2. Review Lesson 1 (Lessons 1, 3, & 6 from CCSS math EOG book) CCSS: 3.OA.1 3.OA.3 3.OA.5 SFO: -I can solve multiplication problems with factors up to 12 using arrays, equations, and area models as shown on graph paper -I can solve multiplication problems using the properties of multiplication Teacher Input: Teacher will review what multiplication is and how you can solve multiplication problems using repeated addition. Teacher will also review important vocabulary including factor, product, and array. Teacher will review drawing arrays and using them to represent multiplication problems. Also, teacher will review finding the area on area models using graph paper. Teacher will review multiplication properties and have students practice identifying them using examples. Assessment: Exit Ticket Independent Practice Problem (Complete on lined paper)

3. EOG Review - Operations and Algebraic Thinking (Day 1) -I can solve multiplication problems with factors up to 12 using arrays, equations, and area models. -I can solve multiplication problems using the properties of multiplication.

4. Vocabulary Review Factor – a number that is multiplied with another number. E.g. 3 x 7 = 21, 3 and 7 are being multiplied and are factors. Product – the answer to a multiplication problem. E.g. 3 x 7 = 21, 21 is product (or answer) of 3 x 7. Array – items arranged in rows and columns. (rows go left to right, columns go up and down)

5. What is Multiplication? Multiplication is simply repeated addition. 3 x 7 = 21 can be read as, “3 groups of 7 equals 21.” This is the same as 7 + 7 + 7 = 21. Let’s solve 4 x 9 with repeated addition: Let’s look at another strategy we can use to solve multiplication.

6. Drawing Arrays Drawing an array is easier than trying to add over and over for larger multiplication problems. Lets draw an array and count the squares to solve this problem: 12 x 9 rowscolumns

7. Area Models Sometimes you will come across an area model such as: Don’t let this confuse you. This is just like an array. You can draw in the rows and columns, use repeated addition, or recall your multiplication facts to solve it! 7 6 ?

8. Properties of Multiplication

9. What are Properties? o Just like addition and subtraction, the operation of multiplication has different properties, or rules. o We have learned about some of these properties already! o Let’s review!

10. Zero Property When you multiply any number by zero, the product is always… ZERO!!!!! 0 x 4 =0 0 x 8 =0 0 x 12 =0 0 x 6 =0 Zeroes clear it out!

11. Identity Property When you multiply a number by 1, the product will always be that number. The number keeps its own identity—it doesn’t change! Multiply by 1—it’s always the same! 1 x 5 = 5 1 x 7 = 7 1 x 9 = 9 1 x 2 = 2

12. Commutative Property What does it mean to “commute”? (Hint: You commute to school and home every day; your parents or guardians most likely commute to work and home each day) RIGHT! To travel back and forth

13. Commutative Property The Commutative Property of Multiplication is similar to the Commutative Property of Addition. –I–In addition, if you change the order of the addends the s ss sum remains the same. –I–In m mm multiplication, if you change the order of the f ff factors the p pp product remains the same. 6 x 8 = 48 8 x 6 = 48 5 x 2 = 10 2 x 5 = 10 9 x 7= 63 7 x 9 = 63

14. Associative Property What does to “associate” mean? (Hint: “I like to associate with my friends at lunch time.” “Since he moved, he doesn’t really associate with the same people any more.”) RIGHT! To “hang out with” or “be friends with” OR the person you hang out with (It can be a verb or a noun)

15. PaulJohnRingo John is “associating” with Paul. Now, John is “associating” with Ringo.

16. It looks like this in math: (4 x 5) x 2 = 5 is “associating” with 4. You can tell by the parentheses, or “arms around” each other. 4 x (5 x 2) Now, 5 is “associating” with 2. The “arms”, or parentheses are around 2.

17. Associative Property grouping The associative property is also known as the grouping property. It is similar to the associative property of addition. – You can change the grouping of the factors and the product will be the same!! Let’s see what this looks like!

