Today we will continue to practice adding, subtracting, multiplying and dividing fractions. The quiz on Thursday went better for some than others, but overall I feel that we still need more practice before moving on. Fraction operations are a huge concept in 6th grade, so we are going to take the extra time to get it right.
Today students will be working in stations. They will be able to use the others in their group for help, but they will each be turning in their own answer sheet and work. The 4 stations will be as follows...
Adding and subtracting fractions with like denominators
Adding and subtracting fractions with unline denominators
Multiplying fractions
Dividing fractions
Each student will work on 3 stations today. Tomorrow they will complete the 4th station. This should give students plenty of time to complete each station. We will grade our answers tomorrow. After completing the stations work, I have prepared a survey for each class that will give us data to use for the next lesson: converting fractions to decimals and percents
Tuesday, February 21, 2012
Wednesday, February 15, 2012
Quiz questions
Here are 4 questions that will appear on the quiz Thursday
1 2/3 x 2 2/5
Answer: 4
4/7 ÷ 2/3
Answer: 6/7
5/12 + 5/12
Answer: 5/6
3/5 + 2/15
Answer: 11/15
Quiz will include multiplication, division, addition, and subtraction of fractions and mixed numbers. All questions will come from examples on my blog or homework/ classwork from the last 2 weeks. Remember, all answers must be given as a simplified (always!) mixed number (when possible)
1 2/3 x 2 2/5
Answer: 4
4/7 ÷ 2/3
Answer: 6/7
5/12 + 5/12
Answer: 5/6
3/5 + 2/15
Answer: 11/15
Quiz will include multiplication, division, addition, and subtraction of fractions and mixed numbers. All questions will come from examples on my blog or homework/ classwork from the last 2 weeks. Remember, all answers must be given as a simplified (always!) mixed number (when possible)
Wednesday Feb 15, 2012
Today we will continue practicing adding and subtracting fractions with unlike denominators. We will review last nights homework (finding the least common multiple of a set of numbers), then use our skills we learned yesterday for some in class practice.
There will be a quiz tomorrow covering multiplying, dividing, adding, and subtracting fractions. The addition and subtraction problems will come from the problems we practice in class today. The multiplication and division will come from homework or classwork from last week. I will post some sample questions later today
There will be a quiz tomorrow covering multiplying, dividing, adding, and subtracting fractions. The addition and subtraction problems will come from the problems we practice in class today. The multiplication and division will come from homework or classwork from last week. I will post some sample questions later today
Tuesday, February 14, 2012
Tuesday Feb 14, 2012
This week we will shift our focus from multiplication and division to addition and subtraction of fractions.
Yesterday we began with adding and subtracting fractions with like denominators. I like to compare adding and subtracting fractions with like denominators to combining like terms. I used the following example in class
If I have 5 apples and add 3 apples, how many apples to I have?
Answer: 8 apples
We can look at fractions with like denominators the same way
If I have 5/10 (five tenths) and I add 3/10 (3 tenths), how many tenths do I have?
Answer: 8/10 (eight tenths)- this can then be simplified to 4/5
I added the numerators, but I do not change the denominators when adding or subtracting fractions with like denominators. Just like when I added 5 apples and 3 apples, the apples did not change, I just have more of them
We did an activity in class where students used graph paper to represent parts of a whole by drawing and shading a given number of boxes to. The parts of the whole that they shaded represents a fraction that was added or subtracted from another fraction.
Today (Tuesday), we will begin adding and subtracting fractions with different denominators. In this case, we must first find a common denominator and rewrite the original fractions as equivalent fractions with common denominators. Once they are rewritten as equivalent fractions with a common denominator, we can add or subtract the numerators and the denominators stay the same. Below are the steps that we are using in class
1.) Convert any mixed numbers to improper fractions
2.) Find a common denominator (LCM of denominators)
3.) Rewrite original fractions as equivalent fractions with a common denominator (multiply top by same # as bottom)
4.) Add or subtract numerators, denominators stay the same
Yesterday we began with adding and subtracting fractions with like denominators. I like to compare adding and subtracting fractions with like denominators to combining like terms. I used the following example in class
If I have 5 apples and add 3 apples, how many apples to I have?
