Lesson 4: Number Lines, Mixed Numbers & Improper Fractions
Grade Level 6
Unit Fractions
Date 11/7/11
Time: 45 minutes
Objectives
SWBAT locate fractions on a number line
SWBAT turn mixed numbers to improper fractions, and vice-versa (apply, CP)
SWBAT create a graphic organizer (in the form of a 12 page Burrito Book) that contains strategies that will help them solve arithmetic problems that involve fractions (create, CP)
SWBAT find relevance in fractions by identifying 2+ ways they use fractions in their everyday lives. (evaluate, A)
Prior Knowledge
-Students should be able to define fraction, numerator and denominator.
-Students should have an assembled Burrito Book (BB).
-Students should have experience working with number lines.
-Students must be able to fluently multiply, divide, add and subtract positive integers.
-Students should have experience factoring.
Materials/Resources
Burrito Book, Whiteboard, dry erase marker, Fractions Detective (lesson 3 homework), Number Line and Mixed Number Conversion Worksheet. math journals, pencils, calculators.
Lesson
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Time
5 min
15 min
10 min
10 min
5 min |
Lesson
Go over objectives Warm-up 1.Think-pair share about Fractions Detective Homework 2. Write and/or draw 3+ examples of fractions that you learned about from your homework, or from listening to others
I do: Fractions on a number line 1. When fractions have the same numerator, the fraction with the larger denominator is smaller. Order from least to greatest: 1/6, 1/9, 1/2 2. When fractions have the same denominator, the fraction with the larger numerator is larger. Order from least to greatest: 5/7, 4/7, 1/7
What do we do when we need to compare fractions with different denominators and numerators? 7/10 and 2/3. Which is bigger? We have to find a common denominator or a common numerator. Find common denominator. Show steps.
Try 2 more problems together: Volunteers come to board and find either common numerator or denominator.
I do: Mixed Numbers to Improper Fractions (and vice-versa) What is a mixed number what is an improper fraction? (Improper numerator is larger than denominator) There is a recipe to turning a mixed number to an improper fraction. Write this in your burrito books: 1.Multiply the denominator and the whole number 2. Add the numerator. 3. Put that number over the denominator. Works every time! Show an example. Draw arrows as you multiply and add.
We do: Mixed Numbers to Improper Fractions Give 2 problems. Volunteers to come to the board. Ask volunteer to say the step s/he is doing as s/he works. Ask what step are you one now? What did you just multiply? If volunteer does not want to narrate for the volunteer: s/he just multiplied the denominator and whole number. Next s/he will add the numerator. Etc.
I do: Improper Fractions to Mixed Numbers How do we go the other way? Write this recipe in your burrito book: 1.Divide the numerator by the denominator. 2.The number of times the numerator goes into the denominator evenly is the whole number. 3.The remainder is the numerator 4. Keep the original denominator. Give an example.
We do: Improper Fractions to Mixed Numbers Give 2 problems. Volunteers to come to the board. Ask volunteer to say the step s/he is doing as s/he works. If volunteer does not want to narrate for the volunteer
Reflect 1. Give homework and directions. 2. On page 10 of BB reflect on what you learned, what you enjoyed, questions you have.
Homework: Comparing/Ordering Fractions and Mixed Number Conversion Worksheet. (Do odds on both sides). |
Monitoring Assessment
1. Listen to pair-sharing, share as a class
Show 2-3 fractions with same numerator, then 2-3 fractions with same denominator. Student volunteers compare/order.
Students guess.
Popsicle sticks to call volunteers. Students may pass.
Check to see if it is in burrito book.
Popsicle stick volunteers. Students may pass.
Check to see if it is in the burrito book
Popsicle stick volunteers. Students may pass. |
Adaptations/Modifications
ESOL Option to draw warm-up activity
TAG Opportunity to volunteer, or opportunity to show strategies/other methods of comparing fractions
Special Needs Option to draw warm-up activity
Literacy Option to draw warm-up activity
Other
Reflection
What's next?
Adding and Subtracting like fractions, greatest common factor, reducing
What worked?
The students grasped the idea of a “recipe” for turning mixed numbers to improper fractions and vice-versa. During the lesson, one of the students asked said, “So, I do this every time? Really? That's easy.” I think I simplified the process for both. I made sure to use the vocabulary we defined the previous lesson, and I used visuals to explain the process (drew arrows, wrote labels, etc.) I am so glad we are using burrito books. I like that later on, when students need to convert improper fractions and mixed numbers to solve multiplication/division problems, I can have them refer to what they wrote. I hope this will give students note-taking and studying skills they can apply to any subject.
What would I change?
After grading that night's homework I learned that I tried to cover too much. The students didn't understand that they needed to find the common denominator/numerator to be able to compare fractions. I suspected they needed more time on the concept, but I needed to move on to converting mixed numbers to improper fractions. Next time I would dedicate an entire lesson to comparing and ordering fractions (since I had to spend the first part of a different lesson reviewing the concept I basically ended up doing so). I would have also liked to teach students how to turn fractions into decimals. I think this is a much more straightforward way to compare fractions. I did not choose this approach because my mentor teacher and I were worried this would confuse the students since they struggled so much with the decimal unit. Looking back, I think connecting the two could have increased their understanding of both concepts.
On the Board Problems (Teacher Notes)
Comparing/Ordering Fractions Examples:
I do: 7/10 and 2/3
You do: DO 2
Order the fractions from least to greatest:
1/6, 1/8, 1/12, 1/4
3/8, 1/5, 2/3
3/8=.375
1/5=.2
2/3=.66667
5/9, 6/11, 9/17
5/9= .5555556
6/11= .54545455
9/17= .5294
Mixed to Improper Examples
I do: 2 and ¾
You do: DO 2
2 and 2/9
4 and 1/3
Improper to Mixed Examples
Improper fraction has a larger numerator than denominator!
I do:
53/7
(answer: 7 and 4/7)
17/6
(answer 2 and 5/6)
20/1=20!!
10/1=10!!
5/1=5!
You do: DO 2
20/7=
13/1=
43/5=
Please wait...