MAT104 Blackboard Assignment:6
Sample Student Response:
Lesson Plan 1
Grade: Fourth Grade
Topic: Adding pairs of fractions with unlike denominators with a common denominator in one of the fractions.
Aim: How do we add fractions with unlike denominators?
Previous Knowledge Assumed: Students are able to: find equivalent fractions, add fractions with like denominators, reduce fractions, find the least common multiple
Materials needed: Hershey Bars, slates, dry erase markers, erasers, worksheets, adding fraction game cards
Motivation: Give each pair of students a Hershey Bar. Instruct one student to eat 1/4 of the bar and the other student to eat 1/4 of the bar. Ask students how much of the bar did they eat in all. Have students tell how they got their answers. Be sure to elicit the addition of fractions with like denominators. Distribute a second candy bar to pairs of students. This time, have one student eat 1/2 and the other student eats 1/4 of the candy bar. Ask the students how much of this candy bar did they eat in all. Discuss how this addition problem differs from the first. Elicit from students the aim: to add fractions with unlike denominators.
Teaching Method/Procedure:
1.Motivational activity
2.Elicit aim
3.Direct instruction: Start with the example from the candy bar. Ask students if we can add these two fractions together, 1/2 + 1/4. Ask why not. Model the procedure for adding fractions with unlike denominators. Find the LCM of both denominators, which will be the LCD. Start with the lower number of the denominators. Find multiples of that number. In this case 4 is a multiple of 2. So we have found the LCD. Convert 1/2 to 2/4. Discuss steps used in the conversion. Add 2/4 + 1/4= 3/4
Put second example on the board: 2/3 + 1/6. Ask students how we would add these two fractions. Elicit steps from students. Model their responses on the board.
Repeat the procedure using the examples: 1/8 + 3/4, 1/5 + 6/10, 3/12 + 2/6
4. Practice - Distribute slates, dry erase markers and erasers to the students. Put examples on the board. Have students write their answers on their slates. Students hold up slates to show their responses. Teacher monitors responses to identify those students having difficulty.
Problems on the board: 1/8 + 3/16, 1/3 + 4/12, 2/6 + 5/12, 2/5 + 4/15
5.Medial summary: Ask students to tell what they have learned about adding fractions with unlike denominators.
6. Practice through game - Play Addition of Fractions Card Game: Two fraction cards are in a plastic bag on pink paper. The yellow card contains the answer. Students take out the pink cards and add the two fractions. Students check their answers against the yellow card. As students play the game, the teacher provides small group instruction for those students who had difficulty earlier in the lesson.
7.Final summary: Have one or two students summarize their learning from the lesson.
What Can Go Wrong? Students may not remember how to add fractions. They may have created their own incorrect strategy. Foe example: 1/2 + 1/4 = 2/6
Students may not be able to find the LCM therefore cannot find the LCD.
Students forget to reduce fractions.
Drills/Problems: Students complete their practice sheet independently as the teacher circulates throughout the room.
Practice sheet
Name______Date______
Directions: Add the fractions. Remember to reduce your answers when possible.
2/3 + 1/6 = ______
2/9 + 2/3 = ______
2/5 + 3/10 = ______
5/8 + 1/4 =______
7/12 + 1/4 = ______
1/9 + 2/3 = ______
Choose one of the above addition fraction problems. Write out your explanation for how you solved the problem.
______
______
Write your addition number sentence for each problem.
Beth ate 1/8 of the Hershey bar. Daniel ate 3/4 of the Hershey bar. How much of the candy bar did they eat in all?
______
Sophia ran 3/10 of a mile. Carole ran 2/5 of a mile. How much did they run in all?
______
On Monday, Mark read 4/9 of his book. On Tuesday, he read 1/3 more. How much of the book has he read?
Homework Worksheet: Addition of fractions with unlike denominators
Name______Date ______
Directions: Add the fractions. Remember to reduce your answer when possible.
3/8 + 2/4 = ______1/2 + 1/10 = ______
3/16 + 5/8 = ______3/5 + 2/15 = ______
2/3 + 4/9 = ______5/6 + 1/12 = ______
3/8 + 6/16 = ______1/8 + 5/24 = ______
Choose one of the addition sentences above. Write how you solved the problem.
