Lesson: Prime Factorization
Lesson Steps: Tuesday
Do Now-8 min
· Students work on 2 problems on do now sheet to review content ( 4 minutes)
· Teacher walks around to check HW for completion and process on do now problems (while students complete problems)
· Pull two sticks – students complete answers on whiteboard – students check work against students boardwork (2 minutes) Teacher walks around still to check understanding while students are working on board.
HW Check- 6 min
· Check All – put up all answers on whiteboard
· Students check all problems on homework (3 minutes – 1 minute front, 1 minute back)
· Teacher walks around while students are checking work to intervene.
· Teacher identifies the one or two most common mistakes on homework and reviews it whole class on transparency. (1 – 2 minutes) Before review – ask students to think about the steps I am taking while I solve the problem(s) – they will share whole class afterwards.
Paper Pass in Transition:
Mental Math: 5min
· Teacher reads and shows problem
· Student pulls a stick to call on student to answer
· Last problem string – all students complete and answer by raising hand – fastest hand called on
Mini-Lesson: (30 mins)
§ Opening: Today we are going to learn a super important theory of mathematics. This theory says that every number can be factored into a product of prime numbers in exactly one way. Before we get started in learning this super important theory – let’s break it down based on our knowledge of vocabulary. What does the word prime mean? What does the word factor mean? What does the word product mean?
§ Launch: pass out calculators to every student.
o Show the following on the overhead: 15 x 28 / 20 x 7 x 3 / 3 x 35 x 4
o Ask students to use calculator to find the products. Ask students what they notice. They all equal 420.
o Tell students there are many ways to write 420 as a product (remind students product means as the answer to a multiplication problem) Can anyone find another way?
o Ask students how they found each product – it students are having trouble explaining their reasoning or stuck on finding different ways to find another product, then elicit:
o The combining strategy – Take parts of the problems we already have and combine them to form a new number (instead of 20 x 7 x 3 - multiple 7 x 3 and make the problem 20 x 21.
o The breaking apart strategy – taking a number and breaking it into two of its factors ( 15 x 28 -à 5 x 3 x 28 if you break 15 apart)
o Display the product puzzle for students – allow them to use their calculators
o Explain that the puzzle is like a word search – except we are going to group together a string of numbers whose product is equal to 1350. The strings can go horizontally, vertically, or around corners.
o Find one for them as an example (top row – circle 5 x 6 x 5 x 9 ) Ask student to use calculators to see if this works.
o Find vertically – 5 x 3 x 10 x 9 - ask student to check if this works
o Allow students to look for some more strings that they find.
o Share whole class some of the strings that are found.
o Take one string from the product puzzle and tell the students we want to break the string down even farther until we have the longest string possible. We will know we have the longest possible string when we break it down all the way to its prime factors.
o Model breaking down the same number in a different way
o Show circling any prime numbers a signal to stop that branch of the tree.
o Take notes of prime factorization and how to walk through the process
o Students will practice making factor trees for different sets of numbers.
§ Wrap Up:
o Discuss how we can write product or primes with exponents as well – demonstrate to students – show students working from string with exponents to longest string. Model for students and complete a couple examples.
§ Key Point: Each number has only one longest string of factors. The prime factorization of any number is unique to that number.
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