Mathematics – United States – Common Core State Standards
4.OA – Operations & Algebraic Thinking
Mathematics
4.OA.1 – Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

1 learning outcomes – click to view
Samples: Multiplicative comparison. Multiplicative comparison (problem solving).

Multiplicative comparisons
 Activities: 2 course, 1 extra


1 learning outcomes – click to view
4.OA.2 – Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. (See Glossary, Table 2. http://www.corestandards.org/thestandards/mathematics/glossary/glossary/ )
4.OA.3 – Solve multistep word problems posed with whole numbers and having wholenumber answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

11 learning outcomes – click to view
Samples: Two step problem solving. Make 100 Answer sheet. Challenge puzzle. Addition of large numbers (puzzle).

Two step problem solving
 Activities: 1 course, 0 extra

Make 100  problem solving
 Activities: 0 course, 2 extra

Challenge puzzle  make 100
 Activities: 1 course, 0 extra

Addition of large numbers (puzzle)
 Activities: 1 course, 0 extra

Addition and subtraction  problem solving
 Activities: 1 course, 0 extra

Adding three numbers  problem solving
 Activities: 2 course, 4 extra

Challenge puzzle  two digit subtraction
 Activities: 1 course, 0 extra

Subtracting from 1000 and 10000 (problem solving)
 Activities: 3 course, 2 extra

Dividing by 8 (problem solving)
 Activities: 3 course, 3 extra

Dividing by 9 (problem solving)
 Activities: 3 course, 6 extra

Balancing equations
 Activities: 2 course, 0 extra


11 learning outcomes – click to view
Mathematics
4.OA.4 – Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given onedigit number. Determine whether a given whole number in the range 1–100 is prime or composite.

8 learning outcomes – click to view
Samples: Factor trees. Factors. Common factors. Prime and Composite Numbers. Factors. Prime numbers.

Factor trees
 Activities: 1 course, 0 extra

Identifying factors
 Activities: 2 course, 1 extra

Common factors
 Activities: 2 course, 0 extra

Prime and Composite Numbers
 Activities: 1 course, 0 extra

Factors
 Activities: 4 course, 2 extra

Prime numbers
 Activities: 2 course, 0 extra

Identifying prime numbers < 100 (puzzle)
 Activities: 1 course, 0 extra

Identifying prime numbers
 Activities: 1 course, 0 extra


8 learning outcomes – click to view
Mathematics
4.OA.5 – Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

4 learning outcomes – click to view
Samples: Patterns created by objects. Number Patterns (2,3,5,10). Number patterns  Identifying the rule.

Explore patterns created by objects
 Activities: 2 course, 0 extra

Number Patterns (2,3,5,10)
 Activities: 2 course, 5 extra

Number patterns  Identifying the rule
 Activities: 2 course, 0 extra

Continue number patterns resulting from addition or subtraction
 Activities: 1 course, 1 extra


4 learning outcomes – click to view
4.NBT – Number & Operations in Base Ten (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.)
Mathematics
4.NBT.1 – Recognize that in a multidigit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
4.NBT.2 – Read and write multidigit whole numbers using baseten numerals, number names, and expanded form. Compare two multidigit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

26 learning outcomes – click to view
Samples: Numbers written in expanded form. Expanded notation. Comparing numbers to 1000 (< = >). Write numbers – to 1000.

