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(MHS) 2

Calculator Enrichment

 Memorial High School
 Squared Up In Mathematics
 Principal: Calvin Rice
 Math Department Lead: Pandora . Walker
Abacus        Slide Rule




            NOW
         TI NSpire
§111.31. through 111.37. (a) Basic understandings.
         Implementation of Texas Essential Knowledge and Skills for
                           Mathematics, Grades 9-12.
The provisions of this subchapter shall be implemented beginning with the 2006-
     2007 school year. This implementation date shall supersede any other
                 implementation dates found in this subchapter.
Tools for algebraic thinking.
Techniques for working with functions and equations are
essential in understanding underlying relationships. Students use a
variety of representations
(concrete, pictorial, numerical, symbolic, graphical, and
verbal), tools, and technology (including, but not limited
to, calculators with graphing capabilities, data collection
devices, and computers) to model mathematical situations to solve
meaningful problems.
Underlying mathematical processes. Many processes underlie all
content areas in mathematics. As they do mathematics, students
continually use problem-solving, language and communication, and
reasoning (justification and proof) to make connections within and
outside mathematics. Students also use multiple
representations, technology, applications and modeling, and
numerical fluency in problem-solving contexts.
Teachers using Technology to support
                       TEKs-TAKs-STAAR
Provide ways to help students that
are deficient.
Reinforces operations with real
number.
Use multiple context to solve
problems; Write, graph, and solve
functions.
Lessen students frustration and
anxiety.
Help students focused on the
lesson longer periods of time.
Help students to retain
information and feel confident
about accuracy of their answers
which lead to
Student being successful on state
test
Basic Calculator FAQ
Q: Why calculator will not turn on?
A: Press 2nd key and blue up arrow, window screen resolution
may be diminished . Then try replacing batteries
Q: How do I change the language back to English?
A: Press the purple APPS key, scroll down to you see language
English and press enter
Q: Why won’t the graph show ?
A: Make sure the equal button is highlighted in y= menu, press
zoom “0” to refocus the window or manually redo window in the
window menu by changing x min-max, x-scale, and y min-max, y
–scale.
A: Sometimes turning off the plots from the y= menu too!
Q: How do I restart the calculator to default settings?
A: Press the 2nd key followed by 7 1 2 enter, done verifies it has
been reset.
Frequently Used Menu‟s

Home Screen “on”        Graph Menu y=„s    Graph Window : Standard 10 x10




Window Menu             Table Setup Menu         Table Window




 http://hotmath.com/graphing_calculators/ti84_movie_index.html
Resetting the Calculator to Defaults
2nd Plus                             Press 1




Press 2

                                                  DONE
Methods For Equations-Expressions
1. Boolean test placed on the home screen an equation
    Example: 2x+10=20 answer choices are a. 1 b. 2 c. 5 d. -6
    A.“0” not a solution, “1” solution. Press 2nd parenthesis to get {}, 2nd Math for =
    B. home screen 2{1,2,5,-6} +10 = 20 press enter {0,0,1,0} so, c. 5 is the correct
2. Equation Solver Press Math key then “0” equation solver shows up on the home
       screen and you are now in a application, not the home screen.
   A. This menu all equations are set equal to “0” by default so, 2x+10-20
   B. Place equation, press enter, place a value for x= -1, press alpha enter, correct x=5,
   C. press up arrow, place a new equation repeat steps A and B or 2nd Mode to exit.
   D. Quadratic answers have two possible solutions so use x=1 then x= -1 to get all
       possible answers.
3. Y= menu multiple representation with connection to graphs, tables, & function rules.
   A. Place any one variable equation, function, or expression in y1=, 2nd graph for values
   B. Place 2x+10 in y1= and 20 in y2=
   C. view table y1= y2 is solution or
   D. 2nd trace 5 enter 3 times it show the graph intersection.
   E. Graph with trace key on to see graph that match identically -0 y1= menu
Home Screen
                                  Get back to home screen
                                  Press 2nd Mode
                                  Change Decimal to Fractions
                                  Press Math to change
                                  Power Key Λ
                                  Underneath Clear key
                                  Square Root Key
                                  Press 2nd x2 √
                                  Insert Key
                                  Place a character into the middle of a
                                     statement, press 2nd then delete key
                                  Clear & Delete Key
                                  Clear removes the entire statement, delete
                                     remove only one character at a time



Home screen is used for basic computation + - X ÷ squaring and square roots
Application are view in the home screen and use variables/letters such as;
          y= equation solver, store / sto features
• The i is the imaginary
  number key
Press 2nd dot next to




Imaginary numbers
EE is the scientific
notation key
Press 2nd to access this
key when you want to
write in scientific like
2.3x105 2.3E5 press
enter and it changes it
to standard notation
230,000
1.05 x10-8 1.05E-8
0.00000105




Scientific notation
Normal                             Sci-Scientific
• Change to radians to             • Use to take a standard
  degrees for trigonometric          notation problem and
  problems
                                     change it to scientific
• Normal to scientific for
  science problems                   notation.
• Polar for advance math           • 270000 converts to 2.7E5
  polar functions                    means 2.7x105
• Float rounds to the indicated    • 0.0001 converts to 1.0E-4
  decimal such as 0 leave it
                                     means 1.0x10-4
  just as it is, 1 rounds to the
  tenth place, 2 to the
  hundredths place…..