Answer: 8 apples
We can look at fractions with like denominators the same way
If I have 5/10 (five tenths) and I add 3/10 (3 tenths), how many tenths do I have?
Answer: 8/10 (eight tenths)- this can then be simplified to 4/5
I added the numerators, but I do not change the denominators when adding or subtracting fractions with like denominators. Just like when I added 5 apples and 3 apples, the apples did not change, I just have more of them
We did an activity in class where students used graph paper to represent parts of a whole by drawing and shading a given number of boxes to. The parts of the whole that they shaded represents a fraction that was added or subtracted from another fraction.
Today (Tuesday), we will begin adding and subtracting fractions with different denominators. In this case, we must first find a common denominator and rewrite the original fractions as equivalent fractions with common denominators. Once they are rewritten as equivalent fractions with a common denominator, we can add or subtract the numerators and the denominators stay the same. Below are the steps that we are using in class
1.) Convert any mixed numbers to improper fractions
2.) Find a common denominator (LCM of denominators)
3.) Rewrite original fractions as equivalent fractions with a common denominator (multiply top by same # as bottom)
4.) Add or subtract numerators, denominators stay the same
Thursday, February 9, 2012
Thursday Feb 9, 2012
Yesterday we got back into the classroom after being out 2 days for ClassScapes testing. Students were given another outline as we practiced multiplying mixed numbers with fractions, whole numbers, and another mixed number. This was mostly review as this did not require learning any new skills, but instead putting some of the previous skills together. Below are the steps we used when multiplying mixed numbers
1.) Convert any mixed numbers into improper fractions
2.) Convert any whole numbers into fractions (put the # over 1)
3.) Simplify if possible
4.) Multiply numerators / multiply denominators
5.) Convert answer to a mixed number (if possible) and simplify
The homework assignment from last night was workbook page 40
Today we will have our lesson on dividing fractions. Dividing fractions is nothing more than multiplying by the reciprocal.
For example
10 ÷ 2 is the same as 10 x ½
15 ÷ 3 is the same as 15 x 1/3
¼ ÷ ½ is the same as ¼ x 2/1
Our steps for dividing fractions are simply "switch and flip"
This means switch the division sign to a multiplication sign, then flip the fraction we are dividing by (the divisor)
Homework tonight is workbook page 41
Tomorrow we will be doing a team activity to practice all of the fraction operations we have learned so far.
Next week we will begin by adding and subtracting like fractions, then move to adding and subtracting unlike fractions
1.) Convert any mixed numbers into improper fractions
2.) Convert any whole numbers into fractions (put the # over 1)
3.) Simplify if possible
4.) Multiply numerators / multiply denominators
5.) Convert answer to a mixed number (if possible) and simplify
The homework assignment from last night was workbook page 40
Today we will have our lesson on dividing fractions. Dividing fractions is nothing more than multiplying by the reciprocal.
For example
10 ÷ 2 is the same as 10 x ½
15 ÷ 3 is the same as 15 x 1/3
¼ ÷ ½ is the same as ¼ x 2/1
Our steps for dividing fractions are simply "switch and flip"
This means switch the division sign to a multiplication sign, then flip the fraction we are dividing by (the divisor)
Homework tonight is workbook page 41
Tomorrow we will be doing a team activity to practice all of the fraction operations we have learned so far.
Next week we will begin by adding and subtracting like fractions, then move to adding and subtracting unlike fractions
Monday, February 6, 2012
Monday Feb 6, 2012
Monday and Tuesday this week students will get a break from the classroom and will be in the computer lab taking their ClassScape mid year assessment. Questions will be EOG style, and will cover material that students have already seen, as well as some material that we have not yet covered.
Last Friday, students recieved their graded quizzes. Overall the scores were good, but there were still way too many "silly" mistakes due to not taking their time or checking answers. I still have a few students that seem to be making up their own way to multiply, simplify, and convert fractions.
I am not one to give much extra credit, but I did give students a chance to EARN some extra points on Friday. After reviewing each question on the quiz, I presented students with 8 questions that were VERY similar to what were on the quiz. There was a possible 10 points to be earned from these questions. I also awarded 1 point each for each of the 3 outlines that students filled out over the last couple of weeks. I reminded students all week that I would be checking to see that they were bringing their materials to class. I was impressed with the number of students that had all 3 outlines completed and organized in their binders.