Numbers written in expanded form
 Activities: 1 course, 0 extra

Expanded notation
 Activities: 3 course, 4 extra

Comparing numbers to 1000 (< = >)
 Activities: 2 course, 1 extra

Writing numbers – to 1000
 Activities: 2 course, 2 extra

Reading numbers – to 1000
 Activities: 1 course, 0 extra

Comparing numbers – to 1000
 Activities: 1 course, 1 extra

Reading numbers to 10,000
 Activities: 1 course, 0 extra

Writing numbers to 10,000
 Activities: 2 course, 0 extra

Comparing numbers – to 10,000
 Activities: 1 course, 0 extra

Representing numbers (thousands)
 Activities: 3 course, 11 extra

Comparing numbers to 10,000 (<,=,>)
 Activities: 1 course, 0 extra

Place value of a digit
 Activities: 3 course, 1 extra

Odd and even numbers
 Activities: 3 course, 2 extra

Challenge puzzle  Odd and Even Numbers
 Activities: 1 course, 0 extra

Write numbers – to 100,000
 Activities: 2 course, 0 extra

Reading numbers – to 100,000
 Activities: 1 course, 0 extra

Comparing numbers – to 100,000
 Activities: 1 course, 0 extra

Reading large numbers
 Activities: 1 course, 0 extra

Ordering large numbers
 Activities: 0 course, 6 extra

Write numbers – to 1,000,000
 Activities: 2 course, 0 extra

Comparing large numbers
 Activities: 2 course, 0 extra

Large numbers presented in tables
 Activities: 1 course, 0 extra

Reading large numbers
 Activities: 1 course, 0 extra

Write numbers – over one million
 Activities: 2 course, 0 extra

Comparing numbers of any size
 Activities: 1 course, 0 extra

Challenge puzzle  flow diagram
 Activities: 1 course, 0 extra


26 learning outcomes – click to view
4.NBT.3 – Use place value understanding to round multidigit whole numbers to any place.

2 learning outcomes – click to view
Samples: Rounding to the nearest 10 (3 digits). Rounding to the nearest hundred. Rounding numbers: Activity 2.

Rounding to the nearest 10
 Activities: 3 course, 3 extra

Rounding to the nearest hundred
 Activities: 3 course, 0 extra


2 learning outcomes – click to view
Mathematics
4.NBT.4 – Fluently add and subtract multidigit whole numbers using the standard algorithm.

9 learning outcomes – click to view
Samples: Subtracting three digit numbers. Subtracting from multiples of one thousand.

Subtracting three digit numbers
 Activities: 2 course, 0 extra

Subtracting from 1000
 Activities: 6 course, 10 extra

Adding three numbers
 Activities: 6 course, 10 extra

Subtracting large numbers
 Activities: 3 course, 14 extra

Adding large numbers
 Activities: 5 course, 29 extra

Addition and subtraction (problem solving)
 Activities: 3 course, 4 extra

Adding large numbers (problem solving)
 Activities: 1 course, 8 extra

Subtracting from 1000 (problem solving)
 Activities: 1 course, 4 extra

Subtracting large numbers
 Activities: 4 course, 6 extra


9 learning outcomes – click to view
4.NBT.5 – Multiply a whole number of up to four digits by a onedigit whole number, and multiply two twodigit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

13 learning outcomes – click to view
Samples: Adding on to Multiples of 10. Multiplying 2 by 1 digit (mental strategy). Multiplying twodigits by onedigit.

Addingon to multiples of ten
 Activities: 2 course, 1 extra

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

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

Multiples of 10 by 1 digit  problem solving
 Activities: 0 course, 1 extra

Arrays
 Activities: 0 course, 1 extra

11x tables
 Activities: 2 course, 1 extra

12x tables
 Activities: 2 course, 1 extra

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

Identifying multiples
 Activities: 1 course, 0 extra


13 learning outcomes – click to view
4.NBT.6 – Find wholenumber quotients and remainders with up to fourdigit dividends and onedigit 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.

10 learning outcomes – click to view
Samples: Division facts. Dividing multiples of 10 by 1 digit. Dividing 3 digits by 1 digit (no remainders).

Division facts
 Activities: 5 course, 9 extra

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

Dividing 3 digits by 1 digit
 Activities: 7 course, 11 extra

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

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

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

Halving numbers
 Activities: 4 course, 5 extra

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


10 learning outcomes – click to view
4.NF – Number & Operations—Fractions (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, 100.)
Mathematics
4.NF.1 – Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

4 learning outcomes – click to view
Samples: Modelling equivalent fractions. Hundredths in their lowest forms. Equivalent fractions.

Modelling equivalent fractions
 Activities: 4 course, 3 extra

Hundredths in their lowest forms
 Activities: 1 course, 0 extra

Equivalent fractions
 Activities: 7 course, 10 extra

Simplifying fractions
 Activities: 4 course, 2 extra


4 learning outcomes – click to view
4.NF.2 – Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

3 learning outcomes – click to view
Samples: Comparing fractions to a half. Hundredths  simplest form. Comparing Fractions.

