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2 TM A Publication of Complete Curriculum Gibraltar, MI 2015 Complete Curriculum All rights reserved; No part of this publication may be reproduced or transmitted in any form or by any means without prior permission from the Publisher or Authorized Agent. Yearly memberships to access over 8,000 lessons, available at Published in electronic format in the U.S.A.

3 Acknowledgments Complete Curriculum s K-12 curriculum has been team-developed by a consortium of teachers, administrators, educational and subject matter specialists, graphic artists and editors. In a collaborative environment, each professional participant contributed to ensuring the quality, integrity and effectiveness of each Compete Curriculum resource was commensurate with the required educational benchmarks and contemporary standards Complete Curriculum had set forth at the onset of this publishing program.

4 TABLE OF CONTENTS AND OBJECTIVES FOURTH GRADE MATH v. 2

5 TABLE OF CONTENTS AND OBJECTIVES FOURTH GRADE MATH v. 2

6 TABLE OF CONTENTS AND OBJECTIVES FOURTH GRADE MATH v. 2

7 TABLE OF CONTENTS AND OBJECTIVES FOURTH GRADE MATH v. 2

8 TABLE OF CONTENTS AND OBJECTIVES FOURTH GRADE MATH v. 2

9 TABLE OF CONTENTS AND OBJECTIVES FOURTH GRADE MATH v. 2

10 TABLE OF CONTENTS AND OBJECTIVES FOURTH GRADE MATH v. 2

11 TABLE OF CONTENTS AND OBJECTIVES FOURTH GRADE MATH v. 2

12 TABLE OF CONTENTS AND OBJECTIVES FOURTH GRADE MATH v. 2

13 TABLE OF CONTENTS AND OBJECTIVES FOURTH GRADE MATH v. 2

14 TABLE OF CONTENTS AND OBJECTIVES FOURTH GRADE MATH v. 2

15 TABLE OF CONTENTS AND OBJECTIVES FOURTH GRADE MATH v. 2

16 TABLE OF CONTENTS AND OBJECTIVES FOURTH GRADE MATH v. 2

17 TABLE OF CONTENTS AND OBJECTIVES FOURTH GRADE MATH v. 2

18 TABLE OF CONTENTS AND OBJECTIVES FOURTH GRADE MATH v. 2

19 TABLE OF CONTENTS AND OBJECTIVES FOURTH GRADE MATH "For web links that may be contained in this text, various links may contain words or symbols that are subject to trademark or other proprietary rights of third parties. No connection or association exists, either expressly or implied, between the author of the present text and the entities associated with the web links used herein. The content of the web links used herein may also be modified without the knowledge of the author of this text, and the author assumes no responsibility for the accuracy, sufficiency or otherwise the content of the web links listed herein." Complete Curriculum recommends that instructors test web links prior to distributing the lesson. If you see a broken link or changed link, please feel free to ompleteurriculu at contactus@completecurriculum.com. v. 2

20 Chart Your Path for Fourth Grade Math! To the Student Each daily Lesson begins with a question. This isn t a trick question you can t study for this question but you do have to think about it before you answer. The more you think, write or talk about your answer, the more relevant the material will become, the more interested you will be in what you are about to learn, and the better you will be able to understand and apply what you are about to learn. v. 2

21 Fourth Grade Math Common Core Alignment Operations and Algebraic Thinking --Use the four operations with whole numbers to solve problems. 4.0A.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. 4.0A.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. Complete Curriculum Lesson 28, 29, 30, 34 32, 33, A.3 Solve multistep word problems posed with whole numbers and dhaving 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 and explain why a rounded solution is appropriate. 34, 37, 43, 45, 52 --Gain familiarity with factors and multiples. 4.0A.4 Find all factor pairs for a whole number in the range Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range is a multiple of a given one-digit number. Determine whether a given whole number in the range is prime or composite. --Generate and analyze patterns. 4.0A.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. Number andoperations in Base Ten --Generalize place value understanding for multi-digit whole numbers. 54,56,57,58,59,60,61,62,63 54, 56, 69, 83, NBT.1 Recognize that in a multi-digit whole number, a digit in 2, 3, 5, 7, 13 one place represents ten times what it represents in the place to its right. For example, recognize that = 10 by applying concepts of place value and division. 4.NBT.2 Read and write multi-digit whole numbers using base-ten , 4, 5, 6, 8, 910, 11, 12, 13 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. 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. 132,