______
Write the rule for adding fractions with unlike denominators.
______
Write your own word problem that includes the addition of fractions with unlike denominators. ______
Lesson Plan 2
Grade: Fourth Grade
Topic: Adding fractions with unlike denominators without a common denominator in the fraction pairs.
Aim: How do we add fractions with unlike denominators without a common denominator in the pairs?
Previous Knowledge Assumed: Students will be able to: find equivalent fractions, add fractions with like denominators, reduce fractions, find the least common multiple, add fractions with unlike denominators with a common denominator in one of the pairs.
Materials: rectangular pieces of paper, spinners with 8 fractions on each, slates, dry erase markers, and erasers
Motivation: Distribute rectangular pieces of paper to pairs of students. One student receives paper divided into thirds; another receives paper divided into fourths. Have students cut sections of the paper on the dotted line. Instruct students to use the pieces of paper to attempt to add 1/3 and 1/4. Discuss student responses. Discuss how this addition problem differs from the problems solved in the previous lesson.
Teaching Method/Procedure:
1.Motivational activity
2.Elicit aim
3.Distribute a rectangular piece of paper divided into twelfths to each pair of students. Have students attempt to add 1/3 and 1/4 by covering the pieces of the rectangle divided into twelfths. Discuss discoveries made by the students. Elicit how we can find the least common denominator from the students.
4.Direct Instruction: Model addition of 1/4+1/3. Instruct students to always begin with the higher denominator. Find multiples of that number. For example: the higher denominator in this problem is 4. The multiples of 4 are 4, 8 and 12. Ask each time if the number is a multiple of the other denominator. Emphasize that once you say yes, you have found the least common denominator. In this case the least common denominator is 12. Have the students convert 1/3 and 1/4 to equivalent fractions with a denominator of 12. Students should determine that 1/3 can be converted to 4/12 and 1/4 can be converted to 3/12. Have the students add these fractions 3/12 + 4/12 = 7/12.
5.Provide another practice problem for the students. The second example is 2/5 + 3/8. Ask students which fraction contains the higher denominator. The students will respond that 8 is the higher denominator. Have the students tell you the multiples of 8. Students will determine that 40 is also a multiple of 5, the smaller denominator. Have them change 2/5 and 3/8 to equivalent fractions with a denominator of 40. The equivalent fraction of 2/5 is 16/40 and the equivalent fraction of 3/8 is 15/40. Have the students add these fractions 16/40 + 15/40 = 31/40.
6.Provide an additional practice problem as reinforcement. Have the students add
1/6 + 3/5. Elicit from the students the steps for solving this problem. Have the students determine the least common denominator by finding multiples of 6. After the students have converted these fractions to equivalent fractions with a common denominator, have the students add the fractions to determine the answer.
7.Medial Summary: At this point in the lesson, elicit the aim from the students and have them explain what they have learned about adding fractions with unlike denominators.
8. Introduce a second method for finding a common denominator. Have the students focus on the previous problem, 2/6 + 3/5. Ask if there is a relationship between the denominators. Elicit from the students that 65 = 30. Elicit from the students that a common denominator can be found by multiplying the denominators. Highlight that a common denominator can always be found by using this method but it might not always be the lowest. Use 1/4 and 1/10 as an example.
9. Distribute slates to students. Students will solve the following problems on their slates using the multiplication of denominators to find their answers.
3/7 + 2/8 = 3/4+ 2/6= 1/5 + 3/9 =
10. Practice through game – Play Addition of Fractions Spinner Game. Give two spinners to each pair of students. Have students add the fractions from the spinners. Each spinner will contain 8 fractions. Students can use either method taught in this lesson to determine a common denominator. Students are required to reduce the fraction to lowest terms. Teacher provides small group instruction for struggling students.
11. Final Summary: Students will summarize the concepts learned in this lesson.
What Can Go Wrong: Students may have difficulty finding the least common multiple. Students may have difficulty converting fractions to equivalent fractions. Students may incorrectly add the fractions without converting to common denominator. Students may forget to reduce fractions to lowest terms.
