1. The number 18 can be written as the product of the primes 2 x 3 x 3. We can say that, “Eighteen can be broken down into three prime factors”. Find three more numbers that can be broken down into exactly three prime factors. Find four numbers between 100 and 300 that can be broken down into exactly five prime factors

2. Applying Primes and HCF/LCM Skills Decide whether worded questions are asking to find LCM or HCF Use appropriate method to find HCF/LCM depending on size of the number Work systematically to problem solve

3. Can explain to others why it is an LCM or HCF question. Can identify which situations need HCF or LCM to solve. Can work out both LCM and HCF then go back to the question to see which one makes more sense. Can draw diagrams or pictures to try to model situations. Can underline key words that help me decide if it is HCF or LCM. Guess which one to use and don’t check answer.

4. Zoe has two large cakes that she wants to share amongst her friends. She doesn’t want any of the cake left. The chocolate cake she has sliced into 24 pieces and the fruit cake into 36 pieces. What’s the largest number of friends she can give cakes to? How many slices of each cake do her friends get? Mr Hussey has two boxes of green pens. One has 28 pens in. The other has 32 pens. He wants to group the pens equally so that there are none left over. What is the largest number of pens that he can have in a group? How many groups of will he have ? A carpenter has two lengths of wood; one is 108cm long and the other is 72cm long. He wants to cut them up to produce smaller pieces of wood to build a shelving unit. The pieces of wood all need to be the same length, with no wood left over. What is the greatest length, in cm, that he can make the shelves? Liz has two pieces of string, one 18 cm long and the other 24 cm long. She wants to cut them up to produce smaller pieces of string that are all of the same length, with no string left over. What is the greatest length, in cm, that she can make them?

5. Tours of the Birmingham Library and the Symphony Hall start from the same location on Broad Street. Tours for the Library leave every 15 minutes. Tours for the Symphony Hall leave every 20 minutes. Q) If the first tours start at 8:30, when is the first time that they leave at the same time? Two neon lights are turned on at the same time. One blinks every 4 seconds. The other blinks every 6 seconds. a)After how many seconds will they blink at the same time? b) In 60 seconds, how many times will they blink at the same time? Aliyah and James are running around a track. Aliya takes 3 minutes to complete a lap. James takes 5 minutes to complete a lap. a) If they started at the same time, after how many minutes will they be at the same place? b) How many laps will Aliya and James each have completed by this time? Alice is stacking two types of boxes in her cupboard. She stacks the red boxes on top of each other. Next to them she stacks the blue boxes. Red boxes are 10cm tall. Blue boxes are 15cm tall. What is the shortest height at which the two stacks will be same height?

6. Question #1 Mrs. Evans has 120 crayons and 30 pieces of paper to give to her students. What is the largest # of students she can have in her class so that each student gets equal # of crayons and equal # of paper.

7. Question #2 Rosa is making a game board that is 16 inches by 24 inches. She wants to use square tiles. What is the larges tile she can use?

8. Question #3 Z100 gave away a Z $100 bill for every 100th caller. Every 30th caller received free concert tickets. How many callers must get through before one of them receives both a coupon and a concert ticket?

9. Question #4 Two bikers are riding a circular path. The first rider completes a round in 12 minutes. The second rider completes a round in 18 minutes. If they both started at the same place and time and go in the same direction, after how many minutes will they meet again at the starting point?

10. Question #5 Sean has 8-inch pieces of toy train track and Ruth has 18-inch pieces of train track. How many of each piece would each child need to build tracks that are equal in length?

11. Question #6 I am planting 50 apple trees and 30 peach trees. I want the same number and type of trees per row. What is the maximum number of trees I can plant per row?

12. The square of a prime number has exactly three factors. Sometimes?Always?Never?

13. 33232 3232 55252 5252

14. pp2p2 p2p2

15. Explain, using diagrams and a concluding sentence why the cube of a prime number has exactly four factors.