Comprehensive Answer Key

Algebra 1 - Unit 1 Materials Key

Slides Key

Slide 3: Warm-Up

The sum of 8 and 5: $8 + 5$
The product of 10 and 3: $10 \times 3$
12 less than 20: $20 - 12$

Slide 7: Independent Practice

RED:

$n + 9$
$6n$
$n - 4$

YELLOW:

$n - 15$
$2n + 1$
$n/8$

GREEN:

$2x + 4$
$4(n + 6)$

Slide 8: Exit Ticket

7 more than x: $x + 7$
Product of 10 and y: $10y$
2 less than twice k: $2k - 2$

Notes/Examples Key

Warm-Up: Total Cost = $12x$
Vocabulary:
- A variable represents an unknown number.
- A coefficient is multiplied by a variable.
- A term is the product of a number and variable.
- An expression contains one or more variables.
Your Turn 1:
- "12 decreased by a number x": $12 - x$
- "the sum of 6 and the product of 2 and y": $6 + 2y$
Your Turn 2:
- "a number cubed": $n^3$
- "9 less than the quotient of 6 and a number": $\frac{6}{n} - 9$
Cool-Down: Total Cans = $s + (s + 50)$

Slides Key

Slide 3: Warm-Up

$5 + 2 \times 10$: 25
$(8 - 3)^2$: 25
$16 \div 4 + 2$: 6

Slide 7: Independent Practice

RED:

17
24
12

YELLOW:

16
63
7

GREEN:

7
15
68

Slide 8: Exit Ticket

Evaluate $5x - 2$ when $x = 6$: 28
Evaluate $a^2 + 9$ when $a = 4$: 25

Notes/Examples Key

Warm-Up: 12 dollars.
Vocabulary:
- To evaluate is to find its numerical value.
- To substitute is to replace a variable.
Order of Operations:
- P - grouping symbols
- E - Exponents
- MD - left to right
- AS - left to right
Your Turn 1: Value is 23.
Your Turn 2: Value is 5.
Cool-Down: Area = 54 cm².

Slides Key

Slide 3: Warm-Up

$x^3 \cdot x^2$: $x^5$
$y^5 / y^3$: $y^2$

Slide 7: Independent Practice

RED:

$x^7$
$y^6$
$a^{12}$

YELLOW:

$20n^8$
$4b^6$
$8c^9$

GREEN:

$12x^3y^7$
$5a^6b^2$
$x^{14}$

Slide 8: Exit Ticket

$n^3 \cdot n^8$: $n^{11}$
$20k^{10} / 5k^2$: $4k^8$
$(p^5)^4$: $p^{20}$

Notes/Examples Key

Warm-Up: $2^4$
Vocabulary: The exponent tells how many times to multiply the base.
Product Rule: add the exponents. (YT1: $a^9$, YT2: $10x^7$)
Quotient Rule: subtract the exponents. (YT1: $z^7$, YT2: $3b^4$)
Power Rule: multiply the exponents. (YT1: $b^{18}$, YT2: $16x^{12}$)
Zero/Negative Rules: Zero power is 1. Negative exponent means reciprocal. (YT1: 1, YT2: $\frac{1}{16}$)
Cool-Down: $9a^4b^{10}$

Slides Key

Slide 8: Independent Practice

RED:

$10a$
$8x + 5$
$3x + 12$

YELLOW:

$-4x + 24$
$2x^2 + 8x$
$7n + 5$

GREEN:

$12n - 1$
$6x - 8$
$-x^2 + 4x$

Slide 9: Exit Ticket

Perimeter: $8x + 6$

Notes/Examples Key

Warm-Up: 5 apples. Can you add apples and oranges? No.
Vocabulary: Like terms have same variables and exponents. A constant has no variable.
Combining Like Terms: (YT1: $10a + b$, YT2: $2x^2 + 5x$)
Distributive Property: You multiply a term across. (YT1: $-4x + 24$, YT2: $21a + 6b$)
Putting It All Together: (YT1: $12n - 1$, YT2: $6x - 8$)
Cool-Down: Perimeter = $8x + 6$

Geometry - Unit 1 Materials Key

Slides Key

Slide 10: Independent Practice

RED 1: H: an angle measures 90°, C: it is a right angle.
RED 2: H: $x = 5$, C: $2x = 10$.
YELLOW 1: If a shape is a square, then it is a rectangle.
YELLOW 2: False. Counterexample: A rhombus.
GREEN: (Answers vary) Ex: If a figure is a triangle, it has 3 sides.

Slide 11: Exit Ticket

H: a student plays basketball, C: they are tall. False, a short person can play basketball (e.g., Muggsy Bogues).

