Transcript Week #2A - MathChow

Algebra 2
Week #2A
Section 4
Autumn, soon.
Week #2A – Section 3
Reflection Question
•
•
Reflection Question for Today: Why are you usually asked to graph the answer
to an inequality rather than the answer to an equation?
Beacause the answer to an equation is only a point. The answer to an inequality is
a range of numbers (or part of a number line).
•
•
•
•
•
•
•
Graph x = all real numbers
<───ι────>
0
Week #2A Section 3
Homework Answers
•
•
Classwork: Why Did the Kangaroo See a Psychiatrist?
He wondered why he was feeling so jumpy.
•
Homework:
CAHSEE #1
CAHSEE #2
1.
o
0
3. - 1 ≤ x ≤ 2
5. x > 5
ı
o
0
5
7. 11b - 12
9. - z2
11. 30
12. 23°
A
D
o
3
2.
● ı o
-2 0 1
4. x < -1 or x > 6
6. x ≤ 4
ı
0
8. 8m + 34
10. - 4w + 66
●
4
Week #2A – Section 4
GOAL: To be able to write algebraic expressions from word expressions.
CA STANDARD (leading to) 1.0: Students will be able to solve equations and
inequalities involving absolute value.
•
WARMUP QUESTIONS
•
1.
3x + 7 = 25
2. 5x – 9 = 11
•
3.
3(4x – 5) = 33
4. 3x – (5x – 9)= 1
•
•
Simplify, using PEMDAS
5.
11 + 35 ÷ 5
6. 8 + 6 ÷ 2 – 1
•
7.
8. 2 + 5 x 3 - 4
8x5÷4
Week #2A – Section 4
GOAL: To be able to write algebraic expressions from word expressions.
CA STANDARD (leading to) 1.0: Students will be able to solve equations and
inequalities involving absolute value.
•
WARMUP QUESTIONS
•
•
•
1.
3x + 7 = 25
3x = 18
x=6
2. 5x – 9 = 11
•
3.
3(4x – 5) = 33
4. 3x – (5x – 9)= 1
•
•
Simplify, using PEMDAS
5.
11 + 35 ÷ 5
6. 8 + 6 ÷ 2 – 1
•
7.
8. 2 + 5 x 3 - 4
8x5÷4
Week #2A – Section 4
GOAL: To be able to write algebraic expressions from word expressions.
CA STANDARD (leading to) 1.0: Students will be able to solve equations and
inequalities involving absolute value.
•
WARMUP QUESTIONS
•
•
•
1.
3x + 7 = 25
3x = 18
x=6
2. 5x – 9 = 11
5x = 20
x=4
•
3.
3(4x – 5) = 33
4. 3x – (5x – 9)= 1
•
•
Simplify, using PEMDAS
5.
11 + 35 ÷ 5
6. 8 + 6 ÷ 2 – 1
•
7.
8. 2 + 5 x 3 - 4
8x5÷4
Week #2A – Section 4
GOAL: To be able to write algebraic expressions from word expressions.
CA STANDARD (leading to) 1.0: Students will be able to solve equations and
inequalities involving absolute value.
•
WARMUP QUESTIONS
•
•
•
1.
3x + 7 = 25
3x = 18
x=6
2. 5x – 9 = 11
5x = 20
x=4
•
•
•
•
3.
3(4x – 5) = 33
12x – 15 = 33
12x = 48
x=4
4. 3x – (5x – 9)= 1
•
•
Simplify, using PEMDAS
5.
11 + 35 ÷ 5
6. 8 + 6 ÷ 2 – 1
•
7.
8. 2 + 5 x 3 - 4
8x5÷4
Week #2A – Section 4
GOAL: To be able to write algebraic expressions from word expressions.
CA STANDARD (leading to) 1.0: Students will be able to solve equations and
inequalities involving absolute value.
•
WARMUP QUESTIONS
•
•
•
1.
3x + 7 = 25
3x = 18
x=6
2. 5x – 9 = 11
5x = 20
x=4
•
•
•
•
•
3.
3(4x – 5) = 33
12x – 15 = 33
12x = 48
x=4
4. 3x – (5x – 9)= 1
3x – 5x + 9 = 1
- 2x + 9 = 1
- 2x = - 8
x=4
•
•
Simplify, using PEMDAS
5.
11 + 35 ÷ 5
6. 8 + 6 ÷ 2 – 1
•
7.
8. 2 + 5 x 3 - 4
8x5÷4
Week #2A – Section 4
GOAL: To be able to write algebraic expressions from word expressions.
CA STANDARD (leading to) 1.0: Students will be able to solve equations and
inequalities involving absolute value.
•
WARMUP QUESTIONS
•
•
•
1.
3x + 7 = 25
3x = 18
x=6
2. 5x – 9 = 11
5x = 20
x=4
•
•
•
•
•
3.
3(4x – 5) = 33
12x – 15 = 33
12x = 48
x=4
4. 3x – (5x – 9)= 1
3x – 5x + 9 = 1
- 2x + 9 = 1
- 2x = - 8
x=4
•
•
•
Simplify, using PEMDAS
5.
11 + 35 ÷ 5
11 + 7 = 18
6. 8 + 6 ÷ 2 – 1
•
7.
8. 2 + 5 x 3 - 4
8x5÷4
Week #2A – Section 4
GOAL: To be able to write algebraic expressions from word expressions.
CA STANDARD (leading to) 1.0: Students will be able to solve equations and
inequalities involving absolute value.