Mode Key
6) Simplify the polynomial.
      −3x(7x − 4) + 6x − (13 − 24x2)

F      3x2 + 18x − 13
G      −24x2 − 15x − 17
H      −24x2 + 10x − 17
J      3x2 + 18x + 13




Simplifying Expression on the
home screen one variable
Which expression is equivalent
                          (3x − 15y) + (9y − 11x)?
                        A     −9x − y
There are 2 variables
                        B     11x − 21y
in the expression
                        C     10x − 4y
                        D     −9x − 26y




Simplifying Expression on the home
screen two or more variables
2005 October Exit
                          28) If (−3.5, y) is a solution to the
                          equation 2x − 5y = 10, what is the
                          value of y?
  One variable is given
  find the other          F       −3.4
                          G       13.75
                          H       −0.6
                          J       −3.75



Simplifying Expression from the
graphing menu y= “one variable only”
What is the value of y if (3, y) is a
Which expression is     solution to the equation 5x − 3y = 18?
equivalent to
5(x2 − 4x) − (x + 1)?
                        F      3
                        G      1
A       5x2 − 21x + 1
B       5x2 − 5x − 1    H      −1
C       5x2 − 21x − 1   J      −11
D       5x2 − 5x + 1



Simplifying/solving Equations on the
home screen one variable using sto
feature and Boolean test “0” or “1”
Objective 2
                         2006 10th Grade
 2003 10th Grade
                         16) Simplify the expression
 10) Simplify the
     expression          6 − 3(5x + 2) − 10x.
 3(x + 1) − 2(3x + 7).
                         F      −25x
 F       −3x − 11        G      5x + 6
 G       −3x − 10
                         H      8 − 25x
 H       −3x − 8
                         J      12 − 25x
 J       −3x + 17



Simplifying/solving Equations using
the y= menu graph/ table
A rectangle has a length of      Simplify the algebraic expression
2x + 1 and a width of 5x − 4.     5(x + 3)(x + 2) − 3(x2 + 2x + 1).
Which expression best describes
the area of the rectangle?        A      2x2 + 7
                                  B      2x2 + 27
F 7x − 3      H 10x2 − 3x − 4     C      2x2 + 7x + 7
G 14x − 6     J 10x2 + 13x − 4    D      2x2 + 19x + 27


    Simplifying/solving Equations using
    the y= menu graph/ table
Which expression can be used to find the values of s(n) in
the table below?
F       3n
G       5n
H       n+4
J       3n + 2




Creating a function rule from
data, patterns, or graphs using stat
menu
2006 10th Grade
38) The squares below show a pattern.
 Which expression can be used to determine
the number of squares at stage n?

F      5n − 3
G      4n − 2
H      2n2
J      n2 + n



Verifying function rules, patterns
or graphs using y= menu
2003 10th Grade
             19) A function is described by the
             equation f (x) = x2 + 5. The
             replacement set for the independent
             variable is {1, 5, 7, 12}. Which of the
             following is contained in the
             corresponding set for the dependent
             variable?

             A       0
             B       6
             C       7
             D       15



Using y= menu to find the domain or
range of a function rule
•
• 2003 10th Grade
• 31) In the equation y = 2x2 − 5x − 18, which is a value of
  x when y = 0?
•
• A −18 C             2
• B 1          D      4




Using y= to answer questions about
functions rules for specific values
Matrix menu                  2004 10th Grade
Press 2nd x-1                24) What is the x-coordinate of the
Edit A using equations       solution to the system of linear
Values given.                equations below?
2 equations with three
values, therefore 2x3        4x + 5y = 8
4 enter 5 enter 8 enter      2x − 3y = −18
2 enter -3 enter -18 enter   F       −4
Go back to home screen
                             G       −3
Press 2nd x-1
Go to math                   H       3
press alpha apps             J       4
Press 2nd x-1
Enter enter

