Let's Talk Word Problems

In class today we completed questions 10, 11, 21 and 33. I'd like to walk you through the process of finding the answers to these problems. Please come to class tomorrow prepared with any questions you may have. 

When solving word problems, remember to distinguish between what you know and what you need to know. Remember to pay attention to clues like "more than" and "less than" that will indicated whether you need to add or subtract. 

10. What we know - There are about 778 million km between the sun and Jupiter. 

                                - This is 550 million km greater than the distance between the sun and Mars. 

      What we need to know - The distance (d) between Mars and the sun. 

Let's set up an equation. Ask the question, what's equal to what here? We know that 778 million km is equal to d (the distance between Mars and the sun) plus an extra 550 million km. 

778 = d + 550

Now, solve for d by subtracting 550 from both sides:

778 - 550 = d + 550 - 550

228 = d

The average distance from Mars to the sun is 228 million km. 

11. What we know - Speed travels through steel @ 5200 m/s

                               - This is 2520 m/s faster than the speed of sound through silver

      What we need to know - The speed of sound through silver (s)

What's equal to what here? We know that 5200 m/s is equal to the speed of sound through silver (s) plus an extra 2520 m/s. 

5200 = s + 2520

Now, solve for s by subtracting 2520 from both sides:

5200 - 2520 = s + 2520 - 2520

2680 = s

The speed of sound through silver is 2,680 m/s.

21. What we know - Distance from Venus to the sun is 108 million km.

                               - This distance is 42 million km less than the distance from Earth to the sun/

      What we need to know - Earth's distance (d) from the sun. 

This is very similar to #10. We know that 108 million km is equal to d (the distance between the Earth and the sun) minus 42 million km. 

108 = d - 42

d = 150 

The average distance from the Earth to the sun is 150 million km. 

33. What we know - In '96, 487m people spoke English. 

                               - This was 512m people fewer than the # of people who spoke Mandarin. 

      What we need to know - How many people spoke Mandarin (n)?

We could think of it like this: If 487 million people spoke English, and that was 512 million people less than those who spoke Mandarin, we must subtract 512 from n to get the 487:

n - 512 = 487 (Answer A)

Worksheet Answers 1 - 9

Hola Amigos,
Please check your answers. Click on the pictures to enlarge (answers are boxed). See the comments if your answer was incorrect and you're not sure where you went wrong. Be sure to come prepared to class tomorrow with any questions you have. See you then!

Questions 1-4 were pretty straight forward. Change addition to adding the opposite, distribute (if necessary), and combine like terms. Sometimes it helps to put negative numbers in parentheses so as not to confuse the signs with adding, subtracting, negatives, etc.

Number 5 was a big more complex. After changing subtraction to adding negatives, we distributed both the 3 and the negative 4 to their respective parentheses. Then we used integer rules to combine like terms. Negative 12 and positive 12 cancel each other out.

Number 6 could have been done two ways. The first way would include all the steps we see above. The second would entail looking at the problem and saying, "If I've got six times g minus h, and I'm taking away six times g minus h, I'll be left with zero."

For 7 - 9, don't forget that there's always an imaginary 1 next to any variable that's by itself. Changing a variable to its negative would mean that invisible 1 turns into a negative 1.

 

Chapter 1 Study Guide

Hello everyone. Don't forget your Chapter 1 Assessment is Monday. Here's what will be on the test:

Variable Expressions
- You'll need to know how to write variable expressions for word phrases. For example:
Write a variable expression for a number n increased by 5.
Well, if we're starting with an unknown number (n) and we're increasing by 5, we must be adding. So n + 5 would be our variable expression.

Order of Operations
***Please remember that you should be using the correct order of operations for any math problem you complete - not just problems that specify that you need to "use order of operations to..."***
- Use PEMDAS
- Remember that MULTIPLICATION and DIVISION  are on the same level and are performed LEFT to RIGHT
- Remember that ADDITION and SUBTRACTION are also on the same level and are performed LEFT to RIGHT

Evaluating Expressions
- To evaluate an expression, substitute a number for each variable. Then solve using order of operations.
Example:
Evaluate 3x + 4 for x = 5. 
1. First, we plug the value in for x: 3 x 5 + 4
2. Next, we multiply: 15 + 4
3. Finally, we add: 19
And voila. We've evaluated the expression.

