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1 Common Core Math Standards 1 st Quarter Study Guide 3 rd Grade Created by Karyn Miller 3 rd Grade Math Teacher WRES Kid Friendly Parent Friendly Detailed Descriptions of Each Standard Examples of Every Standard Practice Problems Included Pictorial Representations Standards Listed on Every Page Bonus Posters Included 33 Jam-Packed Pages of Guidance

2 Common Core Math Standards 1 st Quarter Study Guide 3 rd Grade MCC3.NBT.1 Use place value understanding to round whole numbers to the nearest 10 and 100. When you round a number, you find a number that tells you about how much or about how many. Rounding to the Nearest Ten Step 1 - State the two tens the number is between. Step 2 - Look at the digit in the ones place. Step 3 - If the ones digit is 5 or more, round up to the next ten. If the ones digit is less than 5, the tens digit stays the same (go down). Example: Use place value to round 84 to the nearest ten. Step 1-84 is between 80 and 90 Step 2-4 is in the ones place Step 3-4 is less than 5, so the tens digit stays the same. I will round down to 80. So, 84 rounded to the nearest 10 is 80. Round to the nearest 10: 26, 35, 92, 71, 18, 47, 83, 59

3 MCC3.NBT.1 Use place value understanding to round whole numbers to the nearest 10 and 100. When you round a number, you find a number that tells you about how much or about how many. Rounding to the Nearest Hundred Step 1 - State the two hundreds the number is between. Step 2 - Look at the digit in the tens place. Step 3 - If the tens digit is 5 or more, round up to the next hundred. If the tens digit is less than 5, the hundreds digit stays the same (go down). Example: Use place value to round 372 to the nearest hundred. Step is between 300 and 400 Step 2-7 is in the tens place Step 3-7 is more than 5, so the hundreds digit rounds up to the next hundred. I will round up to 400. So, 372 rounded to the nearest 100 is 400. Practice rounding these numbers to the nearest Now try rounding them to the nearest 10. Page 2

4 MCC3.NBT.1 Use place value understanding to round whole numbers to the nearest 10 and 100. Rounding 3-digit Numbers to the Nearest Ten Step 1 - Cover up the digit in the hundreds place. Step 2 - State the two tens the uncovered 2-digit number is between. Step 3 - Look at the digit in the ones place. Step 4 - If the ones digit is 5 or more, round up to the next ten. If the ones digit is less than 5, the tens digit stays the same (go down). Step 5 - Once you decide what the tens rounds to, uncover the hundreds digit and add it back to the number. Example: Use place value to round 643 to the nearest ten. Step 1 - Cover up 6 and just look at 43 Step 2-43 is between 40 and 50 Step 3-3 is in the ones place Step 4-3 is less than 5, so the tens digit stays the same (rounds down). I will round 43 to 40. Step 5 - Add the 6 hundred back to the number. Instead of just 40, my rounded number will be 640. So, 643 rounded to the nearest 100 is 640. Page 3

5 MCC3.NBT.1 Use place value understanding to round whole numbers to the nearest 10 and 100. Page 4

6 MCC3.NBT.1 Use place value understanding to round whole numbers to the nearest 10 and 100. Page 5

7 MCC3.NBT.1 Use place vale understanding to round whole numbers to the nearest 10 and 100. Page 6

8 MCC3.NBT.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. Addition and Subtraction Strategies Place Value Strategy Breaking Each Number into Expanded Form or Page 7

9 MCC3.NBT.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. Addition and Subtraction Strategies Landmark or Friendly Numbers Strategy Breaking Each Number into Parts That are Easy to Add Break 85 into because it is easy to add 75 to 25. Then I added (like quarters) which was 100. Then I went back and added the other 10 to 100, which was = 110. Landmark or Friendly Numbers That are Easy to Add and Subtract: Numbers that end in 0 Numbers that represent quarters (25, 50, 75, 100) Page 8

10 MCC3.NBT.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. Addition and Subtraction Strategies Adding Up in Chunks Strategy Adding 10 at a time until you get close to the number and then add the remainder Start at 85 and add 10 (95), add 10 more (105) and then add the remaining 5 (110) Page 9

11 MCC3.NBT.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. Addition and Subtraction Strategies Compensation Strategy Adding an amount to one number and subtracting that same amount from the other number to make it easy to add (68 + 2) + (34 2) ( ) + (26 3) Page 10

12 MCC3.NBT.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. Addition and Subtraction Strategies Sketching Strategy Draw base ten blocks to represent each number and then add the value of base ten blocks for the two numbers Page 11

