MTE 280 Mindmap for Elementary Mathematics

Inductive- in a patternDeductive- applying prior knowledge to a situationEx: Formulas

UnDevCarLoUn-understandDev-developCar-carry outLo-look back

H, T, O = F, L, UH= hundredsT= tensO= onesF= flatsL= longsU= units start from the right which is the smallest and move to the left which gets bigger

Going to Base Ten24six to Base Ten2(6)^1 + 4(6)^0=2(6) + 4(1)=16*When leaving Base Ten and going to a different base use downwards division:132 to Base Five5|132five goes into 13 two times with three leftoverfive goes into 32 six times with two leftoverfive goes into 26 five times with one leftoverfive goes into five one time=1012Five

Scratch Method: (the numbers in red represent when you scratch and when it gets to or past ten/the numbers in red go over into the next column and that's where the four comes from)Base Ten6 7 3 3 2 6 4 5 7 6 9 5 34 8Scratch Method: (the numbers in red represent when you scratch and when it gets to or past the specific base/the numbers in red go over into the next column and that's where the three comes from)Base Seven 3 2 1 6 5 4 2 3 5 333Expanded Form: 234+ 56200+30+4 50+6200+80+10=290Friendly Numbers: 34+12+26+43+18+27+1130+10+30+40+20+30+11=171Trade Off:36+2834+30=64Lattice: (add numbers down without carrying/then add diagonal numbers) 37+26 1/ 5/36/3

Algorithms:-efficient-quick-explain place valueLatis:-efficient

Distributive Property: 7(x+3) or 7(5+3)Associative Property:(7+6)+3=7+(6+3)*order does not changeCommutative Property:7+6+3=3+6+7=3+7+6*order does not mater*This also applies to multiplication

Multiplying with Base Ten Blocks:(~=1) 10 ~ ~ ~100 10 10 1010 ~ ~ ~10 ~ ~ ~13(12)=156Area Model for Multiplication: (56)(75) 70 + 550 3500 250+6 420 303750+450 4200

Addition/Subtractionif the fraction is a mixed number you can use the whole number to add or subtract firstin order to complete the fraction part you need to find a common denominator. if they do not then you must find common factors the current denominators haveEXAMPLE:13+2 1/5add the whole numbers first 13+2=15then bring fraction next to whole number13+2 1/5= 15 1/523-4/11this fraction only has 1 whole number and there isn't a common denominatorto change the fraction so we can subtract we would change 23 into 22 11/11. now we have the same denominators and can subtractthe new problem looks like this22 11/11-4/11= 22 7/11Multiplication/Divisionyou don't need common denominators for multiplication and division.for solving mixed number fractions you multiply the denominator to the whole number and then add that to the numerator. you put that total over the original denominatorEXAMPLE 1:6 2/3 x 7 1/53x6+2=2020/35x7+1=3636/5the new problem is 20/3 x 36/5to make the problem easier we can cancel numbers outdiagonal numerators and denominators can cancel20 becomes 4 and 5 becomes 136 becomes 12 and 3 becomes 1this allows students to make big numbers smallerthe answer is 48EXAMPLE 2:3 1/3 divided by 5 5/6you follow the same step as above"for solving mixed number fractions you multiply the denominator to the whole number and then add that to the numerator. you put that total over the original denominator"after that step is done you change the division sign to multiplication and flip the fractionthe final result will be 10/3 x 6/35to make the problem easier we can cancel numbers outdiagonal numerators and denominators can cancel35 becomes 7 and 10 becomes 26 becomes 3 and 3 becomes 1this allows students to make big numbers smallerthe answer is 4/7K.C.F.Keep Change Flip*Helpful way to remember what to do when dividing fractions

Fact FamiliesAddition/Subtraction3 5 83+5=85+3=88-3=58-5=3Multiplication/Division4 6 244x6=246x4=2424/4=624/6=4

Sometimes students struggle knowing which numbers go on the inside and outside of a division problem.Think of your favorite fast food place on the West CoastIn N Out!Example:348/5In N Out5 will be on the outside and 348 will be on the inside!

