
Mathematics
5.NBT.1 – Recognize that in a multidigit 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.

7 learning outcomes – click to view
Samples: Multiplying by 10, 100 and 1000. Multiplying by 100. Multiplying by 10 or 100. Multiplying decimals by 1000.

Multiplying by 10
 Activities: 4 course, 7 extra

Multiplying by 100
 Activities: 3 course, 8 extra

Multiplying by 10 or 100 (problem solving)
 Activities: 3 course, 8 extra

Multiplying decimals by 1000
 Activities: 1 course, 0 extra

Dividing whole numbers by 100
 Activities: 3 course, 0 extra

Multiplying decimals by a whole number
 Activities: 2 course, 6 extra

Multiplying decimals by 10
 Activities: 2 course, 4 extra


7 learning outcomes – click to view
5.NBT.2 – 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 wholenumber exponents to denote powers of 10.

12 learning outcomes – click to view
Samples: Multiplying by 10, 100 and 1000. Multiplying by 100. Multiplying by 10 or 100.

Multiplying by 10
 Activities: 4 course, 7 extra

Multiplying by 100
 Activities: 3 course, 8 extra

Multiplying by 10 or 100 (problem solving)
 Activities: 3 course, 8 extra

Multiplying multiples of 10 (problem solving)
 Activities: 2 course, 1 extra

Multiplying multiples of 10  puzzle
 Activities: 1 course, 0 extra

Multiplying multiples of 10 (missing number)
 Activities: 3 course, 8 extra

Multiplying by multiples of ten
 Activities: 4 course, 12 extra

Dividing multiples of 10 by 1 digit
 Activities: 4 course, 2 extra

Dividing multiples of 10 by 1 digit (problem solving)
 Activities: 0 course, 1 extra

Revision
 Activities: 5 course, 4 extra

Dividing whole numbers by 100
 Activities: 3 course, 0 extra

Long division
 Activities: 3 course, 3 extra


12 learning outcomes – click to view
5.NBT.3 – Read, write, and compare decimals to thousandths.
5.NBT.3.a – Read and write decimals to thousandths using baseten 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).

7 learning outcomes – click to view
Samples: Decimal Numbers  Expanded Form. Common decimals from 0 to 1 (tenths). Compare and order decimals.

Decimal Numbers  Expanded Form
 Activities: 1 course, 0 extra

Common decimals from 0 to 1 (tenths)
 Activities: 4 course, 0 extra

Compare and order decimals
 Activities: 1 course, 1 extra

Read and write decimals in the thousandths
 Activities: 1 course, 0 extra

Comparing decimals in the thousandths
 Activities: 1 course, 0 extra

Place value (thousandths)
 Activities: 1 course, 0 extra

Place value  thousandths
 Activities: 1 course, 0 extra


7 learning outcomes – click to view
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.

5 learning outcomes – click to view
Samples: Compare and order decimals. Read and write decimals in the thousandths. Comparing decimals in the thousandths.

Compare and order decimals
 Activities: 1 course, 1 extra

Read and write decimals in the thousandths
 Activities: 1 course, 0 extra

Comparing decimals in the thousandths
 Activities: 1 course, 0 extra

Place value (thousandths)
 Activities: 1 course, 0 extra

Place value  thousandths
 Activities: 1 course, 0 extra


5 learning outcomes – click to view
5.NBT.4 – Use place value understanding to round decimals to any place.

1 learning outcomes – click to view
Samples: Rounding decimals to whole numbers.

Rounding decimals to whole numbers
 Activities: 1 course, 0 extra


1 learning outcomes – click to view
Mathematics
5.NBT.5 – Fluently multiply multidigit whole numbers using the standard algorithm.

7 learning outcomes – click to view
Samples: Multiplying 2 by 1 digit (mental strategy). Multiplying twodigits by onedigit. Multiplying 2 by 1 digit.

