MTE280 Mindmap1

Bases are a system for counting numbers. There are many different bases. When I write the number 3 we assume that it is in base ten because there is no designated base. (This would be written as a subscript with the number of the base written out in English)Example: 28six

FLU stands for:FlatsLongsUnitsThese are used to groups numbers in their bases.Example:If you are in base five and you have 13 units, you would put the units in columns made up of five units. You would have 2 columns containing 5 units, and you would have 3 single units left over. Each column of 5 units makes 1 long. Each left over unit is 3.The number that makes is 23 because you have 2 longs and 3 units left over.

If you have your long, you determine what base you are in by finding out how many units with fit in that long. You can stack them up next to the long to figure this out.

Downward division is a way to convert from base ten to another base. The method is similar to long division but it works a little differently. You use the normal long division symbol and flip it upside down. The base you want to go to is on the outside and the # from base ten goes on the inside. You then want to see how many times the number 8 (base you are going to) will go into 46 (the number in base ten).Example: Answer:8L46 } 56eight5 } 68 goes into 46 5 times (8x5=40) with 6 left over to make 46.The answer is read from left to right.You can also travel from base ten to another base by counting the numbers up to the desired base and creating longs. Once you create the number of longs to make a flat you convert it to that. You are finished when you have your answer in FLU units.

Distributing a number across an addition or subtraction using multiplication.

https://www.youtube.com/watch?v=u3dexXyyb3c

7+6+3=3+6+7In this property order CAN change

36+28You would cross off the 6 in 36 and subtract 4 to make it 34.You would cross off the 28 and add 2 to make it 30.You then have:34+30You add 30+30+4 to come to your final answer 64This method makes it easier to add big numbers without getting confused from having to "carry numbers" in the traditional adding algorithm.

https://www.youtube.com/watch?v=gTX2CXI1l5k

https://www.youtube.com/watch?v=8-QHQWd4uAs

https://www.youtube.com/watch?v=AJBFxOBxMz8You can use this method to add in different bases as well. You will add up the numbers until you hit the base you are in, and then you make a scratch mark, instead of making a scratch mark every time you hit a two digit number.

https://www.youtube.com/watch?v=fO8vAMIfo_0

https://www.youtube.com/watch?v=Nh540Llr5FY

https://www.youtube.com/watch?v=qdYV6i-kXcA

https://www.youtube.com/watch?v=5ZJlwvJ-7zI

https://www.youtube.com/watch?v=Z3T_NhFlpB0

Positive numbers are denoted by the + signYou can also use colors to denote positive numbers. If you have two color counters, the YELLOW side will be positive.

Negative numbers are denoted by the - signYou can also use colors to denote negative numbers. If you have two color counters, the RED side will be negative.

You start by listing what you want to show- - - - - Then you add in zero pairs (a + above a -) to get to the number of tiles you need to use + +- - - - - - -

KCC is the Keep, Change, Change method. This is used only for subtraction of integers.ex: 50-70Keep the 50Change the sign to +Change to (-70)You would then go on to using the +/- to designate which group is larger.In this case:50 would get one + sign because it is a smaller group of positives(-70) would get two - - signs because it is a larger group of negativesYou write the +/- beneath the numbersYou circle one of each, a plus and a minus since they are next to each other+ and - = Subtract+ and + = Add- and - = AddYou then would do 70-50This equals 20Whatever sign was left out of the circle is the sign for the answerIn this case our answer would be -20 because of the leftover - sign shown beneath (-70)

You would show your -4 tiles- - - -Then you would add 3 more - tiles- - - - - - -This give you the answer of -7

You would start with you three negative tiles- - -Then you would draw a zero bank of 6 + + + + + +- - - - - - - - - Next you would draw a circle around your six positive tiles and attach an arrow to it, which denotes take away.The negative signs left outside of the subtraction circle are your answer. In this case the answer is -9

https://www.youtube.com/watch?v=tW97UU01ShY

https://www.youtube.com/watch?v=oC17dzCzufg

https://www.youtube.com/watch?v=xdzZVpqSUm8*REMEMBER*GCF: same factors, small exponent (S,S)LCM: all factors, large exponent (A,L)

25eight = l l ..... 8+8+5=21There are 2 longs with 5 leftover units. Each long is 8 units, that is why we did 8+8The five leftover units is why we did +5These numbers add up to 21.21 is the base ten number that is = to 25eight

https://www.youtube.com/watch?v=lnC7h6fgglU