Already knew about PEMDASParenthessExponentsM/D Multiplication/DivisionA/S Addition/SubtractionLearned about GEMDASGroupsExponentsM/D Multiplication/DivisionA/S Addition/SubtractionGroups is the stage where you separate each section when you see an addition or subtraction sign and there are other steps in the problemEXAMPLE:-4^2+3x4-5+2x6/3+(-4+1)^2/3anywhere you see an addition or subtraction sign draw a line to separate the group

2- last digit needs to be even (last digit divisible by 2)3- digits add up to multiples of 34- last 2 digits are divisible by 45- if last number ends in a 5 or 0 divisible by 56- if number is divisible by 2 and 3 then its divisible by 68- last 3 digits are divisible by 89- digits add up to multiples of 910- if last number ends in a 0 divisible by 10

When teaching students multiplication there are certain numbers to start with first. They can be broken down into three groups:Group 1 (1,2,5,10)Group 2 (doubles,3,9)Group 3 (4,6,7,8)*The easier multiplication tables will help students with the harder ones. There will only be a few hard ones left once they master the easier ones

DECIMALS- line up whole numbersAdding/Subtracting3.46+8the 8 would have to go underneath the 3 because they are both whole numbers and in order to get the correct answerMultiplication(3.2)(4.5)round each number to the closest whole number3.2=3.04.5=5.0 (you can go either way with this one but I chose to round up)multiply (3.0)(5.0)=15.0(32)(45)=1440place the decimal in between the numbers that would make the most sense and would make the number close enough to 15the decimal would go in between both 4's making the answer 14.40

You can show how to solve fractions by using boxesFor adding and subtracting fractions you make two rectangles.Example:1/4 + 3/7These two fractions don't have the same denominators.The first rectangle you would separate into 4 groups and the second rectangle into 7 groups but going the opposite direction. Shade in the number that the numerator represents for both fractions.For addition the answer requires a third box so you can overlap and get the answer.For subtraction you only need the 2 boxes and what ever you shade in on the second rectangle is what you cross out on the first. Whatever is not crossed out is the answer.For multiplication you only need one box.Draw lines to separate into groups for first fraction.Then do the same thing for the second fraction. Where the shaded parts overlap that is your answerYou can show how to solve decimals by using boxesFor addition/subtraction/multiplication the place value mattersIf the decimals have the same place values you can get away with using one box.If the decimals place values are different you will have to use two boxes

What is 35% of 80?first find what 10% of 80 is.10%=8multiply both by 330%=245% would be half of what 10% is5%=435% of 80=2860% of 3010%=3multiply both by 660%=1840% discount off of $60100% minus 40% would mean you are left paying 60%60% on $6010%=6multiply both by 660%= 36$36 is what you will pay!

Prime numbers- whole number greater than 1 whose only factors are 1 and itselfExamples: 2,3,5,7,11,13,17,19,23,29Composite numbers- positive integer that can be formed by multiplying two smaller positive integersExamples: 4,6,8,9,10,12,14,15,16,18,20Prime Factorization can be done with a factor tree or upside down divisionFactor Tree 24^3 8^2 4^2 22x2x2x3Upside Down Division3|363|122|422x2x3x3

LCM also known as Least Common Multiplenumber with biggest exponentGCF also known as Greatest Common Factornumber with smallest exponentA) 3^2x5^4x11^2x29^4B) 2^4x5x13^2x17^5x29^2C) 2^2x5^7x7^2x13^5GCF is 5 because that's the only number all three groups have in common and its the smallest exponentLCM is 2^4x3^2x5^7x7^2x11^2x13^5x17^5x29^4 because its all the numbers in each three groups with the highest exponents

Fractions- part of a wholeNumerator- number of pieces currently haveDenominator- size/how big the piece/s isComparing Fractions:< less than> greater than= equal to2/3 > 3/8 (anchor)7/8 < 12/13 (missing smaller piece)4/11 > 4/13 (bigger piece)3/7 < 8/15 (anchor)*Show Adding/Subtracting/Multiplying/Dividing Fractions by using a a circle or rectangle and then separate into sections/parts based on fractions in the problem

14 Base five + 10 Base five = 24 Base five110 Base six + 17 Base six = 127 Base six20 base four + 12 Base four + 6 Base four = 38 Base four

25 Base four - 13 Base four = 12 Base four7 Base three - 5 Base three = 2 Base three17 Base five - 11 Base five= 6 Base five

Need to determine how many flats, longs and units are in the given numberExample 1: 22 Base five = 2(5^1) + 2(5^0) = 12Example 2: 72 Base four = 7(4^1) + 2(4^0) = 30

You will start with any number in base ten and have to be given the base you will be converting to.23 to base five *****= 1 long*****= 1 long*****= 1 long*****= 1 long_____________________4 total longs***= 3 units____________________23 to base five= 43 Base five