Grades 6 - 8
1
STANDARDS:
Numbers, Number Sense & Operations
Mathematical Process
TECHNOLOGY:
STANDARDS
Critical Thinking, Problem Solving, & Decision Making
OBJECTIVE:
The students will be able to:
1. Recognize, identify and define all necessary math vocabulary in each OAA question
2. Read each questions with comprehension and have a plan for how to answer the question
3. How to type a square root into the calculator
4. How to identify a perfect square using the calculator
5. How to type an improper fraction into the calculator
6. How to convert a fraction into a decimal using the calculator
7. How to convert a mixed number into an improper fraction using the calculator
8. How to convert an improper fraction into a mixed number using the calculator
9. How to convert a fraction into a decimal using the calculator
10. How to convert a decimal into a fraction using the calculator
11. How to type a percent into the calculator
12. How to convert a percent into a decimal using the calculator
13. How to convert a percent into a fraction using the calculator
14. How to type a scientific notation number into the calculator
15. How to convert a number into scientific notation using the calculator
16. How to type a power/exponent into the calculator
17. How to answer Short-Response Questions using the calculator
18. How to answer Extended-Response Questions using the calculator
19. Identify numbers in the Real Number System
20. Write and/or explain the difference between numbers in the Real Number System
21. Simplify mathematical expressions using Order of Operations
22. Define and identify perfect squares
23. Define a square root
24. Evaluate and estimate a value of a number under a square root
25. Define numbers in Scientific Notation
26. Write numbers in Scientific Notation and/or Standard Notation
27. Perform operations containing Scientific Notation
28. Identify the Law of Exponents
29. Evaluate Mathematical Expressions using the Law of Exponents Rules
30. Define an algebraic equation
31. Solve one-step equations algebraically
32. Solve multi-step equations algebraically
33. Find the percent of a number
34. Find the discount, mark-up & tax rate
35. Set-up and solve proportions
36. Solve word problems applications
E. Kight
Math Coach
March 2010
Grades 6 - 8
2
PROCUDURE:
Calculator Questions
Enclosed is a packed consisting of all released Math OAA questions involving the standard
Number, Number Sense and Operations. For this section, students are able to use their Scientific
Calculators to answer each question.
The students will recall and review all the indicated objectives stated above. Remember to
review Test Taking Strategies with students on how to attempt multiple choice questions and
extended response questions.
For multiple choice questions remember to use POE (process of elimination), WB (work
backwards), Pick a Number, Straight Forward (work the problem out/solve the problem
algebraically), Guess and Check and/or any methods you may have used with your students.
For extended response and short response questions, remember to use any table, charts, graphs,
diagrams, 42 method, Hot-Dog-Bun, Straight Forward (work the problem out/solve the problem)
and/or any methods you have used with your students.
Students should sit in groups of 4 or 5 (depending on the size of the class) and/or traditional
seating arrangements. Students should be given five questions at a time and allowed at most 7
minutes to answer the set of five questions. If students are in groups, the students will answer
each question to the best of their knowledge; discuss what strategies and/or methods should be
used to each question. If students are working individually, they should be prepared to explain
how they arrived to their answer stating what strategies and/methods were used.
Once time is up, each group/student will have an opportunity to report out their answer. The
group/student must state the following:
State their answer.
Explain how they arrived to their answer.
What calculator keystrokes were used?
For further discussion, the teacher could ask other groups/the class as a whole, is their any other
methods/approaches and keystrokes that could have been used to arrived to the correct answer.
Once the first set of five questions are discussed, the teacher will give the students the next set of
five questions and repeat the same line of questioning for discussion.
Remember, each group/student MUST answer a question and each person in the group/student
should have an opportunity to answer a question. This is to assure all students are involved and
engaged in the lesson, which students may still be struggling with concepts and/or calculator
keystrokes.
E. Kight
Math Coach
March 2010
Grades 6 - 8
GUIDED:
PRACTICE
3
1. Which number is not a perfect square?
a) 36
b) 10
c) 25
d) 100
2. Arrange the numbers in order from least to greatest.
22
3, 8 , 2,
8
3. Which number is rational?
18
a) π
b)
c) ¾
d) 0.11121314….
