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# Math Goodies Aligned with the Common Core Standards

Common Core State Standards for Mathematics Grade 5
Domain 5.OA - Operations and Algebraic Thinking
Write and interpret numerical expressions. Lessons
5.OA.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Order of Operations
Order of Operations with Exponents
Order of Operations with Integers
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. Writing Algebraic Expressions
Domain 5.NBT - Number and Operations in Base Ten
Understand the place value system. Lessons
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. Introduction to Decimals
Reading and Writing Decimals
Comparing Decimals
Ordering Decimals
Estimating Decimal Sums
Estimating Decimal Differences
Solving Decimal Word Problems
Practice Exercises for Decimals Part I
Challenge Exercises for Decimals Part I
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 whole-number exponents to denote powers of 10. Multiplying Decimals and Whole Numbers
Dividing Decimals by Whole Numbers
Dividing Decimals by Decimals
Exponents
Patterns with Exponents
5.NBT.3 Read, write, and compare decimals to thousandths. Introduction to Decimals
Reading and Writing Decimals
Comparing Decimals
Ordering Decimals
5.NBT.3.a  Read and write decimals to thousandths using base-ten 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). Introduction to Decimals
Reading and Writing Decimals
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 Decimals
Ordering Decimals
5.NBT.4 Use place value understanding to round decimals to any place. Estimating Decimal Sums
Estimating Decimal Differences
Estimating Decimal Products
Estimating Decimal Quotients
Rounding Decimals Quotients
Perform operations with multi-digit whole numbers and with decimals to hundredths. Lessons
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. Area of a Rectangle
Area of a Parallelogram
Order of Operations
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. Adding Decimals
Subtracting Decimals
Solving Decimal Word Problems
Practice Exercises for Decimals Part I
Challenge Exercises for Decimals Part I
Multiplying Decimals and Whole Numbers
Multiplying Decimals
Dividing Decimals by Whole Numbers
Dividing Decimals by Decimals
Solving More Decimal Word Problems
Practice Exercises for Decimals Part II
Challenge Exercises for Decimals Part II
Domain 5.NF - Number and Operations - Fractions
Use equivalent fractions as a strategy to add and subtract fractions. Lessons
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.) Adding Fractions with Like Denominators
Subtracting Fractions with Like Denominators
Adding and Subtracting Fractions with Unlike Denominators
Adding Mixed Numbers
Subtracting Mixed Numbers
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. Solving Word Problems by Adding and Subtracting Fractions and Mixed Numbers
Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Lessons
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 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Dividing Fractions
Reciprocals
5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Multiplying Fractions
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.) Multiplying Fractions
Multiplying Fractions By Cancelling Common Factors
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. Multiplying Mixed Numbers
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. Patterns and Exponents
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. Multiplying Fractions
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. Multiplying Fractions
Multiplying Mixed Numbers
Solving Problems by Multiplying and Dividing Fractions and Mixed Numbers
5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Dividing Fractions
5.NF.7.a  Interpret division of a unit fraction by a non-zero 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. Dividing Fractions
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. Dividing Fractions
5.NF.7.c  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. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Solving Problems by Multiplying and Dividing Fractions and Mixed Numbers
Domain 5.MD - Measurement and Data

## Convert like measurement units within a given measurement system.

Lessons
5.MD.1 Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Writing Decimals as Percents
Domain 5.G - Geometry
Classify two-dimensional figures into categories based on their properties Lessons
5G.3 Understand that attributes belonging to a category of two-dimensional 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. Perimeter of Polygons
Area of Rectangles
Area of Parallelograms
Area of Triangles
Area of Trapezoids
Practice Exercises for Perimeter & Area
Challenge Exercises for Perimeter & Area
Geometry and a Shoebox Game

Main Standards Page

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Last Modified 05 Mar 2015