Integers, Integers, Errry'thang Integers
You'll need to know how to:
- Compare and order integers (remember, as we go further left on the number line, the values decrease; as we go further to the right, the values increase)
- Find the absolute value (remember, absolute values are ALWAYS POSITIVE and absolute value lines act as grouping symbols, just like parentheses)
- Add and subtract with integers
Quick review: Adding with the same sign - add like normal and keep the sign. 
                       Adding with different signs - find the difference of the absolute values and keep the 
                       sign of the "larger" number
                       Subracting: USE KFC (Keep, Flip, Change); then, use your addition rules.
- Multiply and divide with integers
Quick review: When multiplying OR dividing, if both numbers have the same sign, the answer is 
                        ALWAYS POSITIVE
                        If the numbers have different signs, the answer is ALWAYS NEGATIVE

Patterns & Reasoning
- Use inductive reasoning to find the pattern. Then write the rule. Remember, that's when we use the "Start with .... and then....." model.

The Coordinate Plane
- Coordinates are (x, y) --- Don't forget, you have to walk into the building before you can take the elevator
- Know your quadrants

Study, study, study your notes! See you Monday!

Subtracting Integers

*Please read the post below this one for tonight's KhanAcademy assignment*

Scared of subtraction involving negative integers? Don't be - remember, it's just addition in disguise!

The rule for subtraction is:

Add the OpPoSiTe!


Who likes fried chicken? It's one of my all-time favorites. :)

Img: thebittenword.com

So... what does fried chicken have to do with subtracting integers? Check out this cool chart from passyworldofmathematics.com:


Then, solve your problem as an addition problem. Here are a few examples:

-5 - 3 = ?
-5 + (-3) = -8  ---> Both numbers are the same sign, so we can add like normal and keep the sign.

7 - (-2) = ?
7 + 2 = 9   ---> Again, both numbers are the same sign, so we can add like normal and keep the sign.

4 - 8 = ?
4 + (-8) = ?  ---> Now we've got addition with two different signs, so remember to use your absolute values!
The absolute values are 4 and 8. The difference between 4 and 8 is 4. Now, is it negative or positive? Look at the original number that had the greatest absolute value: -8. Since it's negative, we know the answer is -4.

If you are self-checking subtraction of integers tonight, here are the answers to the Quick Checks from 1-6 (pgs. 30 & 31):

1) a. -5
    b. -1
    c. -3

2) a. -4
    b. -6
    c. 5

3) a. 35
    b. -106
    c. -46

HaPpY SuBtRaCtInG!

Assignment 1, September 2

Assignment 1

Hello all! Welcome to your very first assignment :)

1. Visit KhanAcademy.org.

2. Click the link below to watch your first video. If it does not take you to a video called "Introduction to Order of Operations," go to the search box at the top of the website and type "Introduction to Order of Operations" - then, select the video.

http://www.khanacademy.org/math/arithmetic/order-of-operations/v/introduction-to-order-of-operations

3. After the video, click the gray "Practice" button that appears on the screen. Try to earn as many energy points as you can! Please remember what we talked about in class:PLEASE EXCUSE MY DEAR AUNT SALLY. Remember that the numerator and denominator in a fraction are grouped together (as though they had parentheses).

*If your practice questions give you negative integers and you're not sure how to add/subtract them, just try your best.*

Final Study Guide

Hello all. Here's a quick rundown of the concepts you'll need to review for your final. Remember, we'll be taking a practice final next week in class as we review, so you'll know exactly what type of problems to expect on the real final.

Stuff you need to know:

- Integer operations (adding, subtracting, multiplying, dividing w/integers) - ***You will not be able to use a calculator for this portion of the test***
- Writing/evaluating expressions

- Simplifying variable expressions
- Solving one-step equations (some of your equations will include decimals or fractions)

- GCF and LCM using Prime Factorization

- Mean, median, mode, range

- Exponent rules/simplifying expressions with exponents

- Scientific notation (everyone's favorite! :)

- Comparing and ordering fractions/decimals

- Proportions, similar figures, probability

3rd Quarter Extra Credit Option

Create a blog post for next year's Pre-Algebra class focusing on one concept from Chapter 5. (For example, multiplying fractions.)

Your blog post must:
1. Teach students how to perform the particular math operation you're focusing on
2. Include both words and graphics

You can send this to me digitally or hand me a hard copy.

Due date: Friday, 3/28

This extra credit assignment will be worth one homework grade (it will take the place of a homework assignment if you've missed one) or three points added to your lowest test/quiz grade.