Signed Numbers Showdown • Lesson • Lenny.com
Signed Numbers Showdown A 40-minute collaborative team review lesson targeting integer and rational number addition, subtraction, equivalence, and number line reasoning to prepare students for the unit quiz.
D djaenecke
Signed Numbers Showdown Activity
A 2-page review activity sheet featuring problem rounds that mirror every question type on the Unit 7.5 rational number quiz, formatted with standard student headers and independent/collaborative workspace.
Signed Numbers Showdown Slides
An 8-slide presentation to pace and facilitate the 40-minute review, featuring clear challenge prompts, team discourse norms, and concept checkpoints without role designations.
Signed Numbers Teacher Guide
A 2-page teacher facilitation guide featuring the 40-minute pacing plan, collaborative discussion protocols, common student misconceptions with responsive questions, and complete worked solutions for the review activity.
Signed Numbers Showdown A 40-minute collaborative team review lesson targeting integer and rational number addition, subtraction, equivalence, and number line reasoning to prepare students for the unit quiz.
D djaenecke
Signed Numbers Showdown Activity Review Challenge Unit 7.5 Quiz Prep • 40 Min
Signed Numbers Showdown
Evaluate, compare, and solve rational number expressions and equations.
Name:
Date: Period:
1
Round 1: Value Face-Off (Evaluating Signed Expressions)
Quiz Target 1
Find the exact value of each expression. Then circle the expression with the least value .
Choice A \(-12 - (-12)\)
Value: _____
Choice B \(-4 - 9\)
Value: _____
Choice C \(18 + (-11)\)
Value: _____
Choice D \(-14 + (-5)\)
Value: _____
Conclusion: The expression with the least value is:
A B C D
2
Round 2: Twin Expressions (Equivalence Detective)
Quiz Target 2
Target expression: \(4.2 - 6.8\)
Select all that apply
A. \(6.8 - 4.2\) Reason: ____________________
B. \(-6.8 + 4.2\) Reason: ____________________
C. \(4.2 + (-6.8)\) Reason: ____________________
D. \(4.2 - (-6.8)\) Reason: ____________________
3
Round 3: Variable Crackers (Solving Equations)
Quiz Target 3
Find the value of each variable that makes the equation true. Show all steps.
Problem 3A Integer
\(19 - x = 23\)
\(x =\) ________
Problem 3B Decimal
\(y + (-6.4) = 0\)
\(y =\) ________
Problem 3C Fraction
\(\frac{11}{5} + z = -\frac{4}{5}\)
\(z =\) ________
Unit 7.5 Quiz Review • Page 1 of 2 Show all steps clearly
Part II • Application & Reasoning
Real-World Scenarios & Number Line Logic
Round 4 & 5 Deep Conceptual Mastery
4
Round 4: Arctic Station Temperature Log
Quiz Target 4
The table shows temperatures recorded in an Arctic station. Formula: Midnight Temp + Change = Noon Temp.
Day Midnight Temp (°F) Change to Noon (°F) Noon Temp (°F) Monday -28 +16 -12 Tuesday -16.5 +16.5 Wednesday +14.2 8.2 Thursday -14.8 -26.0 Friday -24.4 +18.1
Saturday Question: At midnight, the temperature was \(-19^\circ\text{F}\). At noon, it was \(12^\circ\text{F}\). How many degrees did the temperature change from midnight to noon?
Change: _____ \(^\circ\text{F}\)
5
Round 5: Number Line Reasoning (Magnitude & Sign)
Quiz Target 5
This number line shows the relative positions of \(p\) and \(q\).
-2 -1 0 1 q p = 0.5
Is the sum \(p + q\) positive, negative, or zero? Circle one:
Positive Negative Zero
Explain how you know using absolute value or distance from 0:
Self-Assessment & Quiz Readiness
How ready do you feel for tomorrow's quiz?
Need Help Pretty Good 100% Ready!
Unit 7.5 Quiz Review • Page 2 of 2 Review Complete
Signed Numbers Showdown Slides Unit 7.5 Quiz Review 40 Minutes • Review Challenge
Signed Numbers
Showdown
Master rational number addition, subtraction, equivalence, and number lines through focused challenge rounds!
5 Rounds All Quiz Targets
Collaboration Discuss & Verify
Goal 100% Quiz Ready
Team Norms How We Work Together
1
Talk Before You Write
• Predict the sign: Will the answer be positive or negative?
• Explain your reasoning: Share the rule or strategy you are using.
Speak your thinking aloud
2
Support & Verify
• Check every sign: Watch out for double negative traps.
• Ask questions: "Why did you add?" or "Can we test that value?"
Confirm every solution together
Golden Rule: Never advance to the next round until both teammates agree and can explain!