 Using matrices to solve systems of
 equations
Summary

• TI-84Plus/NSPIRE
• Strategies to implement in Mathematics 9-12 TEKs
• Strategies for test taking TAKs, STAAR, SAT, ACT, and
  ASVAB
• Other technology tools CBRs, Range, Temperature probes
• Provide students with appropriate calculator methods that can
  extended learning through the curriculum and into science.
• Use technology not to just to get an “answer,” but allows the
  students to verify and analyzed their answers more accurately.
• Share Strategies with students to lessen frustration

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(Mhs)2 calculator enrichment

  • 1. (MHS) 2 Calculator Enrichment Memorial High School Squared Up In Mathematics Principal: Calvin Rice Math Department Lead: Pandora . Walker
  • 2. Abacus Slide Rule NOW TI NSpire
  • 3.
  • 4. §111.31. through 111.37. (a) Basic understandings. Implementation of Texas Essential Knowledge and Skills for Mathematics, Grades 9-12. The provisions of this subchapter shall be implemented beginning with the 2006- 2007 school year. This implementation date shall supersede any other implementation dates found in this subchapter. Tools for algebraic thinking. Techniques for working with functions and equations are essential in understanding underlying relationships. Students use a variety of representations (concrete, pictorial, numerical, symbolic, graphical, and verbal), tools, and technology (including, but not limited to, calculators with graphing capabilities, data collection devices, and computers) to model mathematical situations to solve meaningful problems. Underlying mathematical processes. Many processes underlie all content areas in mathematics. As they do mathematics, students continually use problem-solving, language and communication, and reasoning (justification and proof) to make connections within and outside mathematics. Students also use multiple representations, technology, applications and modeling, and numerical fluency in problem-solving contexts.
  • 5. Teachers using Technology to support TEKs-TAKs-STAAR Provide ways to help students that are deficient. Reinforces operations with real number. Use multiple context to solve problems; Write, graph, and solve functions. Lessen students frustration and anxiety. Help students focused on the lesson longer periods of time. Help students to retain information and feel confident about accuracy of their answers which lead to Student being successful on state test
  • 6. Basic Calculator FAQ Q: Why calculator will not turn on? A: Press 2nd key and blue up arrow, window screen resolution may be diminished . Then try replacing batteries Q: How do I change the language back to English? A: Press the purple APPS key, scroll down to you see language English and press enter Q: Why won’t the graph show ? A: Make sure the equal button is highlighted in y= menu, press zoom “0” to refocus the window or manually redo window in the window menu by changing x min-max, x-scale, and y min-max, y –scale. A: Sometimes turning off the plots from the y= menu too! Q: How do I restart the calculator to default settings? A: Press the 2nd key followed by 7 1 2 enter, done verifies it has been reset.
  • 7. Frequently Used Menu‟s Home Screen “on” Graph Menu y=„s Graph Window : Standard 10 x10 Window Menu Table Setup Menu Table Window http://hotmath.com/graphing_calculators/ti84_movie_index.html
  • 8. Resetting the Calculator to Defaults 2nd Plus Press 1 Press 2 DONE
  • 9. Methods For Equations-Expressions 1. Boolean test placed on the home screen an equation Example: 2x+10=20 answer choices are a. 1 b. 2 c. 5 d. -6 A.“0” not a solution, “1” solution. Press 2nd parenthesis to get {}, 2nd Math for = B. home screen 2{1,2,5,-6} +10 = 20 press enter {0,0,1,0} so, c. 5 is the correct 2. Equation Solver Press Math key then “0” equation solver shows up on the home screen and you are now in a application, not the home screen. A. This menu all equations are set equal to “0” by default so, 2x+10-20 B. Place equation, press enter, place a value for x= -1, press alpha enter, correct x=5, C. press up arrow, place a new equation repeat steps A and B or 2nd Mode to exit. D. Quadratic answers have two possible solutions so use x=1 then x= -1 to get all possible answers. 3. Y= menu multiple representation with connection to graphs, tables, & function rules. A. Place any one variable equation, function, or expression in y1=, 2nd graph for values B. Place 2x+10 in y1= and 20 in y2= C. view table y1= y2 is solution or D. 2nd trace 5 enter 3 times it show the graph intersection. E. Graph with trace key on to see graph that match identically -0 y1= menu
