Using the Language of Comparison and Contrast
Compare and Contrast T-CHART
List the things that are similar or the same for (2 x + 1)( x + 4)
and 2 x 2 + 9 x + 4 on one side of the T- Chart and things that are
different on other side.
Compare
Secondary Mathematics, © 2009
Contrast
COMPARING GRAPHS 1
Tables
Set 1
y = x2
y = 2x2
y = 3x2
y = 4x2
y = 5x2
x
y = x2
y
x
y
x
y = 2x2
y = 3x2
Graph
California Mathematics Project – ELDI-MC Algebra
y
x
y
y = 4x2
x
y
y = 5x2
COMPARING GRAPHS 2
Tables
Set 2
y = -x2
y = -2x2
y = -3x2
y = -4x2
y = -5x2
x
y
y = -x2
x
y
x
y = -2x2
y = -3x2
Graph
California Mathematics Project – ELDI-MC Algebra
y
x
y
y = -4x2
x
y
y = -5x2
COMPARING GRAPHS 3
Set 3
y = .5x2
y = .2x2
y = x2
y = -.5x2
y = -.2x2
x
y = .5x2
y
x
y
y = .2x2
Tables
x
y = x2
Graph
California Mathematics Project – ELDI-MC Algebra
y
x
y
y = -.5x2
x
y
y = -.2x2
COMPARING GRAPHS 4
Set 4
y = x2 + 1
y = x2 + 3
y = x2
y = x2 - 2
y = x2 - 4
x
y
y = x2 + 1
x
Tables
y
x
y = x2 + 3
Graph
California Mathematics Project – ELDI-MC Algebra
y = x2
y
x
y
y = x2 - 2
x
y
y = x2 - 4
COMPARING GRAPHS 5
Set 5
y = x2 - 1x
y = x2 - 2x
y = x2
y = x2 + 2x
y = x2 + 1x
x
y
y = x2 – 1x
x
Tables
y
y = x2 – 2x
Graph
California Mathematics Project – ELDI-MC Algebra
x
y = x2
y
x
y
y = x2 + 2x
x
y
y = x2 +1x
COMPARING GRAPHS 6
Set 6
y = x2
y = -x2
y = x2 - 2
y = x2 + 2
y = x2+ 2x
x
y = x2
y
x
Tables
y
x
y = -x2
y = x2 - 2
Graph
California Mathematics Project – ELDI-MC Algebra
y
x
y
y = x2 + 2
x
y
y = x2+ 2x
The Quadratic Formula
Problem 1 – Write in standard form and solve
using the quadratic formula
Problem 2 – Write in standard form and solve
using the quadratic formula
2x2 = 4x + 30
2q2 – 6 = - 4q
UCPDI/SDMP – A2C
Mathematically Speaking!
Write your name and your partner’s name.
Person #1 explains how to solve the first problem to person #2. Person #2 should mark a tally mark on the chart each
time a vocabulary word is used. Encourage your partner to keep on talking until he or she has used all the target words.
Then person #2 should explain how to solve the second problem while #1 marks on the chart.
Mathematics Vocabulary
coefficient
discriminant
formula
identify
opposite
quadratic
radical
roots
second degree polynomial
square root
standard form
substitute
What did you notice about the explanations?
UCPDI/SDMP – A2C
#1___________________ #2___________________
Algebra Support
Topic: Graphing Quadratic Functions
Quadratic Functions Graph Match Activity
Teacher Instructions:
• Xerox and have students cut apart the following 2 pages of cards. When cutting, tell students to trim
extra off of edges as edges will not match. Place one complete set in an envelope, one envelope per
group (group size: 2 – 4).
• Provide each group with blank answer grids (2 pages) and glue sticks (or tape)
• Students are to match the 4 representations
Variations:
• Leave out of the envelope 2 or three pieces (an equation from one row, a graph from another, a table
from another). Students are required to generate the missing pieces.
• If students are working on graphing, leave out all of the graph pieces and require students to generate.
• If students are working on writing equations, leave out all of the equation pieces and require students
to generate.
LAUSD, Secondary Mathematics © 2009
1Adopted from Algebra Support Module 2
Verbal Description
Tabular
Representation
x
-4
-2
0
2
4
y is always x squared.
The opposite of half the
value of x squared,
when increased by 2
results in the value of y.
The sum of x squared
and y is 4.
y is a sum of 4 and the
square of a number x.
Symbolic
Representation
y
16
4
0
4
16
x
-4
-2
0
2
4
This function is a direct
variation with 4 times
square of a number x.