4. Simplify: 42 * 4-2
a) 0
b) 1
c) 5
d) 25
5. The 200 is between which two consecutive integers?
a) 12 and 13 b) 13 and 14 c) 14 and 15 d) 15 and 16
6. Michael is solving the equation 14x – 12 = 30. The result of his first
step is 14x = 42.
What operation did Michael use in his first step?
a) add 12 to each side
b) subtract 12 from each side
c) multiply both sides by 12
d) divide both sides by 12
7. The product of a number and nine is 288.
Which method can be used to find the value of this number?
a) Multiply the number by 288.
b) Divide 288 by the number.
c) Multiply the number by 9.
d) Divide 288 by 9.
8. Four numbers are shown.
7
-0.35, , 0, 147
12
Explain why each number is a rational or an irrational number.
INDEPENDENT:
PRACTICE
OAA Prep Packet pages 1 – 21; answer all questions
VOCABULARY:
Real number, irrational number, rational number, integer, whole number, counting number,
natural number, absolute value, number line, exponent, power, perfect square, square root,
variable expression, algebraic expression, substitution, evaluate, order of operations, quotient,
product, difference, sum, double, twice, equivalent fraction, equivalent, percent, scientific
notation, ascending, descending, variable, inequality, less than, greater than, sales tax, discount
rate, mark-up rate
E. Kight
Math Coach
March 2010
Grades 6 - 8
4
CALCULATOR KEY STROKES
for
TI-30XIIS CALCULATOR
WHERE ARE YOUR OPERATION KEYS LOCATED
Your operations keys are (+, -, x, ÷). They are located on the right side underneath the red C/CE
button and AC button
WHERE IS YOUR NEGATIVE SIGN LOCATED
Your negative sign (-) is located on the bottom row underneath the number 3.
EX: Type in -10
1. Type in the number 10 ( press 1, then 0)
2. Press the - button once
3. What do you see in your screen? ___________________
EX: Type in -3
1. press the – button once
2. Type in the number 3 (press 3)
3. What do you see in your screen? ___________________
EX: Simplify: 13 + - 7
1. Press the addition operation button (-)
2. Type in 13
3. Type in 7
4. Press the addition operation button (-)
5. Press the = button
6. What is your answer? __________________
EX: Evaluate: -3 + 7 + -12
1. Type in -3
2. Press the addition operation button (+)
3. Type in 7
4. Press the addition operation button (+)
5. Type in -12
6. Press the = button
7. What is your answer? ______________________
EX: Simplify: 2.5 – 3.5 + - 4.5
1. What is your answer? _________________________
E. Kight
Math Coach
March 2010
Grades 6 - 8
5
HOW TO TYPE IN A FRACTION
B
Use the A /C key to type in any fraction (proper or improper fraction)
5
EX: Type in
6
1. Type in the numerator first 5
2. Press the AB/C
3. Type in the denominator 6
4. Your answer should look something like this: 5 ┘6
2
EX: Type in - 3
5
1. Type in the whole number first 3
2. Press the +/- button
3. Press the AB/C
4. Type in the numerator second 2
5. Press the AB/C
6. type in the denominator 5
7. Your answer should look something like this: 3 _ 2 ┘5
8. Is there another way to enter this mixed number? ________________
9. Explain how? ___________________________________________________________
3 2
7 5
Type in the first fraction
Press the subtraction button
Type in the second fraction
Press the = button
What is your answer? ______________________
EX: Simplify:
1.
2.
3.
4.
5.
1
33
5
50
Type in the first fraction
Press the division button
Type in the second fraction
Press the = button
What is your answer? ______________________
EX: Simplify: 2
1.
2.
3.
4.
5.
