This document outlines the schedule and lessons for a math class, including: - Assignments due on Tuesday and Thursday for review packets - Students should wear football attire on Thursday and study for Module 2 - Friday will be the Module 2 assessment - Lesson 19 teaches Euclid's Algorithm as an application of long division to find the greatest common factor of larger numbers. It explores this through examples and relating it to tiling areas without gaps.

1. Module 2 Lesson 19 Day 2.notebook
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Oct 8­8:53 AM
Monday Problem Set Lesson 19 # 2 & 3
Tuesday Review Packet Due Thursday
Wednesday Review Packet Due Thursday
Thursday
Wear football attire today
Study Module 2
Empty Math Binder :)
Friday Module 2 Assessment

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Jan 12­7:26 AM

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MODULE 2 Arithmetic Operations Including
Division of Fractions
Topic D:
Lesson 19: The Euclidean Algorithm as an
Application of the Long Division Algorithm
Student Outcomes
§ Students explore and discover that Euclid’s Algorithm is a more efficient
means to finding the greatest common factor of larger numbers and determine
that Euclid’s Algorithm is based on long division.

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Jan 12­11:31 AM

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Let's go back to Example 1 so we can SEE what it means
Example 1: Euclid’s Algorithm Conceptualized
What is the GCF of 60 & 100? 20
What is the interpretation of the GCF in terms of area? Let’s take a look.
§ Notice that we can use the GCF of 20 to create the largest square tile that will cover the rectangle
without any overlap or gaps. We used a 20 x 20 tile.

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But, what if we didn’t know that? How could we start? Let’s guess!
What is the biggest square tile that we can guess?
Let's try a 60 x 60 tile!
It fits, but there are 40 units left over. Do the division problem to prove this.

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The remainder becomes the new divisor and continues until the remainder is zero.
§ What is the leftover area?
60 x 40
§ What is the largest square tile that we can fit in the leftover area?
40 x 40

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What is the leftover area?
20 x 40
What is the largest square tile that we can fit in the leftover area?
20 x 20
When we divide 40 by 20, there is no remainder. We have tiled the whole
rectangle!
If we had started tiling the whole rectangle with squares, the largest square we
could have used would be 20 by 20.

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Example 4: Area Problems
The greatest common factor has many uses. Among them, the GCF lets us find
out the maximum size of squares that will cover a rectangle. Whenever we
solve problems like this, we cannot have any gaps or any overlapping squares.
Of course, the maximum size squares will be the minimum number of squares
needed.
A rectangular computer table measures 30 inches by 50 inches. We need to
cover it with square tiles. What is the side length of the largest square tile we
can use to completely cover the table, so that there is no overlap or gaps?

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We already know the GCF of (30,50) is 10.
Squares of 10 inches by 10 inches will tile the area.
b. If we use squares that are 10 by 10, how many will we need?
c. If this were a giant chunk of cheese in a factory, would it change the
thinking or the calculations we just did?
d. How many 10 inch ×10 inch squares of cheese could be cut from the giant
30 inch × 50 inch slab?

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Closing
Please take out your exit ticket for Lesson 19, close your
binder, and complete the exit ticket. This will be collected.
Euclid’s Algorithm is used to find the greatest common factor (GCF) of two
whole numbers. The steps are listed on your Student Page and need to be
followed enough times to get a zero remainder. With practice, this can be a
quick method for finding the GCF.

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