Wednesday, August 31, 2011
Homework for 9-1 page 18, items 1 through 9 on the bottom
HW for 9-1 page 18, items 1 through 9 on the bottom
8-31 Math 9 Cornell notes – Rationals, Irrationals, and Reals
8-31 Math 9 Cornell notes – Rationals, Irrationals, and Reals
Today each table studied statements such as pi = 3.14 and 1/3 = .3
Then they gave presentations on which statements were true. Some of the statements had the dotted equal sign which means “approximately equal to” or “almost equal to.”
(drawing of N, W, I circles inside the Rational rectangle) | The decimal equivalents of rational numbers - Can terminate (end), such as ½ = .5 and 3/8 = .375 - Can repeat, such as 2/3 = .66666 . . . and 1/13 = .076923076923. . . - The “. . .” symbol is an ellipsis. It means the idea keeps going. Some square roots, such as those of perfect squares, are rational, such a SQRT (36) = 6 |
(add the Irrational rectangle to the N, W, I, R drawing) | The decimal equivalents of irrational numbers - Never end - Never repeat For example, pi = 3.141592654 . . . And SQRT(2) = 1.414213562. . . Example: SQRT (3) = 1.732050808. . . Example: e = 2.71828. . . |
(drawing of the large Real rectangle which includes the Rational and Irrational rectangles) | Rational numbers combined with Irrational numbers are the Set of Real numbers. None of the N, W, or I numbers is in the Irrational rectangle |
Write an Irrational number | Take all the odd numbers: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, . . . Strike out the perfect squares: 3, 5, 7, , 11, 13, 15, 17, 19, 21 23, , 27. . . Take the square root of any of the remaining numbers. Example: SQRT (23) = 4.795831523. . . is irrational. Example: SQRT (7) = 2.645751311. . . is irrational. |
Tuesday, August 30, 2011
hw for 8-31, page 14 and 15, items 6, 7, 8, 9, 10
hw for 8-31, page 14 and 15, items 6, 7, 8, 9, 10
In the NWIR diagram we did in class, none of the fences crossed. Some Venn diagrams have fences that cross, this makes it possible for some things to be inside two different fences or categories at the same time.
In the NWIR diagram we did in class, none of the fences crossed. Some Venn diagrams have fences that cross, this makes it possible for some things to be inside two different fences or categories at the same time.
Homework due 8-30, page12, items 1, 2, 3, 4, 5
Something like item 3 will appear on a future homework quiz, where you have to look at a pattern to put the proper label at the top of the column.
heading for 1st column: Level (follow the example of the table on page 4)
heading for 2nd column: Number of black squares
heading for 3rd column: Perimeter
heading for 1st column: Level (follow the example of the table on page 4)
heading for 2nd column: Number of black squares
heading for 3rd column: Perimeter
Math Skills 9 Estimation
When you are estimating with mixed fractions, how do you tell whether to round down or to round up? What's the difference between a low fraction and a high fraction?
Consider the numbers (7 and 2/11) and (7 and 7/11). Here are the simple fractions that have 11 in the denominator:
1/11, 2/11, 3/11, 4/11, 5/11, 6/11, 7/11, 8/11, 9/11, 10/11.
Divide this set into halves, a lower half and a higher half:
low: 1/11, 2/11, 3/11, 4/11, 5/11
If one of these is the fraction part of the number, drop the fraction and round down to 7.
high: 6/11, 7/11, 8/11, 9/11, 10/11
If one of these is the fraction part of the number, round up to 8.
Consider the numbers (7 and 2/11) and (7 and 7/11). Here are the simple fractions that have 11 in the denominator:
1/11, 2/11, 3/11, 4/11, 5/11, 6/11, 7/11, 8/11, 9/11, 10/11.
Divide this set into halves, a lower half and a higher half:
low: 1/11, 2/11, 3/11, 4/11, 5/11
If one of these is the fraction part of the number, drop the fraction and round down to 7.
high: 6/11, 7/11, 8/11, 9/11, 10/11
If one of these is the fraction part of the number, round up to 8.
Monday, August 29, 2011
Math 9 homework for 8-30
We all need to make an adjustment to the Springboard textbook. In conventional textbooks, the homework problems are found gathered together on one or two pages after a section. In our Springboard book, homework problems are not found in a separate section. Homework problems can be assigned from the activity items in the text. It is important that you write down both the page and item numbers of homework assignments, and that you not get the two confused.
