Rational Rush Game Slides
Whole-Class Math Arena
Grade 7-8 Math Challenge
LEVELS 1 - 3 + BOSS BATTLE
RATIONAL RUSH
The Ultimate Showdown in Adding & Subtracting Signed Integers, Fractions, and Decimals
Grab Your Dry-Erase Boards & Markers!
Collaborate with your team • Show every step • Lock in answers before the buzzer
Ready to Launch
Mission Briefing
Arena Rules & Scoring
4 Rounds Total
RULE 1
Show All Steps
No mental math guesses allowed! Write down sign conversions, common denominators, and vertical alignment on your board.
RULE 2
Boards Up Together
When the teacher counts down "3-2-1, BOARDS UP!", every team raises their answer simultaneously.
RULE 3
Tiered Bounties
Level 1 = 100 pts • Level 2 = 200 pts • Level 3 = 300 pts • Boss Battle = 500 pts!
Golden Rational Rule: Subtracting a negative number is equivalent to adding its positive opposite!
LEVEL 1
Integer Incline
100 Points
Evaluate the expression completely:
\(-17 - (-25) + (-8)\)
Tip 1: Rewrite the double negative first.
Tip 2: Work left to right with care!
60 Seconds on the Timer • Work with your table team
Advance for Solution Reveal
LEVEL 1 REVEAL
Strategy & Solution
Answer: 0
STEP 1
Fix Double Signs
Subtracting a negative becomes addition:
\(-17 + 25 + (-8)\)
STEP 2
Combine Left to Right
Add \(-17\) and \(25\) (different signs → subtract and keep larger):
\(8 + (-8)\)
STEP 3
Additive Inverse!
Opposites always add to zero:
\(0\)
Award 100 points to every team with 0 and complete step-by-step working!
Up Next: Fraction Foothills
LEVEL 2
Fraction Foothills
200 Points
Find the simplified value:
\(-\frac{3}{5} + \frac{7}{10} - \frac{1}{2}\)
Clue: What is the Least Common Denominator of 5, 10, and 2?
Requirement: Always reduce the final fraction to lowest terms!
90 Seconds • Show common denominator conversions
Advance for Solution Reveal
LEVEL 2 REVEAL
Strategy & Solution
Answer: \(-\frac{2}{5}\)
STEP 1
Convert to LCD (10)
Create equivalent fractions with denominator 10:
\(-\frac{6}{10} + \frac{7}{10} - \frac{5}{10}\)
STEP 2
Combine Numerators
Follow standard integer rules across numerator:
\(\frac{-6 + 7 - 5}{10} = \frac{-4}{10}\)
STEP 3
Simplify to Lowest Terms
Divide both numerator and denominator by 2:
\(-\frac{2}{5}\)
Did any team write \(-0.4\)? That is mathematically equivalent! Award 200 points!
Up Next: Decimal Depths
LEVEL 3
Decimal Depths
300 Points
Deep Sea Exploration Mission
A research submarine starts at an elevation of \(-142.6\text{ meters}\) below sea level. It ascends (climbs) \(58.4\text{ meters}\), and then descends (dives) \(26.75\text{ meters}\).
Mission Goal: Write the expression & find the submarine's final elevation:
\(-142.6 + 58.4 - 26.75\)
90 Seconds • Align decimal points and check signs carefully
Advance for Solution Reveal
LEVEL 3 REVEAL
Strategy & Solution
Answer: \(-110.95\text{ m}\)
STAGE 1
After Ascending (+58.4 m)
Signs are different, so subtract the absolute values:
\(142.60 - 58.40 = 84.20\)
Since \(|-142.6| > 58.4\), the sum remains negative:
\(-84.2\text{ meters}\)
STAGE 2
After Descending (-26.75 m)
Now subtract \(26.75\) (which is adding two negatives):
\(-84.20 + (-26.75)\)
Both are negative → add values together and keep negative:
\(-110.95\text{ meters}\)
Teams need both the correct value \(-110.95\) and units (meters) for full 300 pts!
FINAL ROUND: Boss Battle Ahead!
BOSS BATTLE
The Rational Gauntlet
500 Points
Mixed Format Challenge: Fractions & Decimals United
\(-4\frac{1}{2} - (-3.25) + \left(-\frac{3}{4}\right)\)
Path A: All Decimals
Convert fractions to benchmark decimals (\(0.5\) and \(0.75\)).
Path B: All Fractions
Convert \(3.25\) to \(3\frac{1}{4}\) and use common denominator 4.
2 Full Minutes • All team members must agree on final answer
Advance to Crown the Champions
Victory Debrief
Gauntlet Solved: -2
Grand Answer = -2
Method 1: Decimal Path
\(-4.50 - (-3.25) - 0.75\)
• Double negative: \(-4.50 + 3.25 = -1.25\)
• Subtract \(0.75\): \(-1.25 - 0.75\)
\(= -2.0\) (or \(-2\))
Method 2: Fraction Path
\(-\frac{9}{2} + \frac{13}{4} - \frac{3}{4}\)
• Common denominator: \(-\frac{18}{4} + \frac{13}{4} = -\frac{5}{4}\)
• Subtract: \(-\frac{5}{4} - \frac{3}{4} = -\frac{8}{4}\)
\(= -2\)
Total Up Team Scores!
Maximum possible score: 1,100 Points • Celebrate key strategies used today!
Arena Complete!