1 2 15
2 5 22
1. Type in the first fraction
2. Press the subtraction button
3. Type in the second fraction
4. Press the multiplication button
5. Type in the third fraction
6. Press the = button
7. What is your answer? _________________________
E. Kight
Math Coach
March 2010
EX: Simplify:
Grades 6 - 8
HOW TO REDUCE A FRACTION
B
Use the A /C key to type in any fraction (proper or improper fraction)
EX: Reduce: 12 / 56
1. Type in the fraction
2. Press the = button
3. What is your answer? ____________________
EX: Simplify: 125 / 300
1. Type in the fraction
2. Press the = button
3. What is your answer? ____________________
EX: Reduce: - 48 / 96
1. Press the addition operation button (-) {a negative number can NEVER go in the denominator}
2. Type in the fraction
3. Press the = button
4. What is your answer? ____________________
HOW TO CHANGE A MIXED NUMBER INTO AN IMPROPER FRACTION OR
FRACTION INTO A MIXED NUMBER
B
Use 2ND key & the A /C key to change a mixed number into an improper fraction or an
improper fraction into a mixed number.
2
into an improper fraction
5
Type in the fraction
Press the 2ND button
B
Press the A /C
What is your answer? ________________________
EX: Convert 3
1.
2.
3.
4.
EX: Change -15 / 4 into a mixed number
1. Press the addition operation button (-)
2. Type in the fraction
3. Press the 2ND button
B
4. Press the A /C
5. Press the = button
6. What is your answer? ________________________
1
into an improper fraction
4
Type in the fraction
Press the 2ND button
B
Press the A /C
What is your answer? ________________________
EX: Change 12
1.
2.
3.
4.
E. Kight
Math Coach
March 2010
6
Grades 6 - 8
7
HOW TO CHANGE A FRACTION INTO A DECIMAL
ND
Use the 2
→ PRB key to change a fraction into a decimal (proper, improper, and/or mixed
fraction)
EX: Convert 1/5 into a decimal
1. Type in the fraction
2. Press the = button
ND
3. Press the 2
→ PRB
4. What is your answer? __________________________
1
EX: Change 12 into a decimal
4
1. Type in the fraction
2. Press the = button
ND
3. Press the 2
→ PRB
4. What is your answer? __________________________
2
EX: Convert: 3 into a decimal
5
1. Type in the fraction
2. Press the = button
ND
3. Press the 2
→ PRB
4. What is your answer? __________________________
HOW TO FIND THE VALUE OF AN EXPONENT/POWER
Use the ^ to type in any exponent/power (24, 52, 103)
EX: Evaluate 23
1. Type in the base 2
2. Press the ^ button
3. Type in the exponent 3
4. Press the = button
5. What is your answer? ___________________________
EX: Evaluate 52
1. Type in the base 5
2. Press the ^ button
3. Type in the exponent 2
4. Press the = button
5. What is your answer? ___________________________
E. Kight
Math Coach
March 2010
Grades 6 - 8
EX: Evaluate 22 • 32 • 62
1. Read the problem from left to right
2. Type in the first base 2
3. Press the ^ button
4. Type in the exponent 2
5. Press the X button
6. Type in the second base 3
7. Press the ^ button
8. Type in the exponent 2
9. Press the X button
10. Type in the third base 6
11. Press the ^ button
12. Type in the exponent 2
13. Press the = button
14. What is your answer? ___________________________
HOW TO FIND THE VALUE OF A ROOT
Use the
to find the square root of a number
EX: Simplify: 121
1. Read the problem
2. Type in the radicand 121
3. Press the INV button
4. Press the x2 (above you will see the radical in green)
5. What is your answer? ______________________________
EX: Simplify: 225
1. Read the problem
2. Type in the radicand 225
3. Press the INV button
4. Press the x2 (above you will see the radical in green)
What is your answer? ______________________________
81
EX: Simplify:
6. Read the problem
7. Type in the radicand 81
8. Press the INV button
