Differentiating Instruction● Go to: http://goo.gl/BvCzSw and

complete form (Enter Session Code on board)

● On the post-it notes, please write questions you may have now, if any, about differentiating instruction in a math classroom.

Session Desired Outcome:

Teachers will become familiar with differentiated instruction as modeled in a math demonstration lesson on the fundamental counting principle.

OutcomeDemo Lesson

Bell Work

Find the prime factorizations of: A. 20 B. 30 C. 36 D. 98

Fundamental Counting Principle

Study Questions

First & Last NameMath 1

Essential Question:

Fundamental Counting Principle

Study Questions

First & Last NameMath 1

Essential Question: How many factors does have?Vocabulary:

Factors

Prime numbers

Prime factors

Prime factorization

Fundamental Counting Principle (FCP)

579 532

Fundamental Counting Principle

Study Questions

First & Last NameMath 1

Essential Question: How many factors does have?

579 532

Fundamental Counting Principle

Study Questions

First & Last NameMath 1

Essential Question: How many factors does have?Vocabulary:

Factors

Prime numbers

Prime factors

Prime factorization

Fundamental Counting Principle (FCP)

579 532

Quickwrite:Without doing any

calculations, describe why 212 is much larger than 122.

Fundamental Counting Principle

Study Questions

Practice/Reinforce Sentence Frames

The factors of ____ are _________.

Thumbs up if you agree with what I say.

Fundamental Counting Principle

Study Questions

Practice/Reinforce Sentence Frames

The factors of 10 are 1, 2, 5 & 10.

Repeat together when I hold my arms out.

Fundamental Counting Principle

Study Questions

Practice/Reinforce Sentence Frames

The prime factors of ____ are _________.

Thumbs up if you agree with what I say.

Fundamental Counting Principle

Study Questions

Practice/Reinforce Sentence Frames

The prime factors of 10 are 2 & 5.

Repeat together when I hold my arms out.

Fundamental Counting Principle

Study Questions

Practice/Reinforce Sentence Frames

The prime factors of ____ are _________.

Thumbs up if you agree with what I say.

Fundamental Counting Principle

Study Questions

Practice/Reinforce Sentence Frames

The prime factors of 30 are 2, 3 & 5.

Repeat together when I hold my arms out.

Fundamental Counting Principle

Study Questions

List the factors of 20.

1, 2, 4, 5, 10, 20

20 has 6 factors.

Fundamental Counting Principle

Study Questions

What are the prime factors of 20?

2 & 5

20 has two prime factors.

Fundamental Counting Principle

Study Questions

How many ways can 2 and 5 be used to create the factors of 20?

1 = 2 = 4 = 5 = 10 = 20 =

20 50

Fundamental Counting Principle

Study Questions

How many ways can 2 and 5 be used to create the factors of 20?

1 = 2 = 4 = 5 = 10 = 20 =

20 50

21 50

Fundamental Counting Principle

Study Questions

How many ways can 2 and 5 be used to create the factors of 20?

1 = 2 = 4 = 5 = 10 = 20 =

20 50

21 5002 52

Fundamental Counting Principle

Study Questions

How many ways can 2 and 5 be used to create the factors of 20?

1 = 2 = 4 = 5 = 10 = 20 =

20 50

21 50

22 50

20 51

Fundamental Counting Principle

Study Questions

How many ways can 2 and 5 be used to create the factors of 20?

1 = 2 = 4 = 5 = 10 = 20 =

20 50

21 50

22 50

20 51

21 51

Fundamental Counting Principle

Study Questions

How many ways can 2 and 5 be used to create the factors of 20?

1 = 2 = 4 = 5 = 10 = 20 =

20 50

21 50

22 50

20 51

21 51

22 51

Fundamental Counting Principle

Study Questions

How many ways can 2 and 5 be used to create the factors of 20?

1 = 2 = 4 = 5 = 10 = 20 =

20 50

21 50

22 50

20 51

21 51

22 51

Think about how many ways 2 can be used.

Show on your fingers how many ways 2 can be used.

, , can all be used to create factors of 20.

20

21

22

Fundamental Counting Principle

Study Questions

How many ways can 2 and 5 be used to create the factors of 20?

1 = 2 = 4 = 5 = 10 = 20 =

20 50

21 50

22 50

20 51

21 51

22 51

Think about how many ways 5 can be used.

Show on your fingers how many ways 5 can be used.

