1. Look for a Pattern 1.8 There are no notes for this lesson. This is a problem- solving activity. Whatever approach you or your group chooses in solving a problem MUST BE written, drawn, or illustrated in some way. The method is up to you…… The documentation of your solution is required! First, we’ll try some together.

2. Techniques for Finding the Patterns There is no one “right” way to see a pattern. Everyone has a method that works best for them. During this lesson, we will explore different techniques for solving problems with a variety of pattern-approaches.

3. The Problem………. p. 40 It’s hard to keep something a secret at HMMS. Each person that hears a story repeats it 15 minutes later to two other people. If one student heard something at 8:00 a.m., how many students would know by 9:00 a.m?

4. Make a Table Time8:008:158:308:459:00 New students told 1 Number of students that know 1 Use the facts to create a table 24816 3 7 1531

5. Tree Diagram 8:00 a.m. 8:15 a.m. 8:30 a.m. 8:45 a.m. 9:00 a.m. Sixteen more people!!!!!!!!!!!! 1 2 4 8 16 31

6. We could also use a graph, but it soon becomes useless. 8:00 8:15 8:30 8:45 9:00 9:15 60 56 52 48 44 40 36 32 28 24 20 16 12 8 4 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 New Students Told Total Students that Know Why is this not practical??

7. At what time would 251 people know the news? Continue the chart???? Equation??????????????? WHY????????????????? 9:45 a.m. What techniques did you use? Time9:009:159:309:45 1163264128 13163127255

8. Group Work There is a list of strategies on p. 42 you might want to use when looking for a pattern. With your group, look over problems 1 and 2. If you have time, try 7 and 8 on p. 43. Find solutions to the problems you choose. You may not have time to complete them all. Be creative! We will check these together.

9. Caroline and the Swim meet Week12345678 Laps1361015212836 1+23+36+410+515+621+728+8

10. Student Parade 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 13 We can break this group into 6 pairs of numbers, each with a sum of 13. So, 6(13) = 78

11. Savings 1st2nd3rd4th5 th 6 th 7 th 8 th 9 th 10th 1248163264128256512 1 2 4 8 16 32 64 128 256 512 1023 $10.23

12. Buffet Dinner PeopleCost 1$10 2$20 3$29 4$37 5$44 6$50 7$55 8$59 +9 +8 +7 +6 +5 +4 $80 at the individual price -59 $21 was saved 962 1064 1165 +3 +2 +1 They can only serve 10 without losing money. A party of 11 would cost $66 to serve, but would only have to pay $65.

13. 6 mph 12 mph 12 mph is equal to 12 miles in 60 minutes. 6 mph is equal to 6 miles in 60 minutes. If you divide each number by 6, you know how far he rode in 10 minutes…….2 miles. 2 miles She is only running half this speed, so she will travel just 1 mile… 6 and 60 both divided by 6 shows 1 mile in 10 minutes. 1 mile They are 3 miles apart.

14. Is there a formula for that? YES!!!! d = rt means distance=rate(time) d = rt so the distance they are apart is the sum of the two rates(times) d = ( )(12 ) + ( )( ) 6 d = 2 + 1 d = 3

15. Which set of numbers would match the expression 4x + 3, when x is the previous (first, or starting) number? a) 7, 9, 11, 13 b) 0, 3, 15, 63 c) 1, 8, 15, 19

16. If it takes 12 minutes to cut a pipe into three pieces, how long would it take to cut the pipe into four pieces. 18 minutes One cut gives two pieces, so TWO cuts will give three pieces. This question is about the cuts made.... Two cuts will take 12 minutes……..that is 6 minutes per cut. three cuts will make 4 pieces…..that is 6 minutes per cut. This is where the 18 comes from!!!!!!!!

17. Now what? Using various approaches in problem solving helps you think more flexibly. Tonight’s integer review homework is a different approach to the topics we have covered so far in the chapter.