On Wednesday, we will be back to the classroom to continue our unit on fractions.
Wednesday and Thursday we will begin multiplying mixed numbers, as well as dividing fractions. We will be using the same skills that we learned last week, so I expect students to pick up on multiplying mixed numbers and dividing fractions quickly.
As always, feel free to email me with any questions or concerns that you or your child may have.
nathan.culp@nhcs.net
Last Friday, students recieved their graded quizzes. Overall the scores were good, but there were still way too many "silly" mistakes due to not taking their time or checking answers. I still have a few students that seem to be making up their own way to multiply, simplify, and convert fractions.
I am not one to give much extra credit, but I did give students a chance to EARN some extra points on Friday. After reviewing each question on the quiz, I presented students with 8 questions that were VERY similar to what were on the quiz. There was a possible 10 points to be earned from these questions. I also awarded 1 point each for each of the 3 outlines that students filled out over the last couple of weeks. I reminded students all week that I would be checking to see that they were bringing their materials to class. I was impressed with the number of students that had all 3 outlines completed and organized in their binders.
On Wednesday, we will be back to the classroom to continue our unit on fractions.
Wednesday and Thursday we will begin multiplying mixed numbers, as well as dividing fractions. We will be using the same skills that we learned last week, so I expect students to pick up on multiplying mixed numbers and dividing fractions quickly.
As always, feel free to email me with any questions or concerns that you or your child may have.
nathan.culp@nhcs.net
Wednesday, February 1, 2012
Wednesday Feb. 1, 2012
Yesterday went really well as the response that I got from each class was "wow, this is really easy." Multiplying fractions is simply multiplying across the numerator, and multiplying across the denominator. I created an outline that students filled out during our notes, examples, and practice.
Today, students were split into 6 "stations." Each station focused on a different skill that we have learned over the last week. The quiz tomorrow will be made up of questions from the stations. Below are the questions students saw in class today.
Station 1 – Simplifying fractions by finding the GCF
Pick 4 problems
Find the Greatest Common Factor of each fraction, then simplify
1.) 4/12 GCF = Simplified =
2.) 5/35 GCF = Simplified =
3.) 8/24 GCF = Simplified =
4.) 3/15 GCF = Simplified =
5.) 6/12 GCF = Simplified =
6.) 2/13 GCF = Simplified =
7.) 10/60 GCF = Simplified =
8.) 6/20 GCF = Simplified =
Station 2 – Simplifying fractions by prime factorization
Pick 4 problems
Simplify each fraction by finding the prime factorization of the numerator and denominator, cancel out any possible pairs, then write in simplified form
1.) 27/35
In prime factorization = Simplified =
2.) 16/18
In prime factorization = Simplified =
3.) 20/30
In prime factorization = Simplified =
4.) 64/ 120
In prime factorization = Simplified =
5.) 100/ 150
In prime factorization = Simplified =
6.) 42/56
In prime factorization = Simplified =
7.) 9/24
In prime factorization = Simplified =
8.) 10/36
In prime factorization = Simplified =
Station 3 – Converting improper fractions to mixed numbers
Pick 6 problems
Convert to an improper fraction, then simplify if necessary
1.) 24/9 =
2.) 21/10 =
3.) 15/5 =
4.) 34/6 =
5.) 53/10 =
6.) 8/3 =
7.) 90/25 =
8.) 34/50 =
Station 4 – Converting mixed numbers to improper fractions
Pick 6 problems
1.) 4 2/3 =
2.) 5 1/5 =
3.) 6 5/7 =
4.) 2 4/5 =
5.) 10 2/3 =
6.) 3 1/2 =
7.) 5 3/8 =
8.) 9 1/5 =
Station 5 – Multiplying fractions
Pick 4 problems
Write your answer as a proper fraction or mixed number
1.) 5 x 2/3 =
2.) 7 x 5/8 =
3.) 2 x 7/10 =
4.) 1/3 x 2/5 =
5.) 1/8 x 5/9 =
6.) 4/5 x 1/8 =
7.) 4 x 5/9 =
8.) 1/6 x 5/8 =
Station 6 – Word problems
Pick 3 Problems
HINT: “of” means Multiply
1.) When John asked Brent how much pizza he wanted for lunch, he responded by saying “1/2 of 1/2 of a pizza”. As a fraction, how much pizza did he want for lunch?
