Order of Operations

Margot volunteers at a local bird sanctuary. She just spent two weeks on vacation, so on her first day back she is talking to her supervisor about what she has missed. When Margot left, there were 256 birds. In her absence, 3 birds have each given birth to 5 baby birds, 2 birds were released into the wild and 3 new injured birds were brought in. How can Margot write an expression to figure out the new sanctuary population?

An equation is a number sentence that describes two values that are equal to each other. The values are separated by the "equals" sign, e.g. 3 + 4 = 7. In this case, 3 + 4 and 7 are equal entities. Sometimes you will be given an incomplete equation, which you have to "solve" in order to make both sides equal.

An expression is a number sentence without an equals sign. It can be simplified and/or evaluated, but it cannot be "solved".

Expressions can involve more than one operation, so it is important to know which operation to do first. The order of operations tells you the correct order for completing operations within an expression.

Order of Operations
P - parentheses
E - exponents
MD - multiplication or division, in order from left to right

AS - addition or subtraction, in order from left to right

Now, let's return to Margot and her bountiful birds.

Margot needs to write and evaluate an expression to see how the original population of 256 has changed since 3 birds each gave birth to 5 baby birds, 2 birds were released, and 3 injured birds were brought in.

First, identify the important information in the problem.

256 birds to start

3 birds have 5 babies each

2 birds released

3 birds added

Next, write this as an expression.

256+3×5−2+3

Then, use order of operations to evaluate the expression.

256+3×5−2+3256+15−2+3271−2+3269+3272Multiply 3×5Add 256+15Subtract 271−2Add 269+3===-

The answer is 272.

Margot’s sanctuary now has 272 birds

YOUR TURN: 

Evaluate the following using order of operations

1. 2+3×4+7=––––– 
2. 4+5×2+9−1=––––– 
3. 6×7+2×3=––––– 
4. 4×5+3×1−9=––––– 
5. 5×3×2+5−1=––––– 
6. 4+7×3+8×2=––––– 
7. 9−3×1+4−7=––––– 
8. 10+3×4+2−8=––––– 
9. 11×3+2×4−3=––––– 
10. 6+7×8−9×2 
11. 3+42−5×2+9=––––– 
12. 22+5×2+62−11=––––– 
13. 32×2+4−9=––––– 
14. 6+3×22+7−1=–––––

Original lesson

Scientific Notation

Dear Ayla,

Today, while walking home from school, I got drenched in the rain. I can't believe it! My book bag wasn't zipped all the way, and my papers got soaked. I can't read our homework assignment. Can you send it to me?

Thank you so much!

Jenny

This message is too long to send in a text. Revise it to make it shorter.

We're going to discuss what you did to shorten the message. 

What are examples of other words, phrases, or names that are shortened? 

 Imagine having to write out the numbers we saw in the powers of ten video? 

 

• The population of the world is about 7,117,000,000.

• The distance from Earth to the Sun is about 92,960,000 miles.

• The human body contains approximately 60,000,000,000,000 to 90,000,000,000,000 cells.

• The mass of a particle of dust is 0.000000000753 kg.

• The length of the shortest wavelength of visible light (violet) is 0.0000004 meters.

Write these out in  written form, expanded form, and expanded form with powers of 10. 

There is an easier way to write and say these numbers. Scientific notation is a system developed by scientists and mathematicians to express very large or extreme numbers.

Video time: 

Now, write these numbers out in scientific notation. 

Here's what they should look like: 

The population of the world is about 7,117,000,000.                              (Answer: 7.117 x 109)

The distance from Earth to the Sun is about 92,960,000 miles.                        (Answer: 9.296 x 107)

The human body contains approximately 60,000,000,000,000 to 90,000,000,000,000 cells. 
(Answer: 6.0 x 1013 to 9.0 x 1013)

The mass of a particle of dust is 0.000000000753 kg.                        (Answer: 7.53 x 10-10)

The length of the shortest wavelength of visible light (violet) is 0.0000004 meters.                                                                                                     (Answer: 4.0 x 10-7)

How long is that?

How long is 1000 seconds?

How long is 10 000 seconds?

How long is 100 000 seconds?

How long is 1000 000 seconds?

How long is 10 000 000 seconds?

How long is 100 000 000 seconds?

How long is 1 billion seconds?

Before calculating, make some predictions.

Where would a day fit? (Which "seconds" category)

Where would a year fit?

It's Taco Tuesday!

Do you know whose cheese is on the tacos? 

Scientific Notation

Here are the steps for writing a number in scientific notation.

1. Move the decimal point so that it is to the right of the first non-zero digit of the number. The result should be a number that is at least 1 but less than 10. This will be the first part of your number in scientific notation.
2. Count how many spaces you needed to move your decimal point in step 1. The number of spaces will be your power of 10. If you moved the decimal point to the left, your exponent will be positive. If you moved your decimal point to the right, your exponent will be negative.
3. The number in scientific notation is the decimal number from step 1 multiplied by 10 to the power from step 2.

Converting a Number to Scientific Notation

Large Numbers → Positive Power of Ten

Small Decimal Numbers → Negative Power of Ten

Converting Scientific Notation to Standard Notation

Positive Power of Ten → Move the Decimal to the Right

Negative Power of Ten → Move the Decimal to the Left

Write each number in scientific notation.

1. 0.0000000056731
2. 24,010,000,000
3. 960,000,000,000,000,000
4. 0.0000001245
5. 36,000,000
6. 0.00098
7. 0.000000034
8. 345,000,000

Write each number as a number not in scientific notation.

9. 3.808×1011 
10. 2.1×106 
11. 5.912×108 
12. 6.78×10−6 
13. 5.7×109 
14. 4.5×10−5 

Patterning Bike problems

Mark works at a bike store. He makes $30 per day. For every bike that he sells, he will make $20.

a. What is the unknown? Identify it and create a variable.

b. Is there a constant (an amount that never changes)? What is it?

c. Write an expression for how much Mark can make in one day. (Note: this is the general term) 

d. Last Saturday, Mark sold 5 bikes. How much money did he make that day?

Deposit patterning problem

 

1. Madame opened a savings account on September 1st and made an initial deposit right away and then added a certain amount to the account every two weeks.  The following table shows the account balance after each deposit has been made.  

Biweekly deposit	Balance ($)
1	250
2	375
3	500
4	625

 

1. What was Madame's initial deposit, and how much money did she add to the account each deposit after that?