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November 27, 2006

Last tuesday we began dividing fractions. The students seemed to pick up on this very quickly. We reviewed it in class today and will have a quiz on multiplying and dividing fractions tomorrow. The steps to remember for dividing fractions are the following: 1.KEEP the first fraction as it is. 2. CHANGE the division sign to a multiplication sign. 3. FLIP the second fraction to it's RECIPROCAL. 4. simplify and multiply!!! They have H.W. in their workbook - 'practice' #'s 1-8, 9-23 odds only and #'s 22 and 32. We will continue to build on this skill this week by multiplying and dividing mixed numbers. This will give the students a review on how to convert mixed numbers to fractions and strengthen their multiplication and division facts.

Posted by Jennings at 02:16 PM

November 13, 2006

We continue discussing decimals as a part of a whole just like fractions. Tonight the will be adding and subtracting decimals on their worksheet and tomorrow they will have a short quiz. From here we move on to multiplying and dividing fractions. I think the students will actually find this a little easier than adding and subtracting because we don't have to find a common denominator. Finally we will move on to doing the same with mixed numbers.

Posted by Jennings at 04:16 PM

We have finished our long division unit and we will continue to practice this skill. HW tonight was a worksheet where students are adding and subtracting decimals. As always, we continue on as we review and reinforce all the skills we've learned previously.

Posted by Jennings at 04:11 PM

November 03, 2006

Study guide 6-6 in your workbook to review subtracting mixed number with renaming. #'s 1-9 and 1, 13, 14, 15 and 18.
See 'classwork' section for an explanation of steps. There will be a test next wednesday on adding and subtracting fractions and mixed numbers

Posted by Jennings at 11:59 AM

We are nearing the end of our unit on adding and subtracting fractions and mixed numbers. It is a very difficult concept and there are a great deal of "tricky" problems but we are truly rolling along. Today the students amazed me at how quickly they caught on. We will continue to practice these skills even as we move on. There will be a test next week (Wed.). To help your students prepare I'm going to review the steps they need to remember. They should all have notes but we'll review it here.

** Before you begin---Stack the Fractions!!
1. To add fractions with the same denominator, you just have to add the numerators. 1/4 + 2/4 =3/4.
2. To subtract fractions with the same denominator, you just subtract the numerators 3/4 - 2/4 = 1/4.
3. When the denominators are different, for both addition and subtraction, you need to find a denominator that the two fractions have in common. To do this we need to find the LCD. Students know to list the multiples of each denominator until they find one they have in common. For example 1/3 + 1/4. (The multiples of 3 are:3,6,9,12,15). (The multiples of 4 are: 4/8/12/16). Therefore the smallest multiple they have in common is 12. Now we can change the fractions. To change from 3rds to 12ths we multiply by 4 so we have to do the same to the numerator. 1/3 now becomes 4/12. In addition, to change from 4ths to 12ths we multiplied by 4 so the fraction 1/4 is now 3/12. Now we can add and/or subtract 4/12 and 3/12.
4. One really important fact they need to remember is that answers must ALWAYS be in simplest terms! They know that to do this they must 'bobsled the fraction to it's lowest term!
5. When we are adding and subtracting mixed numbers, we do the same procedure. a) stack the numbers. b) ind the LCD. c) Find and write the equivalent fraction, d) Add or subtract (Fractions FIRST and then the hole numbers! {Don't forget the babies}. e) Simplify * remember you can't have an improper fraction in a mixed number for an answer so 'rename the improper fraction! Students know that to 'rename an improper fraction to a mixed number' they need to divide. For ex. 9/7 - You divide 9 by 7. Your answer will be 1 with 2/7 left over so your mined number is 1 and 2/7.
Ex. 7 9/10 + 3 1/4 - You change the fractions to 7 18/20 + 3 5/20 = 10 23/20 (you divide 23 by 20 and get 1 3/20) Now you replace the 23/20 with 1 3/20 and add it to you whole # 10. Your final answer is 11 3/20.
Believe it or not... we've even gone further than this!!
6. Sometimes when you subtract mixed numbers, there is no fraction on top. For example 23 - 13 3/4. To do this problem we need to create a fraction from the first number because you can't take 3/4 away from nothing. We will 'borrow' 1 from the 23 (making the whole number a 22 now) and make the 1 we borrowed into a fraction. Since we will be needing to subtract 3/4 from this fraction, it makes sense to make the denominator 4. So with a denominator of 4, the way we make it equal to 1 (the 1 we borrowed) we can make the fraction 4/4 (which equals 1). Now our problem will read 22 4/4 - 13 3/4 and we can do this! Today we solved a problem with multiple steps and they did great!
Ex. 15 1/3 - 9 5/6
change to common denominator - 15 2/6 - 9 5/6 (but you can't subtract 5/6 from 2/6)
borrow to make the top # larger - 14 8/6 - 9 5/6
We subtract and get 5 3/6 STILL WE ARE NOT DONE! because 3/6 can be reduced (bobsled) to 1/3 so
Finally our answer is 5 1/3. Yes your students did this on their own. Again, we will continue to practice and reinforce these skills as we continue on. We will be working on some word problems next to help learn how to applay this new knowledge.

Posted by Jennings at 11:54 AM