Annual Garage Sale Ever since last year’s community garage sale. Kyle has been saving $2 coins, $5 bills and $10 bills. Now he has $30 worth of each. He is looking forward to buying some items at this year’s sale. What prices can Kyle pay for exactly, using only $2 coins, $5 bills and $10 bills?

Garage Sale A. What can Kyle pay for using only $2 coins? B. What can he pay for using only $5 bills? C. What can he pay for using only $10 bills? D. Which prices require Kyle to use more than one type of bill or coin? Explain why? E. Write a price that is greater than $100 and that someone can pay using only one type of bill or coin. F. Write a price that is greater than $100 and that someone cannot pay using only one type of bill or coin. Garage Sale Scooter $30 Skateboard$22 Snowboard $59 Baseball Glove $15

A) How many marbles might be in the bag? Do You Remember? A bag of marbles can be divided evenly among two, three or four friends. A) How many marbles might be in the bag? B) What is the least number of marbles that can be in the bag? C) How many marbles would there be if there are between 30 and 40 marbles in the bag? How many marbles would each friend get? Use a diagram or another strategy to show your answer. 2. Suppose that you have three different lengths of linking cubes, as show below. Assume that you have as many of these lengths as you need, but you may not take them apart. Can you make each length below using only one colour? If it is possible, show more than one way 25 cubes 20 cubes 18 cubes 29 cubes 30 cubes 32 cubes

Do You Remember? : The Sequel 3. Find all the possible whole number lengths and widths of rectangles with each area given below. You might draw on centimetre grid paper or use another strategy. 12 cm2 20 cm2 17 cm2 24 cm2

Factors Factors are whole numbers (not including 0) that are multiplied together to give a product - divides into another whole number with no remainder Sometimes represented by F(x) or F(X) Factoring – is breaking a number down into all its factors Examples Factors of 6: F(6): 1, 2, 3, 6 (1x6 = 6), ( 2x3 = 6) Factors of 12: F(12) 1, 2, 3, 4, 6, 12 (1x12 = 12), (2x6 = 12), (3x4 = 12) The common factors of 6 and 12 are: 1, 2,3 and 6.

Find the factors of the following numbers a). 5 = 5x1 F(5) = 1, 5 k). 24 =3x8, 1x24 12x2, 6x4, b). 30 = 5x6, 1x30, 15x2 l). 32=32x1, 8x4 3x10 16x2 c). 42 = 14x3, 1x42, 2x21 m). 4 =2x2, 1x4 7x6. d). 12= 1x12, 4x3, 6x2 n). 13= 1x13 e). 8 = 4x2, 8x1 o). 22= 11x2, 1x22 f). 15 = 5x3, 1x15 p). 6 = 2x3, 1x6 g). 36 =9x4, 6x6, 18x2, q). 9 = 3x3, 1x9 = 36x1, 3x12 h). 40 = 5x8, 4x10, 20x2 r). 16 = 8x2, 4x4, = 40x1, 1x16 i). 18 = 9x2, 3x6, 18x1 s).72 = 18x4, 36x2, 9x8 = 6x12, 1x72 24x3 j). 21 = 3x7, 21x1 t). 100 = 25x4, 10x10, 50x2 = 1x100, 20x5

The Greatest Common Factor The Greatest Common Factor (GCF) is the largest factor that divides all the numbers To find the Greatest Common Factor (GCF) of two numbers: List all the factors of each number If there are no common factors, the GCF is 1 For Example F(18) = 1, 2, 3, 6, 9, 18 F(25) = 1, 5, 25 F(24) = 1, 2, 3, 4, 6, 8, 12, 24 F(17) = 1, 17 The GCF is 6 The GCF is 1

Homework Sept 30 Find the Greatest Common Factor of each. 12 & 15 F(12) = 1, 2, 3,4, 6, 12 The GCF = 3 F(15) = 1, 3, 5, 15 4 & 9 16 & 24 30 & 18 12, 30 & 9

Multiples Multiples is the product of a number and any other whole number. Zero (0) is a multiple of every number A product is the answer to a multiplication question Sometimes represented by M(x) or M(x) For Example Multiples of 4: M(4); 4, 8, 12, 16, 20, 24 … (4x1), (4x2), (4x3), (4x4), (4x5), … Multiples of 6: M(6): 6, 12, 18, 24, … (6x1), (6x2), (6x3), (6x4), (6x5), … A common multiple of 4 and 6 is 24

The Lowest Common Multiple (LCM) The Lowest Common Multiple (LCM) of two numbers is the smallest number (not zero) that is a multiple of all numbers. To find the LCM of two numbers: List the multiples of each number. Sometimes, the LCM will be the numbers multiplied together. For Example: M(2) = 2, 4, 6, 8, 10,12, … M(3) = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, … M(3) = 3, 6, 9, 12, 15, … M(8) = 8, 16, 24, 32 40, 48 … The LCM = 6 The LCM = 24