Notes/Examples Key

Warm-Up: Clean my room.
Propositions: true or false. Truth Value is True (T) or False (F). YT1: No. YT2: True.
Negation: opposite truth value. YT1: It is not raining. YT2: Not all angles are acute.
Compound Statements: Conjunction ($p \land q$) is true if both true. Disjunction ($p \lor q$) is true if at least one is true. YT1: True. YT2: I will study or I will not fail.
Conditionals: Hypothesis is $p$, Conclusion is $q$. YT1: If an animal is a bird, then it has feathers. YT2: H: you have a driver's license, C: you can drive in Virginia.
Truth Values of Conditionals: False only when a true hypothesis leads to a false conclusion. YT1: False. YT2: True.
Cool-Down: If it is not a weekday, then I do not go to school. ($\sim p \rightarrow \sim q$)

Slides Key

Slide 10: Independent Practice

RED: Conv: If it is cold, then it is snowing. Inv: If it is not snowing, then it is not cold.
YELLOW: Conv: If a number is divisible by 5, then it is divisible by 10. (False). Not a biconditional.
GREEN: (Answers vary)

Slide 11: Exit Ticket

Converse: If two angles are congruent, then they are vertical angles.
Contrapositive: If two angles are not congruent, then they are not vertical angles.

Notes/Examples Key

Warm-Up: No, a cat is a mammal but not a dog.
Related Conditionals: Converse (interchanging), Inverse (negating), Contrapositive (interchanging and negating).
Logical Equivalence: Conditional is equivalent to its contrapositive. Converse is equivalent to the inverse.
Biconditionals: True when conditional and converse are true. YT1: Yes; they form congruent adjacent angles. YT2: Yes; No; No, because the converse is false.
Cool-Down: Converse: If the sum of two angles is 90°, then they are complementary. Contrapositive: If the sum of two angles is not 90°, then they are not complementary.

Slides Key

Slide 8: Guided Practice

1. $p \land q$: False. 2. $p \lor q$: True. 3. $\sim p \lor q$: False.

Slide 9: Independent Practice

RED: 1. It is sunny and we go to the park. 2. It is sunny or we do not go to the park.
YELLOW: 1. False. 2. True. 3. False.
GREEN: 1. $p \land q$. 2. True. 3. True.

Slide 10: Exit Ticket

1. "A square is a rectangle and a rectangle is a square." 2. False. 3. True.

Notes/Examples Key

Warm-Up: Someone with muddy shoes came in from outside.
Truth vs Validity: Valid if it follows logically. True if it is factually correct.
Reasoning Types: Inductive (examples), Deductive (logic). YT1: Inductive. YT2: Deductive.
Law of Syllogism: YT1: diagonals are perpendicular. YT2: I can get a job.
Law of Detachment: YT1: has four right angles. YT2: live in Virginia.
Counterexamples: Conclusion is false. YT1: rectangle. YT2: Richmond.
Cool-Down: Maria will buy shoes.

Slides Key

Slide 7: Guided Practice

1. Start with Both (10). 2. Only Dog: $30-10=20$. 3. Only Cat: $22-10=12$. 4. Neither: $50-(20+10+12)=8$. 5. Dog or Cat (Union): $20+10+12=42$.

Slide 8: Independent Practice

RED: 1. In Band: $10+5=15$. 2. In Chorus: $12+5=17$. 3. In Band AND Chorus: 5.
YELLOW: 2. Only Vanilla: $18-6=12$. 3. Neither: $30-(12+6+8)=4$.
GREEN: (Answers vary)

Slide 9: Exit Ticket

Only Dog: $13-5=8$. Only Cat: $9-5=4$. Neither: $20-(8+5+4)=3$. Answer: 3.

Notes/Examples Key

Warm-Up: Two overlapping circles.
Vocabulary: Universal Set (all elements), Subset (within another set), Complement (not in Set A).
Your Turn 1: Only Art: 11. Neither: 4.
Your Turn 2: Only Summer: 18. At least one: 43. Neither: 7.
Cool-Down: 15 students do neither.

Coming Soon!

Algebra 2 content will be available next semester.

Math Foundations - Unit 1 Materials Key

Slides Key

Slide 3: Warm-Up

Do the two '2's in 5,282 mean the same thing? No. The first '2' is in the hundreds place, so its value is 200. The second '2' is in the ones place, so its value is 2.

Slide 8: Independent Practice

RED:

800
9,000
10

YELLOW:

7000 + 300 + 90 + 4
Seven thousand, three hundred ninety-four

GREEN:

5,029
4,612

Slide 9: Exit Ticket

Write 9,205 in:
1. Expanded Form: 9000 + 200 + 5
2. Word Form: Nine thousand, two hundred five

Notes/Examples Key

Objective: To write and understand numbers in standard, expanded, and word form.
We Do 1: In the number 7,462, the digit 4 has a value of 400.
We Do 2: The position of a digit determines its value.
You Do (Expanded Form): For 3,091: $3000 + 90 + 1$.
You Do (Word Form): For 3,091: Three thousand, ninety-one.

