Bridging the Gap for Language Minority Students and ELLs in Math
Notetaking Guide
Ideas/concepts/terms related to English
language learning:
Things to keep in mind about my own
students:
Thoughts on scaffolds that might be
useful:
Things that are good for many students
but might be essential for ELLs:
Things to look up later:
Other/Misc./Don’t-forgets:
Bridging the Gap, Notetaking Guide
Algebra I, Module 3, Lesson 5 from EngageNY.org of the New York State Education
Department is licensed under CC BY-NC-SA 3.0.
1
Algebra I, Module 3, Lesson 5 from EngageNY.org of the New York State Education
Department is licensed under CC BY-NC-SA 3.0.
Listening
Bridging the Gap, Notetaking Guide
Writing
Reading
Which MPs?
Speaking
Scaffold/Idea
2
Algebra 1: The Power of Exponential Growth
Today’s Objective
I will model and solve problems using exponential formulas.
Opening Exercise
Jim rents a bike. He can choose Company 1 or Company 2.
Jim chooses Company 2.
Jim keeps the bike longer than expected. Jim returns the bike 𝟏𝟓 days late.
•
How much money does Jim pay to rent the bike from Company 2?
•
How much money would Jim pay if he used Company 1 instead?
Record your answers by continuing the two tables below. Calculate for Day 5, Day 6, and so on, through
Day 15.
Company 1
Company 2
Day 1
$5
Day 1
$.01
Day 2
$10
Day 2
$.02
Day 3
$15
Day 3
$.04
Day 4
$20
Day 4
$.08
Day 5
Day 5
Day 6
Day 6
Day 7
Day 7
…
…
Day 15
Day 15
The fee increases $5 each day the
bike is late.
•
The fee doubles in amount each day
the bike is late.
How much money does Jim pay to rent the bike from Company 2?
Jim pays _________ to rent the bike from Company 2.
•
How much money would Jim pay if he used Company 1 instead?
If Jim used Company 1 instead, he would pay ________.
Bridging the Gap, Notetaking Guide
Algebra I, Module 3, Lesson 5 from EngageNY.org of the New York State Education
Department is licensed under CC BY-NC-SA 3.0.
3
Example 1
This is a folktale about the game of chess.
A long time ago, the inventor of the game of chess showed the game to the country’s leader, and
the leader was very impressed. The leader told the inventor to think of a prize for his work.
Look at the illustration of the chessboard.
The inventor said he would take one grain of rice on the first square of the chessboard, two
grains of rice on the second square of the chessboard, four grains of rice on the third square,
eight on the fourth square, and so on. The number of grains of rice doubles for each following
square.
The country’s leader was surprised, but he began to count out the rice.
a. Why do you think the country’s leader was surprised?
Bridging the Gap, Notetaking Guide
Algebra I, Module 3, Lesson 5 from EngageNY.org of the New York State Education
Department is licensed under CC BY-NC-SA 3.0.
4
The country’s leader began to count out the grains of rice for each square, but soon ran out. He
would need more rice than they had in the entire country!
b. The first square on the chessboard has one grain of rice, or 20.
The second square has two grains of rice, or 21.
The third square has four grains of rice, or 22.
The fourth square has eight grains of rice, or 23.
Using this information, complete the table (following) to record the number of grains of
rice in each square.
How can we represent the grains of rice as exponential expressions?
1
Square #
Grains of Rice
1
1
2
2
3
4
4
8
5
16
2
3
4
Exponential Expression
5
62 63 64
Bridging the Gap, Notetaking Guide
Algebra I, Module 3, Lesson 5 from EngageNY.org of the New York State Education
Department is licensed under CC BY-NC-SA 3.0.
5
c. Write the exponential expression to describe how much rice is necessary for each of the
last three squares of the board.
Square #
Exponential Expression
62
63
64
Why is the base of the expression 2? You can use the word bank and the sentence starter to
answer this question.
The base of the expression is 2 because…
Word Bank
Nouns
Adjectives
Verbs
base
arithmetic
model
exponent
exponential
formula
formulaic
model
geometric
pattern
successive
sequence
Bridging the Gap, Notetaking Guide
Algebra I, Module 3, Lesson 5 from EngageNY.org of the New York State Education
Department is licensed under CC BY-NC-SA 3.0.
6
What is the explicit formula for the sequence that models the number of rice grains in each
square?
(Use n to represent the number of the square and f(n) to represent the number of rice grains in
that square.)
Would the formula f(n)=2n work? Why or why not?
I think the formula (would/would not) work because…
Bridging the Gap, Notetaking Guide
Algebra I, Module 3, Lesson 5 from EngageNY.org of the New York State Education
Department is licensed under CC BY-NC-SA 3.0.
7
Example 2
What are the differences between 𝑓(𝑛) = 2𝑛 and 𝑓(𝑛) = 2𝑛 ?
a. Complete the tables below, and then graph the points (𝒏, 𝒇(𝒏)) on a
coordinate plane for each of the formulas.
𝑛
−2
𝑓(𝑛)
= 2𝑛
16
15
14
−1
13
0
12
1
11
2
10
3
9
8
7
6
5
4
𝑛
−2
3
𝑓(𝑛)
= 2𝑛
2
1
−1
-6
0
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
-1
1
-2
2
-3
3
-4
-5
b. Describe the change in each sequence when 𝐧 increases by 𝟏 unit for
each sequence.
Bridging the Gap, Notetaking Guide
Algebra I, Module 3, Lesson 5 from EngageNY.org of the New York State Education
Department is licensed under CC BY-NC-SA 3.0.
8
Exercise 1
A typical thickness of tissue paper is 0.001 inches. This is pretty thin, right? Let’s see what
happens when we start folding tissue paper.
How thick is the stack of tissue paper after 1 fold?
How thick is the stack of tissue paper after 2 folds?
How thick is the stack of tissue paper after 5 folds?
Write an explicit formula for the sequence that models the thickness of the folded tissue paper
after n folds.
After how many folds does the stack of folded tissue paper pass the 1-foot mark?
The moon is about 240,000 miles from Earth. Compare the thickness of the tissue paper folded
50 times to the distance from Earth.
Bridging the Gap, Notetaking Guide
Algebra I, Module 3, Lesson 5 from EngageNY.org of the New York State Education
Department is licensed under CC BY-NC-SA 3.0.
9
Exit Ticket
Chain emails are emails with a message suggesting you will have good luck if you forward the
email on to others. Suppose a student started a chain email by sending the message to 3 friends
and asking those friends to each send the same email to 3 more friends exactly 1 day after they
received it.
a. Complete the following table.
Day
1
2
3
4
n
Number of
Emails Sent
b. Write a formula that models the number of people who will receive the email on the nth
day. (Let Day 1 be the day the original email was sent.) Everyone who receives the email
follows the directions.
c. When will more than 100 people receive the chain email? (On which day?)
Reflection
What new ideas or understandings did you have today?
Bridging the Gap, Notetaking Guide
Algebra I, Module 3, Lesson 5 from EngageNY.org of the New York State Education
Department is licensed under CC BY-NC-SA 3.0.
10