Homework for 8-30: page 12; items 1, 2, 3, 4, 5, 6
Hint: Put labels into the blank spaces at the tops of the columns.
Hint for item 5: The graph shown does not start at (0, 0).
Notes on the hw for today, 8-29: page 11, items 17a, 17b, 18
17a. Graph b reflects the intended design model for earning levels. The upward curve shows that you don't just get "more" for getting to the next level, it shows you get "more on top of more", or an increasing, instead of constant, reward.
17b. From the table on page 4, the columns "# of squares added" and "perimeter" look like 17a, straight graph a. The column "total area" looks like the curved graph b in 17a.
18. When playing a game, when you beat a level you are rewarded for recognizing a pattern, To beat the next level, you have to recognize a more difficult pattern. In a math problem, you may have two or more steps which are like levels. You may have to recognize ("beat") increasingly more difficult patterns, from the expression level to the equation level, to the system of equations level, to the feasible/practical level, in order to solve the problem.
Homework for 8-30: page 12; items 1, 2, 3, 4, 5, 6
Hint: Put labels into the blank spaces at the tops of the columns.
Hint for item 5: The graph shown does not start at (0, 0).
Notes on the hw for today, 8-29: page 11, items 17a, 17b, 18
17a. Graph b reflects the intended design model for earning levels. The upward curve shows that you don't just get "more" for getting to the next level, it shows you get "more on top of more", or an increasing, instead of constant, reward.
17b. From the table on page 4, the columns "# of squares added" and "perimeter" look like 17a, straight graph a. The column "total area" looks like the curved graph b in 17a.
18. When playing a game, when you beat a level you are rewarded for recognizing a pattern, To beat the next level, you have to recognize a more difficult pattern. In a math problem, you may have two or more steps which are like levels. You may have to recognize ("beat") increasingly more difficult patterns, from the expression level to the equation level, to the system of equations level, to the feasible/practical level, in order to solve the problem.
Friday, August 26, 2011
Math 9 assignment for Monday 8-29; notes from SBT pages 6-11
Homework for 8-29: page 11, items 17 and 18
9b. total area is L^2 which means L squared
10a. the graph is a line with a slope of 2
10b. the graph a line with a slope of 4, and you run out of room at the top
10c. the graph is not a straight line
13., 14., 15., 16:
a square is missing a smaller square
area of this level (the current level) is L squared
area of the previous level uses the L from the previous level
in math, "previous" means minus 1
if I am talking about level 42, the previous level is 42 minus 1 = level 41
if I am talking about level q, the previous level is q minus 1 = q - 1
area of the previous level is ( L minus 1 ) squared = ( L - 1 )^2
this level's area minus previous level's area = L^2 minus (L - 1)^2
the number of squares addes = L^2 - (L - 1)^2
9b. total area is L^2 which means L squared
10a. the graph is a line with a slope of 2
10b. the graph a line with a slope of 4, and you run out of room at the top
10c. the graph is not a straight line
13., 14., 15., 16:
a square is missing a smaller square
area of this level (the current level) is L squared
area of the previous level uses the L from the previous level
in math, "previous" means minus 1
if I am talking about level 42, the previous level is 42 minus 1 = level 41
if I am talking about level q, the previous level is q minus 1 = q - 1
area of the previous level is ( L minus 1 ) squared = ( L - 1 )^2
this level's area minus previous level's area = L^2 minus (L - 1)^2
the number of squares addes = L^2 - (L - 1)^2
Thursday, August 25, 2011
Math 9 homework assignment for 8-26
Springboard textbook, page 7, item 10, pick one of the three graphing activities a., b., or c. and plot the points required. You will need a completed table from page 4, item 1.
Reflect on our discussion of why we use a blog:
To save _________ .
To actually use _______________ in the classroom and at home.
To build a study __________ that we can share.
So the teacher can include things we talked about that day in class for our ___________ ________ .
To model the way studying and note-taking will be in _____________ .
Reflect on our discussion of why we use a blog:
To save _________ .
To actually use _______________ in the classroom and at home.
To build a study __________ that we can share.
So the teacher can include things we talked about that day in class for our ___________ ________ .