Slides Key

Slide 3: Warm-Up

Quick way to solve 99 + 35? Use a "friendlier" number like 100. (e.g., 100 + 35 = 135, then subtract 1 to get 134).

Slide 8: Independent Practice

RED:

50
90
30

YELLOW:

70 + 20 = 90
100 + 50 = 150

GREEN (152 - 39):

Estimate: 150 - 40 = 110
Calculate: 113
Compare: The answers are close.

Slide 9: Exit Ticket

Estimate total miles for 108 and 295 (round to nearest hundred): 100 + 300 = 400.

Notes/Examples Key

Objective: To use rounding to estimate answers before calculating.
We Do 1: To estimate, you first round the numbers to make them friendly.
We Do 2: The final step is to compare your exact answer and your estimate.
You Do (Estimated Total): For $9.95 + $4.25: $10 + $4 = $14.
You Do (Exact Total): For $9.95 + $4.25: $14.20.

Slides Key

Slide 3: Warm-Up

If you know $4 \times 5 = 20$, what division problem do you know? $20 \div 5 = 4$ or $20 \div 4 = 5$.

Slide 8: Independent Practice

RED:

Missing number for 2, 8, __ is 16.

YELLOW (5, 7, 35):

$5 \times 7 = 35$ and $35 \div 5 = 7$ (other answers valid).

GREEN (6, 8, 48):

$6 \times 8 = 48$, $8 \times 6 = 48$, $48 \div 6 = 8$, $48 \div 8 = 6$.

Slide 9: Exit Ticket

Other three facts for $9 \times 4 = 36$: $4 \times 9 = 36$, $36 \div 9 = 4$, $36 \div 4 = 9$.

Notes/Examples Key

Objective: To understand the inverse relationship between multiplication and division.
We Do 1: Multiplication and Division are called inverses of each other.
You Do (Fact 2): For $6 \times 8 = 48$: $8 \times 6 = 48$.
You Do (Fact 3): For $6 \times 8 = 48$: $48 \div 6 = 8$.
You Do (Fact 4): For $6 \times 8 = 48$: $48 \div 8 = 6$.

Slides Key

Slide 3: Warm-Up

What is $5 + 2 \times 3$? The answer is 11.

Slide 7: Guided Practice ($20 - (3+1) \times 4$)

Parentheses: $(3+1)=4$. Problem becomes $20 - 4 \times 4$.
Multiplication: $4 \times 4=16$. Problem becomes $20 - 16$.
Subtraction: $20 - 16=4$. Final Answer is 4.

Slide 8: Exit Ticket

Solve $16 \div 4 + 2 \times 5$: $4 + 10 = \mathbf{14}$.

Notes/Examples Key

Objective: To apply the order of operations to solve problems with multiple steps.
We Do 1: In PEMDAS, Multiplication and Division are partners done from left to right.
You Do (Step 1): For $20 - (3+1) \times 4$: $20 - 4 \times 4$.
You Do (Step 2): $20 - 16$.
You Do (Final Answer): 4.

Algebra 1 - Unit 1 Materials Key

Slides Key

Slide 3: Warm-Up

Slide 7: Independent Practice

Slide 8: Exit Ticket

Notes/Examples Key

Slides Key

Slide 3: Warm-Up

Slide 7: Independent Practice

Slide 8: Exit Ticket

Notes/Examples Key

Slides Key

Slide 3: Warm-Up

Slide 7: Independent Practice

Slide 8: Exit Ticket

Notes/Examples Key

Slides Key

Slide 8: Independent Practice

Slide 9: Exit Ticket

Notes/Examples Key

Algebra 1 - Quizzes & Tests Key

Geometry - Unit 1 Materials Key

Slides Key

Slide 10: Independent Practice

Slide 11: Exit Ticket

Notes/Examples Key

Slides Key

Slide 10: Independent Practice

Slide 11: Exit Ticket

Notes/Examples Key

Slides Key

Slide 8: Guided Practice

Slide 9: Independent Practice

Slide 10: Exit Ticket

Notes/Examples Key

Slides Key

Slide 7: Guided Practice

Slide 8: Independent Practice

Slide 9: Exit Ticket

Notes/Examples Key

Geometry - Quizzes & Tests Key

Coming Soon!

Math Foundations - Unit 1 Materials Key

Slides Key

Slide 3: Warm-Up

Slide 8: Independent Practice

Slide 9: Exit Ticket

Notes/Examples Key

Slides Key

Slide 3: Warm-Up

Slide 8: Independent Practice

Slide 9: Exit Ticket

Notes/Examples Key

Slides Key

Slide 3: Warm-Up

Slide 8: Independent Practice

Slide 9: Exit Ticket

Notes/Examples Key

Slides Key

Slide 3: Warm-Up

Slide 7: Guided Practice ($20 - (3+1) \times 4$)

Slide 8: Exit Ticket

Notes/Examples Key