2.  Addition 6+4=10  Subtraction 36-10=26  Multiplication 5X6=30  Division 60÷10=6

3.  Addends – the two numbers being added together 6+10=  Sum- the total that results when the addends are combined, the answer 6+10=16  Sign +

4.  Difference – the answer to a subtraction number sentence. 10-3=7  Sign -

5.  Factor- the numbers being multiplied together 5X6=  Product- the result of multiplying the factors, the answer 5X6=30  Sign X

6.  Dividend – the total number being divided into equal groups 48÷6=  Divisor- the number of equal groups being created when dividing up the dividend 48÷6=  Quotient- the answer to a division number sentence 48÷6=8  Sign ÷ =

7.  3+4x4  Begin by laying down 3 tiles. Next create a 4x4 array.  How many tiles are in your model?

8.  3+4x4  Show 3+4 using two colors of tiles for each addend. Next, build an array for this amount times 4.  How many tiles are shown in this model?  What do you notice when you compare the two models? Write an expression to represent each model. Why is order important rather than solving from left to right?

9.  Jay brought some juice boxes to soccer practice to share with his teammates. He had 3 single boxes and 4 multi-packs. There are 6 single boxes in each multi-pack. To determine how many boxes of juice Jay brought to practice, evaluate 3 + 4 × 6.

10.  When solving a problem you should always begin with the expression found within the Parenthesis  3X(4+9)-7=

11.  When solving an expression you should begin solving the part of the problem in the ______________ first.  If you do not begin with the ____________ your answer will not be _______________.

12.  Take two dice.  Roll the dice and create an expression using either multiplication X or division ÷.  Roll the dice again and expand on your expression using addition + and subtraction -.  Choose a place in your expression to add parenthesis.  Solve  Allow your neighbor to try and solve your problem. Are your answers the same? If not discuss.  Now move the parenthesis. Does your answer change? Why or why not?

13.  P= Parenthesis  E= Exponent  M= Multiplication  D= Division  A= Addition  S= Subtraction

14.  Brackets- [ ] are like parenthesis. Anything inside them should be done before you solve exponents, multiplication, division, addition, or subtraction. They often contain an expression that uses parenthesis. 3+[4X9+(9+7-3)]=

15.  Braces- { } are used when an expression contains both parenthesis ( ) and brackets [ ]. 8x{6+[4x(15÷5)-1]x1}  When solving a problem that has Parenthesis, Brackets, and Braces start from the inside and work your way out.

16.  Exponent- shorthand for showing repeated multiplication of the same number by itself. 5 3 = 5 × 5 × 5 = 125 2 4 = 2 × 2 × 2 × 2 = 16

17.  Parenthesis- 3+(56-38)x2  Parenthesis and Brackets- 4x[32+(5x2)-21]  Parenthesis, Brackets, and Braces- 15+{17+[85- (21x2)+4]-12}  Parenthesis, Brackets, Braces, and Exponents 2 3 + {3X(4-1)-3+[3 3 -2]-2}

18.  You can write an expression in word form example- the sum of three and two This expression can then be written using numbers it would be written in number form as 3+2=  Write the number form The product of fifteen and three added to one and subtracted by four

19.  The product of fifteen and three added to one and subtracted by four  You should have written 1+15X3-4  It is important to remember when you need to add parenthesis!!!  Write the number form for The sum of three and seven multiplied by two and subtracted from twenty three

20.  The sum of three and seven multiplied by two and subtracted from twenty three  23-2X(3+7)

21. A function is a rule, sometimes using variables (letters to represent numbers), that changes a number (input), using multiplication, division, addition, and/or subtraction creating a new number (output)

22. In the incomplete equation + 5 = ___, Is the input _____ is the output + 5 is the rule

23. In the incomplete equation + 5 = ___, INPUT 2 into Apply the rule + 5 2 + 5= ____ OUTPUT 7

24. Solving the Rule If you are given the input and the output, you must determine how the number changed using addition, subtraction, multiplication, or division. 6 ______ = 9 7 ________ = 10 The rule must be + 3 because 6 + 3=9 and 7 + 3 = 10 + 3

25. InOut The input is a number going in. Let’s imagine this equation + 5 = ___ The output is the result of applying the rule ( + 5) + 5 is the rule

26. InOut 618 412 5 7 9 30 15 21 3 10

27. InOut 618 412 5 7 9 30

28. InOut 1730 114 10 21 35 19 23 34 22 6

29. InOut 1730 114 10 21 35 19

30. InOut 32 64 9 12 10 1812 6 8 15

31. InOut 32 64 96 128 1510 1812

32. 26 x12 The first step is to make sure the place values are lined up. They don’t have to be but it helps stay oraganized OnesTens

