MAT 280 Mind Map

Professor Miltenberger taught us a very valuable lesson while juggling around the classroom and talking to us. By the time he finished talking to the class ( after walking around us row by row), he asked us to juggle with the 6 cubes he gave us at the beginning of class. Most of us were puzzled and did not know how to juggle ( even though he literally showed us how). But it was a fun and quirky way to start the class and cool first day lesson.

Un - UnderstandDev - Develop a planCar - Carry out the planLO - Look back

We were given 3 categories labeled: Super Easy, Just About Right, and Are You Crazy? and 8 math problems. We were to solve each problem and categorize each as super easy, just about right, or are you crazy based on the level of difficulty we thought it was.These problems included...3x + 5 = 6x – 133/5 + 1/57.76 – 3.9-17 + 43Find 60% of 30    (253) (45)24 – 3/72/3x + 1/5 = 7/10

In class for our group activity we were asked in miles, how long/ tall would 1 billion blocks be? The way we tried to solve this problem as a group was by first, finding the measurement of the blocks. We were given 4 blocks, and assumed (from our eyes view) that 2 of the 4 blocks equal 1 inch. So from there we made a list trying to figure out how many feet are in a mile. None of us knew that answer, so that is where we got stuck, but we established that (from eyes view) 2 blocks = 1 in. 12in. = 1 ft. 1yd. = 36 in./ 3 ft. and our last step was trying to figure out how many feet are in a mile, but we were unfortunately unable to finish the problem before running out of time.

As a class/ small groups we played Buzz. Buzz is a game in which you count up from 1, and once you hit the number 7, multiples of 7, and a number with 7 in it, you say buzz instead of the number.EX: 1,2,3,4,5,6,buzz,8,9,10,11,12,13,buzz,15,16,buzz... 68,69,buzz, buzz, buzz...and the next class we spiced it up a little bit and added bizz to the buzz. We would say bizz for every multiple of 11 and still say buzz for every multiple of 7.EX: 1,2,3,4,5,6,buzz,8,9,10,bizz,12,13,buzz... 20,buzz,bizz,23

This is where we began our journey on learning about bases. Professor Miltenberger told us a FAKE story about how his dog learned how in order to earn treats he would shake his paw in bases. And we did a homework assignment to continue this lesson in which we had to figure out how many treats each animal/Martian would count in their bases.

unit- an individual number/ unitlong- A certain amount of units based on the base (cannot exceed 10)EX: 22 base 7 = 7 units per long ( ///. 3 longs, 1 unit)flat- A collection of longs determined by the base.EX: 113 base 5 (///// ///// ///// ///// // ...) 5 longs of 5 units per flat

finding the number of units in a numberMultiply the number of longs by the Base and adding the units

requires "upside down" divisiondividing the number by it's baseEX: 69 base 8 (divide 69 by 8)

We were shown how to add and subtract different bases and different methods on how to do so including the scratch method and compatible numbers, and expanded form

EXPANDED FORM-a way of writing numbers to see the math value of individual digits.EX: 124 = 100+20+4

left to right is when you add the individual units of a big number.for example, when given a problem such as 347+256 you add them by first adding up the 300 and 200,next adding the 40 and 50, and last adding the 7 and 6. Once you find those numbers, you add them all together and get the answer of 603!

Now trade off is just how it sounds, you are trading off numbers to make your addition a bit easier.EX: 25 +36_i would trade 5 from the 6 in 36 and add them to the 25 making it a full 30 and leaving the bottom as a 31 and add from there so I would not have to carry any numbers making the addition easier.

friendly numbers are groups of two numbers that sendup with the same product after adding them up. like how 3+7 and 2+8 both = 10.for example: 23+12+17+2+24+18the 3 and 7 in 23 and 17 are friendly numbers as are the 2 and 8 in 12 and 18.

Lattice Addition is pretty much the same as the method for multiplication if not the same. You add each individual number to the one at the top or the bottom, depending on whether or not the result is a two or one digit number you place the first number or a 0 at the top half of the square and the 2nd or individual number at the bottom half. You add the digits all up from each square and whatever is left at the bottom is your final answer.

Multiplying by using tiles is pretty easy and fun. Say we get a broblem like 13(16). that means we draw out one horizontal long (10) and 3 units beside it (3) and vertically draw out one vertical long (10) and 6 units below it (6). 13 times 16. Once this diagram is drawn out where the units end (horizontally and vertically) you must draw a straight line down and to the side and make the units meet. leaving you with 1 flat, 9 longs, and 18 units, add them up and you end up with the answer of 208!

area model is a bit like lattice format wise. For every digit there is a square. Ex: 14(21)That would me 10+4 on top with a square under each and a 20 and a 1 on the left side. multiply the 10 and 20 (200) and then multiply 20 and 4 (80). There should be a 200 and 80 in the top 2 squares. Next multiply the 10 and 4 with the 1 leaving you with a 10 and 4 in the bottom squares. Add the top and the bottom (280+14) and you get the answer of 294!

Expanded is when you literally expand the numbers out.(ex: 300+40+7 plus 200+50+6)you add those numbers through long addition thus once again getting the answer of 603.

