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

Math/6 Grade

Compare and Order Integers

26 - 30 Aug 2013

36

15

LEP, IFEP, RFEP, EO

30

36

Learning Outcomes (1a El. 1; 1c El. 2): What are the conceptual understandings, content, and/or procedural knowledge that you want students to learn? What do you want students to understand, know or be able to do in relation to the standard(s)?

The student will be able to:

• 
  Differentiate between the inequality symbols < and >.
  
• 
  Compare two integers, using the proper inequality symbol.
  
• 
  Order a set of integers from least to greatest.
  
• 
  Order a set of integers from greatest to least.
  
• 
  Recognize that Integers get smaller in value as you move to the left, and larger as you move to the right on the number line.
  
• 
  Apply procedures for comparing and ordering integers to complete five interactive exercises
  

The student will be able to:

• 
  Review the definition of absolute value.
  
• 
  Describe the relationship between a negative integer and owing money.
  
• 
  Recognize that the sum of two negative integers is a negative integer.
  
• 
  Perform addition of two negative integers.
  
• 
  Recognize that the sum of two positive integers is a positive integer.
  
• 
  Perform addition of two positive integers.
  
• 
  Describe the procedure for adding integers with unlike signs.
  
• 
  Describe how absolute value concepts are used in this procedure.
  
• 
  Perform addition of integers with unlike signs by applying the procedure.
  
• 
  Differentiate between the sign of an integer and the operation being performed.
  
• 
  Recognize that the sum of any integer and its opposite is equal to zero.
  
• 
  Apply the procedures for adding integers to complete five interactive exercises.
  

The student will be able to:

• 
  Perform subtraction of integers using the number line.
  
• 
  Recognize the need for an arithmetic procedure for subtracting large integers.
  
• 
  Describe the arithmetic procedure for subtracting integers.
  
• 
  Perform subtraction of integers using the arithmetic procedure.
  
• 
  Describe how to convert an integer subtraction problem into an addition problem.
  
• 
  Apply the procedure for subtracting integers to complete five interactive exercises.
  

The student will be able to:

• 
  Restate that the product of two integers with unlike signs is a negative integer.
  
• 
  Restate that the product of two integers with like signs is a positive integer.
  
• 
  Define the Associative Law of Multiplication.
  
• 
  Perform multiplication of two integers with like signs.
  
• 
  Perform multiplication of two integers with unlike signs.
  
• 
  Recognize that the Associative Law of Multiplication applies to integer multiplication.
  
• 
  Perform multiplication of three integers, two at a time, applying the rules for multiplying integers.
  
• 
  Recognize that when multiplying three integers, one can multiply the product of any two by the third.
  
• 
  Apply the procedures for integer multiplication to complete five interactive exercises.
  

The student will be able to:

• 
  Restate that the quotient of two integers with unlike signs is a negative integer.
  
• 
  Restate that the quotient of two integers with like signs is a positive integer.
  
• 
  Perform division of two integers with like signs.
  
• 
  Perform division of two integers with unlike signs.
  
• 
  Describe the procedure for dividing integers with like signs.
  
• 
  Describe the procedure for dividing integers with unlike signs.
  
• 
  Apply the procedures for integer division to complete five interactive exercises.
  

The student will be able to:

• 
  Review the rules and procedures for adding, subtracting, multiplying and dividing integers.
  
• 
  Evaluate ten interactive exercises that provide mixed review of integer operations.
  
• 
  Identify which procedure is needed for each exercise.
  
• 
  Apply the procedures for integer operations to complete each exercise.
  
• 
  Differentiate between the rules and procedures for all integer operations.
  

The student will be able to:

• 
  Examine ten interactive exercises for all topics in this unit.
  
• 
  Determine which concepts and procedures are needed to complete each practice exercise.
  
• 
  Compute answers by applying appropriate formulas and procedures.
  
• 
  Self-assess knowledge and skills acquired from this unit.
  

The student will be able to:

• 
  Evaluate ten interactive exercises with real-world word problems for all topics in this unit.
  
• 
  Analyze each problem to identify the given information.
  
• 
  Formulate a strategy for solving each problem.
  
• 
  Apply strategies to solve routine and non-routine problems.
  
• 
  Synthesize all information presented in this unit.
  
• 
  Connect integers to the real world.
  
• 
  Develop problem-solving skills.
  

The student will be able to:

• 
  Examine the solution for each exercise presented in this unit.
  
• 
  Identify which solutions need to be reviewed.
  
• 
  Compare solutions to completed exercises.
  
• 
  Identify and evaluate incorrect answers.
  
• 
  Amend and label original answers.
  
• 
  Identify areas of strength and weakness.
  
• 
  Decide which concepts, formulas and procedures need to be reviewed from this unit.
  

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.)

Students will be formally assessed by taking the Chapter 2-2 on-line test, the Chapter 2 Standards Practice test and completing the Chapter 2 foldable. Students will be informally assessed by taking the Brain Pop quiz, answering the daily scaffolding questions on an exit slip and showing evidence of completely the homework for lesson 2-2 and 4-9. On page 85 to 87, they will do problems 1 - 44 and on page 218, they will do problems 1 - 23 for homework.
Culminating Activity (1e El. 1): What will be your culminating activity for this lesson?

