Jacob W. by Jake Woodall

Integers and Expressions

jakewoodall08 — 2016-07-18 19:56:15 UTC

When adding negatives you look at the signs and if they are the same sign you add then you put the sign. If the signs are different the numbers cancel eachother out so the highest numbers sign will be the same sign as your answer. Adding negatives=subtraction. For example (-12)+14=2.
When subtracting integers we don't subtract we add the opposite. Also the sign of the bigger number is the sign for the answer. Subtracting negative=adding. For example 4-(-2)=-6 (4+2=6).
When multiplying and deviding integers we use the sleeping dog method. We cover up the sign for integers we are multiplying/deviding. The one that is remaining is the sign for your answer. If you have more than 2 numbers you just do 2 at a time. For example 2 (-6)=12 and -24 ÷ -6= 4.
An integer is a whole number that can be positive, negative, or zero. A synonym 4 integer is unit. They are related because they both represent numbers.
An algebraic expression is a mathematical phrase that can consist of ordinary numbers and variables. For example- (-4)÷(-2). The answer to that expression is positive 2.
A variable is an amount represented by a alphabetical letter that may change within the context of a mathematical problem. And example of a variable is 6Y+4, if Y=2 then the answer to this problem is 16.
Absolute value is the opposite of a number without regard to its sign. An example of absolute value is |3|, the absolute value of 3 is negative 3. (-3).

Integers Grade - 67%

gracynkrajewski — 2016-08-08 15:41:25 UTC

- Absolute value definition and example is incorrect. It is the distance a number is from 0. The absolute value of a number is always positive.
- 3 items were required for each of the 4 terms, not 2.

Operations with rational numbers

jakewoodall08 — 2016-08-27 14:24:55 UTC

(Question 1) To convert a fraction to a decimal you just divide the numerator by the denominator. For example 1÷2=0.5 therefore 1/2=0.5. To convert a decimal to a fraction you must write the decimal divided by 1 like this: decimal/1. Then you multiply both the numerator and the denominator by 10 for every number after the decimal point. This is also true if there are 2 numbers after the decimal then use 100 and also with 3 then use 1000. Lastly you just simplify/reduce the fraction. (Question 2) An example of this is: 0.5/1, 0.5×10=5 and 1×10=10 therefore you would get 5/10 which can be simplified to get you final answer of 1/2. ( Question 3) When you multiply with decimals you multiply as if the decimals are not there and once you have the multiplication answer you count how many numbers were behind the decimals and you move the decimal point that many times to the left in your answer. This is an example of multipying with decimals: 1.5×0.3, you would change it to 15×3=45 then you would see that you have 2 numbers behind the decimal points and you would take 45 and move the decimal 2 times to the left like this 45-> 4.5->0.45 and 0.45 would be your final answer. (Question 5) To convert a mixed number to a improper fraction you must multiply the whole number by the denomonator and then add the numerator and your total to that will be your numerator and you keep the denominator the same. For example in 2 1/2 you would multiply 2×2=4 and 4+1=5 so 5 is your numerator and 2 would still be your denomonator. So your final answer would be 5/2. A common denomonator is a shared multiple of the denomonators of 2 or more frations. An example of a common denominator would be 5/10 and 2/10, and example of what WOULD NOT be considered a common denominator would be 5/3 and 3/8 because 3 dosent go into 8 equally. You can have a common denominator and a improper fraction/mixed number but not always. Equivilent fractions are fractions that look different but show the same ammount. Equivilent fractions can be made by multiplying the denomonator and the numerator by the same number. An example of an equivelent fraction is 1/2 and 5/10 an example of something that IS NOT an equivelent fraction is 1/2 and 3/4. An improper fraction is a fraction in which the numerator is larger than the denomonator, for example 5/2, NOT like this 2/5. Improper fractions can be simplified into mixed numbers. A mixed number is a whole number followed by a fraction such as 2 4/7, NOT like 18/7 (thats an improper fraction). You can turn a mixed number into a improper fraction by multiplying the whole number by the denomerator and then adding the
numerator.

Rational Numbers Grade - 94%

2016-08-29 15:22:37 UTC

- Question 2 is incomplete. An example is given, but you don't explain how to convert it.