22 4.NBT.4 Fluently add and subtract multi-digit whole numbers using 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, the standard algorithm. 24, 25, 26, 27 4.NBT.5 Multiply a whole number of up to four digits by a one-digit 31, 34, 35, 36, 39, 40, 41, 42, 43, 44, whole number, and multiply two two-digit numbers, using strategies 45, 46, 54, 55, 57, 58, 59 based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 4.NBT.6 Find whole-number quotients t and remainders with up to 46, 49, 50-53, 55 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. Number and Operations Fractions --Extend understanding of fraction equivalence and ordering. 4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n 67, 71, 72, 83-85, 87, 88, 90, 91, 92, a)/(n b) by using visual fraction models, with attention to how the 93 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.NF.2 Compare two fractions with different numerators and 67, 71, 79, 80 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. --Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. 4.NF.3 Understand d a fraction a/b with a > 1 as a sum of fractions 1/b. a. Understand addition and subtraction of fractions as joining and 81, 82, 85, 88, 89, 93 separating parts referring to the same whole. b. Decompose a fraction into a sum of fractions with the same 81, 86 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 = /8 = 8/8 + 8/8 + 1/8. c. Add and subtract mixed numbers with like denominators, e.g., by 73, 75, 76, 79 replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. d. Solve word problems involving addition and subtraction of fractions 85, 93 referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. 4.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. 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). *84

23 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.) 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? 84, 86 74, 84, 86 --Understand decimal notation for fractions, and compare decimal fractions. 4.NF.5 Express a fraction with denominator 10 as an equivalent *88, 94, 101, 105 fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/ NF.6 Use decimal notation for fractions with denominators 10 or 94, 95, 96, 97, 100, 101, For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. 4.NF.7 Compare two decimals to hundredths by reasoning about *98, 99, 101, 102, 103, 104, 105 their size. Recognize that comparisons are valid only when the two model and symbol not yet included decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using the number line or another visual model. Measurement and Data --Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. 4.MD.1 Know relative sizes of measurement units within one , 141 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. 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),... 4.MD.2 Use the four operations to solve word problems involving 32, 33, 97, 141 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. 4.MD.3 Apply the area and perimeter formulas for rectangles in 136, 142, 143, 145 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. --Represent and interpret data.

24 4.MD.4 Make a line plot to display a data set of measurements in *85 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. --Geometric measurement: understand concepts of angle and measure angles. 4.MD.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: a. An angle is measured with reference to a circle with its center at *156, 157, 165 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. b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees 4.MD.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. --Geometric measurement: understand concepts of angle and measure angles. 4.MD.7 Recognize angle measure as additive. When an angle is decomposed into non-overlapping 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. Geometry --Draw and identify lines and angles, and classify shapes by properties of their lines and angles. 4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. 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. (Two dimensional shapes should include special triangles, e.g., equilateral, isosceles, scalene, and special quadrilaterals, e.g., rhombus, square, rectangle, parallelogram, trapezoid.) 4.G.3 Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. *156, 157, 165 *156, 157, 165 *156, 157, , 157, 158, 164, , 155, ,

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152 STUDENT MANUAL FOURTH GRADE MATH LESSON 36-1 Lesson 36 Multiplication Algorithm Here are a few problems you should be able to do using mental math to prepare you for learning the standard algorithms x 4 = 2. 8 x 10 = 3. 2 x 10 = x 6 = x 9 = In this Lesson, you are going to learn another way to multiply 2-digit numbers by 1-digit numbers. The method you are going to learn in this Lesson is called the standard algorithm. A standard algorithm is the set of steps and rules used to solve a problem. Example 1 Multiply: 28 x 4= Start by solving using the distributive property. You will use the distributive property to help you understand the standard algorithm. 28 = tens x 4 = 8 tens = 80 8 x 4 = = 112 Now you will learn the standard algorithm. 28 x 4