We will be doing the line Plot activity.

Language Objective (1b El. 1; 1c El. 2): What language forms and functions will make content comprehensible for English Learners and Standard English Learners?
English Learners will use the Noteables Interactive Study, the Interactive classroom power point presentation, the English-Spanish Math tutor and the Math word wall illustrating the vocabulary being used in this lesson.

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.
   

The academic language taught in is lesson includes Measure of Central Tendency, mean, median, and mode. We will use Level III to Level VI questions for critical thinking by Bloom’s Taxonomy.

It is the number with minus sign The number is a negative integer.

I guess where the number goes I will extrapolate a value and determine its position on the number line.

We put the numbers in a bracket The numbers in ordered pairs are located in a parenthesis.

The bars make it positive Numbers in the parallel bars indicate the absolute value.

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.
  

1. 
   Arithmetic prerequisites: Students should understand sums, differences, and quotients for all activities. They should know the concepts of addition, subtraction, multiplication, and division.
   
2. 
   Technological prerequisites: Each student or group of students working together will need a computer with a Java-capable browser. Students should be comfortable using the computer and browser. Calculators may be helpful for solving problems that arise in discussions. Students will be using their laptops and Alpha Smart 3000s.
   

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?

• 
  Understand that positive and negative numbers are used together to describe quantities having opposite directions or values; use positive and negative numbers to represent quantities in real-wold contexts, explaining the meaning of 0 in each situation.
  
• 
  Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
  
• 
  Understand ordering and absolute value of rational numbers.
  
• 
  Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.
  

What student misunderstandings/misconceptions do you anticipate, and how will you address those (1d, El. 4)?

A common mistake that students make when working with integers are:

• 
  Recognizing opposite signs of numbers on each side of zero on the number line is the number itself. -(-3) = 3
  
• 
  Knowing that the absolute value of a positive or negative integer is always positive.
  
• 
  Knowing that terms such as greater, larger, above, up will mean the value of the integer is positive.
  
• 
  Knowing that the terms such as less, below, down, under will mean the value of the integer is negative.
  
• 
  Temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge represents integer quantities having opposite directions or values.
  

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

Grouping (1d El. 3): How will you group students (whole class, small groups, pairs)? How will you use data to assist you in forming these groups?

• 
  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)
  

Student and Teacher Interactions (1a El. 2; 1b El. 2, 4; 1d El. 1, 2, 3): Outline your sequence of instructional activities using your preferred lesson format (e.g.: Understanding by Design, BTSA, NBC, Writer’s Workshop, etc.)

 
Standard: NS 1.1,2.4

1. 
   Students will need access to a Java-capable browser
   
2. 
   Students will need pencil and paper.
   
3. 
   Students will need copies of the following worksheet:
   
   1. 
      The Measures activity
      

Integer, rational number, compare and order, absolute value, number line, ordered pairs, positive number, negative number, extrapolate, coordinate plane, credit, debit, below sea level, elevation

1. 
   Focus and Review Remind students of what they have learned in previous lessons that will be pertinent to this lesson and/or have them begin to think about the words and ideas of this lesson:
   
   1. 
      Does anyone know how to draw a number line?
      
2. 
   


   
3. 
   Objectives: Let the students know what they will be doing and learning today. Say something like this:
   
   1. 
      Today, class, we are going to learn about comparing integers. I want you to work with your team and develop a method to compare and order numbers and fractions on a number line. What math symbols could we use to show that a number is larger or smaller than another number? (15 min)
      

4. 
   Teacher Input
   
   1. 
      Lead a discussion, or the instructor can prepare a "live" discussion, to deepen and formalize the students' intuitive understanding of mean, median, and mode. (10-20 min)
      
5. 
   
   
6. 
   Guided Practice
   
   1. 
      Introduce and develop the concepts of Comparing and Ordering numbers by having them do the Guided practices work foudn in Lesson 2-2 Comparing and Order Integers and lesson 4-9 Comparing and Ordering Rational Numbers.
      
7. 
   
   
8. 
   Independent Practice
   
   1. 
      Have the students either individually or in groups read and try to solve problems 1 - 44 on page 85 and 87, problems 1-23, page 218(30 min)
      
9. 
   
   
10. 
    Closure
    
    1. 
       You may wish to bring the class back together for a discussion of the findings. Once the students have been allowed to share what they found, summarize the results of the lesson. Students will record their work by using Cornell note taking method. The Recorder will read the best summary developed in each group.(10 min)
       
11. 
    
    

Student will showcase their skills on how to Compare and Order Integers from what they have learned and performed on ST Math.

This lesson introduced the students to some basic ways of describing sets of data. The next lesson will be on determining the Greatest Common Factor starting on page 186.

• 
  Students will get a set of temperature data and determine what the final temperature will be at the end of the day. They will get temperature above and below zero and must correctly solve the real life situation.
  
• 
  Students will get story problem which deals with elevation above and below sea level. They must determine the correct altitude from all the data.
  
