Elementary Mathematics

An issue with division is that students dont know how to set up or write the problem correctly. Division is for example 20 divided by 5, would break down into 20 divided into 5 groups. (example below)xxxxx xxxxx xxxxx xxxxx

Multiplication Lattice12x13 12 Multiply the 1 on the right column with the 2 1 on the top column. Then multiply the 1 on 3 the right column with the 1 on the top column. Next multiply the 3 on the right column with the 2 on the top column. Then multiply the 3 on the right column with the 1 on the top column. should look like this on the inside of the box, 12 36Next you would add diagonally, so it would be 6, then 2+3, lastly it would be 1. Your answer would be 176

Sub Alt Algo Expanded Formexample: 536- 304 918-213500+30+6 900+10+8300+0 200+10+3-------------- -------------200+30+6=236 700+0+5=705Equal Addends (Subtractends)Whatever you add to one number you add to the other numberEx:53+2-28+2--------55-30-----25

Building Integers examples, building -3 with 7 tiles. --- -- ++ building 2 using 10 tiles++ ++++ ----

solving adding integers examples ++ - 35+(-24)= 35 -24 --------- 11 it would be positive because the plus sign that is not bold is the sign that we would be using. The bold positive and negative sign, equal each other out. If you notice the larger number, that is positive, has the 2 plus signs above it, the smaller number, negative only has the one negative sign. If the larger number was negative, it would have two negative signs. example-- +-26 +(2)= -26 + 2 ----------- -24

divisibilty rules2 is divisible if the numbers end in 0,2,4,6,83 is divisible by 3 if the sum of digits are divisible by 3 ex:156=124 is divisible if the last 2 digits are divisible by 4 ex:394165 is divisible if the last digits are 0 or 56 is divisible by 6 if 2 and 3 works, 7 no rule, not divisible8 is divisible if the last 3 digits are divisible by 8 ex: 256489 is divisible by 9 if the digits are divisible by 9 ex :2736=1810 is divisible by 10 if the last digit is 0 ex: 9290

When we teach Solving subtraction and multiplication integers I think that its important to show that we have to start at "0" to show that sometimes we have to subtract (take away) from a number that doesnt have value.Here are some examples-2-(-4) would be stated, 2 negatives take away 4 negatives4-6 would be stated 4 positives take away 6 positivesmultiplication would be shown as5(-2)= 5 groups of negative 2 that would be -10-- -- -- -- --

Add/Sub/Mult/ Division examples -- - you would add-45-(-60)=-105 -45 + -60 ---------- -105-++-27-(43)=16 you would subtract(take away) 43 -27 --------- 16multiplication-5(30)= -1505(30)= 150 If the signs are different, the answer will be negative, signs are the same, it will be positive. division-25 divided by 5 = -525 divided by 5= 5

Fractions into to Algorithms The numerator tells us the number of thing that we have, the denominator tells us the size of the things or pieces. examples 7/11 would be bigger than 15/34 because seven is over half15/16 would be bigger than 5/6 because one small piece is missingaddition 8+ 10 15/34= 18 15/34 *add the whole numbers 8 and 10. then there is no fraction to add to 15/34 so that would stay the same. subtraction 10- 15/34=take 1 from 10 making it 9 34/34-15/34= 9 19/34

Multiplying/Dividing FractionsMULTIPLICATION2/4 x3/8= 6/32 DIVISION 10/9 divided by 16/21Keep change to x(multiply) and flip10/9 x 21/16, you would then simplify, using the "1" method, ( i don't know how to show that here!!) problem would end up:5/3x7/8 =35/24 = 1 11/24

adding, subtracting and multiplying decimals. (diagrams are close to how we would work fractions)0.2+0.3=0.5 correct way to line up the decimals0.2+ 0.3-------- 0.5 0.7-0.6=0.10.7- 0.6--------0.1

with multiplication its easier to estimate and then work the problem,1.7(10.2)= estimation 2(10)=20 17x102---------340017------------ 17.4

Order of Operations, Instead of PEMDAS we use something similar G(group) E(exponents)MD(multiply/divide) and AS (add and subtract) examples:(-4)^2=16 which could also look like this 0(-4)^2=165*4/2*6/5*3 (/=divide symbol)20/210*660/512*3=36

scientific method is a number between 1-10, you always multiply by 10's and there are exponents, negative and positive.Example 2.5x10^5= 250,0002.5x10^-5= 0.000025-2.5x10^5=-250,000