Equations

jakewoodall08 — 2016-10-10 15:49:00 UTC

Essential Question 1
step 1: make the repeating decimal into a variable such as X. step 2: find the repeating digits in the repeating decimal. step 3: put the repeating digit(s) to the left of the decimal point. step 4: put the repeating digit(s) on the right side of the decimal point. step 5: Subtract the left sides of the two equations. Then subtract the right sides of the two equations
. As you subtract, just make sure that the difference is a positive number for both sides.
For Example: 0.33333
0.33333 = X
10X=3.3333
X=0.33333
your equations are: 10X=3.3333 and X=0.33333.
But you are not finished, you have to subtract X from 10X.
So basically it's 10X-X=9X and you have to subtract from both sides so the 0.33333s cancel out so you just have two 3s. Then you have to solve for X so you divide both sides by nine: 9X/9=X and 3/9= 3/9, so you get three ninths (3/9) as you answer.

Essential Question 2
step 1: first you have to find the closest perfect square that is less than your number. step 2: you have to find the nearest perfect square that is greater than your number. step 3: you can figure out that your number is greater than the greatest square root that is less than your number. you can also discover that the closest perfect square larger than your number has a larger square root. So then you know your number has an integer in between your other numbers integer's. For example: say my number is 27. The nearest perfect square that is less than 27 is 25 being 5 squared. The nearest perfect square that is greater than 27 is 36 being 6 squared. Therefore since 27 is in-between 25 and 36 I can conclude the 27 is in-between 5 squared and 6 squared.

Square Root
A number that makes a specific amount when multiplied by itself. An example of a square route is 25 = 5 squared because 5 multiplied by itself is equal to 25. The opposite of finding square root is squaring a number.

Repeating Decimal
A repeating decimal is a decimal with a repeating pattern. A repeating decimal can also be known as a number with a decimal with a pattern that repeats forever. An example of a repeating decimal is 0.55555.

Cube Root
A number that produces a different number when cubed. When doing cubed root you just have to figure out what number can be cubed to equal your number. If your number is not a perfect square then you can estimate it by discovering its nearest larger and smaller perfect squares. Cube root is related to square root because it is basically the same thing except the numbers are cubed instead of squared. A synonym for cube root is multiplying a number by itself 3 times (cubing it) to equal a cube.

Additive Inverse
The additive inverse is the distance a number is from zero. A synonym for additive inverse is the opposite of your number. An example of an additive inverse is say your number is 15, the additive inverse of 15 is negative 15 because you have to subtract 15 to get Zero.

Multiplicative inverse
The multiplicative inverse of a fraction is found by flipping it upside down. An example of this is say your fraction is 1/5, then your multiplicative inverse is 5/1 (5). A synonym for multiplicative inverse is multiplicative inverse property.

Equations Grade - 95%

2016-10-11 15:16:44 UTC

-Missing explanations when giving synonyms.

Inequalities

jakewoodall08 — 2016-10-23 21:26:17 UTC

Essential question 1. You flip the inequality sign when the variable has a negative in front of it. An example of this is -8/X is greater than or equal to -32. We know the answer to this is X is greater than or equal to 4.
3 Descriptive words per symbol-
Starting with less than, other words you can use are below, fewer, or smaller. An example statment for less than would be, "I have fewer than 5 pencils." And here is my number line for that exmple;
<-○
|---|---|
4 5 6
Next we have greater than, other words for greater than are: above, more than, larger than, bigger, over, and exeed. An example of a greater than statement would be i have more than 3 peices of candy. My number line for greater than is:
○->

|--|--|
2 3 4
Next we have less than or equal to, a few synonyms for that is no more than, at most, below or equal to, not greater than, not exeeding (doesn't exeed), up to, maximum, and limit. An example of this is 8 apples weighs no more than 10 pounds. The number line for this looks like:

<-●

|---|---|
7, 8, 9
And lastly we have greater than or equal to, also know as: at least, no less than, above or equal to, and minimum. An example of this is i have no more than 6 games. The number line 4 this is:
●->

|---|---|
5, 6, 7.
Vocabulary-
Soulution set,
A solution set is a set of answers (values) that have potential to be the solution (make an inequality correct/true). An example of a solution set for the inequality X>5 is 6, 7, and 8, not -2, 3, and 1. In my opinion the opposite of a solition set is an answer because you have 1 solution instead of several.
Inequality-
An inequality is the relationship between 2 expressions that are not equal. An example of an inequality is X>13. In an inequality you do not use equal signs so that is how it differs from equasions.

Inequalities Grade - 100%

2016-10-31 15:38:00 UTC

- An inequality symbol is flipped when you multiply or divide both sides by a negative. Your answer is still correct, but make sure you know that those are the two operations.

Proportional Reasoning

jakewoodall08 — 2016-10-31 21:09:25 UTC

Essential Question 1,
The 4 types of slope are positive (/), negitive (\), zero (-), and undefined (|). Positive slope means the slope is incraseing. Negitive slope means slope is decreasing. Zero slope means just a change on the X axis, and undefined slopes are just change on the Y axis.

