Maria has taught University level psychology and mathematics courses for over 20 years. They have a Doctorate in Education from Nova Southeastern University, a Master of Arts in Human Factors Psychology from George Mason University and a Bachelor of Arts in Psychology from Flagler College.
After this lesson, students will be able to:
- Demonstrate an understanding of the addition of mixed numbers
- Identify at least one method for how to add mixed numbers
- Define the term 'mixed number'
Warm-up and Instructions - 20 minutes
Activity 1 - 30-45 minutes
Activity 2- 30 - 45 minutes
Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)
Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.
- Printed transcripts of the video lesson Mixed Numbers: How to Add, Subtract, Multiply & Divide (edit out the sections 'Multiplying Mixed Numbers', 'Dividing Mixed Numbers' and 'Borrowing with Mixed Numbers').
- Hard copies of the lesson quiz (change all operations to addition)
- Audio/Video equipment
- Poster paper
- Art supplies
- Review the parts of a fraction: numerator and denominator.
- Review the concept of mixed numbers. Ask:
- What does the large number represent?
- What is the other part of a mixed number?
- Review how to add fractions. Ask:
- What is the most important rule when adding fractions? (The fractions must have a common denominator.)
- How do you get a common denominator for fractions?
- Is there another way?
- On the board, review all ideas students have for how to add fractions and how to find common denominators. This should be a review.
- Allow students to offer sample problems to be worked on.
- Tell your students that you are going to be continuing to learn more about mixed numbers today; specifically, you will focus on how to add mixed numbers.
- Hand out the transcripts of the video lesson.
- Start video. Pause at time marker 1:50. Discuss:
- Is everyone clear on how to change a mixed number to an improper fraction?
- How might this be helpful when adding fractions?
- Skip to time marker 3:59, 'Adding & Subtracting Common Denominators'. Play the video pausing at time marker 4:31.
- Point out that adding happens twice: between the whole numbers and between the numerators (but not the denominators).
- Pause the instruction to give students time to practice this concept. Practice by asking a group of students to go to the board and write up their own sample problem of mixed numbers with common denominators and then solve the problem. Ask:
- You've all done well when the denominators are the same, but what if they weren't the same?
- Restart the video at marker 4:54, 'Adding & Subtracting Unlike Denominators'. Pause at time marker 5:07. Ask students to write down the steps to adding mixed numbers with unlike denominators. Discuss:
- Is this process different from what you had to do for adding regular fractions before?
- How do you think the whole number impacts the process?
- Continue the video and stop at time marker 5:42.
- Select a few students to write mixed fraction addition with unlike denominator problems on the board. Tell the students to solve their problems using the same steps shown in the video.
- Give an example of a word problem using mixed number addition:
- If a farmer gets 3 ½ buckets of milk from his cow on Saturday and only 2 ¼ buckets of milk on Sunday, how much milk did he get over the weekend? 5 ¾
- Allow students time to review the concepts and ask questions before taking the quiz.
- Hand out the lesson quiz. Go over each question and answer with the class after they have finished it.
Activity 1 - I'll Do It My Way
- For this activity, you should remind students that everyone thinks a little differently. Reinforce that it is okay to have a different method for solving problems than the one shown in class as long as it works.
- Pair students and give each pair a piece of poster board.
- Instruct students to create a poster explaining the method to add mixed numbers. Encourage them to come up with an alternative method to the one shown in the lesson.
- Allow time for students to present their work to the class.
Activity 2 - Test Me
Students should construct a practice quiz/worksheet of mixed number addition. Each student should:
- List at least ten problems
- Vary the degree of difficulty
- Include at least one word problem
- Include an answer key on the back of their worksheet
Instruct students to swap papers, and solve their classmates' worksheets.
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