Part II

Day 7: Adding and subtracting fractions of common denominators.

Standards:  5.2.8

Focus Question: What process do I use to add or subtract fractions with common denominators?

Objective 1:  Name the parts of a fraction. (numerator/denominator)

·         The teacher will display a bridge map showing the parts of a fraction, and discuss the meaning of each part.  The students will replicate the bridge map in notes.  To practice this skill the students will play “Around the World”.  In order to play, one student will stand beside another student and will be presented a question by the teacher.  The student to answer first will move on to the next student.  The first student to get back to their own seat will win.  The teacher will show a fraction and ask for the students to identify the number that coordinates with the bridge map segment. ( Ex.) Which part of the fraction shows the numerator?)

_____3_______^__numerator_____^_pieces selected___________^ members selected

          4                  denominator          pieces whole is divided into     members in group

Objective 2:  Use concrete models to demonstrate what each part of a fraction represents and what the shadow fraction is.

The teacher will provide the steps to follow when representing part of a group as a fraction:

A)   Determine number of members in group. (denominator)

B)    Determine number of members specified (numerator)

C)    Determine “shadow fraction” – the fraction of the group that is NOT specified

·         The teacher will display a map of the United States, and guide the students in representing the number of states beginning with “M” as a fraction.  Demonstrate that the number of states NOT starting with an M is the shadow fraction.

·         The students will answer the following questions in fraction form independently and name the shadow fraction for each answer.

A)   What fraction of the states begin with the word “New”?…..What fraction does not?  (shadow)

B)    What fraction of the states border South Carolina? ….What fraction do not?  (shadow)

C)    What fraction of our class are boys?  girls? (shadow)

·         The students will be grouped into groups of 4-5 and answer the following questions in fraction form and the shadow fraction:

A)   What fraction of your group are boys? girls? (shadow fraction)

B)    What fraction of your group has tennis shoes on?…..shadow fraction?

C)    What fraction of your group has blue eyes? ……shadow fraction ?  (those without blue eyes)

D)    What fraction of your group has on red?…..shadow fraction?  (those without red)

Homework:  DR 9-5

Materials:     Fraction cards for “Around the World”

Copies of maps with state names

List of states in alphabetical order

Assessment: Class discussion of USA fractions, Independent work on USA fractions, Group work

Day 8:

Objective:  Add/Subtract fractions with common denominators, add shadow fractions

Focus Question: What process do I use to add or subtract fraction with common denominators?

Standards:  5.2.8

·         The teacher presents the rules for adding/subtracting fractions (the denominator does not change, the numerators will be added or subtracted).

·         The teacher will model this rule with an analogy.  The denominator will serve as a highway number and the numerator will be the amount of people in a car.  (The amount of people in a car can change as you add to it or subtract, but the highway number will not change.)

·         Model that shadow fractions, when added, equal one whole

·         Give fraction problems on the board the students will complete independently (or give copies of “Fishing for Sums and Differences), then check work as selected students solve the problem on the board.

         (get problems from “Fishing for Sums and Differences”)

Homework:  DR 10-1 (Do not have to put in simplest form as directions say)

Materials Needed: copies of “fishing for Sums and Differences”  (optional…you can just write some of the problems on the board)

Assessment: Independent work on “Fishing for Sums and Differences”

Day 9:  Equivalent Fractions

Objective:  The students will calculate equivalent fractions and represent on concrete model.

Focus Question: How can concrete models representations help me calculate equivalent fractions?

Standards:  5.2.4

·         Explain that we need to find equivalent fractions because:

1.     The denominator has to be the same to add two fractions ex:  1/2  + 3/8

2.     In order to reduce fractions to put them in simplest form.

·         The students will make “Fraction Fringe” booklets for ½ and 1/3  base.

·         The students could manipulate their “Fraction Fringe” booklet to create the various equivalent fractions for 8/16 and record their answers (4/8, 2/4, ½). (The students can problem solve to identify the rule for creating equivalent fractions.)

·         Once the students are given a chance to identify the rule to create equivalent fractions, the teacher will model this rule on the overhead by writing out each step.  (The numerator and denominator should be multiplied or divided by the same number……Like brothers and sisters….to keep it fair, what you do for one you have to do for the other)

·         Write the next fractions in the pattern:  3/4,  6/8,  ………

1/2,  2/4,  …..

·         The students will calculate equivalent fractions by either multiplying or dividing and check answers by using their fraction fringe. (page 354 #15 – 33 odd)

Homework:  DR 9-9

Materials:  Materials for making Fraction Fringe books

Assessment: Fraction Fringe booklets and independent use of fraction fringe booklet

Day 10:  Reduce Fractions

Objective: The students will find the GCF (Greatest Common Factor) and use this to reduce fractions.

