Prime Factorization

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Objective

SWBAT calculate the prime factorization of integers in exponential form by using the tree method (factor out a negative).

Big Idea

Students work on a real world application task using prime factorization and the tree method to solve

Do Now

10 minutes

Students enter silently according to the Daily Entrance Routine. For today’s warm up I decide to pull three most commonly missed problems on the multiple choice section of the mock assessment. Before students begin I let them know that these three questions were modeled after the most highly missed on the test. I share their percentage by class for each question. I challenge students to earn a percentage of students answering correctly as a class. If this target percentage is met, each student gets a piece of candy and the students who answered correctly also get an achievement point. Since this is a class goal, students are allowed to work in groups of four for 5 – 6 minutes to complete the problems on the do now and submit their answers into Senteo clickers.

The following list reflects the strategies and feedback I gave students based on the mistakes most commonly being made on these questions:

Question #1: These first two question pose a great opportunity to push MP8, attention to precision. The mistakes I see my students making the most when I look closely at their work are small and can easily be caught if students are checking their solutions along the way. This is a habit that cannot bloom from one day to the next, but instead requires constant reminders.

Question #2: Substitution of negative numbers and operations with fractions are two skills affecting mastery within this question. Again, students are also not showing all of the steps when simplifying.

Question #3: The third question is all about the number line. I show students the distance between the two temperatures in question and push them to draw and label the number lines on their own. I am watching out for students who require remediation in more basic skills such as identifying integers on the number line, or drawing number lines properly. There are a few students drawing number lines with positive numbers to the left and negatives to the right.

We review the answers and strategies for each question in the last 3 – 4 minutes of this class, allowing students more time to explain how they solved.  

Class Notes

15 minutes

All students return to their seats and receive class notes. I decided to include a lot of content to save time on copying notes. This is a review lesson including prime factorization and factor trees. I am taking a day to review this strategy to address the factoring component of this unit.

We begin by defining prime factorization, the tree method, and negative numbers. I share a question from a sample CCSS document about volume and missing dimensions. I explain to students that this is also an example of the kinds of word problems that need mastery from most of the grade, based on their mock and unit assessments data.

I use the words factor and multiple many times, asking different students each time to identify each in a list of numbers or to tell me the difference between the two. The difference between these two words is a common misconception in this grade each year. The same can be said of the words prime and composite. There is a ton of vocabulary to practice today so I push myself to let students do most of the talking, encouraging with questions only.

  • What is a factor? A multiple?
  • What is the smallest prime number?
  • What is the smallest composite number?
  • Why isn’t 1 prime?
  • What about zero? Negative numbers? Fractions/decimals?
    • Refer back to the definition “… to attain a whole number answer”
    • How many factors does 10 have?
    • Does a factor have to be a whole number?
    • What is exponential notation?

 

I do model what the tree method looks like in the first example and in the negative number example. Then students get 5 minutes to work through the rest of the notes independently/silently. Students can ask questions, and my help will guide them through their own notes to encourage their use. 

Task

20 minutes

Students return to their seats and are given their “Task” paper. If is divided into two sections: a real world application problem for factoring and a skills section for practice. Students must work with their neighbors to complete the questions. I have one class that has been doing well when given a difficult problem to solve in groups, but my other two classes don’t do as well. They freeze up and are afraid to take any steps, exclaiming defeat rather quickly. The skills section of this class work does not have to be completed second. Students may begin with this section to get ready for the task problem. After 10 minutes, I will stop class to allow 3 – 4 minutes of questions about the task problem. Then, students will be allowed to continue working together after also being advised that this assignment will be collected for a grade. Work must be shown.

Closing

10 minutes

Any students allowed to work in booths will be asked to return to their seats. They will be given the remainder of class time to work silently on completing this task. I will be distributing homework during this time.

I will be grading this question using the three point rubric provided by the state of NY.