Talent Management Division Supporting All Employees 333 South Beaudry Avenue, 14

Math/6 Grade

Multiplying Fractions and Mixed Numbers

September 2013

1

15

9

0

LEP, IFEP, RFEP, EO

18

36

3

Assessment (1e El. 1): What formal or informal assessment at the close of the lesson will serve as evidence that students have met the lesson objectives (e.g.: student work, exit slip, etc.)

Informal assessment will involve students constructing the Foldables and keeping their notes about Multiplying Fractions and Mixed Numbers on the tabs. They will also take a review quiz on Brain Pop. There will be an exit question which involves a problem from their homework and they will also work with multiplying fractions in ST Math which is part of the Blended Learning component with technology.

We will be implementing the English Learner Master Plan fully in each lesson plan. Our sources will be SDAIE/Access to Core-Instructional/Observation Tools, using the LAUSD Teaching & Learning Framework Rubrics, Blended Learning, AVID strategies, and incorporating the eight mathematical practices establish by Common Core Standards.

For English Language learners we will be decoding the vocabulary throughout the lesson. Each student will work in Cooperative Learning teams and be required to make a word web. Students write the words on a large sheet of paper and they must provide the main concepts, supporting elements, and bridges showing relationships between ideas in a concept. The Math Department has developed a "Story Problem" template. It works perfectly for English Language learners. The template has 6 main areas as follows:

1. 
   Rewrite the problem (1 point) - students are required to rewrite the formal standard in their own words.
   
2. 
   Restate the Final Question (4 points) - Students must put the final question in this area and put it in their own words. They are asked "What are you solving for?"
   
3. 
   Model/Picture/Graph (4 points) - This area is for Kinesthetic Learners where they can visualize the problem.
   
4. 
   Show Your Work (4 points) - In this area of the template the students puts down all their math work and calculations.
   
5. 
   Solution (4 points) - What is the final solution? Write in 1 sentence.
   
6. 
   Reflection & Analysis (3 points) - In this area we check for understanding from our English Learners. What was the TOPIC of this problem? What did you learn from this problem? What was easy or hard? Why was it easy or hard? Explain.
   

Academic Language taught or reviewed (1a El.1; 1c El. 1; 1c El. 2): What academic language will be taught or reviewed?

In data-driven differentiated instruction we have noticed students who need work on their everyday English patterns. We will form collaborative learning groups so that these English Learners can see peer-editing from other students with similar grammar needs. The teacher will read the lessons aloud and have students use the vocabulary words in a sentence and paste them on a word web.

The vocabulary words in this lesson are listed below:

Multiplication

Mixed Numbers

Equation

Home Language Academic English

I multiply two fractions to get the answer. I multiplied two fractions to get the answer. (Past tense)

I solve problems involve multiplication. I solve problems involving multiplication. (Gerund)

The fraction has numbers and a fraction. The fraction contains mixed numbers. (Target vocabulary)

Some other methods we will be using to decode the English language for our English learners are listed below:

• 
  Students will highlight words and phrases they do not know before the lessons.
  
• 
  We will emphasize root words, break them apart and show what the prefix and suffix of words mean.
  
• 
  Students will be required to read out loud in class at least 5 minutes per period and 30 minutes at home.
  
• 
  Teachers will provide immediate feedback if words are mispronounced or spelled incorrectly.
  
• 
  Model pronunciation of math vocabulary, formulas, and graphic displays.
  
• 
  Give verbal praise to all students each and every day.
  
• 
  Students will use target vocabulary using the correct gerund, possessive nouns, and past tense.
  
• 
  Students will use the story problem template to reinforce critical thinking and language objectives.
  

.

Students apply their understanding of fractions and fraction models to represent the multiplying and dividing of fractions with unlike denominators as equivalent calculations with like denominators. They develop fluency in calculating the products of fractions, and make reasonable estimates of them. Students also use the meaning of fractions, of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures for multiplying and dividing fractions make sense. (Note: this is limited to the case of dividing unit fractions by whole numbers and whole numbers by unit fractions.)

Prior Knowledge (1b El. 1; 1c El. 2; 1e El. 4): What do students know and understand in relation to the objectives? What data (formal or informal) provides evidence for their prior knowledge?

Students should know how to write a mixed number as an improper fraction. It will require them to be proficient in Multiplication. They will compete in Multiplication contest amongst their class teams and other Math classrooms. We will utilize a multiplication ball that has numerous Math problems on the exterior and the student must solve the multiplication problem based on where their left thumb falls.