2.) There are 280 students in the sixth grade. 1/8th of them picked reading as their favorite subject. How many of them picked reading as their favorite subject?
3.) John broke a candy bar into 4 equal pieces. He ate 1/2 of one of those pieces. How much of the total candy bar did he eat? (Answer will be a fraction)
4.) Ryan told his teacher that he completed 1/3 of the 96 questions on his test. How many did he complete?
5.) When Ben asked Jarrod how many tacos he could eat, he replied with “nine halves”. How could he show this number as a mixed number?
6.) There are 50 states on the United States of America. As a fraction, 4/25 of the states begin with the letter “M”. How many states begin with M?
Today, students were split into 6 "stations." Each station focused on a different skill that we have learned over the last week. The quiz tomorrow will be made up of questions from the stations. Below are the questions students saw in class today.
Station 1 – Simplifying fractions by finding the GCF
Pick 4 problems
Find the Greatest Common Factor of each fraction, then simplify
1.) 4/12 GCF = Simplified =
2.) 5/35 GCF = Simplified =
3.) 8/24 GCF = Simplified =
4.) 3/15 GCF = Simplified =
5.) 6/12 GCF = Simplified =
6.) 2/13 GCF = Simplified =
7.) 10/60 GCF = Simplified =
8.) 6/20 GCF = Simplified =
Station 2 – Simplifying fractions by prime factorization
Pick 4 problems
Simplify each fraction by finding the prime factorization of the numerator and denominator, cancel out any possible pairs, then write in simplified form
1.) 27/35
In prime factorization = Simplified =
2.) 16/18
In prime factorization = Simplified =
3.) 20/30
In prime factorization = Simplified =
4.) 64/ 120
In prime factorization = Simplified =
5.) 100/ 150
In prime factorization = Simplified =
6.) 42/56
In prime factorization = Simplified =
7.) 9/24
In prime factorization = Simplified =
8.) 10/36
In prime factorization = Simplified =
Station 3 – Converting improper fractions to mixed numbers
Pick 6 problems
Convert to an improper fraction, then simplify if necessary
1.) 24/9 =
2.) 21/10 =
3.) 15/5 =
4.) 34/6 =
5.) 53/10 =
6.) 8/3 =
7.) 90/25 =
8.) 34/50 =
Station 4 – Converting mixed numbers to improper fractions
Pick 6 problems
1.) 4 2/3 =
2.) 5 1/5 =
3.) 6 5/7 =
4.) 2 4/5 =
5.) 10 2/3 =
6.) 3 1/2 =
7.) 5 3/8 =
8.) 9 1/5 =
Station 5 – Multiplying fractions
Pick 4 problems
Write your answer as a proper fraction or mixed number
1.) 5 x 2/3 =
2.) 7 x 5/8 =
3.) 2 x 7/10 =
4.) 1/3 x 2/5 =
5.) 1/8 x 5/9 =
6.) 4/5 x 1/8 =
7.) 4 x 5/9 =
8.) 1/6 x 5/8 =
Station 6 – Word problems
Pick 3 Problems
HINT: “of” means Multiply
1.) When John asked Brent how much pizza he wanted for lunch, he responded by saying “1/2 of 1/2 of a pizza”. As a fraction, how much pizza did he want for lunch?
2.) There are 280 students in the sixth grade. 1/8th of them picked reading as their favorite subject. How many of them picked reading as their favorite subject?
3.) John broke a candy bar into 4 equal pieces. He ate 1/2 of one of those pieces. How much of the total candy bar did he eat? (Answer will be a fraction)
4.) Ryan told his teacher that he completed 1/3 of the 96 questions on his test. How many did he complete?
5.) When Ben asked Jarrod how many tacos he could eat, he replied with “nine halves”. How could he show this number as a mixed number?
6.) There are 50 states on the United States of America. As a fraction, 4/25 of the states begin with the letter “M”. How many states begin with M?
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