33. 26 x12 Begin with multiplying the bottom factor’s one’s place with the top factors one’s place. Think, 2 x 6 equals 12. Because there is still the tens place to multiply, you must regroup the 1. 2 1

34. 26 x12 Next, multiply the 2 and the other 2. Then, remember to add the 1 ten from the first step. Think, 2x2=4+1=5 2 1 5

35. 26 x12 Next, because we are multiplying tens, we need to use a 0 for a place holder. Place the 0 under the 2 in the products line. Cross out your regrouped ten from before. 2 1 5 0

36. 26 x12 Next, begin to multiply the 1 in the tens place with ones in the top factor. Think 1x6=6. 25 06

37. 26 x12 Think 1x2=2. 25 062 Next, begin to multiply the 1 in the tens place with tens in the top factor.

38. 26 x12 Finally, add the two products to find the final product. 25 062+ 213 1 Add the ones place. Regroup if necessary. Add the tens place. Regroup if necessary.. Add the hundreds place. Regroup if necessary.

41. 1. Divide 2. Multiply 3. Subtract 4. Bring down 5. Repeat or Remainder

42.  Before you begin dividing write the first 9 multiples for the divisor. 21168 42189 63 84 105 126 147 2 1) 9 4 8

43.  Divide 21 into first number in the dividend. 2 1) 9 4 8 21 will not go into 9 so place a 0 over the 9 then you look at 94. 0 4 1. Write your multiples then Divide The 4 th multiple 84 is the closest write this multiple above the 4. Which multiple of 21 is closest to 94 without being greater?

44.  Multiply the divisor times the first number in your quotient. Write your answer directly under the 94 or the number you just divided into. 21 x4 84 2. Multiply 2 1) 9 4 8 4 84

45.  Draw a line under the 84. Write a subtraction sign next to the 84. 3. Subtract Subtract 84 from 94. Write your answer directly below the 84. 1 2 1) 9 4 8 4 84 0

46.  Go to the next number in the dividend to the right of the 4. Write an arrow under that number. 4. Bring down Bring the 8 down next to the 10. 1 2 1) 9 4 8 4 8 0 4 8

47.  This is where you decide whether you repeat the 5 steps of division. If your divisor can divide into your new number, 108, or if you have numbers in the dividend that have not been brought down, you repeat the 5 steps of division. 5. Repeat or Remainder 1 2 1) 9 4 8 4 8 0 4 8

48.  Divide 21 into your new number, 108. Place your answer directly above the 8 in your quotient. 1. Divide 1 2 1) 9 4 8 4 8 0 4 8 Which multiple of 21 is closest to 108 without being greater? 5

49.  Multiply your divisor, 21, with your new number in the quotient, 5. Place your product directly under the 108. 2. Multiply 1 2 1) 9 4 8 4 8 0 4 8 5 1 0 5

50.  Draw a line under the bottom number, 105. Draw a subtraction sign. 3. Subtract Subtract 3 2 1) 9 4 8 4 8 0 4 8 5 15 1 0

51.  Since there is nothing to bring down, go to step five. 4. Bring down 3 2 1) 9 4 8 4 8 0 4 8 5 15 1 0

52.  If the 21 will not divide into your new number, 3, & there is nothing to bring down, you are done. 5. Repeat or Remainder 3 8 15 1 0 2 1) 9 4 8 0 84 45 Write your left over 3 as the remainder next to the 5. R3

53. 53 Place Value The place of a digit in a number determines its value. Let’s Take a Look…

54. 54 Ones Tens Hundreds, Thousands Ones Tens Hundreds Ones Tens Hundreds Millions,

55. 55Ones,Thousands O T HMillions, O T H O T H 8 9 2 4 0 9 So, in the number 892,409, the place of the digit 2 is “Thousands” and the value is 2,000.

56. 56Ones,Thousands O T HMillions, O T H O T H 5 7 4 3 1 8 6 What is the place of the digit 5? Millions What is the value of the digit 5? 5,000,000

57. 57 What can I do to be sure I don’t make a careless mistake when trying to figure out a digit’s place and value?

58. 58 Decimal- All numbers have a decimal!!!!!!!! A decimal point is a symbol used to separate whole numbers from fractional parts. Let’s Take a Look…

59. 59 Ones Tens Hundreds Thousandths Hundredths Tenths Decimals (Fractional parts) The very important little decimal point

60. 60 Confused by decimals? Think of them like money… If this represents a whole, or “one” then… This shows a tenTH, because it takes 10 of them to make a whole This shows a hundredTH, because it takes 100 of them to make a whole

61. 61 How can thinking of decimals in terms of money help me understand them better?