Multiplying a twodigit number by a onedigit number
 Activities: 1 course, 2 extra

Multiplying a twodigit number by a onedigit number  written strategy
 Activities: 4 course, 10 extra

Multiplying a twodigit number by a onedigit number  mental strategy
 Activities: 3 course, 10 extra

Multiplying 2 digits by a 1 digit number  Puzzle
 Activities: 1 course, 0 extra

Multiplying 2 by 1 digit (missing number)
 Activities: 2 course, 7 extra

Multiplying by 2 digit numbers (problem solving)
 Activities: 1 course, 4 extra

Multiplying twodigit numbers
 Activities: 5 course, 10 extra


7 learning outcomes – click to view
5.NBT.6 – Find wholenumber quotients of whole numbers with up to fourdigit dividends and twodigit 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.

12 learning outcomes – click to view
Samples: Challenge Puzzle  Division of a large number by a one digit number.

Division puzzle
 Activities: 1 course, 0 extra

Multiplying multiples of 10 (missing number)
 Activities: 3 course, 8 extra

Multiplying 2 by 1 digit (missing number)
 Activities: 2 course, 7 extra

Dividing multiples of 10 by 1 digit
 Activities: 4 course, 2 extra

Dividing multiples of 10 by 1 digit (problem solving)
 Activities: 0 course, 1 extra

Dividing 3 digits by 1 digit (problem solving)
 Activities: 0 course, 2 extra

Division (with remainders)
 Activities: 3 course, 7 extra

Dividing 4digit numbers by 1digit numbers
 Activities: 4 course, 5 extra

Dividing large numbers (problem solving)
 Activities: 1 course, 3 extra

Long division
 Activities: 3 course, 3 extra

Long division  problem solving
 Activities: 0 course, 4 extra


12 learning outcomes – click to view
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.

8 learning outcomes – click to view
Samples: Adding Decimals. Subtracting Decimals. Multiplying Decimals By A Single Digit Number. Dividing a whole number by 10.

Adding decimals
 Activities: 5 course, 3 extra

Subtracting decimals
 Activities: 4 course, 3 extra

Multiplying decimals by a whole number
 Activities: 2 course, 6 extra

Dividing whole numbers by 10 (problem solving)
 Activities: 5 course, 0 extra

Matching fractions, decimals and percentages.
 Activities: 3 course, 6 extra

Percentages as Decimals
 Activities: 1 course, 0 extra

Multiplying decimals by decimals
 Activities: 0 course, 1 extra

Changing mixed fractions to decimals
 Activities: 0 course, 1 extra


8 learning outcomes – click to view
5.NF – Number & Operations—Fractions
Mathematics
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. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

3 learning outcomes – click to view
Samples: Adding and Subtracting Related Fractions. Adding mixed fractions. Adding fractions. Adding fractions (with hints).

Adding and subtracting related fractions
 Activities: 5 course, 1 extra

Adding mixed fractions
 Activities: 1 course, 0 extra

Adding and subtracting fractions
 Activities: 3 course, 0 extra


3 learning outcomes – click to view
5.NF.2 – 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. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.
Mathematics
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. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

3 learning outcomes – click to view
Samples: Converting Improper Fractions. Converting mixed numbers to improper fractions tutorial.

Improper and mixed number fractions
 Activities: 6 course, 1 extra

Converting mixed numbers to improper frac.
 Activities: 0 course, 1 extra

Division answers as fractions
 Activities: 2 course, 0 extra


3 learning outcomes – click to view
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) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)

2 learning outcomes – click to view
Samples: Dividing whole numbers by fractions. Multiplying and Dividing Fractions.

Dividing whole numbers by fractions
 Activities: 3 course, 0 extra

Multiplying and Dividing Fractions
 Activities: 4 course, 0 extra


2 learning outcomes – click to view
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.

3 learning outcomes – click to view
Samples: Calculating area. Area (problem solving). Area of Squares and Rectangles. Area of Squares and Rectangles.

Calculating area (squares and rectangles)
 Activities: 5 course, 8 extra

Area (problem solving)
 Activities: 2 course, 7 extra

Area of Squares and Rectangles
 Activities: 0 course, 1 extra


3 learning outcomes – click to view
5.NF.5 – Interpret multiplication as scaling (resizing), by:
5.NF.5.a – Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
5.NF.5.b – Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.