13 MCC3.MD.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step how many more and how many less problems using information presented in scaled bar graphs. Picture Graphs Students should be able to answer questions about pictographs regardless of how many each picture stands for, but paying very close attention to the key to answer questions accurately. How many more students play basketball than hockey? How many fewer students play football than baseball? Page 12

14 MCC3.MD.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step how many more and how many less problems using information presented in scaled bar graphs. Bar Graphs Students should be able to answer questions about bar regardless of what scale is used. How many more students chose purple than red? How many fewer students chose green than blue? Page 13

15 MCC3.OA.1 Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. x means groups of 5 groups of 7 5 x 7 = 35 Page 14

16 MCC3.OA.2 Interpret whole number quotients of whole numbers, e.g., interpret 56 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. 56 gumdrops shared equally by 8 friends 56 8 = 7 8 groups of 7 Page 15

17 Steps to Solve Story Problems GET READY! 1.Read the Whole PROBLEM. 2.Underline the QUESTION. 3.Circle the Important NUMBERS. 4.Draw a PICTURE. 5.Reread the PROBLEM. 6.Check your ANSWER. 7.Write a Number SENTENCE. 8.Box the ANSWER. Callback Story Problem Fun Remember to make sure your answer makes sense and answers the question from the story problem. Page 16

18 MCC3.OA.2 Interpret whole number quotients of whole numbers, e.g., interpret 56 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. EXAMPLE Four friends share 24 marbles equally. How many marbles will each person get? Think: They have to share them equally, so I need to make a pile for each person. Then I need to pass them out until I don t have any left. Now I can see that each friend will get 6 marbles each. Number Sentence: 24 4 = 6 4 groups of 6 Page 17

19 MCC3.OA.2 Interpret whole number quotients of whole numbers, e.g., interpret 56 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. Now You Try Five students earned 30 stickers that they had to share equally. How many stickers will each student get? Think: They have to share them equally, so I need to make a pile for each person. Then I need to pass them out until I don t have any left. Now I can see that each friend will get stickers each. Number Sentence: = groups of Page 18

20 MCC3.OA.2 Interpret whole number quotients of whole numbers, e.g., interpret 56 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. 56 gumdrops with each friend getting 8 gumdrops each 56 8 = 7 7 groups with 8 in EACH group Page 19

21 MCC3.OA.2 Interpret whole number quotients of whole numbers, e.g., interpret 56 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. EXAMPLE Ella bakes 18 cupcakes. She puts 3 cupcakes on each plate to cool. How many plates will she use? Think: I need to put 3 cupcakes on each plate and count by 3s until I get to 18. Now I can see that each plate has 3 cupcakes on it, and Ella had to use 6 plates. Number Sentence: 18 3 = 6 6 groups of 3 Page 20

22 MCC3.OA.2 Interpret whole number quotients of whole numbers, e.g., interpret 56 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. Now You Try A group of 8 people want to ride the Ferris wheel. Two people will fit in each seat. How many seats will they need? Think: I need to put 2 people in each seat and count by 2s until I get to 8. Now I can see that each seat has people on it, and they used seats all together. Number Sentence: = groups of Page 21

23 MCC3.OA.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent a problem. Array An equal number of rows and columns, where the row is named first in the number sentence. (Row x Column = Total) Lucy works at a cookie store. She places cookies on a cookie sheet to bake. She places the cookies in 2 rows of 4 cookies. How many cookies can she bake on one cookie sheet? 2 X 4 = 8 2 rows of 4 Page 22

24 Arrays An arrangement that shows objects in rows and columns which will form a square or a rectangle 3 x 4 Means 3 rows with 4 in each row Row 1 Row 2 Row Answer = 12 Page 23

25 MCC3.OA.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent a problem. Equal Groups An equal number of objects in each group (Groups x Objects = Total) Barry has some comic books. He puts them in 3 equal piles. He puts 5 in each pile. How many comic books does Barry have? 3 X 5 = 15 3 groups of 5 Page 24

26 MCC3.OA.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent a problem. Repeated Addition An equal number of objects in each group (Group + Group + Group + Group = Total) Mr. Carson was cleaning out his closet. He packed 2 shoes in each of his 5 shoeboxes to organize his closet. How many shoes did he pack up in all? = 10 5 groups of 2 Page 25

27 MCC3.OA.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent a problem. Number Line Equal jumps on a number line (Number skip counting by X Number of jumps = Total) Mrs. Baxter buys 3 packages of mangos to make a large fruit salad. Each package contains 2 mangos. How many mangos does Mrs. Baxter have in all? X 3 = 6 3 groups of 2 Page 26