•
WARMUP QUESTIONS
•
•
•
1.
3x + 7 = 25
3x = 18
x=6
2. 5x – 9 = 11
5x = 20
x=4
•
•
•
•
•
3.
3(4x – 5) = 33
12x – 15 = 33
12x = 48
x=4
4. 3x – (5x – 9)= 1
3x – 5x + 9 = 1
- 2x + 9 = 1
- 2x = - 8
x=4
•
•
•
Simplify, using PEMDAS
5.
11 + 35 ÷ 5
11 + 7 = 18
6. 8 + 6 ÷ 2 – 1
8 + 3 – 1 = 10
•
7.
8. 2 + 5 x 3 - 4
8x5÷4
Week #2A – Section 4
GOAL: To be able to write algebraic expressions from word expressions.
CA STANDARD (leading to) 1.0: Students will be able to solve equations and
inequalities involving absolute value.
•
WARMUP QUESTIONS
•
•
•
1.
3x + 7 = 25
3x = 18
x=6
2. 5x – 9 = 11
5x = 20
x=4
•
•
•
•
•
3.
3(4x – 5) = 33
12x – 15 = 33
12x = 48
x=4
4. 3x – (5x – 9)= 1
3x – 5x + 9 = 1
- 2x + 9 = 1
- 2x = - 8
x=4
•
•
•
Simplify, using PEMDAS
5.
11 + 35 ÷ 5
11 + 7 = 18
6. 8 + 6 ÷ 2 – 1
8 + 3 – 1 = 10
•
•
7.
8. 2 + 5 x 3 – 4
8x5÷4
40 ÷ 4 = 10
Week #2A – Section 4
GOAL: To be able to write algebraic expressions from word expressions.
CA STANDARD (leading to) 1.0: Students will be able to solve equations and
inequalities involving absolute value.
•
WARMUP QUESTIONS
•
•
•
1.
3x + 7 = 25
3x = 18
x=6
2. 5x – 9 = 11
5x = 20
x=4
•
•
•
•
•
3.
3(4x – 5) = 33
12x – 15 = 33
12x = 48
x=4
4. 3x – (5x – 9)= 1
3x – 5x + 9 = 1
- 2x + 9 = 1
- 2x = - 8
x=4
•
•
•
Simplify, using PEMDAS
5.
11 + 35 ÷ 5
11 + 7 = 18
•
•
7.
8x5÷4
40 ÷ 4 = 10
6. 8 + 6 ÷ 2 – 1
8 + 3 – 1 = 10
8. 2 + 5 x 3 – 4
2 + 15 – 4 = 13
Same symbols in any language.
Week #2A Section #4 Notes
VOCABULARY
Algebraic Expressions
Algebraic expression a variable or any combination of variables and numbers
Week #2A Section #4 Notes
EXAMPLES
•
•
•
•
•
•
•
•
Algebraic Expressions
Change these expressions into mathematical symbols.
Twice a number plus four ________________
Half the sum of a number and four ________________
The product of a number and five less than a number _______________
Week #2A Section #4 Notes
Algebraic Expressions
EXAMPLES
•
•
•
•
•
•
•
•
Change these expressions into mathematical symbols.
Twice a number plus four 2n + 4
Half the sum of a number and four ________________
The product of a number and five less than a number _______________
Week #2A Section #4 Notes
Algebraic Expressions
EXAMPLES
•
•
•
•
•
•
•
•
Change these expressions into mathematical symbols.
Twice a number plus four 2n + 4
Half the sum of a number and four n + 4 or ½(n + 4)
2
The product of a number and five less than a number _______________
Week #2A Section #4 Notes
Algebraic Expressions
EXAMPLES
•
•
•
•
•
•
•
•
Change these expressions into mathematical symbols.
Twice a number plus four 2n + 4
Half the sum of a number and four n + 4 or ½(n + 4)
2
The product of a number and five less than a number n(n – 5) = n2 – 5n
Week #2A Section #4 Notes
REAL LIFE
Algebraic Expressions
1. You’re playing cards with your brother and sister. Your final score
is twice as much as your brother’s, but his is only a third of your
sister’s. If you scored 60 points, how many points did you sister
score?
Guess who’s winning.
Week #2A Section #4 Notes
REAL LIFE
Algebraic Expressions
1. You’re playing cards with your brother and sister. Your final score
is twice as much as your brother’s, but his is only a third of your
sister’s. If you scored 60 points, how many points did you sister
score?
You – 60 points
Brother -
Week #2A Section #4 Notes
REAL LIFE
Algebraic Expressions
1. You’re playing cards with your brother and sister. Your final score
is twice as much as your brother’s, but his is only a third of your
sister’s. If you scored 60 points, how many points did you sister
score?
You – 60 points
Brother – 30 points
Sister -
Week #2A Section #4 Notes
REAL LIFE
Algebraic Expressions
1. You’re playing cards with your brother and sister. Your final score
is twice as much as your brother’s, but his is only a third of your
sister’s. If you scored 60 points, how many points did you sister
score?
You – 60 points
Brother – 30 points
Sister - 90 points WINNER!
Classwork Instructions
Note: you will not be cutting this out!
1. Number all problems.
2. Mark equations with an E and expressions with an X. Count how
many there are of each.
3. On the back of the notes, evaluate all expressions using the
numbers shown there for each variable.
4. On the back of the problem sheet, solve all of the equations.