18. Let’s multiply 3 factors! There are different ways that you can find the product of 3 x 4 x 2 You can multiply 3 x 4 first.3 x 4 = 12 Then multiply that product by 2. 12 x 2 = 24 You can group the factors differently and get the same product! You can multiply 4 x 2 first. 4 x 2 = 8 Then multiply that product by 3. 8 x 3 = 24

19. Let’s try more! 5 x 2 x 2 = 2 x 6 x 2 = 4 x 5 x 1 = 3 x 3 x 4 =

20. Distributive Property Watch this video: http://www.brainpop.com/math/numbersandoperat ions/distributiveproperty/ http://www.brainpop.com/math/numbersandoperat ions/distributiveproperty/ This property helps us solve challenging problems: 4 x 27 4 x (25 + 2) = (4 x 25) + (4 x 2) = 100 + 8 = 108 Can we solve 6 x 13?

21. Exit Ticket Solve the following problems: 1. 2. Which number sentence can be used to solve 7 x 23? a.(7 + 20) x (7 + 3)c. (7 x 10) + (7 x 13) b.(7 x 2) + (7 x 3)d. 7 x (7 x 23)

22. Review Lesson 2 (Lessons 2 & 4 from CCSS math EOG book) CCSS: 3.OA.2 3.OA.3 SFO: -I can solve division problems using equations and arrays Teacher Input: Teacher will review what division is and how you can solve division problems using arrays. Teacher will review important vocabulary including dividend, quotient, divisor. Teacher will use area models where students are given the total area of a shape and one dimension and students have to find the other dimension by dividing. Assessment: Exit Ticket Independent Practice Problem (Complete on lined paper)

23. EOG Review – Operations and Algebraic Thinking (Day 2) - I can solve division problems using equations and arrays.

24. Vocabulary Review Dividend – a number that is divided into group. E.g. In 18 divided by 6, 18 is the dividend. Divisor – the number of groups something is divided into. E.g. 18 divided by 6, 6 is the divisor. Quotient – the answer to a division problem.

25. What is Division? Division is simply splitting a number into equal groups. (It is also repeated subtraction!) 21 ÷ 3 = 7 can be read as, “21 items split into 3 equal groups will leave 7 items in each group” We can test this by placing an item into each group until we run out of item.

26. Using Arrays We can build an array to help us to solve division problems: 48 ÷ 6 For this problem, I am going to start with 6 rows, and continue adding items to each row until I get to 48. The number of columns created is the answer to the problem.

27. Area Models Sometimes you will see division represented as an area model: How would you solve this problem? 637 ?

28. Exit Ticket Solve the following problems: 1. 2.

29. Review Lesson 3 (Lessons 5 & 7 from CCSS math EOG book) CCSS: 3.OA.4 3.OA.6 3.OA.7 SFO: -I can find the unknown value of multiplication and division problems -I can solve multiplication and division problems using related facts Teacher Input: -Teacher will review finding the unknown value of multiplication and division problems. Teacher wlll review with students that you can use inverse operations to solve these problems. Teacher will also show students how they can use models (pictures) to represent multiplication and division problems. Assessment: Exit Ticket Independent Practice Problem (Complete on lined paper)

30. Strategies to Solve Multiplication Problems Skip Count Repeated Addition Use Doubles/Break Apart Draw a Picture Use the Inverse Operation

31. Skip Count Example: 5 x 6 Start at 6 and skip count 5 times and you will get your answer! 6, 12, 18, 24, 30

32. Repeated Addition Ex. 5 x 6 Add 6 five times and you will get your answer! 0+6=6, 6+6=12, 12+6=18, 18+6=24, 24+6=30

33. Use Doubles Example: 5 x 6 Break the six apart into two numbers that are the same: 3 and 3 since 3 + 3 equals 6. 5x6 = (5x3) + (5x3) = 15 + 15 = 30 How else could you break apart the 6?? Try this one using this method: 23 x 4

34. Draw a Picture or Array Example: 5 x 6 You will need 5 groups with 6 in each group or 5 rows with 6 columns.

35. Inverse Operation Example: 5 x 6 The inverse operation of multiplication is division. ? ÷ 5 = 6 or ? ÷ 6 = 5 30!!!

36. Strategies to Solve Division Problems Skip Count Backward Use Repeated Subtraction Draw a Picture Use the Inverse Operation

37. Skip Count Backward Example: 30 ÷ 6 Start at 30 and skip count backward by 6 five times. 30, 24, 18, 12, 6 How many times did it take you?

