BELLWORK

p. 347 2-70 to 2-72 When you solve a puzzle, is there always one answer?  To a crossword puzzle with words, this is typically true.  There is only one way that the letters can be entered so that everything will work and match the clues.  But in a number puzzle there may be more than one answer that fits the clues.  As you work today, think about and discuss with your team whether there is more than one way to solve a problem and how you know this to be true.

2-70. There are several ways to write the dimensions of the rectangle at right. How many ways can you write the dimensions of the generic rectangle below? Draw a new rectangle for each way.

2-70. (cont.) The factor on the short side of each of the rectangles you drew in part (a) had to be a factor of both 120 and 18.  When two products share the same factor, that factor is called a common factor.  What do you think is meant by the greatest common factor of 120 and 18?  What is the GCF for 120 and 18? 

2-71. In problem 2-70, the greatest common factor and its generic rectangle could be used to write a multiplication sentence with parentheses: 120 + 18 = 6 (20 + 3)

2-71. (cont.) For each generic rectangle below, draw as many rectangles with different dimensions as you can. Then use the greatest common factor for the numbers in each rectangle to write a multiplication sentence with parentheses.

2-72. Ethan thinks that 5(13) can be found by adding 50+15. Is Ethan correct? Draw a diagram to demonstrate Ethan’s idea OR show where he went wrong. Write a multiplication sentence with parentheses to represent Ethan’s generic rectangle.

2-73. Use Ethan’s idea to draw a generic rectangle to find each product below. Then write a multiplication sentence with parentheses for each one. 7(1+11) 5(500 + 4) 3 • 206

2-74. LEARNING LOG Discuss the idea of a greatest common factor with your team. Then write a definition for greatest common factor in your Learning Log. Create your own example to help explain your definition. Title this entry “Greatest Common Factor” and include today’s date.

What about the Greatest Common Factor (GCF) of 6 and 8? PRACTICE REVIEW What about the Greatest Common Factor (GCF) of 6 and 8? The GCF is the product of all the numbers on the left. 2 6 8 The GCF of 6 and 8 is 2. 3 4 Becky Afghani, LBUSD Math Curriculum Office, 2003

Which numbers in the ladder give you the GCF? PRACTICE REVIEW Which numbers in the ladder give you the GCF? Multiply the numbers on the left only for the GCF. # # # # # # # # # # # Becky Afghani, LBUSD Math Curriculum Office, 2003

Let’s try some bigger numbers. PRACTICE REVIEW Let’s try some bigger numbers. Divide out all the common factors down the left side. 2 24 60 What number goes into both 24 and 60? Does any # besides 1 go into both 12 and 30? 2 12 30 How about 6 and 15? Anything else? 3 6 15 No? You’re done. 2 5 Becky Afghani, LBUSD Math Curriculum Office, 2003

= 12 24 60 2 12 30 6 15 3 5 Find the GCF. PRACTICE REVIEW The GCF of x The GCF of 24 and 60 is 12. 24 60 2 12 30 6 15 3 5 = 12 Becky Afghani, LBUSD Math Curriculum Office, 2003

PRACTICE Use any method of your choice to find the Greatest Common Factor (GCF). 1) 54 and 45 2) 25 and 55 3) 126 and 374 4) 8 and 50 5) 210 and 20

HOMEWORK