3 learning outcomes – click to view
Samples: Fractions. Fractions Problem Solving. Multiplying and Dividing Fractions. Fractions Problem Solving.

Multiplying fractions by a whole number  visual
 Activities: 1 course, 0 extra

Multiplying fractions
 Activities: 0 course, 3 extra

Multiplying and Dividing Fractions
 Activities: 4 course, 0 extra


3 learning outcomes – click to view
5.NF.6 – Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
5.NF.7 – Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. (Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.)
5.NF.7.a – Interpret division of a unit fraction by a nonzero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.

5 learning outcomes – click to view
Samples: Fractions of a number. Division  Answers as fractions. Fractions Problem Solving.

Fractions of a number
 Activities: 11 course, 2 extra

Division answers as fractions
 Activities: 2 course, 0 extra

Multiplying fractions
 Activities: 0 course, 3 extra

Dividing whole numbers by fractions
 Activities: 3 course, 0 extra

Multiplying and Dividing Fractions
 Activities: 4 course, 0 extra


5 learning outcomes – click to view
5.NF.7.b – Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.

2 learning outcomes – click to view
Samples: Fractions Problem Solving. Multiplying and Dividing Fractions. Fractions Problem Solving. Multiplying fractions.

Multiplying fractions
 Activities: 0 course, 3 extra

Multiplying and Dividing Fractions
 Activities: 4 course, 0 extra


2 learning outcomes – click to view
5.NF.7.c – Solve real world problems involving division of unit fractions by nonzero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3cup servings are in 2 cups of raisins?

1 learning outcomes – click to view
Samples: Dividing whole numbers by fractions. Divide whole numbers by fractions (problem solving).

Dividing whole numbers by fractions
 Activities: 3 course, 0 extra


1 learning outcomes – click to view
5.MD – Measurement & Data
Mathematics
5.MD.1 – Convert among differentsized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multistep, real world problems.

5 learning outcomes – click to view
Samples: Converting between kilometers and meters. Converting between units of volume: Activity 2.

Converting between kilometers and meters
 Activities: 2 course, 0 extra

Problem solving : Volume
 Activities: 0 course, 5 extra

Converting between grams and kilograms
 Activities: 1 course, 0 extra

Length  problem solving
 Activities: 4 course, 1 extra

Length  problem solving
 Activities: 4 course, 4 extra


5 learning outcomes – click to view
Mathematics
5.MD.2 – Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.

3 learning outcomes – click to view
Samples: Interpreting Dot Plots. Interpret a dot plot. Line graphs. Display data using dot plots. Line Plots. Line graphs.

Dot plots
 Activities: 1 course, 1 extra

Dot plots
 Activities: 1 course, 2 extra

Line graphs
 Activities: 2 course, 0 extra


3 learning outcomes – click to view
Mathematics
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.

4 learning outcomes – click to view
Samples: Calculating volume. Volume Extension. Drawing 3D objects. Matching  threedimensional objects with their nets.

Volume of rectangular prisms
 Activities: 4 course, 6 extra

Volume
 Activities: 0 course, 2 extra

Drawing threedimensional objects
 Activities: 11 course, 9 extra

Nets of three dimensional objects
 Activities: 4 course, 4 extra


4 learning outcomes – click to view
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.

4 learning outcomes – click to view
Samples: Calculate the volume of a stack  record in cubic centimeters. Volume and Capacity. Calculating volume.

Measure volume using centicubes
 Activities: 4 course, 5 extra

Volume and Capacity
 Activities: 2 course, 7 extra

Volume of rectangular prisms
 Activities: 4 course, 6 extra

Volume
 Activities: 0 course, 2 extra


4 learning outcomes – click to view
5.MD.4 – Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

6 learning outcomes – click to view
Samples: Calculate the volume of a stack  record in cubic centimeters.