, can both be used to create factors of 20.

50

51

Fundamental Counting Principle

Study Questions

, , can all be used to create factors of 20.

20

21

22

, can both be used to create factors of 20.

50

51

There are three ways to use 2 and two ways to use 5.

Fundamental Counting Principle

Study Questions

____________ x ____________ = ___________ Ways to use 2 Ways to use 5 Factors of 20

Fundamental Counting Principle

Study Questions

____3_______ x ____________ = ___________ Ways to use 2 Ways to use 5 Factors of 20

Fundamental Counting Principle

Study Questions

____3_______ x _____2______ = ___________ Ways to use 2 Ways to use 5 Factors of 20

Fundamental Counting Principle

Study Questions

____3_______ x _____2______ = ____6______ Ways to use 2 Ways to use 5 Factors of 20

Fundamental Counting Principle

Study Questions

Fundamental Counting Principle

Study Questions

How many kinds of pizzas can be created with:3 meats – pepperoni, seafood, ground beef (or none)2 veggies – mushrooms, olives (or no veggies)1 cheese – cheese (or no cheese)

No doubling up (and no meat, no veggies, and no cheese counts as a choice). __4___ x ____3______ x ___2___ = __24____ Meats Veggies Cheese Pizzas

Study Questions

How many kinds of pizzas can be created with:3 meats – pepperoni, seafood, ground beef (or none)2 veggies – mushrooms, olives (or no veggies)1 cheese – cheese (or no cheese)

No doubling up (and no meat, no veggies, and no cheese counts as a choice). __4___ x ____3______ x ___2___ = __24____ Meats Veggies Cheese Pizzas

Work with a partner to construct a visual in your notes that would represent this problem.

Fundamental Counting Principle

Study Questions

Return to the Essential Question. How many factors does have?A. 30B. 315C. 480D. 630

29 37 55

Fundamental Counting Principle

Study Questions

Dyads create/exchange example problems.

Verify solution with table group.

These ideas are critical to enabling “Public Key Encryption.” Without the understanding of very large prime numbers and the Fundamental Counting Principle, you would not be able to use the ATM or make purchases online.

Fundamental Counting Principle

1. Respond to the essential questions.

2. List five key phrases or words from your notes.

3. Use your five key phrases or words to write three to five complete sentences summarizing your notes and answering the essential questions.

GIST Summary

Study Questions Can “cover” standards-based

content while ensuring that students are active and engaged

Fundamental Counting Principle

Study Questions

Ticket out the door: Write your answer on a sticky note—do not put your name on it.

How many factors does 24•32•53 have?

On your way to break, put your note on the Parking Lot/Community Forum.

Fundamental Counting Principle

Reflection Question:

How does the prior activity provide access for AEL (Academic English Learners), Special Education and GATE students?

ELD Identifiers: ● Emerging: AELs need substantial support

● Expanding: AELs need moderate support

● Bridging: AELs need light support

ELD StandardsPart 1: Interacting in a meaningful way● A: Collaboration

○ 1 - Exchanging information and ideas: Contribute to class, group, and partner discussions, including sustained dialogue, by following turn taking rules, asking relevant ‐questions, affirming others, and adding relevant information.

● C: Productive○ 9 - Presenting: Plan and deliver brief oral presentations on a variety of topics and

content areas (e.g., retelling a story, explaining a science process, etc.). ○ 12 - Selecting language resources: Use a growing number of general academic and

domain specific words in order to add detail, create an effect (e.g., using the word ‐suddenly to signal a change), or create shades of meaning (e.g., scurry versus dash) while speaking and writing.

Link to full document: Grades 6-8, Grades 9-12

Universal Design for Learning (UDL) Principles: Video on UDL (4 minutes)1. Provide Multiple Means of Representations - The

what of teaching and learning, content

2. Provide Multiple Means of Action and Expression - The how of teaching and learning, process

3. Provide Multiple Means of Engagement - The why of teaching and learning, product

GATE (link to Ca Math Framework on GATE, start at bottom of page 1)

● Depth

● Pacing

● Complexity

● Novelty

RUSD Lesson Template (see page 2)● Sample Lesson: 8th Grade, Unit 1:

Representing and Combining Transformations

Pick a topic/lesson and expand to include strategies

Closing:

● Post parking lot questions that we have not answered (YET) during this session.

Resources:● UDL Presentation