Finding common denominators - Reasons:
(1) To accurately compare the relative value of 2 fractions (when denominator is same - same sized pieces- the one with the bigger numerator is larger...has more of these same sized pieces!) or
(2) to add & subtract fractions finding common denominators becomes essential because you need to be adding up (or subtracting) the same sized pieces or your answer won't make any sense!
Strategy/Example #1:
1/3 + 2/9 = _____
- Hmmm, well, since the denominator of the 1st fraction is a FACTOR of the second I should be able to use multiplication to create my common denom. because 3x3=9! Don't forget, to get an EQUIVALENT fraction (we don't want to add up a non-equivalent fraction, that would change the actual value of the problem!) we need to multiply the numerator and the denominator by the same #
1 x 3
__ = 3/9 and now we just substitute 3/9 into our original problem for 1/3
3 x 3
3/9 + 2/9 = 5/9 (remember, only add the denominators because that is how many pieces you
are adding - if you added the denominators you'd be changing the size of
your pieces which would, in effect, be making your sum of less value!)
Strategy/example #2:
1/5 + 2/4 = ____ well, neither denominator is a factor of the other so we have to find a
common multiple of both - easiest way to do this is to multiply 2
numbers together!! Here, like this:
1 x 4
___ = 4/20
5 x 4
2 x 5
__ = 10/20
4 x 5
Now, we can substitute our new, fancy equivalent fractions with common denominators in for the old ones and we get
4/20 + 10/20 = 14/20 which reduces to 7/10
Note: you can also use division to reduce fractions in order to find a common denominator - make sure you divide the numerator and the denominator by the same # and that the they are both divisible by that number!
Monday, October 17, 2011
Friday, October 7, 2011
Tuesday, October 4, 2011
Science: Mass, Volume, and Density
Density, the measure of mass per unit volume, can be found by simply dividing the mass of an object by it's volume.
M/V=D
If you HAVE the density and volume and you want to figure out the MASS of an object, take your density and multiply it by your volume.
D x V = M
And if your looking for the VOLUME and you have the mass and density, just divide the mass by the density.
M/D = V
Remember, volume is the amount of SPACE something takes up, mass is a measure for how much matter is in an object and density is a measure of mass per volume. I also like to think of my garbage can after I forget to take out the garbage the previous week - the bin is the same size (volume) but I've been forced to increase the amount of matter (mass) in that same space thus increasing it's DENSITY!
oh, yeah...units we've been using in class:
* the gram(g) is a unit of MASS
* cubic centimeters (cm^3) or milliliters (mL) are units of VOLUME
* and grams per milliliter (g/mL) and grams per cubic centimeter (g/cm^3) is for DESNSITY
M/V=D
If you HAVE the density and volume and you want to figure out the MASS of an object, take your density and multiply it by your volume.
D x V = M
And if your looking for the VOLUME and you have the mass and density, just divide the mass by the density.
M/D = V
Remember, volume is the amount of SPACE something takes up, mass is a measure for how much matter is in an object and density is a measure of mass per volume. I also like to think of my garbage can after I forget to take out the garbage the previous week - the bin is the same size (volume) but I've been forced to increase the amount of matter (mass) in that same space thus increasing it's DENSITY!
oh, yeah...units we've been using in class:
* the gram(g) is a unit of MASS
* cubic centimeters (cm^3) or milliliters (mL) are units of VOLUME
* and grams per milliliter (g/mL) and grams per cubic centimeter (g/cm^3) is for DESNSITY
Wednesday, September 28, 2011
Inv.1.3 (9/28 Homework)
Investigation 1.3 (purple worksheet) Tips/Hints: Use Soleil's Strategy for finding the value of a fractional portion!
Steps
1) Identify the fraction represented if it's not given
2) Identify the value of the whole or the total
3) Divide your whole by the denominator of the fraction you "have"
4) Multiply the quotient from step 3 by your numerator
Example: Billy bought a bag of 20 cookies and ate 3/4 of it.
20 /4 = 5
3 x 5 = 15 cookies eaten by Billy
*Note on division: When you divide, the divisor (in this case 4) chops the dividend (in this case 20) into 4 groups and gives you the value of 1 of these groups (the quotient or answer)....OR you could say you can create 5 groups of 4 out of 20....OR if you had to SHARE 20 things among 4 people each person gets 5. Grouping or Sharing - whichever makes more sense to YOU!