Essential Question 2,
The different parts of a linear equation are the y cordinant (y), the slope (m), the x intercept (x), and the y intercept (b). So when you write out your equation it looks like this: Y=MX+B.

Essential Question 3,
For 2 figures to be simlar the only difference (not required) is size. (You also may have to rotate the figure.) An example of this is ● and • that.

Vocabulary Word 1, (unit rate)
Unit rate is comparing two different numbers when they are combined with each other. An example of unit rate would be like 45 miles in an hour or it would be 45 miles per hour. A synonym for unit rate would be a percentage.

Vocabulary word 2, (proportion)
A proportion is a name we give to equivalent fractions or 2 ratios that equal the same thing. An example of a proportion is 1/2=2/4. And an antonym for proportion is an unbalance, or unequal.

Vocabulary Word 3, (scale factor)
A scale factor is the ratio of any 2 corresponding lengths in 2 similar geometric shapes. Here is a link to a website with an example on it and also it is very good on information too. A synonym for scale factor is multiplier.

Vocabulary Word 4, (constant of proportionality)
A constant of proportionality is when one variable is always the product of the other and a constant. An example of this is X=KY but only if X and Y are proportional. A synonym for constant of proportionality is poportionality constant, or the coefficient of proportionality.

Proportional Reasoning Grade - 71%

2016-11-18 16:34:07 UTC

- Missing pictures and values for slope essential question.
- x in the equation represents the x coordinate, not the intercept.
- Similar shapes also have congruent corresponding angles and proportional corresponding sides. Missing an example as well.
- Antonym and synonyms require an explanation to receive full credit.

Geometric Properties

jakewoodall08 — 2017-02-07 20:50:05 UTC

Adjacent angles- Adjacent angles are angles that are next to each other. For example, if I had a 90 degree angle named ABC and within there is a 45 degree angle named JBC and ABC are adjacent angles. Here is a picture giving an example of adjacent angles. http://image.tutorvista.com/content/feed/tvcs/adjacent20angles20Theorem202.GIF

Complementary angles- complementary angles are two angles that add up to 90 degrees. For example two 45 degree angles put together is a 90 degree or complementary angle, because 45+45=90. Here is a link to an example picture. https://d2gne97vdumgn3.cloudfront.net/api/file/MctYSJdSSE6NHboFp39J

Supplementary angles- 2 angles whose sum reach 180 degrees. For example, two 90 degree angles put together is a supplementary angle because 90+90=180. Here is a link to an example picture. http://www.softschools.com/math/geometry/topics/images/supplementary_and_complementary_angles_image1.png

Vertical angles- vertical angles are 2 angles opposite each other when 2 lines cross, they also share the same vertex. A synonym for Vertical angles is upright angles because vertical and upright have very similar meanings. Here is a link to a picture of vertical angles. https://www.mathsisfun.com/geometry/images/vertically-opposite.gif

Triangle sum theorem- the triangle sum theorem is that three interior angles add up to 180 degrees. An example of the triangle sum theorem is two 45 degree angles and a 90 degree angle if they are all interior angles and u add them all together then u get 180 degrees. Here is an example picture showing what i'm explaining.
https://nzmaths.co.nz/sites/default/files/images/Simple1_2.jpg

Corresponding angle- angles that occupy the same relative position at each intersection where a straight line crosses 2 others. If the 2 lines are parallel, the corresponding angles are the same. An example of corosponding angles is if there was a 45 degree angle crossing through 2 parrallel lines. Here is an example picture of corosponding angles. https://i.ytimg.com/vi/fhvR6lzy_jg/hqdefault.jpg

Geometric Properties Grade - 89%

2017-02-16 18:29:12 UTC

- upright does not have anything to do with vertical angles.
- example for corresponding angles does not make sense.