Round 1 • 6 Minutes Evaluate & Compare
Value Face-Off: Which has the least value?
Choice A \(-12 - (-12)\) Subtracting negative
Choice B \(-4 - 9\) Starting negative & going left
Choice C \(18 + (-11)\) Positive + Negative
Choice D \(-14 + (-5)\) Adding two negatives
Concept Check: "Least value" means farthest to the LEFT on the number line! Calculate All 4!
Round 2 • 6 Minutes Equivalence Detective
Twin Expressions: Target is
\(4.2 - 6.8\)
Which expressions have the exact same value ? Select all that apply.
A. \(6.8 - 4.2\) Subtraction commutative?
B. \(-6.8 + 4.2\) Reordered addition?
C. \(4.2 + (-6.8)\) Add the opposite?
D. \(4.2 - (-6.8)\) Subtract a negative?
Key Principle: Subtracting a number is identical to adding its opposite! \(a - b = a + (-b)\)
Round 3 • 7 Minutes Solve For The Unknown
Variable Crackers: Solve For the Variable
Find the value of each variable that makes the equation true:
3A • Integer Trap
\(19 - x = 23\)
What number must be subtracted from 19 to get 23?
3B • Additive Inverse
\(y + (-6.4) = 0\)
What number cancels with \(-6.4\) to make 0?
3C • Fraction Operations
\(\frac{11}{5} + z = -\frac{4}{5}\)
Signed Numbers Teacher Guide Teacher Facilitation Guide Amplify Grade 7 • Unit 7.5 Quiz Review
Signed Numbers Showdown Facilitation
40-Minute Review Plan • Pacing, Math Discourse Stems & Misconception Matrix
Total Duration 40 Minutes
⏱ 40-Minute Pacing Guide
Time Phase Teacher Moves & Student Actions 0:00 - 0:05 Launch & Norms Slides 1–2. Group students into pairs or triads. Establish collaborative norm: "Discuss strategy and sign prediction aloud before recording work." 0:05 - 0:11 Round 1: Value Slide 3. Evaluating 4 expressions. Students calculate and verify values together. Emphasize "least value" means farthest left on the number line. 0:11 - 0:17 Round 2: Twins Slide 4. Groups identify equivalent forms. Reinforce \(a - b = a + (-b)\). Highlight why subtraction is not commutative. 0:17 - 0:24 Round 3: Equations Slide 5. Solve integer, decimal, and fraction equations. Direct students to substitute values back into original equations to self-check. 0:24 - 0:32 Round 4: Arctic Log Slide 6. Real-world context. Guide backward reasoning: \(\text{Change} = \text{End} - \text{Start}\) and \(\text{Start} = \text{End} - \text{Change}\). 0:32 - 0:37 Round 5: Logic Slide 7. Number line reasoning. Ensure students explain using "absolute value" or "distance from zero." 0:37 - 0:40 Debrief & Collect Slide 8. Review top 3 traps. Collect activity mats to spot-check students needing quick morning check-in.
🗣 Accountable Math Talk Stems (Display on Board)
Guiding Questions:
"Why did you rewrite that minus sign as adding a negative?"
"Which number has the larger distance from zero?"
"Can we plug that answer back in to make sure it equals the right side?"
Reasoning & Explanation Stems:
"I know the sign is negative because the negative number has a greater absolute value."
"Subtracting \(-12\) is the same as adding \(+12\)."
"Because noon was higher than midnight, the change had to be positive."
Common Quiz Misconceptions & Responsive Questions
Trap: Conflating "Least Value" with "Smallest Magnitude"
Students often pick \(0\) or a small positive number instead of a large negative like \(-19\).
Subtract \(\frac{11}{5}\) from both sides carefully!
Verification Tip: Substitute your answer back into the equation to check it! Plug & Check
Round 4 • 8 Minutes Real-World Application
Arctic Freeze: Temperature Changes Midnight Temp + Temperature Change = Noon Temp Formula
Finding Noon Temp (Forward) Start with Midnight and ADD the change.
Finding Missing Values (Backward) Missing Change = Noon Temp - Midnight Temp
Saturday Alert: From \(-19^\circ\text{F}\) to \(12^\circ\text{F}\). Did it get warmer or colder? Change must be positive!
Round 5 • 6 Minutes Conceptual Reasoning
Number Line Duel: Relative Magnitudes Point \(p = 0.5\) and point \(q\) is located to the left of \(-1\). Is \(p + q\) positive, negative, or zero?
Distance of \(p\) from 0 0.5 units
Distance of \(q\) from 0 More than 1.0 unit!
