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

ORDER OF OPERATIONS

There are 4 operations in mathematics

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

Addition Terms

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 +

Subtraction Terms Difference – the answer to a subtraction

number sentence. 10-3=7 Sign -

Multiplication Terms Factor- the numbers being multiplied

together 5X6= Product- the result of multiplying the

factors, the answer 5X6=30 Sign X

Division Terms 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 ÷

=

Order of Operations 3+4x4 Begin by laying down 3

tiles. Next create a 4x4 array.

How many tiles are in your model?

Order of Operations 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?

Order of Operations 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.

Parenthesis

When solving a problem you should always begin with the expression found within the Parenthesis

3X(4+9)-7=

Order of Operations 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 _______________.

Order of Operations 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?

PEMDASPlease Excuse My Dear Aunt Sally P= Parenthesis E= Exponent M= Multiplication D= Division A= Addition S= Subtraction

Brackets 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)]=

Braces 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.

Exponents Exponent- shorthand for showing

repeated multiplication of the same number by itself.53 = 5 × 5 × 5 = 12524 = 2 × 2 × 2 × 2 = 16

Practice 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 23+ {3X(4-1)-3+[33-2]-2}

Using Words to Write Expressions

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 formThe product of fifteen and three added to

one and subtracted by four


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 forThe sum of three and seven multiplied by

two and subtracted from twenty three


The sum of three and seven multiplied by two and subtracted from twenty three

23-2X(3+7)

What is a Function?

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)

FunctionsIn the incomplete equation + 5 = ___ ,

Is the input_____ is the output

+ 5 is the rule

Practice using a FunctionIn the incomplete equation + 5 = ___ ,

INPUT 2 into

Apply the rule + 52 + 5= ____ OUTPUT7

Practice using a FunctionSolving 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 + 3

Function Tables

In Out

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

Function TablesIn Out

6 184 1257

930

1521

310

The rule is x 3

In Out

6 184 1257

930


17 301 141021

3519

2334

226

The rule is + 13

In Out

17 301 141021

3519


3 26 4912

1018 12

6 8

15

RULE (___+____)÷3

In Out

3 26 49 612 815 1018 12

Multiplication AlgorithmSteps

26x12

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


26x12

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


26x12

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


26x12

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

50


26x12

Next, begin to multiply the 1 in the tens place with ones in the top factor.

Think 1x6=6.

2506


26x12

Think 1x2=2.

25062

Next, begin to multiply the 1 in the tens place with tens in the top factor.


26x12

Finally, add the two products to find the final product.

25062+ 2131

Add the ones place. Regroup if necessary.Add the tens place. Regroup if necessary..Add the hundreds place. Regroup if necessary.

THE PRODUCT IS 312

Division AlgorithmWith 2 Digit Divisor

Division AlgorithmWith 2 Digit Divisor

1. Divide2. Multiply3. Subtract4. Bring down5. Repeat orRemainder

2 Digit Division Before you begin

dividing write the first 9 multiples for the divisor.

21 16842 1896384105126147

2 1) 9 4 8

Step 1 in 2 Digit Long Division

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 thenyou look at 94.

0 4

1. Write your multiples then Divide

• The 4th multiple 84 is the closest write this multiple above the 4.

•Which multiple of 21 is closest to 94 without being greater?

Step 2 in 2 Digit Division

Multiply the divisor times the first number in your quotient.

• Write your answer directly

under the 94 or the number

you just divided into.

21x484

2. Multiply 2 1) 9 4 8

48 4


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.

12 1) 9 4 8

48 4

0


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.

12 1) 9 4 8

48

04

8


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 84

804

8


Divide 21 into your new number, 108.

• Place your answer directly above the 8 in your quotient.

1. Divide

12 1) 9 4 8

48

04

8• Which multiple of 21 is closest to 108 without being greater?

5


Multiply your divisor, 21, with your new number in the quotient, 5.

• Place your product directly under the 108.

2. Multiply

12 1) 9 4 8

48

04

8

5

1 0 5


Draw a line under the bottom number, 105.

• Draw a subtraction sign.

3. Subtract

• Subtract

3

2 1) 9 4 84

804

8

5

1 51

0


Since there is nothing to bring down, go to step five.

4. Bring down

3

2 1) 9 4 84

804

8

5

1 51

0


If the 21 will not divide into your new number, 3, & there is nothing to bring down, you are done.

5. Repeat or Remainder

38

1 51

0

2 1) 9 4 80

844 5

• Write your left over 3 as the remainder next to the 5.

R3

53

Place & ValuePlace Value The place of a digit in a number determines its value.

Let’s Take a Look…

54

Ones

OnesTens

Hundreds,

Thousands

OnesTens

Hundreds

OnesTens

Hundreds

Millions

,

55

By using the place value chart, we can determine the place and value of any

digit within a number.

Ones

,Thousands

OTH

Millions

, OTH OTH8 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

Let’s try using the chart!

Ones

,Thousands

OTH

Millions

, OTH OTH

5 7 4 3 1 8 6

What is the place of the digit 5?

MillionsWhat is the value of the digit 5?

5,000,000

57

THINK…

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

Place & Value - Decimals

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

Whole Numbers

OnesTens

Hundreds

ThousandthsHundredths

Tenths

Decimals(Fractional

parts)

The very important little decimal point

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

THINK…

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

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

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