To model the way studying and note-taking will be in _____________ .
Word wall 8-25
educated guess - attempting to find an answer by applying additional knowledge, mathematics, and research.; better than a blind guess or a flip the coin guess.
expense - the cost of doing something or getting something.
extensive - done with more detail, more preparation, more resources, or better tools. Remodeling a kitchen is more extensive work than fixing a faucet.
hypothesis - an educated guess that is designed to be tested.
incidentals - small expenses that are unexpected or that are not planned for, such as bus fare, snacks, tips.
linear programming - the "programming" is a rigorous procedure for mathematically allocating resources; the "linear" refers to modeling processes and relationships with equations of the form y = mx + b or Ax + By = C
predict - to make an educated guess about a quantity or a behavior as you extend a table of data or extend a time frame.
expense - the cost of doing something or getting something.
extensive - done with more detail, more preparation, more resources, or better tools. Remodeling a kitchen is more extensive work than fixing a faucet.
hypothesis - an educated guess that is designed to be tested.
incidentals - small expenses that are unexpected or that are not planned for, such as bus fare, snacks, tips.
linear programming - the "programming" is a rigorous procedure for mathematically allocating resources; the "linear" refers to modeling processes and relationships with equations of the form y = mx + b or Ax + By = C
predict - to make an educated guess about a quantity or a behavior as you extend a table of data or extend a time frame.
Math Skills fraction and decimal equivalents
Recognition of common fraction and decimal equivalents
½ = .5 | 2/2 = 1.00 |
1/3 = .333 . . . repeats | 2/3 = .666 . . . repeats | 3/3 = 1.00 |
¼ = .25 | 2/4 = .5 | ¾ = .75 | 4/4 = 1.00 |
1/5 = .2 | 2/5 = .4 | 3/5 = .6 | 4/5 = .8 | 5/5 = 1.0 |
1/6 = .166 . . . | 2/6 = .333 . . . | 3/6 = .5 | 4/6 = .666 . . . | 5/6 = .833 . . . | 6/6 = 1.0 |
1/8 = .125 | 2/8 = .25 | 3/8 = .375 | 4/8 = .5 | 5/8 = .625 | 6/8 = .75 | 7/8 = .875 | 8/8 = 1.0 |
.1 | .2 | .3 | .4 | .5 | .6 | .7 | .8 | .9 | 1.0 |
Unacceptable testing behavior
You will get a YWLCS demerit if you do any of the following during a test, benchmark assessment, or diagnostic assessment:
Not having a pencil.
Talking to other students.
Reading out loud.
Asking for or giving assistance on a question.
Asking for a calculator.
Not following instructions.
Arguing with a proctor (test administrator).
Multiple choice tests are an essentail part of schooling. You will take them to get ready for college, you will take them to get into college, you will take them to qualify for courses in college, and you will take them to qualify for employment. We administer the tests not just to evaluate your skills, but to expose you to a proper and rigorous testing environment.
If you display unacceptable testing behavior beyond the math skills class, you may be asked to leave the room, thus forfeiting a chance to be evaluated, and possibly losing money (test fees) and time (you'll have to wait months for a testing date).
I wrote demerits for some students during Math Skills testing today. I encourage students to show leadership by giving proper respect to the testing process.
Not having a pencil.
Talking to other students.
Reading out loud.
Asking for or giving assistance on a question.
Asking for a calculator.
Not following instructions.
Arguing with a proctor (test administrator).
Multiple choice tests are an essentail part of schooling. You will take them to get ready for college, you will take them to get into college, you will take them to qualify for courses in college, and you will take them to qualify for employment. We administer the tests not just to evaluate your skills, but to expose you to a proper and rigorous testing environment.
If you display unacceptable testing behavior beyond the math skills class, you may be asked to leave the room, thus forfeiting a chance to be evaluated, and possibly losing money (test fees) and time (you'll have to wait months for a testing date).
I wrote demerits for some students during Math Skills testing today. I encourage students to show leadership by giving proper respect to the testing process.
Recognize the distributive property and "undistribution"
After distribution,we got these expressions:
a. 3(x) + 3(8)
b. -10y + xy
c. 6w + 9z
Write the expressions before the distributive property was applied.
