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Math Goodies Aligned with the Common Core Standards


Common Core State Standards for Mathematics Grade 4
Domain 4.OA - Operations and Algebraic Thinking
Use the four operations with whole numbers to solve problems. Lessons
4.OA.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 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. Writing Algebraic Equations
Challenge Exercises for Perimeter & Area
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. Writing Algebraic Equations
Multiplying Decimals and Whole Numbers
Multiplying Decimals
Dividing Decimals by Whole Numbers
Dividing Decimals by Decimals
Solving More Decimal Word Problems
4.OA.3 Solve multistep word problems posed with whole numbers and having whole-number 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. Divisibility
Order of Operations
Order of Operations with Exponents
Order of Operations with Integers
Writing Algebraic Equations
Non-Routine Mean
Estimating Decimal Sums
Estimating Decimal Differences
Estimating Decimal Products
Estimating Decimal Quotients
Gain familiarity with factors and multiples. Lessons
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 one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. Factors and GCF
Multiples and LCM
Prime and Composite Numbers
Practice Exercises for Number Theory
Challenge Exercises for Number Theory
The Sieve of Eratosthenes Worksheet & Answer Key
Generate and analyze patterns. Lessons
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. Exponents
Patterns and Exponents
Practice Exercises for Number Theory
Challenge Exercises for Number Theory
Multiplying Decimals and Whole Numbers
Dividing Decimals by Whole Numbers
Dividing Decimals by Decimals
Domain 4.NBT - Number and Operations in Base Ten
Generalize place value understanding for multi-digit whole numbers. Lessons
4.NBT.1 Recognize that in a multi-digit 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. Introduction to Decimals
Reading and Writing Decimals
Multiplying Decimals and Whole Numbers
Dividing Decimals by Whole Numbers
4.NBT.2 Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Introduction to Decimals
Reading and Writing Decimals
Comparing Decimals
4.NBT.3 Use place value understanding to round multi-digit whole numbers to any place.  
Use place value understanding and properties of operations to perform multi-digit arithmetic. Lessons
4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit 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. Area of a Rectangle
Area of a Parallelogram
Order of Operations
4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-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. Factors and GCF
Divisibility
Dividing Decimals by Whole Numbers
Dividing Decimals by Decimals
Domain 4.NF - Number and Operations - Fractions
Extend understanding of fraction equivalence and ordering. Lessons
4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x 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. Introduction to Fractions
Classifying Fractions
Equivalent Fractions
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. Comparing Fractions
Ordering Fractions
Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. Lessons
4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Adding and Subtracting Fractions and Mixed Numbers
  4.NF.3a  Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Adding Fractions with Like Denominators
Subtracting Fractions with Like Denominators
  4.NF.3b  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. Converting Fractions to Mixed Numbers
Converting Mixed Numbers to Fractions
  4.NF.3c  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. Adding Mixed Numbers
Subtracting Mixed Numbers
  4.NF.3d  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. Adding Fractions with Like Denominators
Subtracting Fractions with Like Denominators
Solving Word Problems by Adding and Subtracting Fractions and Mixed Numbers
4.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Multiplying and Dividing Fractions and Mixed Numbers
  4.NF.4a  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 x (1/4), recording the conclusion by the equation 5/4 = 5 x (1/4). Multiplying Fractions
  4.NF.4b  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 x (2/5) as 6 x (1/5), recognizing this product as 6/5. (In general, n x (a/b) = (n x a)/b.) Multiplying Fractions By Cancelling Common Factors
  4.NF.4c  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? Multiplying Fractions
Solving Problems by Multiplying and Dividing Fractions and Mixed Numbers
Understand decimal notation for fractions, and compare decimal fractions. Lessons
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. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. Writing Fractions as Percents
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. The Meaning of Percent
Writing Percents as Decimals
Percents Less Than 1 or Greater Than 100
Introduction to Decimals
Read and Write Decimals
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. Comparing Decimals
Ordering Decimals
Solving Decimal Word Problems
Practice Exercises for Decimals Part I
Challenge Exercises for Decimals Part I
Domain 4.MD - Measurement and Data
Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Lessons
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 two-column table. Converting Mixed Numbers to Fractions
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. Comparing Fractions
Adding Decimals
Subtracting Decimals
Multiplying Decimals and Whole Numbers
Dividing Decimals by Decimals
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. Area of a Rectangle
Challenge Exercises for Perimeter & Area
Geometric measurement: understand concepts of angle and measure angles. Lessons
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 "one-degree angle," and can be used to measure angles. Constructing Circle Graphs
  4.MD.5.b   An angle that turns through n one-degree angles is said to have an angle measure of n degrees. Constructing Circle Graphs
4.MD.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. Constructing Circle Graphs
Domain 4.G - Geometry
Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Lessons
4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. Geometry and the Circle
Area of a Parallelogram
Area of a Trapezoid
4.G.2 Classify two-dimensional 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. Area of a Triangle
Geometry and a Shoebox


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