# Distance, Rate, and Time Learning Log

Distance rate and time are all units of measuring somethings rate, where rate is the actual rate. In equation, the rate is distance over time, or r = d/t, where r is rate, d is distance, and t is time. For example, say you have a mouse that can run 10 feet every  7 seconds, the rate would be 10/7, so the rate would be about 1.428 feet per 7 seconds, so the unit rate would be 0.204 ft every hour.

# Multiplication Equations Learning Log

Solving an equation using multiplication is really easy, depending on the equation. For example, say you have the problem

5/7d = 15

You know you need to multiply d with 5/7 to get 15, so you would use multiplication. You multiply the denominator (7), with 15 in this problem, and your result is 105. So that is your answer, d = 105. Lets Check, 105/7 = 15, you can go check on a calculator. Basically, you use multiplication to solve a problem when you have a numeral less than the final result, and you need to multiply the less numeral with a fraction. However, there is another way to solve the 5/7d = 15 problem. It’s addition. 5/7 + q = 15, s if you calculate, q is 14 2/7.

# Representations, Center, Shape, and Spread of Data Learning Log

Different types of graphs exist, and each of them shows things better than others. Maximum, Minimum, Mode, Range, Median, and Mean, all of them are shown clearly in some and not s clearly on others. For example, a box plot shows the exact Median always no matter what because it is based around it, while a steam and leaf plot can show the maximum minimum and range clearly, and still a histogram can show a sort of idea of where all the data in centralised, the sort of “mode”. For showing shape, instantly throw the box plot out, because it doesn’t show shape. Anyways, a histogram and a steam and leaf plot both show the shape of the information, where the stem and leaf plot is basically a histogram with bins of 10.

# Mean Absolute Deviation Learning Log

The Absolute Deviation is the Mean of the distance each information piece is from the informations mean. I mean, say you have the information 11, 12, 14, 15. The mean is 13, so we need to find the distances. 11 and 15 are 2 numerals away from 13, and 12 and 14 are online 1 numeral away, so we add that up. 1+1+2+2 = 6/4 = 1.5. So 1.5 is the Absolute Deviation for that information. This can help to tell how dynamically far away each information piece can be, like if we added the information 1 and 25, which are both 12 away from 13, it would become 30/4 which would become 5, because the information is a lot more dynamic.

# Mean and Median Learning Log

There is something called the Mean, and something called the Median. And I don’t mean Mean, in math, the Mean means average. The Median, however, is just the center of all the information, it’s the information that stands in the middle of all of the information. Both, can show the middle of the information, but there are times where it is better to use one than the other and times where both are extremely close to each other. For example, say you have the information :

11,12,13,13,13,17,17,19,21

In the set of information above, you should be using the median, which is 13, because if you used the Mean, it would be lower than 16 because 11,12,13,13 and 13 of the question would partially lean it towards one direction, making the Mean lower. However, in other informations, like these :

20,20,21,21,21,22,22,23,23

It’s better to use the mean because the median would be 21, which you know is not the average of all the information. So using the mean would be a better substitute to find the “typical” information.

# Distributive Property

Distributive property is showing an expression without a parentheses, and instead multiply the factor with each expression inside the parentheses. For example in the expression 4(7x+6) the distributive property would multiply 7 by 4 and 6 by 4, so the new expression would be 28x + 24. The expressions are equivalent, just shown in different “formats”.

# Inverse operations

Inverse operations are basically the opposite of the original operation. For example, if you add add “X”, the inverse operations is to subtract “X”. Similarly, it also works vice versa. Multiplication and division are also inverses. Inverse operations undo the previous operations, making both operations cancelled from the question. Follow the examples below:

10 +4 = 14 – 4 = 10

See above how the subtraction undid what the addition did to the original number. That is called inverse operations. A multiplication and division inverse operation is:

2*4 = 8 ÷ 4 = 2

See how the division undo’s the multiplication? This works the other way round too. You subtract then add, or divide then multiply. That, is inverse operations.

# Using a Super Giant One Learning Log Using  a SUPER GIANT ONE is really quite simple. It’s easier to teach while showing an example than to explain it.

Say you want to divide 5/6 by 11/17. You would confusingly represent the problem as 5/6/11/17 (The red line is the divide line, while the black line is part of representing the fraction). You would want to make the denominator 1, so you find the reciprocal of the denominator fraction, which in this case is 17/11. Then you would show it confusingly, just try to follow:

5/6     x  17/11 = 85/66                                                                                                                                                                                                                                                                 11/17  x 17/11 =     1

If you have followed above, the denominator should always equal 1, and the numerator is the answer to the problem. This is because any number divided  by 1 has a result of the same as the original number. So our answer is 85/66, or 1 and 19/66. You always find the reciprocal of the denominator because when you multiply a fraction by it’s reciprocal, it will always have a result of one, meaning all you have to do is multiply the numerator with the reciprocal of the denominator.

# Algebra Tiles Learning Log

Today in math we used algebra tiles to learn about variables and showing algebraic expressions. We used algebra tiles. We had small unit tiles, tiles that equal 5 units, an x tile, and x2 tiles. We used these tiles to show algebraic expressions, like 1*3+5+3x+2x2 . Our feeble learnings let us understand how algebraic equations worked.