Now, some of you will read the example problem and say "of" means multiply, which it mostly does....but this would require the students to divide the fraction and then multiply by the fractions decimal equivalent (i.e.: 0.75 x 20 = 15). While this way is more efficient, we haven't studied place value yet so I'm not ready to explain WHY this works to the students yet.
2) Identify the value of the whole or the total
3) Divide your whole by the denominator of the fraction you "have"
4) Multiply the quotient from step 3 by your numerator
Example: Billy bought a bag of 20 cookies and ate 3/4 of it.
20 /4 = 5
3 x 5 = 15 cookies eaten by Billy
*Note on division: When you divide, the divisor (in this case 4) chops the dividend (in this case 20) into 4 groups and gives you the value of 1 of these groups (the quotient or answer)....OR you could say you can create 5 groups of 4 out of 20....OR if you had to SHARE 20 things among 4 people each person gets 5. Grouping or Sharing - whichever makes more sense to YOU!
Now, some of you will read the example problem and say "of" means multiply, which it mostly does....but this would require the students to divide the fraction and then multiply by the fractions decimal equivalent (i.e.: 0.75 x 20 = 15). While this way is more efficient, we haven't studied place value yet so I'm not ready to explain WHY this works to the students yet.
Monday, September 26, 2011
Hint for tonight's Green worksheet homework - Like mentioned in class today, you can always find common multiples of 2 numbers by multiplying them by EACH OTHER
Example:
If I wanted to find common multiples of 4 and 5....4x5=20
20 is thus a common multiple of BOTH! To find more common multiples I would then just count by 20's. So additional common multiples would be 40, 60, 80, etc.
Example:
If I wanted to find common multiples of 4 and 5....4x5=20
20 is thus a common multiple of BOTH! To find more common multiples I would then just count by 20's. So additional common multiples would be 40, 60, 80, etc.
Thursday, September 22, 2011
Factor Game Rules
These are the rules to the Factor Game - if your sixth grader can explain them to you without this all the better! Let them teach you...you never learn something better than when you have to teach it!
1) Player A chooses a # on the game board and circles it.
2) Using a different color (or "circling" it with a square works too), Player B circles all of the factors of the # A chose (can't circle the number itself even though it is a factor because it has already been taken - a number can't be circled twice!) You get the value of the numbers you circle as points.
3) Player B now circles a new number and Player A circles all of the factors of the number that are not already circled.
4) The players take turns choosing numbers and circling factors.
5) IF a player circles a number that has no factors left because they have already been circled that player DOES NOT get the points for that number and then loses their next turn. You have to pick a number that has factors your opponent can circle!
6) THE GAME ENDS when you cannot do the latter, i.e. when there are no numbers left with uncircled factors.
7) Total up the points and see who wins! Winner does tacky victory dance!
1) Player A chooses a # on the game board and circles it.
2) Using a different color (or "circling" it with a square works too), Player B circles all of the factors of the # A chose (can't circle the number itself even though it is a factor because it has already been taken - a number can't be circled twice!) You get the value of the numbers you circle as points.
3) Player B now circles a new number and Player A circles all of the factors of the number that are not already circled.
4) The players take turns choosing numbers and circling factors.
5) IF a player circles a number that has no factors left because they have already been circled that player DOES NOT get the points for that number and then loses their next turn. You have to pick a number that has factors your opponent can circle!
6) THE GAME ENDS when you cannot do the latter, i.e. when there are no numbers left with uncircled factors.
7) Total up the points and see who wins! Winner does tacky victory dance!
Monday, September 19, 2011
Hola!
Switching gears...going to be working on identifying factors and multiples for about a week.
Example:
Switching gears...going to be working on identifying factors and multiples for about a week.
Example:
3 x 4 = 12
3 and 4 are both factors of 12
12 is a multiple of both 3 and 4.
It's all about perspective...if you're looking for factors of a PARTICULAR number just think of all of the whole numbers you can multiply together to GET that number. Those are the factors (hint: factors ALWAYS come in pairs)
On the other hand, if you have a particular number and want to find the multiples of that number, just start multiplying that number by ANY WHOLE NUMBER and the product will be a multiple of that number. See example above!
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