Because \(|q| > |p|\), the negative number pulls farther from 0. The sum MUST be NEGATIVE!
Quiz Explanation Trap: Don't just say "it's negative" — explain using DISTANCE! Explain Why
Final 5 Minutes • Debrief Quiz Readiness Locked In
Top 3 Quiz Traps to Dodge Tomorrow
Double Negatives \(a - (-b)\) turns into addition: \(a + b\). It does not stay negative!
Order in Subtraction \(3.5 - 4.7 \neq 4.7 - 3.5\). Subtraction is NOT commutative!
Change vs. Value Temperature change = \(\text{End} - \text{Start}\). Watch out for double negative subtraction!
Turn in your completed Review Mat!
Teacher Question: "On a thermometer or vertical number line, which number is located deepest in the freeze?"
Trap: Treating Subtraction as Commutative
Students think \(3.5 - 4.7\) is the same as \(4.7 - 3.5\).
Teacher Question: "Does having $3.50 and spending $4.70 leave you with the same balance as having $4.70 and spending $3.50?"
Trap: Subtracting Forward on Missing Start Temperatures
When given change \(+14.2\) and noon \(8.2\), students add \(8.2 + 14.2 = 22.4\) instead of subtracting.
Teacher Question: "If it warmed up by 14 degrees to reach 8 degrees, was it colder or warmer at midnight?"
Signed Numbers Showdown Facilitation • Page 1 of 2 Turn Over for Complete Worked Solutions & Key
Complete Activity Solutions & Quiz Crosswalk Exact step-by-step solutions, point distributions, and quiz alignment.
Verification 100% Quiz Aligned
Round 1 Key (Quiz Item 1 Alignment) Correct: D
\(= -12 + 12 = \mathbf{0}\)
\(= -4 + (-9) = \mathbf{-13}\)
\(= 18 - 11 = \mathbf{7}\)
\(= \mathbf{-19}\) (Least!)
Comparison on number line: \(-19 < -13 < 0 < 7\). \(-19\) is farthest left.
Round 2 Key (Quiz Item 2 Alignment) Target: \(4.2 - 6.8 = -2.6\)
A: \(6.8 - 4.2 = +2.6\) Not equivalent (opposite sign; subtraction not commutative).
B: \(-6.8 + 4.2 = -2.6\) ✓ EQUIVALENT Addition is commutative: \(4.2 + (-6.8) = -6.8 + 4.2\).
C: \(4.2 + (-6.8) = -2.6\) ✓ EQUIVALENT Definition of subtraction: \(a - b = a + (-b)\).
D: \(4.2 - (-6.8) = 4.2 + 6.8 = 11.0\) Not equivalent (subtracting negative adds positive).
Round 3 Key (Quiz Item 3 Alignment) One-Step Rational Equations
Check: \(19 - (-4) = 19 + 4 = 23\) ✓
Additive inverse property
Check: \(6.4 + (-6.4) = 0\) ✓
3C: \(\frac{11}{5} + z = -\frac{4}{5}\)
\(z = -\frac{4}{5} - \frac{11}{5} = -\frac{15}{5}\)
Check: \(\frac{11}{5} + (-3) = \frac{11-15}{5} = -\frac{4}{5}\) ✓
Round 4 Key (Quiz Item 4 Alignment) Arctic Temperature Data
Tuesday Noon: \(-16.5 + 16.5 = \mathbf{0^\circ\text{F}}\)Wednesday Midnight: \(8.2 - 14.2 = \mathbf{-6.0^\circ\text{F}}\)Thursday Change: \(-26.0 - (-14.8) = \mathbf{-11.2^\circ\text{F}}\)Friday Noon: \(-24.4 + 18.1 = \mathbf{-6.3^\circ\text{F}}\) Saturday Prompt Solution:
Midnight: \(-19^\circ\text{F}\), Noon: \(12^\circ\text{F}\)
\(\text{Change} = 12 - (-19) = 12 + 19 = \mathbf{+31^\circ\text{F}}\)
Explanation: The temperature had to increase by 19° to reach 0°F, then increase another 12° to reach 12°F, giving a total change of \(19 + 12 = 31^\circ\text{F}\).
Round 5 Key (Quiz Item 5 Alignment) Correct: Negative
Exemplary Student Explanation (Rubric: 2 pts):
"The sum \(p + q\) is negative . Point \(p\) has a value of \(+0.5\), so its distance from zero is \(0.5\). Point \(q\) is located to the left of \(-1\), so its distance from zero (its absolute value) is greater than \(1.0\). Because \(|q| > |p|\), the negative number has a greater magnitude and determines the sign of the sum."
Signed Numbers Showdown Facilitation • Page 2 of 2 Ready for Classroom Implementation