Comparing fractions
 Activities: 4 course, 0 extra

Tenths and hundredths
 Activities: 4 course, 4 extra

Comparing fractions
 Activities: 4 course, 2 extra


3 learning outcomes – click to view
Mathematics
4.NF.3 – Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
4.NF.3.a – Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
4.NF.3.b – Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

3 learning outcomes – click to view
Samples: Adding fractions  same denominators. Adding fraction with common denominators tutorial.

Adding and subtracting fractions  same denominator
 Activities: 5 course, 0 extra

Add and subtract fractions (same denominators)
 Activities: 0 course, 3 extra

Adding and subtracting related fractions
 Activities: 6 course, 1 extra


3 learning outcomes – click to view
4.NF.3.c – Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

4 learning outcomes – click to view
Samples: Adding fraction with common denominators tutorial. Converting Improper Fractions.

Add and subtract fractions (same denominators)
 Activities: 0 course, 3 extra

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

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

Adding mixed fractions
 Activities: 1 course, 0 extra


4 learning outcomes – click to view
4.NF.3.d – Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

2 learning outcomes – click to view
Samples: Adding fraction with common denominators tutorial. Adding and subtracting related fractions.

Add and subtract fractions (same denominators)
 Activities: 0 course, 3 extra

Adding and subtracting related fractions
 Activities: 6 course, 1 extra


2 learning outcomes – click to view
4.NF.4 – Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
4.NF.4.a – Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).

2 learning outcomes – click to view
Samples: Fractions. Fractions of a number. Simple fractions of quantities. Fractions of numbers. Fractions of quantities.

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

Fractions of a number
 Activities: 11 course, 2 extra


2 learning outcomes – click to view
4.NF.4.b – Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)

2 learning outcomes – click to view
Samples: Fractions. Fractions of a number. Simple fractions of quantities. Fractions of numbers. Fractions of quantities.

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

Fractions of a number
 Activities: 11 course, 2 extra


2 learning outcomes – click to view
4.NF.4.c – Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?
Mathematics
4.NF.5 – Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. (Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.) For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

1 learning outcomes – click to view
Samples: Hundredths  simplest form. Tenths and hundredths. Tenths and hundreds (problem solving).

Tenths and hundredths
 Activities: 4 course, 4 extra


1 learning outcomes – click to view
4.NF.6 – Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.

3 learning outcomes – click to view
Samples: Converting 10ths and 100ths to decimals. Placing Decimals On A Number Line. Comparing fractions and decimals.

Converting 10ths and 100ths to decimals
 Activities: 1 course, 0 extra

Decimals on a number line.
 Activities: 2 course, 2 extra

Comparing fractions and decimals (10ths 100ths)
 Activities: 1 course, 0 extra


3 learning outcomes – click to view
4.NF.7 – Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

4 learning outcomes – click to view
Samples: Compare and order decimals. Comparing Fractions. Comparing fractions to a half. Equivalent fractions.

Compare and order decimals
 Activities: 1 course, 1 extra

Comparing fractions
 Activities: 4 course, 2 extra

Comparing fractions
 Activities: 4 course, 0 extra

Equivalent fractions
 Activities: 7 course, 10 extra


4 learning outcomes – click to view
4.MD – Measurement & Data
Mathematics
4.MD.1 – Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a twocolumn table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...

9 learning outcomes – click to view
Samples: Converting between grams and kilograms. Common fractions of a kilogram. Convert Tonnes To Kilograms.

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

Convert units of mass  between kilograms and grams
 Activities: 6 course, 22 extra

Convert units of mass  between kilograms and tonnes
 Activities: 2 course, 11 extra

Convert between units of mass
 Activities: 1 course, 0 extra

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

Converting between metric units of length.
 Activities: 1 course, 8 extra

Problem solving : Volume
 Activities: 0 course, 5 extra

Converting between units of time
 Activities: 2 course, 0 extra

Convert between units of time
 Activities: 2 course, 1 extra


9 learning outcomes – click to view
4.MD.2 – Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

3 learning outcomes – click to view
Samples: Volume and Capacity. Calculating cost according to weight  US units tutorial. Time  'am' and 'pm': Activity 1.