Future Lessons: Adding Mixed Numbers With Unlike Denominators
Drills/Problems:
Students complete their work independently as the teacher circulates throughout the room.
Practice Sheet- Class Work
Name______Date______
Directions: Add fractions. Remember to reduce your answers when possible.
2/3 + 1/4 = ______
2/7 + 3/5 = ______
3/8 + 3/7 =______
1/2 + 2/9 = ______
1/9 + 2/8 =______
Choose one of the above addition fraction problems. Write out your explanation for how you solved the problem.
______
Write your addition number sentence for each problem.
Dave ate 1/2 of a small pizza. Betty ate 3/12 of the same pizza. How much of the pizza did they eat in all?
Susan walked 2/3 of a mile. Joe walked 1/7 of a mile. How much did they walk in all?
______
Bob did 1/8 of his homework. Then he did 5/9 of his homework. How much of his homework did he complete?
Bonus Problem: Find several pairs of fractions with different denominators that have a sum of 4/5. ______
Homework
Name______Date______
Directions: Add the fractions. Remember to reduce when possible.
1/2 + 1/4 =______2/5 + 1/3 =______
1/6 + 1/4=______5/6 + 7/8= ______
2/3 + 1/4=______7/10 + 3/4=______
1/9 + 5/6=______1/5 +1/9 =______
Choose one of the above addition fraction problems. Write out your explanation for how you solved the problem.
______
Write your addition number sentence for each problem.
Dave walked ½ of a mile to the grocery store and 1/3 of a mile to the hardware store. How far did he walk in all? ______
Mary walked 1/8 of a mile to the grocery store. She then walked 1/5 of a mile more to the library. How far did she walk in all? ______
On Saturday, Frank read 3/5 of his book. He read 2/9 more on Sunday. How much of his book did he read in all? ______
Christina helped her father with some repair work. She worked 1/2 hour on Monday and 2/5 of an hour on Tuesday. How long did she work with her father in all? ______
To repair his doghouse, Jim nailed two boards together. One board was 1/4 inch thick and the other board was 1/3 inch thick. What was the total thickness of the two boards?
______
NCTM or Traditional Approach
I believe my lesson plans on the addition of fractions with unlike denominators incorporate both the positive aspects of NCTM and the more traditional approach. The teacher assumes the role of facilitator as well as provides direct instruction. The students work independently and cooperatively, use the language of math, make discoveries and practice what they have learned.
The motivation in both lessons is aligned with NCTM standards. It includes hands-on experience, cooperative learning, problem solving, as well as discussion of mathematical reasoning. It affords students the opportunity to make some discoveries on their own. Students are required to use prior knowledge as they attempt to find their answers.
The teaching method/procedure fuses NCTM standards and a conventional approach. Step 3 in lesson one and steps 4, 5, 6 and 8 in lesson 2 incorporate direct instruction and modeling by the teacher as prescribed by traditionalists. The teacher questions and elicits responses from the students while guiding them in the correct direction. Step 4 in the first lesson and step 9 in the second lesson satisfy both traditionalists and NCTM. Students practice what they have learned but in a more interactive and “fun” way. The medial summary in both lessons is aligned with NCTM standards when students are required to present their knowledge in their own words. The Addition of Fraction Card Game and the Addition of Fractions Spinner Game are also aligned with NCTM. Students develop and apply necessary skills as they build a stronger foundation for adding fractions. While engaging in the game, they integrate their knowledge, share their ideas and develop greater mathematical understanding. The final summaries follow NCTM. Students must verbalize their understanding and share their own thoughts about their learning.
As prescribed by the traditional approach, the first part of the class work sheets and homework sheets provide the opportunity to develop proficiency through practice. In addition, the teacher is able to assess student progress and provide feedback. NCTM standards are met in the remaining sections of the practice sheets and homework. Students are required to synthesize their knowledge and use higher level thinking skills as they give a written explanation of their mathematical reasoning.
Throughout the lessons, the balance of NCTM standards and traditional approach addresses parental concerns. There is a higher level of expectation and a more supportive environment for all students. There is a clear understanding of what students need to learn and a challenge to help them to learn it well.
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