153 STUDENT MANUAL FOURTH GRADE MATH LESSON 36-2 Step 1: When you set up the problem, place the number with more digits on the top, and the number with fewer digits on the bottom. Line up your numbers so that the numbers in the ones place are lined up as shown. 28 x 4 Step 2: Multiply the 4 x 8. The product is 32. Place the 2 (the ones place) under the 4. Carry the 3 to the tens column (place it above the 2). 28 x 4 2 Step 3: Multiply the 2 x 4. The product is 8. Add the 8 (the product) to the 3 that was carried over to the tens place. The sum is 11. Place the 1 Your product is x Now, compare the two methods. In the distributive property method you multiplied 2 tens x 4 and 8 x 4. In the algorithm, you multiplied 4 x 8 and 2 x 4. In both methods, you multiply the same digits. The algorithm allows you to multiply just the digits, not groups of tens and ones; therefore, it is often considered the faster method. Example 2 Use the algorithm to multiply 32 x 9. Step 1: Set up your problem. Step 2: Multiply the two numbers in the ones place. Carry your tens place if needed.

154 STUDENT MANUAL FOURTH GRADE MATH LESSON 36-3 Step 3: Multiply the single digit times the digit in the tens place. Add the product to the carried number if needed x Notice that in this Example, we had to carry. We carry when we multiply two numbers together and find a number that s larger than 10. When we carry, we take the digit representing the ten s place and write it above the next number to be multiplied. In this case, we multiplied 9 by 2 and got 18, so we carried the 1 (representing 10) and put it over the 3 (the next digit to be multiplied). We then added that number to the next product, in this case = 28. Here s another example: 5 27 x Since 7 x 8 is 56, we carried the 5 and added that to 8 x 2 (16) to get 21.

155 STUDENT MANUAL FOURTH GRADE MATH LESSON 36-4 Practice Use the algorithm to solve x 5 = 2. 8 x 10 = Lesson Wrap-Up: The standard algorithm is the most common method used for multiplication because it is a fast way to solve problems.

156 STUDENT MANUAL FOURTH GRADE MATH LESSON 36-5 Worksheet 36 Directions: Use the algorithm to solve the following problems. Remember to set up the problems correctly x 8 = x 4 = x 4 =

157 STUDENT MANUAL FOURTH GRADE MATH LESSON x 5 = x 9 = x 6 =

158 STUDENT MANUAL FOURTH GRADE MATH LESSON x 2 = x 1 = x 7 =

159 STUDENT MANUAL FOURTH GRADE MATH LESSON x 3 = x 8 = x 7 =

160 STUDENT MANUAL FOURTH GRADE MATH LESSON x 6 = x 9 = x 0 =

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169 STUDENT MANUAL FOURTH GRADE MATH LESSON 40-1 Lesson 40 Multiplication: 3 Digit Times 1 Digit Here are a few problems you should be able to do using mental math to prepare you for learning the standard algorithms. Multiply the numbers and then add zeroes to the end of the answer x 2 = (200) 2. 7 x 100 = (700) 3. 4 x 100 = (400) x 3 = (300) x 5 = (500) In this Lesson, you are going to use the standard algorithm to solve 3-digit numbers multiplied by 1-digit numbers. Example 524 x 3 = Step 1: Step 2: Step 3: Step 4: x Set up your problem. Multiply the two numbers in the ones place. Carry your tens place if needed. Multiply the single digit times the digit in the tens place. Add the product to the carried number if needed. Carry the tens place number of the product if needed. Multiply the single digit number times the digit in the hundreds place. Add the carried number if needed.

170 STUDENT MANUAL FOURTH GRADE MATH LESSON 40-2 Practice Use the standard algorithm to multiply x 4 = x 123 = 861 Lesson Wrap-Up: The standard algorithm makes multiplying large numbers fast and easy. Multiply 365 by how many years old you are. That s how many days you have been alive!

171 STUDENT MANUAL FOURTH GRADE MATH LESSON 40-3 Worksheet What is the difference between using the standard algorithm for a 2-digit times a 1-digit and using the standard algorithm for a 3-digit times a 1-digit? Answers will vary 2. You have used the standard algorithm for a 2-digit and a 3-digit times a 1-digit. How do you think the steps would change if you were multiplying a 4-digit number times a 1-digit number? Answers will vary Directions: Multiply using the standard algorithm x 7 = 2947

