Class Profile
Teacher Name:
W. Martin / Subject/Grade Level:
Math/6 Grade
Greatest Common Factor / Lesson Date/Time:
August 2013
Class Composition (Record in numbers)
Male:
36 / FBB:
1 / Basic:
15 / Adv:
9 / SWD:
0 / Language Proficiency Levels:
LEP, IFEP, RFEP, EO
Female:
30 / BB:
15 / Prof:
36 / GATE:
3 / ELs:
2
/ SELs:
1
/ Other: ADHD
Instructional Goals and Objectives
Standards (1a El.1): What standard(s) or portion of a standard does your lesson address?
CCSS.Math.Content.6.NS.B.4
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)?
Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).
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.)
Formal assessment will be a written test of at least 10 problems from the student's homework assignment. The homework consist of 44 problems located on page 188 to 189. Students must be able to perform the following steps:
  • Steps for Finding the Greatest Common Factor
The greatest common factor, or GCF, of a set of numbers is the largest number that every number in that set can be divided evenly by. Your teacher will usually ask you to find the GCF of just two numbers, but sometimes you'll find it for three or more numbers. No matter how many numbers you're finding the GCF for, the steps are always the same.
  • List the Factors for Each Number in Your Set
First, write down a list of the factors for each number you're given. A number's factors are all of the numbers that it can be divided evenly by. For example, let's say you're finding the GCF of nine and 18. You would list all of the factors of nine, which are one, three and nine. Then you'd list the factors of 18, which are one, two, three, six, nine and 18.
  • Compare Your Lists of Factors
Next, compare the lists of factors you made for each number. To find the GCF, look for the biggest number that is on both lists.
Informal assessment will involve students constructing the Foldables and keeping their notes about the Greatest Common Factor 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 line plots in ST Math which is part of the Blended Learning component with technology.
Language Objective (1b El. 1; 1c El. 2): What language forms and functions will make content comprehensible for English Learners and Standard English Learners?
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:
Greatest Common Factor
Prime Factorization
Least Common Multiple
Distributive Property
Common Factor
Home LanguageAcademic English
Find the big numberFind the Greatest Common Factor
I used the disturbing propertyI used the distributive property
You have find the same factorYou have to find the common factor
I am using the greater than factorI am using the greatest common factor
We found the number that barely wentWe found the largest number divisible by the two whole numbers
I put the numbers in a listI wrote down the common factors in a list
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.
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Student Progress
Prerequisite Skills (1a El. 1): What prerequisite skills are essential for students to be successful in accomplishing the objectives?
In order to master the Greatest Common Factor component in the CCSS Number System standard in Grade 6, students must have the following prerequisite skill sets mastered by Grade 5:
  • Deep understanding of basic mathematic vocabulary, symbols and operations such as addition, subtraction, multiplication, and division. (5NS 2.1)
  • Students must be able to organize and display single-variable data on graphs and explain which type of graphs are appropriate for the various data sets. (Standard 5SDAP1.2)
  • They must have some understanding of how to compute and compare and order to show that they may differ. (Standard 5SDAP1.1)
  • Identify ordered pairs of data from a graph and interpret the meaning of data in terms of situations depicted by the graph. (Standard 5 SDAP1.4)
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?
In order for students to understand the concept of Greatest Common Factor, they must practice finding the GCF for at least 50 or more pairs of whole numbers. They must follow basic steps as outlined in the lesson below:
  • Practice Finding the GCF
Below are some examples to help you practice finding the GCF. In each example, we'll follow these steps:
  1. List the factors for each number in the set.
  2. Compare the lists to see which numbers are on all of them.
  3. Find the largest number that appears on all lists. That number is the GCF.
Example 1: Find the GCF of 24 and 32
First, we'll list the factors for each number. The factors of 24 are one, two, three, four, six, eight, 12 and 24. For 32, the factors are one, two, four, eight, 16 and 32.
Next, we'll find the largest number that's on both lists of factors. One, two, four and eight are all factors of both 24 and 32. However, eight is the largest number on both lists, so it is the GCF.
Example 2: Find the GCF of 15 and 17
We'll begin by listing all the factors of 15 and 17. One, three, five and 15 are the factors of 15. The number 17 is prime, so it only has two factors: one and 17. Next, we'll compare the two lists. The only number that appears on both lists of factors is one, so it is the GCF of 15 and 17.
Example 3: Find the GCF of 12, 15 and 18
Remember that your teacher might ask you to find the GCF of three or more numbers. Here's how you figure it out:
First, list the factors of each number, just like you did before. Twelve's factors are one, two, three, four, six and 12. The number 15 has one, three, five and 15 as its factors. Finally, the factors of 18 are one, two, three, six, nine and 18.