28 MCC3.OA.5 Apply properties of operations as strategies to multiply and divide. Examples: If 6x4=24 is known, then 4x6=24 is also known. (Commutative Property of Multiplication). 3x5x2 can be found by 3x5=15, then 15x2=30, or by 5x2=10, then 3x10=30. (Associative Property of Multiplication). Knowing that 8 x 5 = 40 and 8 x 2 = 16, one can find 8 x 7 as 8 x (5 + 2) = (8 x 5) + (8 x 2) = = 56. (Distributive Property of Multiplication). Commutative Property of Multiplication (Flip Flop Property) States that the order of the numbers (factors) does not matter when you are multiplying numbers 5 x 4 = 4 x 5 5 x 4 = 20 4 x 5 = 20 Page 27

29 Flip Flop Property Also Known As Commutative Property 5 x 4 Has the Same Value as 4 x 5 Either way you compute it, you still get 20. Page 28

30 MCC3.OA.5 Apply properties of operations as strategies to multiply and divide. Examples: If 6x4=24 is known, then 4x6=24 is also known. (Commutative Property of Multiplication). 3x5x2 can be found by 3x5=15, then 15x2=30, or by 5x2=10, then 3x10=30. (Associative Property of Multiplication). Knowing that 8 x 5 = 40 and 8 x 2 = 16, one can find 8 x 7 as 8 x (5 + 2) = (8 x 5) + (8 x 2) = = 56. (Distributive Property of Multiplication). Associative Property of Multiplication (Friendship Property) States that the product stays the same when the grouping of the factors is changed (5 x 2) x 3 = (5 x 3) x 2 10 x 3 = 15 x 2 30 = 30 Give it a try: (4 x 2) x 5 = (4 x 5) x 2 x = x = or (6 x 4) x 2 = (6 x 2) x 4 x 2 = x 4 = Page 29

31 MCC3.OA.5 Apply properties of operations as strategies to multiply and divide. Examples: If 6x4=24 is known, then 4x6=24 is also known. (Commutative Property of Multiplication). 3x5x2 can be found by 3x5=15, then 15x2=30, or by 5x2=10, then 3x10=30. (Associative Property of Multiplication). Knowing that 8 x 5 = 40 and 8 x 2 = 16, one can find 8 x 7 as 8 x (5 + 2) = (8 x 5) + (8 x 2) = = 56. (Distributive Property of Multiplication). Distributive Property of Multiplication (Stretch it Out) Students use this strategy for using products they know to solve products they don t know. 7 x 6 7 x 5 = 35 7 x 1 = = 42 or 7 x 6 7 x 3 = 21 7 x 3 = = 42 or 7 x 6 5 x 6 = 30 2 x 6 = = 42 Page 30

32 MCC3.OA.5 Apply properties of operations as strategies to multiply and divide. Examples: If 6x4=24 is known, then 4x6=24 is also known. (Commutative Property of Multiplication). 3x5x2 can be found by 3x5=15, then 15x2=30, or by 5x2=10, then 3x10=30. (Associative Property of Multiplication). Knowing that 8 x 5 = 40 and 8 x 2 = 16, one can find 8 x 7 as 8 x (5 + 2) = (8 x 5) + (8 x 2) = = 56. (Distributive Property of Multiplication). Distributive Property of Multiplication (Stretch it Out) Students use this strategy for using products they know to solve products they don t know. Give it a try: 8 x 6 x = x = + = or 9 x 7 x = x = + = Page 31

33 MCC3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 x? = 48, 5 = 3, 6 x 6 =?. Determine the Unknown in a Multiplication or Division Equation 2 x c = 16 c = 8 b x 8 = 80 b = 10 Give it a try: 21 a = 7 a = or c x 5 = 45 c = Page 32

34 MCC3.OA.6 Understand division as an unknown factor problem. For example, find 32 8 by finding the number that makes 32 when multiplied by 8. Fact Families Multiplication and Division are Inverse Operations of Each Other 4 x 3 = 12 3 x 4 = = = 3 Give it a try: 5 x 7 = 35 x = = = or 3 x 6 = 18 x = = = Page 33

35 This study guide is a culmination of all the standards taught during the 1 st 9 weeks in 3 rd Grade Math this year, in the format that is was taught with kid friendly terms they understand and use. I created this file for my students to review for our system-wide end of the 9 weeks testing, in addition to providing my parents with a resource that is easy to understand so they can help their children when they are at home. We do not have a Common Core textbook yet, so this resource should prove invaluable to my parents during this transition. I hope you find it just as useful, as I tried to make it kid & parent friendly, and also included examples for practice. Karyn Miller 3 rd Grade Math Teacher Whitesville Road Elementary School LaGrange, GA