What student misunderstandings/misconceptions do you anticipate, and how will you address those (1d, El. 4)?
Students may have some difficulty understanding how to multiply fractions and mixed numbers. I will address these by:

1. 
   Having the students work with a variety of manipulative.
   
2. 
   Students will have fractions strips available for them to model the problems.
   
3. 
   I will remind the students that multiplication is repeated addition.
   
4. 
   Students will work with ST Math and be involve in interactive learning with technology on multiplying fractions.
   
5. 
   Students will interact with numerous multiplying fraction lessons on the computer embedded in my lesson plan.
   

Students will need:

• 
  Paper and pencil
  
• 
  ruler
  
• 
  hand calculator
  

• 
  fraction manipulative.
  
• 
  5-Minute Check Transparency
  
• 
  Interactive Classroom CD-ROM
  
• 
  Computer and LCD projector
  

• 
  ca.gr6math.com
  
• 
  Extra Examples, Chapter 5, lesson 5.
  
• 
  Self-Check Quiz, Chapter 5, lesson 5.
  

Structures/procedures (1d El. 4): What structures and classroom routines/procedures will increase academic engaged time in this lesson?

1. 
   Capture the Kids' Heart Social Contract - this contract is an agreed upon norms on how students will behave and interact with other students as they learn the lessons in the classroom.
   
2. 
   Class Rules - defines the classroom routine and daily procedures which are common in most classrooms with respects to using the restroom, medical emergencies, acquiring classroom material, etc.
   
3. 
   Kagan's Cooperative Learning strategies - this program contains a self-contained body of structures used to engage and motivate students. Each structure is designed to engage students in team and class building activities. The specific structures we will use in this lesson plan to engage students to process information is as follows:
   

• 
  One - Stray
  
• 
  Quiz-Quiz-Trade
  
• 
  Rally Coach
  
• 
  Round Robin
  
• 
  Think-Write-Round Robin
  
• 
  Inside - Outside Circle
  

Students will sit in small groups of four students per team. Kagan Cooperative Learning program recommends the first group be randomly selected. They should remain in this small group for about 6 weeks. The structures activities are perform in pairs and the culminating activities are whole class involvement. Each four student team has been assigned a job. At each table, there is a Coach, Recorder, Material Monitor, and a Quiet Captain. I will continue to use the data acquired from the "My Data" website and Common Assessments from the Partnership to assist me in forming groups when the students are able to work effectively as a team and a class. I will also monitor their progress on homework assignments, Common Assessment tests, ST Math, data compiled by our school data specialist, and Math Department data and analysis.

• 
  What opportunities will you provide for students to make sense of what they are learning and construct new knowledge? (1d El.1)
  
• 
  How will you make content relevant to students’ interests and cultural heritage? (1b El.4)
  
• 
  What strategies, linked to lesson objectives, will you use to maximize participation of all students for the entire instructional block? (e.g. discussion, student talk, inquiry, questioning, reflection) (1d El.1; 1a El. 2)
  
• 
  What opportunities are you providing for students to engage in higher level thinking (e.g. analysis, synthesis, application) (1d. El1)
  
• 
  What questions do you plan to ask students so that they can demonstrate their reasoning? (1d. El 1)
  

Students will learn how to solve problems involving Multiplication of positive fractions and explain why a particular operation was used for a given situation. They will also explain the meaning of multiplication of positive fractions and perform the calculations.

1. 
   What is a Mixed number? Can you write a mixed number into an improper fraction?
   
2. 
   I am going to put these fractions on the board and lets see how fast your team can convert them into improper fractions. They are: 2 3/4, 1 7/8, 3 4/7, and 5 1/6.
   
3. 
   Remember you must multiply the whole number and denominator. Then add the numerator.
   

Have students go to the math lab in room 105 and interact with the following math lessons:

1. 
   Multiply Fractions - Index of four activities
   
2. 
   ST Math - multiplying fractions in room 105 computer lab.
   
3. 
   Students will work in teams to complete the multiplying fraction homework of problems 1 to 31 on page 255 in their Math Text books.
   
4. 
   Students will perform a variety of Kagan teambuilding activities using what they have learned in Chapter 5-5/.
   
5. 
   Students will use the Alpha Smart 3000 to check their answers. They will also use hand calculators to check their answers.
   
6. 
   Students will solve a Story Problem dealing with multiplying fractions and illustrate it on a Story problem template.
   

Students are required to interact with ST Math for at least 2 hours each week. They will work on multiplying fractions and mixed numbers.