Now, instead of comparing just two lists, you'll have to compare three. The numbers one and three are on all three lists, so they are the common factors of 12, 15 and 18. Since three is larger than one, three is the GCF of this set of numbers.
  • Tip: Some numbers, like two and six, appeared on two of the three lists, but that's not good enough. To be the greatest common factor, a number must be a factor of every number in the set that you're given, and it must be largest of all of the numbers that fit this description.
What student misunderstandings/misconceptions do you anticipate, and how will you address those (1d, El. 4)?
Many students misunderstand that the number they have determined as the GCF is not actually the greatest number. They may be finding just a common factor or the least common multiple. There may be instances were there are no common factors between the set of numbers. They must understand that this process enhances their ability to simply fractions which will be in the next lesson.
Students will be working in teams and each team will pass their work to an adjacent team for peer assessment. I will also allow students to check their work by using calculators and other math tools.
Procedures
Materials (1d El. 2): What materials, resources, and/or technology will be used in the lesson? How will they support the instructional outcomes for this lesson?
Students will need:
  • Paper and pencil
  • ruler
  • hand calculator
Teacher will need:
  • colored post-its
  • 5-Minute Check Transparency
  • Interactive Classroom CD-ROM
  • Computer and LCD projector
Technology Tools for Students
  • ca.gr6math.com
  • Extra Examples, Chapter 4, lesson 2 and 4
  • Self-Check Quiz, Chapter 4, lesson 2 and 4
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:
  • Mix-Pair-Share
  • Quiz-Quiz-Trade
  • Rally Coach
  • Round Robin
  • Think-Write-Round Robin
  • Timed Pair Share
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?
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 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, the three District Math Periodic tests they take each school year, and data that shows high-risk students
Instructional Sequence
Consider the following questions when designing your plan:
  • 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)
(These questions do not need to be answered directly but are important guiding questions to support your lesson design. You may be asked to respond to these questions during your pre-observation conference.)
SUBJECT: Math
GRADE LEVEL: 6th grade
LESSON TOPIC: Greatest Common Factor
STANDARD:CCSS.Math.Content.6.NS.B.4
ACADEMIC CONTENT STANDARDS: Find the greatest common factor of two whole numbers less than or equal to 100.
PACING: Regular: 5 periods, Block: Math Intervention
LEARNING OBJECTIVES/OUTCOMES: Students will find the Greatest Common Factor of two whole numbers less than or equal to 100.
ENGAGEMENT: Involve in the students in finding the Greatest Common Factor of a list of number sets. Say, "Okay today we are going to find out what team can figure out the GCF of the numbers on the board the fastest and most accurately. The winner gets to go to lunch early and does not have to do any homework tonight. Who wants to be a part of this activity?" Most of the students will be waving their hands. I will have each team organize their strategy to solve the problems. Most students will have problems organizing who will work the problems and check them before the time runs out. I will give them 15 minutes for this activity.
CONTENT SPECIFIC QUESTIONS:
1.What are all the factors listed for these two whole numbers?
2.What is the least common multiple?
3.Can you show me how we can use prime factorization?
4.Can you use the factor tree to find the GCF?
5.Can you use the distributive property?
What are the students going to learn? They will learn how to find the Greatest Common Factor by using the distributive property, prime factorization, the factoring tree, or any other method they have discovered to compute the GCF of two whole numbers less than or equal to 100.

How will they know they learned it? They will must accomplish at least 70 percent proficiency on a written test that covers the standard. Students will also complete a Story Problem worksheet that contains an "Essential Question". The essential question will be "Can you find the GCF of two whole numbers less than or equal to 100?"

What will do if they have learned it?

Students will use their acquired knowledge to perform more advanced calculations involving finding the least common multiple and to simplify fractions which will be presented in the next lesson. Lesson 4-4.

Students will look at a Brain Pop on Factoring integers and take Cornell notes on what they have learned. Use the KWL chart and Story Problem Template to organize what you have learned

What will do if they have failed?

Students will be tutored and take a retest on Monday.

Intensive Intervention - Math Triumphs

Student On-line tutoring - ca.gr6math.com

Students will complete their Foldables and put the standards and an examples of their work on GCF on the foldable. They will also will explore ST Math and solve problems dealing with Greatest Common Factor, Factoring, and Least Common Multiple for at least 90 minutes this week. They will be given extra credit if they complete the extra work at the pace the Partnership has assigned for students in 2013-2014.