Transcript Group Lesson: Problem Solving

Look for a Pattern 1.8
There are no notes for this lesson. This is a problemsolving 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.
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.
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?
Make a Table
Time
New
students told
Number of
students
that know
Use the facts
to create a
table
8:00
1
1
8:15
8:30
8:45
9:00
2
4
8
16
3
7
15
31
Tree Diagram
8:00 a.m.
1
8:15 a.m.
2
4
8:30 a.m.
8
16
8:45 a.m.
31
9:00 a.m.
Sixteen more people!!!!!!!!!!!!
At what time would 251 people know the news?
Continue the chart???? Equation???????????????
WHY?????????????????
9:45 a.m.
What techniques did you use?
Time
9:00 9:15 9:30 9:45
1
16
32
64
128
1
31
63
127
255
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.
Caroline and the Swim meet
Week
1
2
3
4
5
6
7
8
Laps
1
3
6
10
15
21
28
36
1+2
3+3
6+4
10+5
15+6
21+7
28+8
Student Parade
12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 =
13
13
13
We can break this group into 6 pairs of numbers, each
with a sum of 13. So, 6(13) = 78
Buffet Dinner
People Cost
1
$10
2
$20
3
$29
4
$37
5
$44
6
$50
7
$55
8
$59
+9
+8
+7
+6
$80 at the individual price
-59
$21 was saved
+5
+4
+3
9
62
10
64
11
65
+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.
If you divide each number by
6, you know how far he rode
in 10 minutes…….2 miles.
12 mph is equal to
12 miles in 60 minutes.
They are 3
miles apart.
12 mph
1 mile
6 mph
2 miles
6 mph is equal to
6 miles in 60 minutes.
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.
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 = ( 1 )(12 ) + ( 1)(6 )
6
6
d=2+1
d=3
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
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
This question is about the cuts made . . . .
One cut gives two pieces, so TWO cuts will give three pieces.
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!!!!!!!!
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.