Hint - distribution means something outside the parentheses was shared in multiplication by two things inside the parentheses. When we undo a distribution ("undistribute" or factor) we move something that multiplies from two position inside the parentheses to one psoition in front of or outside the parentheses.
a. 3 ( x + 8 )
b. y (-10 + x )
c. 3 ( 2w + 3z )
a. 3(x) + 3(8)
b. -10y + xy
c. 6w + 9z
Write the expressions before the distributive property was applied.
Hint - distribution means something outside the parentheses was shared in multiplication by two things inside the parentheses. When we undo a distribution ("undistribute" or factor) we move something that multiplies from two position inside the parentheses to one psoition in front of or outside the parentheses.
a. 3 ( x + 8 )
b. y (-10 + x )
c. 3 ( 2w + 3z )
Wednesday, August 24, 2011
Skills 9 Number categories notes from 8-23
Natural numbers | We counted objects in nature 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, . . . many |
Whole numbers (add the thing with the “hole”) | We invented zero to represent what is left when all is taken 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, . . . |
Integers | We invented negative numbers to represent what things or money we owe . . . , -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, . . . |
Rational numbers | Add fractions to the integers F R A C T I O N R A T I O Integer over integer except you can’t use 0 in the denominator Integer / integer An integer divided by an integer ½, 4/3, -5/-5 0/-6 2/43 |
Decimals are rational | .2 = 1/5 .375 = 3/8 .94 = 94/100 Decimals are ratios with ten or a power of ten in the denominator |
Rational decimals can repeat | Repeat means the same digit or set of digits repeats forever going right 1/3 = .333333333333333333333333333333333333333333333333333… |
Rational decimals can terminate | Terminate means to come to an end when going right 7/8 = .875 |
All integers are rational | 1 = 7/7 3 = 27/9 10 = 10,000/1,000 4.0 = 40/10 0 = 0/17 |
Not all rationals are integers | The ratio 5/12 can’t be simplified into a number |
Irrational | A decimal that doesn’t repeat, and it never ends going right Pi = 3.14159. . . . . Most square roots SQRT(3) SQRT (17) Many sides of triangles |
1-1 For the Love of the Game hw for 8-25
Math 9 Algebra 1 homework due Thursday 8-25
Springboard textbook (SBT) page 4, 5, 6, items (problems) 3 through 9
expression | Variables operating with numbers, but no equal sign |
equation | Has an equal sign in the middle Has an expression on the left and an expression on the right |
Define variables | Use the word “let” to assign a variable to a thing or quantity |
I thought you multiply to get perimeter | Perimeter is length of the fence that goes around an object. If you make squares out of sticks, you add all the sticks on the outside edge of the square. |
Characteristics of a pattern | Example: 2 4 6 8 . . . Something connects things in a pattern You do something consistent from one thing to the next You can use a pattern to figure out more things or to predict more things |
HW hint for 7b, 7c, 8
Let L = the level number
Let S = the number of squares added
S = (L – 1) + L
S = L – 1 + L
Combine terms and you get _______________
or
S is an odd number, and you make odd numbers by adding 1 to even numbers
You can make an even number from any integer by ______________________
The expression _____ always gives you an even number
Graphing age and height
Math 9 Algebra 1 homework for 8-24
Find 7 to 10 people. For each person, write down their age in years and months, and their height in inches. Make a graph with age along the x-axis and height along the y-axis. Plot the age and height information as dots showing ordered pairs of numbers
Hints:
“Plot a point” means use age for x and height for y.
If you are fourteen years old and your birthday was in May, it has been 3 months since your birthday (June, July, August) so you are 14 years and 3 months old.
If you are 5 feet 3 inches tall, 5 times 12 inches per foot = 60 inches, and add the other 3 inches, so you are 53 inches tall.
Thursday, August 18, 2011
Parents Meet Teachers Night Micro-Lesson
A circle has a radius of 10 meters, and the length of the given chord PQ is 16 meters. If O marks the center of the circle, what is the length of segment OA?
A. 2(sqrt3)
B. 6
C. 12
D. 4(sqrt21)
E. 36
B. 6
C. 12
D. 4(sqrt21)
E. 36
Saturday, August 13, 2011
Mirth Math Inspire
Welcome to 9th grade math at YWLCS. I look forward to meeting parents on Thursday, August 18.
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