Reflection: How do you know your answer is reasonable?
Common NYS Trap Question
Q2. Which expression is equivalent to \( -2(4x - 6) - 5x \)?
A \( -13x - 12 \)
B \( -13x + 12 \)
C \( 3x - 12 \)
D \( 3x + 12 \)
Show distribution and sign tracking...
Q3. Midnight temp: \( -4^\circ\text{F} \). Noon: \( +15^\circ\text{F} \). 8 PM: \( -7^\circ\text{F} \). Final temp?
Q4. Recipe: \( 3/4 \) cup sugar for every \( 1/2 \) cup flour. Sugar needed for 1 cup flour?
A \( 3/8 \) cup
B \( 1 \frac{1}{4} \) cups
C \( 1 \frac{1}{2} \) cups
D \( 2 \) cups
Q5. Solve the inequality: \( -5x + 10 > 35 \)
Conceptual Explanation: Does the inequality sign change? Why or why not?
Q6. Bag: 4 red, 6 blue, 2 green. Probability of choosing a marble that is NOT blue?
E1. Distance between \( -8 \) and \( 5 \) on a number line?
A -13
B -3
C 3
D 13
E2. Calculate: \( -2^4 \) vs \( (-2)^4 \)
Metacognition: Which type of mistake would most likely lead to a wrong answer here?
SIGN ERROR
ORDER OF OPERATIONS
MISREADING THE QUESTION
Blueprint Final Sweep
Check Signs (+/-) Order of Ops Reasonability
Do Now:
1: A | 2: -23 ft | 3: Used Subtr. before Mult. | 4: e.g. \( -2-3 = -5 \)
Error Lab:
001: Subtr neg = add (+3) | 002: Distribute to both terms (+20) | 003: Div by time (2 m/hr)
Micro-Drill:
A: 9, 5, -6.8, -5.5 | B: -5/12, 4 | C: -17
Guided Practice:
Q1: $6.75 | Q2: B | Q3: 4°F | Q4: C | Q5: x < -5 (flip for div by neg) | Q6: 1/2
Exit Ticket:
E1: D (13) | E2: -16 vs 16. Power only applies to base; parens include sign.
What is the value of the expression below? \( -8 + 3(-4 + 1) \)
Show steps and sign track here...
Q1. A bank account has a balance of \( -\$15.50 \). A deposit of \( \$45.00 \) is made, followed by a withdrawal of \( \$22.75 \). What is the new balance in the account?
Reasonableness Check: Is your final answer positive or negative? Explain why.
TRAP QUESTION: COMMON NYS ERROR ANALYSIS
Q2. Which expression is equivalent to \( -2(4x - 6) - 5x \)?
A \( -13x - 12 \)
B \( -13x + 12 \)
C \( -3x - 12 \)
D \( -3x + 12 \)
Show your work...
Q3. At midnight, the temperature was \( -4^\circ\text{F} \). By noon, the temperature had increased by \( 15^\circ\text{F} \). By 8:00 p.m., the temperature had decreased by \( 7^\circ\text{F} \). What was the temperature at 8:00 p.m.?
Q4. A recipe calls for \( \frac{3}{4} \) cup of sugar for every \( \frac{1}{2} \) cup of flour. How many cups of sugar are needed for 1 cup of flour?
A \( \frac{3}{8} \text{ cup} \)
B \( \frac{2}{3} \text{ cup} \)
C \( 1 \frac{1}{4} \text{ cups} \)
D \( 1 \frac{1}{2} \text{ cups} \)
Q5. Solve the inequality below. **Explain why the inequality sign changes (or does not change)** during your solution process.
\( -5x + 10 > 35 \)
Conceptual Explanation:
Q6. A bag contains 4 red marbles, 6 blue marbles, and 2 green marbles. If one marble is chosen at random, what is the probability that it is NOT blue?
E1. Which value represents the distance between \( -8 \) and \( 5 \) on a number line?
