Quizzles!

Bellringer:


Classwork:

State the following If/Then statements as converse, inverse, and contrapositives.

If there are clouds in the sky, then it will rain.

If this is geometry class, then my teacher is Mr. Ryals.

If today is Tuesday, then tomorrow is Wednesday.

Also, complete these quizzle squares:



Notes:

Converse: reverse the if and the then.

Inverse: make the if and the then negative.

Contrapositive: reverse the if and the then and make both parts negative.



EX: If today is Tuesday the tomorrow is Wednesday.

The CONVERSE is: If tomorrow is Wednesday then today is Tuesday.

The INVERSE is: if today is not Tuesday then tomorrow is not Wednesday.

The CONTRAPOSITIVE: is if tomorrow isn't Friday then today isn't Tuesday


WHEN YOU CHANGE A STATEMENT IT MAY CHANGE THE TRUTHFULNESS OF THE STATEMENT.

Homework:

Two 3-square quizzles.

Test 1

Test on Nth Terms and Patterns covering what we learned this week.

Test 1 Review Key

Test 1 Review

Nth Term/Patterns

A new worksheet for extra practice.


Defining patterns in words.


Nth term handout.


Test 1 Review.
If you can complete this, you will be able to complete the test with no problems. Check back at 9:30 pm for answer key!

Frankenstein Tables!

Bellringer:


Homework:

Complete Nth term/Pattern Worksheet. ALL.

Classwork:

Begin Nth term/Pattern Worksheet.

Notes:

change in y/change in x = ∆y/∆x = rise/run = slope = m

Linear v. Non-Linear: An equation can be identified as linear if the equation can be written as y = mx + b. If there is an exponent on a variable (x², x³, etc.) The equation is not linear. Linear equations look like a line if you graph them. Non-linear equations have curves in their graphs.

Advanced math notation: "∆" stands for "the change in." When talking about out Frankenstein tables we use ∆x and ∆y.

∆y represents the change in y from position to position in the pattern. ∆x is change in x from position to position (many times 1).

Nth Term

Bellringer:


Homework:

How many triangles will there be in figure 7? Figure 57?


Classwork:

What is the formula for the top (using 'n')? What is the formula for the bottom (using 'n')?


Notes:

Today we discussed "nth" term rules. Basically we want to be able to write patterns in mathematical terms, instead of in sentences. We do this because it is much easier to use a formula to solve a pattern.

What I mean by solving a pattern is that sometimes you will be given a pattern, like 1, 2, 3, 4, ... and asked what the 40th number will be. In this case we can see that the first number is one, the second number is two, et cetera. Therefore, the 40th number will be 40. Mathematically the formula for this is:

n

"n" stands for the position a number falls into (i.e. First, second, third, ...), so when we plug in "1" for "n" because we want to know the first number we get: 1. Let's try a different one.

2, 3, 4, 5, ...

This pattern still increases by one each time, however, in order to get from our "n's" to our pattern we now have to add one. The formula for this is:

n + 1

Finally a more difficult pattern. 1, 4, 9, 16. Remember, n stands for the position of each number in the pattern. That means the the "n" for 1 is 1. The "n" for 4 is 2, the "n" for 9 is 3 and the "n" for 16 is 4. The question, again, is how can we turn the "n" into the pattern number. Let's try a few options.

The second number is 4, it's "n" is 2. Mathematically, what can we do to the number 2 to get it to become a 4. There are 3 options. The first is to add 2.:

2 + 2 = 4

This works for 2, but does it fit the pattern? If I add 2 to 3 (for the next part of the pattern) do I get 9?

3 + 2 = 5
3 + 2 ≠ 9

So, +2 does not give us the formula. The next option to get from 2 ("n") to 4 is to multiply by 2.

2 x 2 = 4

Does this work with 3?

2 x 3 = 6
2 x 3 ≠ 9

No. The last option is to multiply the "n" by itself.

2 x 2 = 4 or 2² = 4

It works for two, but will it work for 3?

3 x 3 = 9 or 3² = 9

Yes, it works for 3. It also works for the rest of the pattern. Therefore, the correct formula for this pattern is:

n²

Why bother finding nth terms? Many lines of work, including epidemiology (studying the spread of diseases) use formulas to describe complex patterns that occur in nature. This allows doctors to use patterns without having to write out entire sequences.

Inductive Reasoning

Homework:

Worksheet on inductive reasoning. Find the next number in the pattern and EXPLAIN how it was found.

Notes:

Deductive reasoning-A form of reasoning by which each conclusion follows from the previous one. (i.e. Memorizing the alphabet, multiplication tables, counting)

Inductive reasoning-A form of reasoning in which a conclusion is reached based on a pattern present in numerous observations. (i.e. 4, 7, 10, 13 have nothing in common, except they are 3 apart from each other.)

Sequences - a string of numbers that are tied together with some sort of consistent rule.