Focus Question: What strategies can I use to reduce fractions?

Standards:  5.2.9

·         The teacher will model how to find GCF using a factor rainbow and how it is used to reduce fractions (Divide numerator and denominator by the GCF).  Emphasize the importance of using divisibility rules to ensure that factor rainbows are complete

·         Define composite numbers as those with a colorful rainbow (more than 1 & itself as a factor), and prime numbers as those with a plain factor rainbow (only 1 & itself as factors)

·         Students will be grouped into pairs.  Each student will be given (or draw from a bag) a number to list factors of. The students will meet together to find the largest factor in common.  Give bigger numbers to students needing a challenge.

·         Students will use their original numbers to create a fraction, and use GCF to reduce that fraction.  Students should then determine if the fraction is indeed in simplest form

·         Independent practice will be provided.  Page 362 #23 – 34

Homework:  DR 9-10

Materials:  Cards with numbers on them ex:  56,84, 64, 93, 99, 132, 174, 216, 84, 45, 32, 54, 30, 72, 24, 40, 30, 90, 63, 18, 27, 18, 12, 48, 36, 42

Assessment: Independent practice on page 362

Day 11:  LCM and common denominators

Objective:  The students will find LCM and use it to create common denominators in order to add fractions.

Focus Question: What strategies will I use to find the LCM and create common denominators in order to add fractions without common denominators?

STANDARDS:  5.2.7

·         The teacher will model the difference between GCF and LCM.  The teacher will list the multiples of two given numbers and find the smallest common multiple.  Then, model how to use this to achieve common denominators.  (Show both skip counting or multiplying methods)

·         Explain that we need to find common denominators in order to put fractions in a format that we can add or subtract since they have to have the same denominator to add or subtract.

·         The students will get back into pairs, and each student will be given (or draw from a bag)a fraction with unlike denominators.  The students will have to find the multiples of their denominator.  Then, compare results with partner to find the LCM, and use this to create equivalent fractions with common denominators.

·         Independent practice will be provided with teacher assistance as needed (pg. 339 #12-28 even)

·         Early finishers or challenge:  switch roles and make up problems like:  “I’m thinking of 3 numbers greater than 6, whose LCM is 12.  What is the number?”  A partner must then find the answer then switch roles.

Homework:  DR 9-3

Materials:  cards with fractions on them ex:  ¼, 3/5, 4/5, 5/6, 3/7, 5/7, 2/14, 7/9, 1/6, 7/8, 12/24, 1/6, 2.9, 3/8, 2/3, 5/6, 5/9, ¾, 24/7, 3/10, 7/10   ….make up any others & repeat any

Assessment: Class work, Group activity, Independent practice

Day 12:  Add fractions with unlike denominators

Objective:  The students will add fractions with unlike denominators

Focus Question: How can I apply the strategies to find LCM to add fractions with unlike denominators?

Standards:  5.2.8

·         The teacher will model how to use LCM and equivalent fractions to add/subtract fractions with unlike denominators, using overhead fraction strips to show the equivalent fractions the addends are being changed to.  ½ + 1/3 = 5/6       ½ + 1/5 = 7/10      ½ + 2/3 = 7/6      ¼ + 3/8 = 5/8     2/3 + 4/6 = 8/6

·         (optional) The students will use their fraction strips to add fractions with unlike denominators, then add by finding LCM changing fractions to equivalent fractions in order to give them like denominators.

·         Students will be given more problems to complete independently or guided as needed – (above problems &/or DR 10-6 even).

·         Challenge:  The students will complete an AIMS activity puzzle “The Little T” in which they have to align fractions in a T so that the sum of the fractions in each of the two arms are the same.  (See attached)  Faster paced students will complete the puzzle alone, while students who need more guidance will receive a puzzle that is partially completed.  THIS IS A TIME CONSUMING AND GREAT CHALLENGE – IF THEY DON’T FINISH YOU MAY WANT TO KEEP COPIES OF THIS ON HAND FOR STUDENTS NEEDING CHALLENGE IN FUTURE LESSONS.

Homework:  DR 10-6 odd

Materials:     Overhead fraction strips

Precut paper fraction strips (optional)

“Little T Puzzle” and answers

Practice problems to add that will work with overhead strip fractions

Assessment: Independent work, AIMS activity

Day 13:  Subtract fractions with unlike denominators

Objective:  The students will subtract fractions with unlike denominators

Focus Question: How will I subtraction fractions without common denominators?

