Mathematics Topics

Expanded form of Base 10For example:3562 base 103000+500+60+2 is the expanded formAnother example:5347 base 105000+300+40+7 is the expanded form

Converting from Base 10 to any baseExample 235 to Base 4Start with listing the 4 powers that are needed for the problem4^3 = 644^2 = 164^1 = 44^0 = 1Then see how many times the biggest number (64) goes into the base 10 number (235). In this case it is 3 times.64*3 = 192235-192 = 43Then you move onto the next number (16). 16 can go into 43 2 times.16*2 = 3243-32 = 11Then see how many times 4 can go into 11. 2 times.4*2 = 811-8 =3And finally see how many times 1 can go into 3. 3 times.1*3 = 33-3 = 0So 235 is 3223three.The link will bring up more examples

Converting any base to Base 10441three to Base 10We start by creating a chart with the powers 3^0, 3^1, and 3^2. Then you match the place values of the numbers (441)3^2 3^1 3^04 4 1Then we create the equation(4*9) + (4*3) + (1*1)36 + 12 + 149441three is 49 in Base 10

Subtraction with Non-Base 10 with blocks431eight - 43eightFor the number 431, the 1 is the units place, the 3 is for the longs, and the 4 is for the flats.We start by placing 4 flats, 3 longs, and 1 unit onto a flat surface. We then begin with the units. We cannot take 3 units away from 1. We must break a long down into units.Now we have 4 flats, 2 longs, and 9 units. We can subtract the 3 units from the 9 units. We have 6 units left over.We have 4 flats, 2 longs, and 6 units. We have to subtract 4 longs. To do that we must break down one of the flats. We now have 3 flats, 10 longs, and 6 units. We can subtract the 4 longs from 10 longs. We then are left with 3 flats, 6 longs, and 6 units.366eight is our answer

Base 20,1

Base 30,1,2

Base 40,1,2,3

Base 50,1,2,3,4

Base 60,1,2,3,4,5

Base 70,1,2,3,4,5,6,

Base 80,1,2,3,4,5,6,7

Base 90,1,2,3,4,5,6,7,8

Base 100,1,2,3,4,5,6,7,8,9

Zero Pair Example5+ -3 = 21+1+1+1+1-1+-1+-1These cancel out to leave 1+1 = 2These pairs are zero pairs

The Big 7 This is an easier way for students to divide numbers.Example:137/3 Students like to work with the number 10. So if we use 10's while dividing, it is easier for them.Create the division problem like a normal long division problem. The first step is to multiply 10 *3 to get 30. We then subtract the 30 from the 137 to get 107. We then multiply 10*3 = 30 and subtract the 30 from 107 to get 77. Then multiply 10 *3= 30 and subtract 30 from 77 to get 47. Then multiply 10*3 = 30 and subtract 30 from 47 to get 17. We then move down to the next easier number for kids, which is 5. 5*3 =15 and we subtract 15 from 17 to get a remainder of 2. Then you add up all of the number to get 45 with a remainder of 2.

To show -4 with 8 counters, you would use 6 negative counters and 2 positive counters- - - - - - ++This cancels out 2 pairs, and leaves 4 negatives. -6+2=-4

To show 3 with 11 counters you would need 7 positive counters and 4 negative counters+++++++----This cancels out 4 pairs and leave 3 positive counters7 + (-4) = 3

Show 5+-3=2 with counters+++++- - - Three pairs are cancelled out and 2 is left over

Show -5 with 7 counters- - - - - -+-6 + 1 = -5One pair cancels out leaving -5

-8/2Switch the division to multiplication 2* ? = -8? = -4So you must have 2 groups of negative 4---- ----

Show -10/5Switch it to multiplication 5* ? = -10? = -2So you have 5 groups of negative 2-- -- -- -- --

Adding FractionsExample(-2/3) + (1/5)Find common denominator (-2/3) turns into (-10/15)(1/5) turns into (3/15)(-10/15) + (3/15) = -7/15Just add straight across. Don't change the denominator.

Example #2(1/2) + (1/6)(1/2) turns into (3/6)(1/6) stays (1/6)(3/6) + (1/6) = (4/6) = (2/3)

Example(12/42) and (10/35)Find the LCMthe factors are 2*3*5*7=210(12/42) turns into 60/210(10/35) turns into 60/210these fractions are equal

An integer is a whole number (not a fraction)1,2,3,4,...

-2 *3This means that you have -( 2*3).So you start with 2 groups of positive 3+++ +++You need to take the opposite of the groups, so that makes the positive negative--- --- The final answer would be -6The opposite of 2 groups of 3

How to word -2 * -3You start with 2 groups of negative 3--- --- But you need to take the opposite of the negative, which makes it positive.+++ +++So -2*-3 = 6The opposite of 2 groups of -3

A proportions is a statement that says that two ratios are equal.Example 1/3 = 2/6

Number line with division12/40 1 2 3 4 5 6 7 8 9 10 11 12We start at 12 and take 4 steps towards 0. That puts us at 8. Then takes another 4 steps. That puts us at 4. Take another 4 steps. That puts us at 0.So 12/4 = 3

Problem Solving in math is when you look at a problem and determine the best way to start the problem is. Then you solve the problem and double check your answer. When you double check your answer, and you get the same thing you started with, that's how you know you got it correct.