Measure volume using centicubes
 Activities: 4 course, 5 extra

Choosing appropriate units for measuring volume (mL or L)
 Activities: 1 course, 0 extra

Volume and Capacity
 Activities: 2 course, 7 extra

Volume of rectangular prisms
 Activities: 4 course, 6 extra

Volume
 Activities: 0 course, 2 extra

Volume of a Cylinder
 Activities: 0 course, 1 extra


6 learning outcomes – click to view
5.MD.5 – Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
5.MD.5.b – Find the volume of a right rectangular prism with wholenumber 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 wholenumber products as volumes, e.g., to represent the associative property of multiplication.

5 learning outcomes – click to view
Samples: Calculating volume. Calculate the volume of a stack  record in cubic centimeters. Volume and Capacity.

Volume of rectangular prisms
 Activities: 4 course, 6 extra

Measure volume using centicubes
 Activities: 4 course, 5 extra

Volume and Capacity
 Activities: 2 course, 7 extra

Volume
 Activities: 0 course, 2 extra

Volume of a Cylinder
 Activities: 0 course, 1 extra


5 learning outcomes – click to view
5.MD.5.c – Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with wholenumber edge lengths in the context of solving real world and mathematical problems.

5 learning outcomes – click to view
Samples: Calculating volume. Matching  threedimensional objects with their nets. Naming prisms and pyramids.

Volume of rectangular prisms
 Activities: 4 course, 6 extra

Nets of three dimensional objects
 Activities: 4 course, 4 extra

Prisms and pyramids
 Activities: 2 course, 8 extra

Challenge Puzzle  prisms and pyramids
 Activities: 1 course, 0 extra

Volume and Capacity
 Activities: 2 course, 7 extra


5 learning outcomes – click to view
5.MD.5.d – Recognize volume as additive. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms by adding the volumes of the nonoverlapping parts, applying this technique to solve real world problems.

3 learning outcomes – click to view
Samples: Calculating volume. Volume and Capacity. Volume Extension. Calculating the volume of rectangular prisms.

Volume of rectangular prisms
 Activities: 4 course, 6 extra

Volume and Capacity
 Activities: 2 course, 7 extra

Volume
 Activities: 0 course, 2 extra


3 learning outcomes – click to view
5.MD – Measurement & Data
Mathematics
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., xaxis and xcoordinate, yaxis and ycoordinate).

1 learning outcomes – click to view
Samples: Cartesian Plane  Identify location. Cartesian Plane  Identify coordinates. Cartesian planes  lines and shapes.

Cartesian Planes
 Activities: 3 course, 5 extra


1 learning outcomes – click to view
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.

2 learning outcomes – click to view
Samples: Using grid references. Using Coordinates to Read a Map. Maps (coordinates). Describe locations using grid reference.

Using grid references
 Activities: 2 course, 10 extra

Location using a grid reference.
 Activities: 1 course, 1 extra


2 learning outcomes – click to view
Mathematics
5.G.3 – Understand that attributes belonging to a category of twodimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.

4 learning outcomes – click to view
Samples: Properties of twodimensional shapes. Grouping shapes based on attributes. Constructing 2D shapes.

Attributes of two dimensional shapes
 Activities: 2 course, 0 extra

Grouping shapes based on attributes
 Activities: 1 course, 0 extra

Construct and draw two dimensional shapes
 Activities: 3 course, 3 extra

Naming triangles
 Activities: 3 course, 1 extra


4 learning outcomes – click to view
5.G.4 – Classify twodimensional figures in a hierarchy based on properties.

5 learning outcomes – click to view
Samples: Splitting shapes. Constructing 2D shapes. Properties of twodimensional shapes. Grouping shapes based on attributes.

Splitting shapes
 Activities: 2 course, 0 extra

Construct and draw two dimensional shapes
 Activities: 3 course, 3 extra

Attributes of two dimensional shapes
 Activities: 2 course, 0 extra

Grouping shapes based on attributes
 Activities: 1 course, 0 extra

Naming triangles
 Activities: 3 course, 1 extra


5 learning outcomes – click to view