A \( -13 \)
B \( -3 \)
C \( 3 \)
D \( 13 \)
E2. Calculate the value of both expressions below: \( -2^4 \) and \( (-2)^4 \)
Metacognition: Which error would most likely lead to a wrong answer on E2?
SIGN ERROR
ORDER OF OPERATIONS
MISREADING THE QUESTION
Blueprint Submission Sweep
Verify Signs Show All Steps Units Included
Do Now:
1: A | 2: -23 ft | 3: Used Subtr. before Mult. | 4: e.g., \( -2-3 = -5 \)
Error Lab:
001: Subtr neg = add (\( 3 \)) | 002: Distribute to both (\( -4x + 20 \)) | 003: Div by time (\( 2 \text{ m/hr} \))
Micro-Drill:
A: \( 9, 5, -6.8, -5.5 \) | B: \( -5/12, 4 \) | C: \( -17 \)
Guided Practice:
Q1: \( \$6.75 \) | Q2: B | Q3: \( 4^\circ\text{F} \) | Q4: D | Q5: \( x < -5 \) (flip for div by neg) | Q6: \( 1/2 \) or \( 6/12 \)
Exit Ticket:
E1: D (\( 13 \)) | E2: \( -16 \text{ vs } 16 \). Power only applies to base; parens include sign.
Q2. Which expression is equivalent to -2(4x - 6) - 5x?
A -13x - 12
B -13x + 12
C -3x - 12
D -3x + 12
Q3. At midnight, the temperature was -4°F. By noon, the temperature had increased by 15°F. By 8:00 p.m., the temperature had decreased by 7°F. What was the temperature at 8:00 p.m.?
Q4. A recipe calls for 3/4 cup of sugar for every 1/2 cup of flour. How many cups of sugar are needed for 1 cup of flour?
A 3/8 cup
B 2/3 cup
C 1 1/4 cups
D 1 1/2 cups
Q5. Solve the inequality below. **Explain why the inequality sign changes (or does not change)**.
-5x + 10 > 35
Conceptual Explanation:
Q6. A bag contains 4 red marbles, 6 blue marbles, and 2 green marbles. If one marble is chosen at random, what is the probability that it is NOT blue?
E1. Which expression represents the distance, in units, between -8 and 5 on a number line?
A | -8 - 5 |
B | -8 + 5 |
C -8 - 5
D -8 + 5
E2. At 6:00 a.m., the temp was -12°F. By noon, it increased by 18°F. From noon to 4:00 p.m., it decreased by 5.5°F. What was the temp at 4:00 p.m.?
Metacognitive Tracking:
Which part was the most challenging?
Increasing Temp
Decreasing Temp
Decimal Signs
Blueprint Submission Sweep
Verify Signs Show Steps Check Units
DO NOW :
1: A | 2: -23 ft | 3: Used Subtr. before Mult. | 4: e.g., -2 - 3 = -5
ERROR LAB :
001: Subtr neg = add (3) | 002: Distribute to both (-4x + 20) | 003: Div by time (2 m/hr)
MICRO DRILL :
A: 9, 5, -6.8, -5.5 | B: -5/12, 4 | C: -17
GUIDED PRACTICE :
Q1: $6.75 | Q2: B | Q3: 4°F | Q4: D | Q5: x < -5 (flip for div by neg) | Q6: 1/2 or 6/12
EXIT TICKET :
E1: A (| -8 - 5 | = 13) | E2: 0.5°F (-12 + 18 - 5.5 = 6 - 5.5 = 0.5)
Q5 (The 'Why'):
NYS is moving toward conceptual explanations. If a student can solve but can't explain the sign change, they haven't mastered the concept. **Key Phrase:** "Dividing by a negative reverses the order of the number line."
Use the final 5 minutes to discuss the strategy selection and results from the exit ticket.
Rational Number Blueprint Workshop - Teacher Facilitation Edition