Standards:  5.2.8

·         The teacher will model how to use LCM and equivalent fractions to subtract fractions with unlike denominators, using overhead fraction strips to show the equivalent fractions the fractions in the problem are being changed to.  1/2  - 1/3= 1/6,       1/2  - 2/5 = 1/10,         2/3 – ½ = 1/6

·         The students will use their fraction strips (optional) to subtract fractions with unlike denominators, then subtract by finding LCM changing fractions to equivalent fractions in order to give them like denominators.

·         Practice:  DR 10 – 7 Even problems

Homework:  DR 10-7 Odd Problems

Materials:     Overhead fraction strips

                Precut paper fraction strips

Assessment: Activity with Fraction strips, DR 10-7

Day 14:  Models of fraction problems

Objective: Create models to represent adding, subtracting, and shadow fractions

Focus Question: How can the strategy of creating models help me add or subtract fractions?

Standards: 5.1.8

·         HOOK:  Ask students, what number of students prefer the new Nintendo Wii to the new X-Box 360?  Separate onto different sides of the room to create a model for the fraction of those liking each.  Explain that we can draw models to represent fractions and addition and subtraction of fractions.

·         Draw representations on the board of the following problems:  ¼ + 2/4,     6/10 – 2/5,    3/8 – 1/8,    1/3 + ½  , 

·         Draw a representation of the shadow fraction of:  5/8,    ¾

·         Have students draw models of the following problems:  pg. 398 #1,2,5,6,20,22   and the shadow fractions of 1/7 & 3/5.

Homework: 

Materials:  Colored Pencils

Assessment: Drawings, Independent practice Pg 398

Day 15:  Compare and Order Fractions

Objective: The students will compare fractions by using the correct sign:  <, >, or =, and put fractions in greatest to least, or least to greatest order, as directed.

Focus Question: What process will I use to compare fractions by using the correct signs: <,> or =.

Standards:  5.2.4

·         Teacher models using cross multiplication to compare fractions.      2/7            9/11

2 x 11                 9 x 7

   22        <             63

Therefore 2/7 < 9/11

          Multiply numerator of one fraction times denominator of other fraction.  Record the answer under the fraction for which you used the numerator.  The fraction with the greatest product written under it is the greater fraction.

·         Students play “Dueling Fractions”.  Students are each given a bag of fractions written on index cards.  They pull out a card and compare their fraction with their partner’s fraction by recording them and placing the appropriate sign in between them after cross multiplying.  Students can then use their “fraction fringe” to check for accuracy of comparisons.  They can keep track of who has the higher fractions and keep score to determine the “winner”.

·         As faster learning students use up all fractions in their bag, they can strategically add more fractions to their bag so as to attempt having higher value fractions than their partner.

·         Higher level students will share strategies for coming up with higher value fractions.

·         Students will then be provided with independent practice in class.

Homework:  DR 9-6

Materials:  Bag w various fractions in it for each student

Assessment: Observation made during game, Independent practice

Day 16:  Review for Test

Objective:  Review for test on :  parts of a fraction, adding and subtracting fractions with like and unlike denominators, LCM, GCF, equivalent fractions, comparing and reducing fractions, Name fractions represented in a picture or model

Focus Question: How can I apply the strategies I have learned to find parts of a fraction, adding and subtracting fractions with like and unlike denominators, LCM, GCF, equivalent fractions, comparing and reducing fractions, Name fractions represented in a picture or model

Standards: 5.2.8, 5.2.4, 5.2.9, 5.2.7, 5.1.8

·         After writing the problems below (not answers) on the board vertically, have students follow the following steps to add or subtract and put answer in simplest form:

1.      Find the LCM of denominators

2.     Find equivalent fractions with common denominators

3.     Add or subtract the fractions

4.     Find the GCF of the numerator and denominator in the answer

5.     Reduce the sum or difference to simplest form

·         Play “Who has I have”:

1.      Pass out cards with questions (see attached chart to make cards)

2.     Have all students find answer to the questions on the cards as the question is called out

3.     Whoever is holding the card with the answer call out “I have…..”

4.     That person then reads the question on their card as all solve & wait for someone to call out they have the answer.  Keep repeating until all cards have been read and solved.

Homework:  Page 417 D & E

Materials:     Who Has I Have cards

                Copies of Fraction Part I Pretest

6/10 – 2/5 =  2/10 = 1/5             6/8 – 1/3 =  10/24 = 5/12   7/8 – 3/4  = 1/8         

2/3 + 8/12 = 16/12 = 4/3 = 1 1/3     

16/32 – 1/4 = 8/32 = 1/4             2/4 + 2/9 = 26/36 = 13/18           9/10 – 1/4 =  13/20      

 3/10 + 3/5 = 9/10

Assessment: “Who Has, I Have” game, class work

“Who Has I Have” Cards