38. Repeated Subtraction Example: 30 ÷ 6 Subtract 6 five times. 30-6=24, 24-6=18, 18-6=12, 12-6=6, 6-6=0

39. Draw a Picture Example: 30 ÷ 6 Split 30 into 6 groups. Count how many is in each group when you are finished. Go ahead and try!

40. Inverse Operation Example: 30 ÷ 6 The inverse operation of division is multiplication! So… 6 x ? = 30

41. Practice Directions: Solve each of the following problems using one of the strategies we discussed. Write what strategy you used. 6 x 7 9 x 11 7 x 4 8 x 6 40 ÷ 5 72 ÷ 8 25 ÷ 5 81 ÷ 9 Challenge: 61 x 425 x 3 46 x 539 x 8

42. Exit Ticket Solve the following problems. 1.What is the inverse operation of division? 2.What is the inverse operation of multiplication? 3.Solve 7 x 7 4.Solve 56 ÷ 8 5.Write the related multiplication equation for 24 ÷ 6 = 4. 6.Write the related division equation for 5 x 6 = 30

43. Review Lesson 4 (Lessons 8 & 9 from, CCSS math EOG book) CCSS: 3.OA.8 3.OA.9 SFO: -I can solve two step word problems that use all 4 operations -I can understand the order of operations -I can use patterns to identify missing numbers Teacher Input: -Review with students key words to identify each operation in an operation and also review any word problem strategy you use. Teacher will practice solving multi-step word problems. Students will have to write the equation that represents each word problem. Also have students write the equations letting “ x ” represent the unknown value. Teacher will then practice using input/output tables, pictures, and numbers to find the patterns and identify missing numbers. Teacher will practice identifying the rule with a group of numbers after identifying the pattern. Assessment: Exit Ticket Independent

44. Two Step Word Problems What are two step word problems? They are word problems that involve more than one step. They might involve also using more than one operation. Let’s review the ways to solve word problems: Draw a picture x, ÷, +, - Make a chart or table Find a pattern Work Backwards Guess and Check Make a list Use an equation Can you think of any more?

45. Let’s Review Word Problem Word Clues

46. Let’s Review Our Word Problem Strategy: UPS Check

47. Let’s try one together… On a nature walk, Tim drew pictures in his notebook of things he saw. He drew 2 leaves on each of the 6 pages. He also drew 8 insects. How many total leaves and insects did Tim draw?

48. Let’s try another… Rachel picked 42 flowers. She places those flowers in 7 vases, putting the same number of flowers in each vase. Then she gave 4 of those vases of flowers to her friends. How many flowers did Rachel give to her friends?

49. You try one! Eli loves model cars. He has 21 red model cars and 14 black model cars. He put the same number of model cars on each of 5 shelves. How many cars did Eli put on each shelf?

50. Order of Operations Let’s review the steps…. ( ) X OR ÷ + OR -

51. Let’s do a couple together… 4 x (6+3) ÷ 2 – 5 = ________ 15 ÷ 3 + (26 – 11) x 4 = _________

52. You Try… 5 x (10 + 30) – 20 = _________ 30 – 12 + (24 ÷ 6) x 2 = _________

53. Patterns A pattern is an ordered set of numbers, shapes, or objects. There are many different kinds of patterns. Some patterns may increase, some may decrease. Example: 2, 5, 8, 11, 14 What is the pattern? Does it increase or decrease and by what?

54. Examples 11, 9, 7, 5, 3 What is the pattern? 15, 20, 25, 30, 35, 40 What is the pattern?

55. You try this one… Identify the pattern and draw what the next set of shapes would look like.

56. Find the Pattern 24 68 1012 1416 1820

57. Find the pattern and answer these questions! The product of two (even, odd) numbers is always an even number. The product of two odd numbers is always an (even, odd) number. The product of an even number and an odd number is always an (even, odd) number.

58. Exit Ticket 1.Jack and Jane were mowing lawns to earn extra money. Jack mowed 6 lawns for 1 week and earned $5 per lawn. Jane mowed 4 lawns for 2 weeks and earned $6 per lawn. Who made more money mowing lawns? How much more? 1.Solve. 4 x 9 – (20 ÷ 2) + 6 2.Identify the pattern and find the missing number. 16, 22, 28, _____, 40