Graph
y = x2
y
64
16
0
16
64
x
-4
-2
0
2
4
y
-6
0
2
0
-6
x
-4
-2
0
2
4
y
-12
0
4
0
-12
x
-4
-2
0
2
4
LAUSD, Secondary Mathematics © 2009
y = 4x2
1
y = − x2 + 2
2
y = − x2 + 4
y
20
8
4
8
20
y = x2 + 4
2Adopted from Algebra Support Module 2
y is equal to the sum of 2
and twice the square of a
number x.
x
y
-4
34
-2
10
0
2
2
10
4
34
Double the square of x is
equal to y increased by 3.
x
-4
-2
0
2
4
y is equal to the opposite
of a square of a number x
.
x
-4
-2
0
2
4
y
29
5
-3
5
29
y = 2 x2 − 3
y
-16
-4
0
-4
-16
The difference of y and
double the square of a
number x equals the sum
of 4 and triple a number
x.
x
-4
-2
0
2
4
y
24
6
4
18
48
The sum of y and half of
a number squared equals
the sum of that number
and 2
x
-4
-2
0
2
4
y
-10
-2
2
2
-2
LAUSD, Secondary Mathematics © 2009
y = 2x2 + 2
y = − x2
y = 2 x 2 + 3x + 4
1
y = − x2 + x + 2
2
3Adopted from Algebra Support Module 2
Verbal Description
Tabular
Representation
LAUSD, Secondary Mathematics © 2009
Graph
Symbolic
Representation
4Adopted from Algebra Support Module 2
Using the Language of Comparison and Contrast
Page 1
Listening & Speaking
On Your Own
1. Think about how (2 x + 1)( x + 4) and 2 x 2 + 9 x + 4 compare.
2. Fill in the blanks for both the Comparison Questions.
Comparison Questions
Initiator:
How are _________________ and _________________ similar?
Responder:
_________________ and _________________ are similar because both
_________________________________________________________.
Initiator:
What do _________________ and _________________ have in common?
Responder:
Both _________________ and _________________ have/are ___________________
_________________________________________________________.
Initiator:
How is ___________________ like ___________________?
Responder:
Like _________________, _________________ is/has ___________________
_________________________________________________________.
Initiator:
What is a significant similarity between ___________________ and ___________________?
Responder:
A significant similarity between _________________ and _________________ is
_________________________________________________________.
Initiator:
What is another important comparison between _________________ and _________________?
Responder:
Another important comparison between _________________ and _________________ is
_________________ because ___________________________________________________.
With Your Partner: practice speaking and listening to the language of comparison.
1. First Partner 1 one reads the Initiator questions and Partner 2 answers as the Responder.
2. Then switch roles: Partner 2 is the Initiator and Partner 1 is the Responder.
Using the Language of Comparison and Contrast
Page 2
Listening & Speaking
On Your Own
1. Think about how (2 x + 1)( x + 4) and 2 x 2 + 9 x + 4 contrast.
2. Fill in the blanks for both the Contrast Questions.
Contrast Questions
Initiator:
How are _________________ and _________________ different?
Responder:
_________________ and _________________ are different because they have/are
_________________________________________________________.
Initiator:
What makes _________________ unlike _________________?
Responder:
_________________ and _________________ are dissimilar because ___________________
_________________________________________________________.
Initiator:
How else do___________________ and ___________________ differ?
Responder:
Unlike _________________, _________________ is/has ___________________
_________________________________________________________.
Initiator:
What is a major difference between ___________________ and ___________________?
Responder:
A major difference between _________________ and _________________ is
_________________________________________________________.
Initiator:
What is another significant difference between _________________ and _________________?
Responder:
Another important difference between _________________ and _________________ is
_________________ because ___________________________________________________.
With Your Partner: practice speaking and listening to the language of contrast.
1. First Partner 1 one reads the Initiator questions and Partner 2 answers as the Responder.
2. Then switch roles: Partner 2 is the Initiator and Partner 1 is the Responder.
Using the Language of Comparison and Contrast
Page 3
Writing & Reading
On Your Own: Fill in the blanks of the Comparison/Contrast Paragraph Frame.
Comparison/Contrast Paragraph Frame
_________________ and _________________ are similar. Each (is/has) _________________
__________________________________. Like _________________, _________________ also has
__________________________________. A significant similarity between the two is
__________________________________ _________________. Although they share many similarities,
_________________ differs from _________________ because __________________________________.
An important difference between the two is __________________________________. Perhaps the most
significant difference is ____________________________________________________________________.
On Your Own: Write your paragraph.
With Your Partner: Reading the language of comparison and contrast.
1. First Partner 1 one reads her/his paragraph to Partner 2.
2. Then Partner 2 one reads her/his paragraph to Partner 1.