  • 10. Home Screen Get back to home screen Press 2nd Mode Change Decimal to Fractions Press Math to change Power Key Λ Underneath Clear key Square Root Key Press 2nd x2 √ Insert Key Place a character into the middle of a statement, press 2nd then delete key Clear & Delete Key Clear removes the entire statement, delete remove only one character at a time Home screen is used for basic computation + - X ÷ squaring and square roots Application are view in the home screen and use variables/letters such as; y= equation solver, store / sto features
  • 11. • The i is the imaginary number key Press 2nd dot next to Imaginary numbers
  • 12. EE is the scientific notation key Press 2nd to access this key when you want to write in scientific like 2.3x105 2.3E5 press enter and it changes it to standard notation 230,000 1.05 x10-8 1.05E-8 0.00000105 Scientific notation
  • 13. Normal Sci-Scientific • Change to radians to • Use to take a standard degrees for trigonometric notation problem and problems change it to scientific • Normal to scientific for science problems notation. • Polar for advance math • 270000 converts to 2.7E5 polar functions means 2.7x105 • Float rounds to the indicated • 0.0001 converts to 1.0E-4 decimal such as 0 leave it means 1.0x10-4 just as it is, 1 rounds to the tenth place, 2 to the hundredths place….. Mode Key
  • 14. 6) Simplify the polynomial. −3x(7x − 4) + 6x − (13 − 24x2) F 3x2 + 18x − 13 G −24x2 − 15x − 17 H −24x2 + 10x − 17 J 3x2 + 18x + 13 Simplifying Expression on the home screen one variable
  • 15. Which expression is equivalent (3x − 15y) + (9y − 11x)? A −9x − y There are 2 variables B 11x − 21y in the expression C 10x − 4y D −9x − 26y Simplifying Expression on the home screen two or more variables
  • 16. 2005 October Exit 28) If (−3.5, y) is a solution to the equation 2x − 5y = 10, what is the value of y? One variable is given find the other F −3.4 G 13.75 H −0.6 J −3.75 Simplifying Expression from the graphing menu y= “one variable only”
  • 17. What is the value of y if (3, y) is a Which expression is solution to the equation 5x − 3y = 18? equivalent to 5(x2 − 4x) − (x + 1)? F 3 G 1 A 5x2 − 21x + 1 B 5x2 − 5x − 1 H −1 C 5x2 − 21x − 1 J −11 D 5x2 − 5x + 1 Simplifying/solving Equations on the home screen one variable using sto feature and Boolean test “0” or “1”
  • 18. Objective 2 2006 10th Grade 2003 10th Grade 16) Simplify the expression 10) Simplify the expression 6 − 3(5x + 2) − 10x. 3(x + 1) − 2(3x + 7). F −25x F −3x − 11 G 5x + 6 G −3x − 10 H 8 − 25x H −3x − 8 J 12 − 25x J −3x + 17 Simplifying/solving Equations using the y= menu graph/ table
  • 19. A rectangle has a length of Simplify the algebraic expression 2x + 1 and a width of 5x − 4. 5(x + 3)(x + 2) − 3(x2 + 2x + 1). Which expression best describes the area of the rectangle? A 2x2 + 7 B 2x2 + 27 F 7x − 3 H 10x2 − 3x − 4 C 2x2 + 7x + 7 G 14x − 6 J 10x2 + 13x − 4 D 2x2 + 19x + 27 Simplifying/solving Equations using the y= menu graph/ table
  • 20. Which expression can be used to find the values of s(n) in the table below? F 3n G 5n H n+4 J 3n + 2 Creating a function rule from data, patterns, or graphs using stat menu
  • 21. 2006 10th Grade 38) The squares below show a pattern. Which expression can be used to determine the number of squares at stage n? F 5n − 3 G 4n − 2 H 2n2 J n2 + n Verifying function rules, patterns or graphs using y= menu
  • 22. 2003 10th Grade 19) A function is described by the equation f (x) = x2 + 5. The replacement set for the independent variable is {1, 5, 7, 12}. Which of the following is contained in the corresponding set for the dependent variable? A 0 B 6 C 7 D 15 Using y= menu to find the domain or range of a function rule
  • 23. • • 2003 10th Grade • 31) In the equation y = 2x2 − 5x − 18, which is a value of x when y = 0? • • A −18 C 2 • B 1 D 4 Using y= to answer questions about functions rules for specific values
  • 24. Matrix menu 2004 10th Grade Press 2nd x-1 24) What is the x-coordinate of the Edit A using equations solution to the system of linear Values given. equations below? 2 equations with three values, therefore 2x3 4x + 5y = 8 4 enter 5 enter 8 enter 2x − 3y = −18 2 enter -3 enter -18 enter F −4 Go back to home screen G −3 Press 2nd x-1 Go to math H 3 press alpha apps J 4 Press 2nd x-1 Enter enter Using matrices to solve systems of equations
  • 25. Summary • TI-84Plus/NSPIRE • Strategies to implement in Mathematics 9-12 TEKs • Strategies for test taking TAKs, STAAR, SAT, ACT, and ASVAB • Other technology tools CBRs, Range, Temperature probes • Provide students with appropriate calculator methods that can extended learning through the curriculum and into science. • Use technology not to just to get an “answer,” but allows the students to verify and analyzed their answers more accurately. • Share Strategies with students to lessen frustration