Dividing Fractions

Quote of the day:

• Student: "Why do I have to do this?"  
• Teacher:"Because it is my job to make you college and work force ready."

Dividing Fractions Using Models

Staring with whole numbers

Dividing with decimals

When dividing fractions, we are redefining our whole

Below are slides of a ppt presentation that I found online that help show dividing fractions, here's the link.

www.district87.org/staff/powelln/Eureka/.../division%20lesson.ppt

This explanation helped me visualize what was happening.

Homework - Beckman pg 233 #4 a-d

Fractions and Decimals

Fractions of Whole Numbers

1. There are 15 cars in Michael's matchbox car collection. Two-thirds of the cars are red.  How many red cars does he have?

Unit Parts Without Subdivisions

• You have 3/4 of a pizza left.  If you give 1/3 of the leftover pizza to your brother, how much of a whole pizza will your brother get?
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• Someone ate 1/10 of the loaf of bread, leaving 9/10.  If you use 2/3 of what is left to make French toast how much of a whole loaf have your used?

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• Gloria used 2 1/2 tubes of blue paint to paint the sky in her picture.  Each tube holds 4/5 ounce of paint.  How many ounces of blue paint did Gloria use?

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Subdividing the Unit Parts

• Zack had 2/3 of the lawn left to cut.  After lunch, he cut 3/4 of the grass he had left.  How much of the whole lawn did Zack cut after lunch?

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• The zookeeper had a huge bottle of the animals' favorite liquid treat, Zoo Cola.  The monkey drank 1/5 of the bottle.  The zebra drank 2/3 of what was left.  How much of the bottle did the zebra drink?

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Role of Estimation   

Predict with will happen. Rounding a tool that can be used to help estimate, but rounding isn't estimating.  Rounding is the process to help estimate.

If students understand benchmark fractions, that will help them when it comes to estimating.

• Addition 
•  3/4 + 7/5 .....7/5 is more than a whole, 3/4 is almost a whole.  I can estimate that my answer will  be more than a whole.  (Benchmark close to 1)
• Subtraction
• The same as addition, or at least pretty darn close.
• Multiplication

• In fractions there is an influction point, it is 1.  
• Alice in Wonderland Fractions
• How Tall is Alice
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• 1st number in multiplication is our starting part.  The second number is doing the work.  We compare to where we start to where we end.  If I am multiplying by something greater than one, then my answer will be greater than my starting point.  If I multiply by something smaller than one, my answer will be smaller than my starting number.
• 4/5 x 4/9 = the answer will be less than 4/5 because 4/9 is less than 4/5.  The answer is a lot smaller than 4/5.
• 4/5 x 1/15 = 1/15 is smaller than 4/5, the answer to this question will be smaller than the answer for 4/5 x 4/9.
• When asking kids to estimate, you don't want an answer, you want AN ESTIMATION
• Division
• a divided by 5 = a x 1/b
• 12 divided by 3 = 12 x 1/3
• When dividing fractions, you are multiplying by the reciprocal 
• Multiplication rules apply for division when estimating

• Models for Dividing Fractions


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Where Does the Decimal Go? (pg. 343 Van de Wall)

• 24 x 63 = 1512
• 0.24 x 6.3 = 1.512, the decimal goes between the 1 and the 5 because the number one thousandths smaller (compare to the problem w/out decimals)
• 24 x 0.63 = this answer is one hundreths smaller so the answer is 15.12
• 2.4 x 63 = this answer is one tenths smaller so the answer is 151.2
• 0.24 x 0.63 = this answer is one ten thousandths smaller so the answer is .1512

The key to decimals is understanding the base 10 system.

Homework

• Journal Entry
• Beckman pg 206-207 1, 3, 6
• Reading (Parker) 150 - 154

Finding the GCF Using the Upside Down Cake Method

I have refered to this method in earlier notes, but here is a great video and explanation of using the upside down cake method.

Reflection for January 12th Class

I really enjoyed the class activities that we did during class tonight.  I liked learning how Steve teaches fractions with is students.  He introduces adding fractions using an area model, then teaches subtracting fractions using an area model and then he continues to teach them together.  This is a teaching strategy I hadn't thought of before.  Steve said that he teaches fractions this way, so students don't see adding and subtracting as having two different rules.  Students learn that they have to do the same thing when adding and subtracting (using common denominators) fractions, the operation just changes.

Something that I have always had a difficult time with is explaining to students why we use common denominators, or why we change mixed numbers to improper fractions.  Using the area model to add and subtract fractions helped me as a teacher see what was happening, and I can see how that will help my students understand why we use common denominators.  I really like the visual representation, this is something I didn't always do when I was teaching fractions.

January 12, 2010

Fractions

Why do teachers struggle teaching fractions?

• They are very abstract
• They change appearance.   For example, 1/2 can be 4/8 or 9/ 18
• Lots of steps to remember
• Parents feel helpless when it comes to helping student with fractions
• There is a cultural fear or phobia of fractions

Equivalent Fractions

• Why? 
• Why is 3/2 equivalent to 9/6? These fractions represent the same amount.  If we divided 3 by 2, the answer is 1.5. Same for 9 divided by 6.

Simplifying Fractions

• Cake Method - helps students simply fractions

Example of simplifying using the cake method.

It is a good idea to mix in improper fractions with the other fractions.  That way there is one rule instead of students thinking there are two rules to remember.

Adding Fractions

• If students can count, they can add fractions.
• Drawing models
• 2/3 + 4/5 = 
• 7/4 + 1/3 = 25/12



draw model for 7/4 and 1/3



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Adding Fractions Using the Area Model - practice problems.

Subtracting Fractions

• The model is the same as what we did for adding subtractions.  The difference is, rather than counting the number of squares that are shaded, you cancel out boxes, and then count what shaded box which is last.



Subtracting Fractions  Using the Area Model - practice worksheet

When teaching adding and subtracting fractions, start with using the area models.  Teach them separate.  Then, teach adding and subtracting together.  

• Mixed Practice - Draw the area model AND then rewrite the problem based on the new model.

Adding and Subtracting Fractions - Developing the Algorithm

Homework

• Beckman Hardcover - pg 130 #s 1, 2, 3, 4, 16. 17
• Van de Wall 342-345

Number Rights

This link will take you to a great video that talks about how important each number is on the number line.

Math Snacks

January 5, 2011

Great Benchmark Fraction Activities


Hundredths disk -

• Cut out the pink and white circles
• Cut along the dotted line
• Put the circles together

Students look at the side that doesn't have lines and predict sizes of different fractions such as 2/5 1/4 30/100, 16/32.  Students then turn the circles over and see if they are correct.

Organize fractions, percentages and decimals into equal groups.

• Strategies
• Elimination - do what you know first
• Organize cards

Best Match

• Strategies
• Students will take what they know about fractions, decimals and percentages and order them on the numberline.  For example, they will start ordering the fractions, and then when they need to place decimals on that same numberline they may either try to look at each decimal as a fraction or each fraction as a decimal.  (1/4 is the same as .25 so .267 would be places after 1/4 or .25)
• Students can take fractions and relate them to fractions that they know.  For example, 2/7 is close close 2/8 which is 1/4.  9/11 is close to 9/12 which is 3/4. AKA - Friendly fractions

I have/Who has activity

• Each student is given a card that says something like, "I have 0.84 (eighty-four hundredths) Who has the fraction equivalent for 0.04 (four hundredths)?  The student who has the equivalent fraction will read what is on their card.  This is a great way to help students practice mastery and automaticity.  This will give students a chance to practice doing math mentally.

Worksheet

Homework:

Read Van de Wall section on adding fractions pgs 312 - 317