Example 1:5, 7, 11, 17, 25 the next numbers will be 35, 47, 61 the pattern is to add the next even numbers.

Example 2:7, -7, 14, -42, 168 the pattern is to multiply by next negative integers. The next numbers will be -840 ,5040, -35280.

Example 3: 100, 97, 88, 61 the next numbers would be -20, -263, -992. The pattern is to subtract by the next power of three.

Tips to figure out patterns with shapes:
Look for: counter clockwise and clockwise changes, count sides, count lines , changes in direction.

Pop-Quiz and New Books!

Classwork:

Today we had an activity schedule for PBS testing.

We reviewed homework if there were questions, and then took a pop quiz.

Finally textbooks were distributed. We have a classroom set of books so you can leave your personal books at home for the year! No more lugging books back and forth from home!

Homework:

Do what you have to to successfully find this site, and complete the homework from 8/20. I also recommend that you either become a follower of MrRyals.com to receive email updates or subsrcibe at the bottom for real-time, bookmarked browsing.

Algebra I Review, part 2

Homework:

Solve. This will be collected Monday (8/24).

1. 4z= 132

2. -6 = c + 4

3. x/2 = -40

4. 4.6 + z = 3.6

5. w - 5 = -13

6. -m = 5

7. c/7 + 2 = 1

8. 5(z + 3) = 12

9. 6 - 3a/2 = -6

10. 4x + 2(x - 3) = 0

11. (3 + m)/2 = 5

12. 4(t - 7) + 6 = 30

13. 12 ∙ b ∙ 13 = 338

14. 4(5n + 7) - 3n = 3(4n - 9)

15. 12 - 23c = 7(9-c)

16. 4.7(2f - 0.5) = -6(1.6f - 8.3f)

Notes:

Variable ∙ Variable = Variable2

z ∙ z = z2

Distributive Property: Multiply the number, variable or sign (+ or -) on the outside of the parenthesis to every number on the inside of the parenthesis.

Example:

z(7-2z)
7z-2z2

Classwork:

Simplify:

1. -m + 4 +7m

2. 6x - 9x +x

3. 3z + 6 - 3z - 7

4. d/5 + 2d/7

5. 3.1 + 7.5y - 8y

6. 2.5(4z - 18) + 12

7. 6h - 3h(h + 1)

8. 3 - (2x - 7)

9. 8 + 3(y - 4)

10. 9k - 2(3k - 5) - 10

11. 5(r + 1) - (r - 3)

12. x(2x - 6) + x2

13. 2(n + 8 ) + 3n(n - 5)

Algebra I Review, part 1

Homework:

Create and solve 5 single-step and 3 two-step linear equations to be turned in. Don't forget the heading!

Notes:

Basic Rules of Algebra:

Commutative: a + b = b + a; ab = ba
Associative: (a + b) + c = a + (b + c); (ab)c = a(bc)
Distributive: a(b +c) = ab + ac; a(b – c) = ab – ac
Identity: a + 0 = a; a ∙ 1 = a
Inverse: a + (-a) = 0; a ∙ 1/a = 1
Multiplication:
(-1)a = -a
(-1)(-a) = a
a ∙ 0 = 0
(-a)(b) = -ab
(-a)(-b) = ab

Equations of Lines:

Slope-intercept form: y = mx + b
General form: Ax + By + C = 0
Point-slope form: y – y1 = m(x – x1) [(x1,y1) point on line]
Horizontal line: y = b
Vertical line: x = a

Distance formula: √(x2 – x1) + (y2 – y1)
Midpoint formula: x1 + x2 , y1 + y2
2 2

Problem Solving:

1. Understand the problem. Read the problem carefully. Decide what information you are given and what information you need to find. Eliminate unnecessary information.
2. Make a plan to solve the problem. Choose a strategy. PEMA. Equation/formula. Look for a pattern. Break into simpler parts. Work backwards. Make a table.
3. Carry out the plan to solve the problem.
4. Check to see if your answer in reasonable.

Solving Linear Equations

1. Get x by itself.

x+12=25 x-6=0 -36/-9=-9x/-9

-12 -12 +6 +6 x=4

x=13 x=6

-32x/-32=4/-32 -6=x+4 3x-4=20

x=-0.125 -4 -4 +4 +4

-10=x 3x/3 24/3

x=8

First Day of Class!

Your first assignment is to bring in a box of tissues (3rd & 4th) or a roll of paper towels (5th). This assignment is not required and is for extra credit on your first test.

Today's lesson was about Class Procedures and Rules.

Email lesson notes to Mr. Ryals at trey.ryals@jppss.k12.la.us

Welcome to Bonnabel!

My name is Mr. Ryals, and I'll be teaching 3 sections of Geometry this year! Class notes and assignments will be posted on here daily, so be sure to check back! That especially goes if you are absent.