Expand the numbersEx: 324(65)300+20+4 60+5Multiply the 60 and the 5 and the bottom by each top number (300, 20, 4) add those numbers60(300) = 1800060(20) = 120060(4) = 2405(300) = 150060(20) = 1005(4) = 20add all of the numbers thus getting the answer of 21,060

5/12 + 7/10find two common multiple that goes into each denominator12= 2x610= 2x5now multiply the numerator and denominator of 5/12 by 5 and 7/10 by 6making the denominator of each faction 60.25/60 + 42/60and the answer will be 67/60 or 1 7/60

15 - 4/13step one: turning the 15 into a fraction14 13/1314 13/13 - 4/13step two: move the whole number off to the sidestep three: subtract 13/13 and 4/13 making it 9/13step four: bring back the 14 making the answer 14 9/13

5 1/4 x 4 2/7Step 1: use upwards multiplication on each fraction.step 2: multiply 4 and 5 and add the 1 making it 21/4 and do the same with the other fraction. multiply 4 and 7 and add the 2 making the problem 16/721/4 x 16/4find common multiples for the numerators to match the denominators3*7/4 x 4*4/7make long 1s when canceling out whole numbers.leaving you with 4 x 3which = 12

Divisibility Rules2- if last digit is even3- sum of digit is divisible by 94- if the last 2 digits are divisible by 4 the whole number is5- ends in 5 or 06- is divisible by 2 and 3 it is divisible by 68- last 3 digits are divisible by 89- sum of digits are divisible by 910- ends in 0

35/4Step 1: 4 goes into 35 8 timesso you write 8 off to the sideStep 2: subtract 32 from the 35 (while doing the subtraction above the fraction line) leaving you with 3.Step 3: with that remainder of 3, you use it to fill in the fraction. making the answer 8 3/4

Adding decimalswhen adding decimals, the decimals must line upFor example: if given the problem5.23 + 4.16when adding line up the decimals5.23+4.16_____9.39

Subtracting decimalswhen Subtracting decimals, its the same process as addition of decimals. the decimals must line upFor example: if given the problem9.73 - 4.51now line them up...9.73-4.51_______5.22

Multiplying Decimals(6.42)(4.2)round the whole numbers and multiply them(6)(4)24The answer will be something equivalent to 24

40% of $70turn the 40% to a 10%, and the 70 to a 7 (10% of 70)multiply each side by 4and theres your answer(should be 28)40% of $7010% = 7x X_4____4__40% = 28

(14)(21)for this problem we will be doing area models which are kind of like algebra tiles.14 = 10 + 421+ 20 =1So for each group of numbers we have a box (a 2x2 graph)the top of the graph will have 10+4 with a square under each and 20 + 1 on the left side. multiply the 10 and 20 (200) and then multiply 20 and 4 (80). There should be a 200 and 80 in the top 2 squares. Next multiply the 10 and 4 with the 1 leaving you with a 10 and 4 in the bottom squares. Add the top and the bottom (280+14) and you get the answer of 294!

EX:5-8+++++- - - - - - - --3EX:-5 using 9 tiles+ +- - - - - - --5EX: 2(3)two groups of 3+++ +++ +++EX:-7+4++++ - - - - - - --3

Keep,Change, ChangeEx: 2 - (5)+ sub - -12+ (-20)-8

EX:2(-4)2 groups of -4_ _ _ __ _ _ _-8

Least Common Multiple (LCM)A common multiple is a number that is a multiple of two or more numbers. Common multiples of 2 and 3 are 0, 6, 12, 18, ...EX:16=  2*2*2*224=  2*2*2*3We can multiply 16 by 3 (the only prime factor of 24 not shared by 16), to find the LCM: 3 * 16 = 48.

Greatest Common Factor (GCF)the greatest factor that is common to two or more numbers (they share it).EX:16=  2*2*2*224=  2*2*2*3There are three 2's common to both numbers, so 2*2*2 = 8 is the "greatest common factor" (GCF) of 16 and 24.

Finding which prime numbers multiply together to make the original number.EX: 24 6 * 4 2*3 2*22*2*2*3 = 24

+ + = ++ - = -- - = +- + + -

EX:36^6 6^ ^3 3 3 33*3*3*3 = 36

EX: 482 l 48 2 l 24 2 l 12 2 l 6 32*2*2*2*3 = 48

12 bars with 12 different colorseach color bar represents a number out of 12red- 1/12orange- 2/12 - 1/6yellow- 3/12 - 1/4neon- 4/12 - 1/3green- 5/12fusia- 6/12 - 1/2lavender - 7/12purple- 8/12 - 2/3light blue- 9/12- 3/4blue- 10/12 - 5/6brown- 11/12gray- 12/12 - 1

EX:13/ 14 > 9/10because its missing a smaller piece11/19 > 8/17because anchor 1/2 (half)

3 squares2/3 +1/4draw 2 squaressq 1: 3 bars going horizontally, and shade in 2 barssq 2: 4 bars going vertically, and shade in 1 barnext on each square, merge the bars, so that on the first and second squares there are bars facing both horizontally and vertically. (making each square have 12 internal squares)Lastly, re draw the square w/ 12 internal squares again, and fill in how many squares were filled each original model.sq 1 should have 8 squares shaded, and sq 2 should have 3 shaded, thus having 11 squares shaded in the 3rd square, making the final answer 11/12.

2 squaresEx:1/2 - 1/5sq 1: has 2 bars going horizontally, with one bar shadedsq 2: has 5 bars going vertically, with 1 bar shadednext on each square, merge the bars, so that on the first and second squares there are bars facing both horizontally and vertically. (making each square have 10 internal squares)subtract 2 squares from each side, making the answer 3/10

1 square(1/2)(3/4)one square with 2 horizontal lines in it (with one bar shaded in), and 4 vertical (with 3 bars shaded in), making the square have 8 internal squares.Now the squares that are double shaded are what make up the answer to this problem. 3 squares are double shaded, making the answer 3/8.