Transcript Sequences - Teaching Portfolio

Sequences
Arithmetic Sequences
Solving
word problems.
By Irma Crespo 2010
A Review
• A sequence is an ordered list of numbers.
1 Triangle
2 Triangles
3 Triangles
3 Sticks
5 Sticks
7 Sticks
Number of Triangles
Number of Sticks
• 3, 5, 7, 9, 11, 13, 15,…
+2 +2 +2 +2 +2 +2
The difference is called
the common difference.
• An arithmetic sequence
is a sequence with
common difference.
Remember Our Easy Tricks
• Only think addition to get the next term.
• Common difference means the terms in a sequence are
either increasing or decreasing at the same amount.
• If term 1 and the common difference are the same, the
expression is common difference times the term number (n).
• If term 1 and the common difference are NOT the same, the
expression consists of the common difference times the term
number (n) and the number added to the common difference
to get the first term. The expression should be in this order.
Oh,No! Oh,Yes!
Word Problem
• The cost of a taxi ride for 1,2,3, and 4 miles are shown
in this arithmetic sequence. What would be the cost of
a 9-mile ride?
Costs of a Taxi Ride
Miles (m)
Costs in $
1
2
3
4
5.25
7.00
8.75
10.50
Let’s Solve It
• Find the common difference.
+1
Miles (m)
Costs in $
+1
+1
1
2
3
5.25
7.00
8.75
+1.75
+1.75
4
10.50
Wait!!!
+1.75
We are not
done yet!
The common difference is $1.75.
The common difference is $1.75 times the miles (m).
So, the expression is $1.75m.
Is the common difference the same as the cost in 1 mile? No.
Let’s Solve It
• We have $1.75m. Next, find a number you can add to
the common difference that gives the cost at 1 mile.
Miles (m)
Costs in $
1
2
3
4
5.25
7.00
8.75
10.50
How much can you add to $1.75 to get the cost at 1 mile,
which is $5.25? $1.75 + $3.50
?
= $5.25
• So, the expression is $1.75m + $3.50.
• And the cost at 9 miles is: ($1.75)(9) + $3.50 = $19.25
On the White Board
• If Luther continues
the pattern shown in
the table, how many
minutes will he
spend jogging each
day during his 5th
week?
Week
(n)
Time Jogging
1
2
3
4
5
8
16
24
32
4?0
(minutes)
Expression: 8n
The 5th week: 8(5) = 40
Practice, Practice,Practice
• Complete the worksheet.
• You have a choice to work on your own
or to work with a partner.
• Completed worksheets are submitted
for grading.
• Solutions are discussed the next day.
Time is up!
Main Resources
LINEAR FUNCTIONS (Chapter 9) LESSON PLAN by
• Math Connects: Concepts, Skills, and Problem Solving
Teacher Edition; Course 3, Volume 2
Columbus:McGraw-Hill, 2009.
POWERPOINT CREATED by
• Irma Crespo. University of Michigan-Dearborn,
School of Education; Winter, 2010.