Volume and Capacity
 Activities: 2 course, 7 extra

Mass (problem solving)
 Activities: 0 course, 2 extra

Use a.m. and p.m.
 Activities: 0 course, 2 extra


3 learning outcomes – click to view
4.MD.3 – Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

4 learning outcomes – click to view
Samples: Perimeter. Challenge puzzle perimeter. Area. Area (problem solving). Perimeter of squares and rectangles.

Perimeter of squares and rectangles.
 Activities: 3 course, 5 extra

Challenge puzzle perimeter
 Activities: 1 course, 0 extra

Area
 Activities: 1 course, 0 extra

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


4 learning outcomes – click to view
Mathematics
4.MD.4 – Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.
Mathematics
4.MD.5 – Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
4.MD.5.a – An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “onedegree angle,” and can be used to measure angles.

2 learning outcomes – click to view
Samples: Angles within a circle. Parts of a circle. Parts of a circle. Learn the parts of a circle. Parts of a circle.

Angles within a circle
 Activities: 1 course, 0 extra

Parts of a Circle
 Activities: 5 course, 0 extra


2 learning outcomes – click to view
4.MD.5.b – An angle that turns through n onedegree angles is said to have an angle measure of n degrees.
4.MD.6 – Measure angles in wholenumber degrees using a protractor. Sketch angles of specified measure.

6 learning outcomes – click to view
Samples: Comparing angles. Right angles in shapes. Measuring obtuse angles using a protractor. Estimating the size of angles.

Comparing angles
 Activities: 2 course, 1 extra

Comparing to a right angle
 Activities: 4 course, 3 extra

Measuring obtuse angles using a protractor
 Activities: 1 course, 3 extra

Estimate the size of angles.
 Activities: 1 course, 0 extra

Measure and classify angles.
 Activities: 1 course, 2 extra

Angles in shapes
 Activities: 1 course, 0 extra


6 learning outcomes – click to view
4.MD.7 – Recognize angle measure as additive. When an angle is decomposed into nonoverlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

8 learning outcomes – click to view
Samples: Angles on a straight line. Measuring obtuse angles using a protractor. Estimating the size of angles.

Angles on a straight line
 Activities: 2 course, 1 extra

Measuring obtuse angles using a protractor
 Activities: 1 course, 3 extra

Estimate the size of angles.
 Activities: 1 course, 0 extra

Angles within a circle
 Activities: 1 course, 0 extra

Naming angles
 Activities: 5 course, 3 extra

Naming angles within shapes
 Activities: 1 course, 0 extra

Measure and classify angles.
 Activities: 1 course, 2 extra

Angles in shapes
 Activities: 1 course, 0 extra


8 learning outcomes – click to view
4.G – Geometry
Mathematics
4.G.1 – Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures.

3 learning outcomes – click to view
Samples: Identifying types of lines. Types of angles. Naming angles within shapes. Identifying lines.

Identifying types of lines
 Activities: 2 course, 2 extra

Naming angles
 Activities: 5 course, 3 extra

Naming angles within shapes
 Activities: 1 course, 0 extra


3 learning outcomes – click to view
4.G.2 – Classify twodimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

6 learning outcomes – click to view
Samples: Comparing angles. Right angles in shapes. Identifying types of lines. Properties of twodimensional shapes.

Comparing angles
 Activities: 2 course, 1 extra

Comparing to a right angle
 Activities: 4 course, 3 extra

Identifying types of lines
 Activities: 2 course, 2 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


6 learning outcomes – click to view
4.G.3 – Recognize a line of symmetry for a twodimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify linesymmetric figures and draw lines of symmetry.

4 learning outcomes – click to view
Samples: Symmetry in the environment. Creating Symmetrical Drawings and Patterns. Identify line of symmetry.

Symmetry  manmade structures
 Activities: 0 course, 1 extra

Drawing symmetrical pictures
 Activities: 0 course, 4 extra

Lines of symmetry
 Activities: 1 course, 1 extra

Rotational symmetry
 Activities: 2 course, 1 extra


4 learning outcomes – click to view