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6th grade math

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 on: November 03, 2006

7th grade math

We continue to work on our long division. It gets a little easier every day. This skill needs to be practiced every day. In addition, we began a very special project. It involves math, technology and food. What a great combination! Your children will tell you more about it as we proceed.

posted on: October 24, 2006

Adding and subtracting fractions

After a week of finding equivalent fractions, I think we've just about got it! Now we can begin to apply what we've learned. We have discovered that we can add and subtract fractions with 'like' denominators just by adding or subtracting the numerators. However, if the denominators are not the same...we first have to find the 'least common denominator' so they will be the same. The first step in doing this is to "Stack" the fractions so they are one on top of another. Out to the side, we find the (LCD) Least common denominator. {This is exactly the same as finding the least common multiple. Students list the multiples of the larger number first and then see if the smaller number is a factor as well}. After we find a common denominator, we multiply each numerator by the same number we used to get the denominator (what you do to the bottom, you must do to the top). Now you have created equivalent fractions. Now we can add or subtract the numerators. DON'T FORGET TO SIMPLIFY YOUR ANSWER!! (double bobsled).

posted on: October 24, 2006

comparing fractions

This week we've been learning how to find equivalent fractions and how to reduce fractions to their simplest terms. We've been using fraction stacks and paper cutting activities along with a great deal of in-class examples. This process can be confusing, but the students seem to be 'getting it'.

Fractions that name the same number. To find an equivalent fraction, you multiply or divide the numerator AND the denominator of a fraction by the SAME number ( not zero). Ex. 5/6 = x/18 we multiplied 6 x 3 to get 18, therefore we must multiply 5 by the same thing. 3x5 - 15 so our numerator will be 15. therefore 5/6 = 15/18.
To find all the equivalent fractions you could just keep multiplying the fractions.

To reduce a fraction or ratio to it's simplest form, we used the double'bobsled'. 4/16 if you bobsled 4 and look for a number that can 'go into both', starting with the lowest prime number and working your way up. We divide 4 and 16 by two and our answers will be 2/16. We know that we can further bobsled so we divide 2 and 16 by 2 and we get 1 and 8. Therefore, our reduced fraction is 1/8. 4/16 = 1/8. It's really simple once you've worked out a few. The students caught on quickly. If the numbers can not be bobsledded then the number is already in simplest form. Sometimes the number is given as a ratio or other than fraction form. If this is the case, the answer should be given as the original ratio. Ex. 4:16 = 4/16 = 4 out of 16 - 4 to 16. These are all the same ratios just written a different way!.

posted on: October 11, 2006

6th grade classwork (parents can help)

We have been working on a bobsled method to find the prime factors of a number. Bobsled is a reverse division where you divide only by prime numbers. I tell the students to always write the first 7 or 8 prime numbers on top of their papers for a reminder...they all know them (2,3,5,7,11,13,17,19,23..). Today we began doing double bobsleds where we find the prime factors of two numbers and then find the prime factors that they share. For ex. if we wanted to find the GCF (greatest common factor) of 27 and 45. We first divide 27 by it's prime factors and get 3x3x3. When we divide 45 by it's prime factors (bobsled) we get 3x3x5. * you stop dividing when the last number is prime. Next we look for the 'common' numbers or pairs. There are 2 pairs of 3 so we write 3x3 and multiply. The answer is 9. 9 is the largest factor that can go into both 27 and 45 evenly. GCF=9 Sometimes you get numbers like 14 and 33. Their GCF is 1 because they share no other common factors. Tomorrow we will be learning to triple bobsled. The idea is basically the same but all three numbers will have to share a common factor! So far our class is really showing they understand this concept!

posted on: September 21, 2006

picto & circle graphs

we're almost at the end of our data analysis unit. We can create, read and analyze many different types of graphs. Today we were quizzed on pictographs and circle (or Pie) graphs. There will be a unit test later this week.

posted on: September 05, 2006

performance based assessment - graphing activity

Our classes have been buzzing with activity. The students are putting to use the skills they learned regarding creating and analyzing graphs. They've been counting and sorting, calculating and graphing their M&M's. They're doing a great job and you can see by their almost finished projects that they have learned and can understand how to create and analyze bar graphs. This assignment will be considered an authentic task and therefore graded as a major test!

posted on: August 31, 2006

6th grade math

Todays Objective: Introduction to Unit 1 - Data Analysis. Students practiced reading from charts. A parent letter was placed in the classwork section of their notebooks. This letter will help explain the unit and gives great websites connected to our text for practice and games.

posted on: August 21, 2006

7th grade math

Today we continued pre-testing for goals! We reviewed multiplication facts 0,1,2,5 and 10. Friday is DEAR time in math. Always come to class with a novel to read!

posted on: August 18, 2006

6th grade math

Today in class we discussed grades. The students exchanged a phone number with a study buddy and recorded my blog address and e-mail address ( I distributed their workbooks and syllabi to be signed. Friday is DEAR (drop everything and read) time in math - please always come to class with a novel to read.

posted on: August 18, 2006

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