2 and 3 Dimensional Shapes

jakewoodall08 — 2017-04-21 20:04:53 UTC

2d/3d Grade - 100%

Essential Question 1: For inscribed shapes you must find the area of both shapes and subtract the inside shape area from the outside shape area. With composite shapes you add the areas of both simple shapes that make up the composite shape. The difference is finding the extra area instead of finding the total area. For example with composite shapes like a trapezoid with a triangle and a rectangle put together. The height of the rectangle and triangle are 3 and the length of the rectangle is 4, and the base of the triangle is 2. So the area of the triangle is 3u^2 and the area of the rectangle is 12u^2 so you add 12u^2 and 3u^2 and you get your area of your trapezoid as 15u^2. For the inscribed figure say you have a square inside of a circle, the radius of the circle is 4 and the length of the square is 3. So we find the area of the circle (3.14 x radius^2) which is 50.24u^2. Then we find the area of the square (base x height) which is 9u^2. Then we subtract the area of the square from the area of the circle, and we get 41.24u^2 which is the area not taken up by the square inside the circle.
Essential Question 2: (for rectangle and triangle) When you multiply the dimensions by the scale factor(s) then you multiply your scale factors together to get what your old area was multiplied by to get your new area. For example with rectangles, say you have a 2 x 4 and 4 x 8 rectangles. The scale factors in this case are both 2, so 2 x 2= 4. This tells us that our 4 x 8 is 4 times the area of our area on our 2 x 4. Now for the triangles. Say we have a triangle with a base of 3 and a height of 4, we also have a triangle with a base of 6 and a height of 8. The scale factors of the base and height are both 2 and if we multiply 2 x 2 then we get 4 which is what our area scale factor is (the new area is 4 times the size of the old area).
Area of a Triangle: (Base x Height)/2. For example (4 x 5) / 2 = 10u^2 as your area.
Area of a Trapezoid: Area= (Base 1 + Base 2)/2 x Height. For example (6 + 9) / 2 x 5 = 37.5u^2.
Volume of a triangular prism: 1/2 (base x height) x Length. For example 1/2 (2 x 7) x 6= 42u^2.
Volume of a Sphere: Volume= 4/3 x PI x radius^3. For example 4/3 x 3.14 x 2^3= 33.49u^3
Surface Area of a Cylinder: 2 x PI x Radius^2 + PI x Diameter x Height. For example 2 x 3.14 x 4^2 + 3.14 x 8 x 3= 175.84u^2.

Area of a Rectangle: Base x Height. For example 4 x 3 = 12 u^2.
Area of a Circle: PI x Radius^2. For example 3.14 x 3^2 = 28.26u^2.
Volume of a Cylinder: Volume= PI x Radius^2 x Height. For example 3.14 x 3^2 x 9= 254.34u^3.
Volume of a Square Pyramid: length x Width x Height / 3. For example (3 x 3 x 8) / 3 = 24u^3.
Surface Area of a Square Pyramid: Base^2 + (2 x base x height). For example 3^2 + ( 2 x 3 x 10)= 69u2.
Area of a Parallelogram: Base x height. For example 3 x 3 = 9u^2.
Circumference of a circle: PI x Diameter. For example 3.14 x 2= 6.28u.
Volume of a Cone: Volume= (PI x Radius^2 x Height) /3. For example (3.14 x 3^2 x 9) /3= 84.78u^3.
Triangular Prism Surface Area: Base x height + Height(side 1+side 2+side 3). For example 3 x 4+(6x3+6x3+6x3)= 66u^2.
Rectangular Prism Surface Area: 2(L*W+L*H+W*H). For example 2(3 x 2 + 3 x 6 + 6 x 2) and that would give us our surface area of 72u^2.

Exponents and Scientific Notation

jakewoodall08 — 2017-05-01 20:05:12 UTC

Grade - 97%
- The exponent applies to everything inside the parenthesis.

Essential Question 1: They can determine whether the answer is negative or positive. For example, (-3)^2 vs. -3^2 the difference between them is that with parentheses the answer is positive, and without parentheses your answer is negative.
Essential Question 2: We use powers of ten in writing numbers in scientific notation because the base ten decimal system. The ten tells you that you aren't changing the digits but you are changing where the decimal is with the exponent on the ten.
Base: A base is the bottom value of the exponent that is multiplied by itself when the exponent is in expanded form. A synonym to a base would be a bottom of something (in this case it is a value). They are alike because the base is the bottom of the exponent. A example of a base would be in bold: 9.099 x 10^8. In this case our base is 10.
Exponent: An exponent is a number of times you multiply the base by itself in expanded form. A synonym for an exponent is a power of a number (how many times the number is multiplied by itself). An example of a Exponent would be in bold: 8 x 10^2. In this case the 2 is our exponent.
Zero Exponent: a zero exponent is when the base has an exponent of zero. When the exponent is zero the simplified answer will always be 1. For example 10^0 or 5^0, they both equal 1. A non example of a zero exponent would be 8^1 because that would equal 8 not 1. A Correct example would be 8^0 which equals 1.
Scientific Notation: Using base 10 and exponents to change the length of a number by moving the decimal. For example you could take 867,000,000,000 and convert it to 8.67 x 10^11 because you moved your decimal to the left 11 times so your exponent increased by 11. An example of non scientific notation would be 36.8 x 10^4, A correct example of scientific notation would be 3.68 x 10^5 because you cant have a number with 2 or more digits in front of the decimal.