172 STUDENT MANUAL FOURTH GRADE MATH LESSON x 6 = x 3 = x 4 = 2008

173 STUDENT MANUAL FOURTH GRADE MATH LESSON x 3 = x 2 = x 9 = x 7 = 3374

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175 STUDENT MANUAL FOURTH GRADE MATH LESSON 42-1 Lesson 42 Multiplication: 3 Digit Times 2 Digit In this Lesson, you will use the standard algorithm to multiply 3-digit numbers by 2-digit numbers. You will see that many of the steps are the same as when multiplying by a 1-digit number. Example x 45 = Step 1: Step 2: Set up your problem. 123 x 45 Multiply the two numbers in the ones place. Carry your tens place if needed x Step 3: Multiply the single digit times the digit in the tens place. Add the product to the carried number if needed. Carry the tens place number of the product if needed x Step 4: When you move to the tens place of the second number, place a 0 as a place holder for the ones place below the first product you found x

176 STUDENT MANUAL FOURTH GRADE MATH LESSON 42-2 Step 5: Multiply the number in the tens place of the bottom number by numbers in the top number in the same way you did for the ones place x Step 6: Add the two products. The sum is your answer. 123 x is your product. Notice that when you multiplied 3 by 5 and by 4, you had to carry a one each time. Once you ve carried a number and used it, cross it out or erase it don t use it again! Example x 16 = 1. Set up your problem. 2. Multiply 6 x 2 = 12. Put the 2 in the ones place, carry the 1 to the tens place. 3. Multiply 6 x 4 = 24. Add the carried 1. (25) Place the 5 in the tens place, carry the 2 to the hundreds place. 4. Multiply 6 x 3 = 18. Add the carried 2. (20) Place the 0 in the hundreds place and the 2 in the thousands place. 5. Put a zero in the ones place under the Multiply 1 x 2 = 2. Place the 2 in the tens place.

177 STUDENT MANUAL FOURTH GRADE MATH LESSON Multiply 1 x 4 = 4. Place the 4 in the hundreds place. 8. Multiply 1 x 3 = 3. Place the 3 in the thousands place. 9. Add the two products. 342 x is your product. You can check to see if your answer seems correct by estimating. This is done by rounding each number to the nearest hundred or the nearest ten. So for: 342 x 16 = You would round 342 to 300 and you would round 16 to 20. So the problem would be: 300 x 20 = 6000 (You multiply the 2 numbers and add how many zeroes there are in the problem to the end of the answer.) Since 5472 is close to 6000, your answer is probably correct. Practice 2 Multiply using the standard algorithm and check the answer by estimation x 15 =

178 STUDENT MANUAL FOURTH GRADE MATH LESSON x 467 = Lesson Wrap-Up: You will use multiplication often outside of the classroom. The standard algorithm will help you solve these real world problems. Look at the nutrition label on a box of cereal. Multiply the number of calories per serving by the number of servings in the box. How many calories are in the whole box?

179 STUDENT MANUAL FOURTH GRADE MATH LESSON 42-5 Worksheet 42 Directions: Multiply using the standard algorithm and check your answer by estimating x 42 = x 11 =

180 STUDENT MANUAL FOURTH GRADE MATH LESSON x 81 = x 674 =

181 STUDENT MANUAL FOURTH GRADE MATH LESSON x 12 = 6. Matt makes $115 a week. How much would he make in 52 weeks?

182 STUDENT MANUAL FOURTH GRADE MATH LESSON There are 150 marbles in a box of marbles. How many marbles would you have if you bought 15 boxes of marbles? 8. Each student in Mr. Smith s class has 115 trading cards. If there are 22 people in the class, how many trading cards do they have all together?

183 STUDENT MANUAL FOURTH GRADE MATH LESSON A pack of paper comes with 215 sheets of paper. If your mom bought you 19 packs, how many sheets of paper would you have? 10. There are 456 sprinkles on each cupcake. If you and your friends eat 14 cupcakes, how many sprinkles did you eat?

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Page 1 of 11. Curriculum Map: Grade 4 Math Course: Math 4 Sub-topic: General. Grade(s): None specified

Page 1 of 11. Curriculum Map: Grade 4 Math Course: Math 4 Sub-topic: General. Grade(s): None specified Curriculum Map: Grade 4 Math Course: Math 4 Sub-topic: General Grade(s): None specified Unit: Creating a Community of Mathematical Thinkers Timeline: Week 1 The purpose of the Establishing a Community