Assessment: (1 hour)

Students will copy and answer the five problems on Lesson 5-5, Multiplying Fractions and Mixed Numbers on the Glencoe McGraw Hill math web site. They must achieve 70% proficiency to be considered in mastering this standard.

Grading

Each problem is worth 1 point.

B - 2 wrong

C - 3 wrong

D - 4 wrong

F - 5 wrong

100 to 90 = A

89 to 80 = B

79 to 70 = C

69 to 60 = D

Below 60 = F

In this lesson to help English Learners and Standard English Learners access the content will be using essential techniques as defined Doug Lemov's book called "Teach Like a Champion: The essential Techniques. In the Structuring and Delivering Your Lessons section, our group has decided to use the following techniques:

• Technique 12: The Hook

• Technique 13: Name the Steps

• Technique 16: Break it Down

• Technique 18: Check for Understanding

• Technique 20: Exit Ticket

As our English Learners perform their math work, we will look at the following processes:

1. Show students and model the work - we will tell students what they have to do each day by having a White Board Configuration Model that shows what is expected of them each day and in every class. We will also provide them with an agenda and class syllabus so they can take it home so that their parents can monitor their progress.

2. Start each day by having students read their work and share with other students. An Alpha Smart word processer is available for each student so they can type their work in the unit and use the spell checking application to check for misspelled words. A Spanish/English Dictionary is available for each students as well as the Math curriculum is bilingual in text.

3. Define Pattern - I will help the students find their way through their text book. They will have a Brainstorming and Scavenger Hunt exercise that is designed for them to explore all the areas of their math book so they know how to use the Table of Contents, Glossary, Appendix, workbooks and on-line material that is provided with their text books.

4. English Learners will not be required to read a large amount of text at one time.

5. Students will be encouraged to mark up the text, use highlighters, post-its and Cornell notes to highlight important points.

6. Teachers will use their personal experiences if appropriate to enhance the learning experience.

7. English learners will be able to illustrate what they have learned by creating stories or using the Story Problem templates.

8. There will be a daily review of the math vocabulary words, formulas, symbols, story problems, common assessments, and technical training using Math programs.

9. Students will be provide a feedback "Parking Lot" area where they can post matters of concern on the board to get help before and after class.

Ms. Howell and Mrs. King and Mrs. Doyle are the designated RSP teachers and City Year associate assisting me with students who need modifications and/or accommodations. As a rule of thumb, we allow these students to have more time to master the material. Some strategies we are using that seems to increase productivity in these students are:

• We do not take off for spelling and minor mathematical errors.

• Allow them to read with a study buddy

• Encourage peer-tutoring with students that have similar abilities.

• Do not require oral reading or physical presentations.

• Give constant praise each day.

• Allow students to access and leave the classroom at an earlier time.

• Place these students closer to the front of the classroom.

• Allow students to make up the test or take an oral assessment.

• Limit classroom distracters.

• Stand by the student when giving the lecture or classroom directions.

• Look for limiting or aggressive body language.

Students were given a challenge by the Principal to develop a Power Point Presentation that illustrates their ability to learn while using technology. Students will be encouraged to use Microsoft Excel spread sheet programs to develop strategies to solve fraction problems, graphs, and manipulate data by interjecting formulas and equations. Any successful work produced by these students will be assessed as extra credit to increase their Grade Point Average.

If the entire class achieves mastery, they usually rewarded with a Class Pizza Party. Students can also be quite beneficial by show casing their talents by assisting their peers in mastering the math concepts. The homework assignments and Story Problems will be placed on the bulletin board to model extraordinary work for other students.

1. 
   The Math Department routinely engages math teachers to collaborate and develop Math Rubrics that are used to distinguish mastery/proficiency from non-mastery/below proficiency. As a general rule, the Department has used 70% mastery of the material as a proficient level.
   
2. 
   Graded work is posted in the classroom so that the student can clearly see what an "A" paper ranks and how an "F" paper ranks by the teacher's assessment. Graded work in combination with the Grading Rubrics is the best tool for students to gauge their work.
   
3. 
   Math teachers should model out the problem before allowing students to work them out.
   
4. 
   Through Differentiated Instruction, teachers should be able distinguish mastery and proficiency on a given standard. Usually students are successful with Core and Advanced level questions on their homework and assessment challenges.
   
5. 
   In this lessons, students will be required to solve problems involving multiplication of positive fractions in the Exercises. They will have to verbally justify their answers and critique other team mate's work.
   
