compare and contrast t-chart

Using the Language of Comparison and Contrast

Compare and Contrast T-CHART List the things that are similar or the same for and on one side of the T- Chart and things that are different on other side.

(2 1)( 4)x x+ +22 9x x+ + 4

Compare Contrast

Secondary Mathematics, © 2009

California Mathematics Project – ELDI-MC Algebra

COMPARING GRAPHS 1

Tables Set 1 x y x y x y x y x y y = x2 y = 2x2 y = 3x2 y = 4x2 y = 5x2

y = x2 y = 2x2 y = 3x2 y = 4x2 y = 5x2

Graph


COMPARING GRAPHS 2

Tables Set 2 x y x y x y x y x y y = -x2 y = -2x2 y = -3x2 y = -4x2 y = -5x2

y = -x2 y = -2x2 y = -3x2 y = -4x2 y = -5x2

Graph


COMPARING GRAPHS 3

Tables Set 3 x y x y x y x y x y y = .5x2 y = .2x2 y = x2 y = -.5x2 y = -.2x2

y = .5x2 y = .2x2 y = x2 y = -.5x2 y = -.2x2

Graph


COMPARING GRAPHS 4

Tables Set 4 x y x y x y x y x y y = x2 + 1 y = x2 + 3 y = x2 y = x2 - 2 y = x2 - 4

y = x2 + 1 y = x2 + 3 y = x2 y = x2 - 2 y = x2 - 4

Graph


COMPARING GRAPHS 5

Tables Set 5 x y x y x y x y x y y = x2 - 1x y = x2 - 2x y = x2 y = x2 + 2x y = x2 + 1x

y = x2 – 1x y = x2 – 2x y = x2 y = x2 + 2x y = x2 +1x

Graph


COMPARING GRAPHS 6

Tables Set 6 x y x y x y x y x y y = x2 y = -x2 y = x2 - 2 y = x2 + 2 y = x2+ 2x

y = x2 y = -x2 y = x2 - 2 y = x2 + 2 y = x2+ 2x

Graph

The Quadratic Formula

Problem 1 – Write in standard form and solve using the quadratic formula 2x2 = 4x + 30

Problem 2 – Write in standard form and solve using the quadratic formula

2q2 – 6 = - 4q

UCPDI/SDMP – A2C

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 #1___________________ #2___________________ coefficient discriminant formula identify opposite quadratic radical roots second degree polynomial square root standard form substitute What did you notice about the explanations?

LAUSD, Secondary Mathematics © 2009 Adopted from Algebra Support Module 2 1

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.

Verbal Description Tabular

Representation Graph Symbolic

Representation


y is always x squared.

2y x=

This function is a direct variation with 4 times square of a number x.

x y -4 64 -2 16 0

x y -4 16 -2 4 0 0

2 4 4 16

0 2 16 4 64

24y x=

The opposite of half the value of x squared, when increased by 2 results in the value of y.

x y

-4 -6 -2 0 0 2 2 0 4 -6

21 22

y x= − +

The sum of x squared and y is 4.

2 4y x= − +

x y -4 -12 -2 0 0 4 2 0 4 -12

y is a sum of 4 and the square of a number x.

x y -4 20-2 8 0 4 2 8 4 20

2 4y x= +

y is equal to the sum of 2 and twice the square of a number x.

22 2y x= +

Double the square of x is equal to y increased by 3.

x y

-4 34 -2 10

0 2 2 10 4 34

x y


-4 29 -2 5 0 -3 2

22 3y x= −

5 4 29

y is equal to the opposite of a square of a number x .

2y x= −

The difference of y and double the square of a number x equals the sum of 4 and triple a number x.

x y -4 24 -2 6 0 4 2 18 4 48

x y -4 -16 -2 -4 0 0 2 -4 4 -16

22 3y x x= + + 4

x y -4 -10 -2 -2 0 2 2 2 4 -2

21 2

2y x x= − + +

The sum of y and half of a number squared equals the sum of that number and 2


Verbal Description Tabular Representation

Graph Symbolic Representation

Using the Language of Comparison and Contrast Page 1

Listening & Speaking On Your Own

1. Think about how and 4(2 1)( 4)x x+ + 22 9x x+ + 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.


Listening & Speaking On Your Own

1. Think about how and 4(2 1)( 4)x x+ + 22 9x x+ + 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.


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.

compare and contrast t-chart

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