• 
  Students will get a story problem dealing with a real life banking and accounting issue. They will get credit and debit amounts and must determine their final budget.
  
• 
  The entire class will compete on Comparing and Ordering themselves based on height, weight, birthdays, and number of siblings in the family.
  

Kinesthetic Learners

• 
  To create a line plot using classroom data, draw a number line on the board with a scale from 0 to 5.
  
• 
  Give each student a sticky note and ask them to write the number of siblings they have on it. Allow students to use a thermometer or a graphing program to show values.
  
• 
  Then have each student come to the board and add their response to the line plot.
  

• 
  Ask the students to explain what the term "below sea level" means?
  
• 
  Have students draw the absolute value sign.
  
• 
  Make sure students can draw the number line correctly, neatly, and place values on it accurately.
  

• 
  The most frequent response is only 1 sibling
  
• 
  Students will forget that a negative value means a lower altitude.
  
• 
  Most of the students will want to use graphs and post its instead of showing the work.
  
• 
  Most students will do the guided practice work but may not finish the homework or make the foldable.
  
• 
  Many students will forget to do the summary on the Cornell notes.
  

• 
  Explain why it is important to order the data before performing computations.
  
• 
  Why is it important to understand the positive and negative numbers if you are in a profession that deals with mountain climbing, flying an airplane, working in a bank, constructing a building, traveling to another country?
  
• 
  What would happen if we did not compare and order data?
  

• 
  Using the vocabulary of the lesson, have students work as a team to make a word web.
  
• 
  Have four or five students write simultaneously on a large sheet of paper or on the board.
  
• 
  Have them provide main concepts, supporting elements, and bridges showing relationships between ideas in a concept.
  
• 
  Group students according to the Kagan Cooperative Learning Strategy.
  
• 
  Have students fill in the Story board template
  
• 
  Students must document notes on the Cornell note taking template.
  
• 
  Have students do the interactive lessons on computer for lesson 2-2.
  
• 
  Students must take the vocabulary word, define it, and use it properly in a sentence.
  
• 
  Students will find similar words in the vocabulary by using a thesaurus.
  
• 
  Make exit tickets on the vocabulary word for students.
  
• 
  Construct a visual word wall of all terms being learned during the first 5 weeks.
  
• 
  Reinforce basic terms by integrating Math Triumphs work from Math intervention class.
  
• 
  Allow students to use the Spectrum and Test-Ready material if available.
  

Time for a given activity (if applicable)

• 
  I will reduce quantity students read at one time.
  
• 
  Modify materials to student’s reading decoding level.
  
• 
  Emphasize and highlight important points.
  
• 
  Explain root words and review vocabulary daily.
  

Students with Disabilities (1b El. 3): What modifications and/or accommodations are needed for students with disabilities in this lesson?

• 
  Do not take off for spelling and minor mathematic errors.
  
• 
  Allow a reading buddy and peer tutoring.
  
• 
  Do not require oral reading.
  
• 
  Provide more oral instructions.
  
• 
  Allow for a make up test or open book test.
  

Enrichment (1b El. 3): How will you enrich and deepen learning opportunities for students who have already achieved mastery?

• 
  Allow students to work with ST Math program after they have finished the assignment.
  
• 
  Give students extra credit for volunteering as a peer tutor and helping others with homework.
  
• 
  Reward students with Pirate Coins, Student of the Month, or Pizza Party.
  
• 
  Allow students to develop an activity that uses the Comparing and Ordering skills they have learned.
  
• 
  Allow students to analyze the “My Data” information and use Comparing and Ordering skills.
  

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 construct line plots in the Exercises. They will have to verbally justify why selecting a line plot is appropriate to display the data.
   
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:
   
   • 
     LAUSD Periodic Math Assessments
     
   • 
     D.A.R.T.S
     
   • 
     ST Math
     
   • 
     Math Text book Tests
     
   • 
     CST
     

1. 
   Post student work on the bulletin board that illustrates how tests are assessed by the grading rubrics.
   
2. 
   Post A, B, C, D, and F graded papers so students can gauge their work.
   
3. 
   Post sample work provided by other teachers and also material received in the Math Professional Development meetings.
   
4. 
   Post the Story Problems and the Problem of the Week assignments and solutions.
   

What evidence will let you know that all (EL, Sp Ed, etc.) students understand how to demonstrate proficiency/mastery?(1e El.2)

I will see increased student motivation, attendance, and a willingness to focus on the math material.

I will see increase student rigor and coherence.

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

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.

1. 
   I will engage the students in a few Brain Pop activities that will test their abilities in Comparing and Ordering Integers.
   
2. 
   I will have the students create a method to determine what number is the Greatest Common Factor in a group of numbers.
   
3. 
   I will have each team journal the Pros and Cons of this activity on their Alpha Smart keyboards and we will have a group discussion and a debate on what is the best way to analyze data.
   
4. 
   I will have students look at similar fractions and have them figure out a method to simplify them.
   

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

I will expect at least 70% overall success for Chapter 2-2 and if I fall short of my goal, the lesson will be revisited the following Monday.