6. 
   The data for class performance is routinely placed on performance spreadsheets and analyzed by the Math Department. Each math teacher is able to print out these performance spreadsheets and post them in their classroom. There are spread sheets available for:
   
   • 
     Common Assessments by the Partnership
     
   • 
     My Data
     
   • 
     ST Math Syllabus and Standards Mastery results
     
   • 
     Math Text book Tests
     
   • 
     CST data from 5th grade data for Math and ELA
     
   • 
     SMARTER Balanced Assessment - Mathematics
     

Special Needs and English Language learners will show evidence that they have demonstrated proficiency/mastery if they can perform the following tasks:

1. 
   Write down the target vocabulary and use the words correctly in a complete sentence.
   
2. 
   Compute at least five simple fractions using multiplication.
   
3. 
   Identify a mixed number and improper fraction by pointing it out on a sheet of paper.
   
4. 
   Be able to participate in the Kagan team building exercises for this lesson.
   
5. 
   Give a reasonable explanation on what they believe a mixed number and improper fraction means to them.
   
6. 
   Answer at least 3 out of the 5 questions located on page 255 in the section called "Check for Understand".
   
7. 
   Work on a team, make a foldable, and use the vocabulary words in a word web.
   

What opportunities will students have to self- or peer assess? (1e El. 3)

At the end of each week, students are given an opportunity to provide feedback on their learning experiences for that week. Students are given an Alpha Smart word processer where they can type their concerns or critique their peers performance. Each Alpha Smart is downloaded to the teacher's main computer for quality control purposes and editing. The classroom composition can be published in a weekly progress report or projected on the screen and read by an electronic word recognition reading program. Students are also allow to grade their peers quizzes, homework, and test. They are provided with a 10 week course syllabus that requires them to chart their daily homework, test grades, and work habit grades. Parents are required to initial the syllabus each week showing evidence they are aware of their child's academic progress. In the Blended component of the math curriculum, students engage in ST Math. Each time they log out the program keeps track of their academic progress. Students are able to access their abilities on how their peers are progressing through the course work. Progress reports are generated by the School counselors which are given to students so that they may chart their daily progress, period by period. This process is generally used for struggling students or students that exhibit behavioral problems that inhibit them to learn effectively in the classroom.

During the lesson, what are some of the different strategies you will use to check for understanding? (1e El. 3, El. 4)

Thumbs Check - if students are understanding the lesson I will tell them to give me a "thumbs up". If they do not understand, then they will give me the "thumbs down". If they are a little confused, then they give me the "sideways thumb" and swing it back and forth.

2. Body Language Check - if students are easily distracted, yawning, sleeping, appear easily frustrated, not completing the work, consistently failing the tests, exhibiting excessive motor activity, grimacing, frequently tardy or absent from class, and shy, this gives me clues that they are not understanding the lesson. In these situations, students are asked to repeat the directions verbally or write them down on a piece of paper so that I can check for understanding.

3. Pointing - students are told to point to a required text or problem so that I know they are focused on the material.

4. Showcasing - students are allow to pick a math problem they can explain and use that for their "exit ticket" when it is time to leave the classroom.

5. Stand-by-the-door - I stand by the door and ask the students a warm up question before they enter the classroom. If they fail to answer the question, they must fall in the back of the line.

6. Wiggle the Pencil - this technique is much like the thumb check except for the student is required to wiggle their pencils in their fingers if they understand the material.

I will prepare the class for the next lesson which is "Dividing Fractions and Mixed Numbers". This lesson will go more in depth from the concepts students mastered in the last lesson. They will be dividing fractions and mixed numbers. Once again, they must understand computing and performing simple multiplication of fractions involves mastering multiplication skills and understanding fractions. Dividing fractions will involve understanding how to invert the second fraction or utilize the reciprocal.

How will you record and utilize evidence of student learning to inform your next steps? (1e El. 4, 1e El. 3)

All grades are recorded on a Microsoft Excel spreadsheet which tells the following?

• 
  Computes the student G.P.A.
  
• 
  Computes the classroom passing rate.
  
• 
  Charts a visible Pie Graph illustrating students who are passing or failing the curriculum.
  
• 
  Records the progress scores for each student for the entire school year.
  

Grades Verification - all grades are recorded on ISIS. Teachers can print out student grades and analyze the measure of central tendency for grade marks per classroom. With a normal distribution of grade marks, if the data is distributed in the D and F range, I will have to revisit the this standard for at least two more days in the following week.