9. Press the x2 (above you will see the radical in green)
10. Press the Press the +/- button once
What is your answer? ______________________________
E. Kight
Math Coach
March 2010
8
Grades 6 - 8
HOW TO CHANGE A NUMBER INTO SCIENTIFIC NOTATION
Use the SCI to change a number into scientific notation. Remember your answer should
ALWAYS be written in the form a X 10n
EX: Express 123,000,000 in scientific notation
1. Read the problem
2. Type in the number 123,000,000
3. Press the = button
4. Press the INV button
5. Press the • (the decimal point) button (above you will see the letters SCI in green)
6. What do you see? 1.2308
8
7. Re-write your answer in scientific notation form. 1.23 X 10
EX: Express 0.000045 in scientific notation
1. Read the problem
2. Type in the number 0.000045
3. Press the = button
4. Press the INV button
5. Press the • (the decimal point) button (above you will see the letters SCI in green)
6. What do you see? 4.5-05
-5
7. Re-write your answer in scientific notation form. 4.5 X 10
EX: Express 2,500,000,000 in scientific notation
8. Read the problem
9. Type in the number 2,500,000,000
10. Press the = button
11. Press the INV button
12. Press the • (the decimal point) button (above you will see the letters SCI in green)
13. What do you see? 2.509
9
14. Re-write your answer in scientific notation form. 2.5 X 10
HOW TO CHANGE A PERCENT INTO A DECIMAL
Use the % to change a percent into a decimal
EX: Change 25% into a decimal
1. Type in the number 25
2. Press the INV button
3. Press the = (above you will see the % in green)
4. What is your answer? ________________________
E. Kight
Math Coach
March 2010
9
Grades 6 - 8
EX: Change 38% into a decimal
1. Type in the number 38
2. Press the INV button
3. Press the = (above you will see the % in green)
4. What is your answer? ________________________
1
EX: Change 33 % into a decimal
3
1
1. Type in the number 33 %
3
2. Press the INV button
3. Press the = (above you will see the % in green)
4. What is your answer? ________________________
E. Kight
Math Coach
March 2010
10
Grades 6 - 8
11
Name ____________________________________
Date ___________________
Teacher ___________________________________
Period __________________
SCIENTIFIC CALCULATOR WORKSHEET
Directions: Answer each question. Be sure to show your work where necessary.
1. Question 27
Benchmark A
Spring 2009
2. Question 1
Benchmark E
March 2008
3. Question 6
Benchmark C
Spring 2009
E. Kight
Math Coach
March 2010
Grades 6 - 8
4. Question 1
Benchmark E
March 2006
5. Question 13
Benchmark H
January 2005
6. Question 37
Benchmark A
March 2005
E. Kight
Math Coach
March 2010
12
Grades 6 - 8
7. Question 18
Benchmark A
Spring 2007
8. Question 28
Benchmark H
Spring 2007
9. Question 1
Benchmark I
Spring 2009
E. Kight
Math Coach
March 2010
13
Grades 6 - 8
10. Question 7
Benchmark I
January 2005
11. Question 1
Benchmark E
March 2008
12. Question 5
Benchmark E
March 2005
E. Kight
Math Coach
March 2010
14
Grades 6 - 8
13. Question 9
Benchmark E
Spring 2009
14. Question 28
Benchmark E
March 2006
15. Question 5
Benchmark H
Fall 2005
E. Kight
Math Coach
March 2010
15
Grades 6 - 8
16. Question 1
Benchmark I
March 2005
17. Question 33
Benchmark I
March 2005
18. Question 37
Benchmark I
March 2005
E. Kight
Math Coach
March 2010
16
Grades 6 - 8
19. Question 1
Benchmark I
Spring 2007
20. Question 6
Benchmark E
March 2008
21. Question 4
Benchmark E
March 2006
E. Kight
Math Coach
March 2010
17
Grades 6 - 8
22. Question 29
Benchmark E
March 2006
23. Question 24
Benchmark G
March 2006
24. Question 1
Benchmark H
March 2006
E. Kight
Math Coach
March 2010
18
Grades 6 - 8
25. Question 33
Benchmark I
March 2008
E. Kight
Math Coach
March 2010
19