Integer Gridlock Slides Session 01 Grade 7 Math Review Arena
Combat Math
INTEGER GRIDLOCK
Dominate the matrix using integer operations, absolute value shields, and high-speed mental math strategy.
Mental Fluency
3 Differentiated Tiers
Team Arena Play
Turn on mental math instincts • Keep recording sheet ready Arena Status: READY
01
Rules of Engagement
Protocol Briefing
1. Draw Numbers
Draw 3 number cards from your deck (positive and negative integers -12 to +12).
Example: [-4], [+6], [-2]
2. Build Target
Combine your numbers using \(+\), \(-\), \(\times\), or \(\div\) to hit an open grid coordinate.
\((-4 \times -2) + 6 = 14\)
3. Claim Grid
Justify your mental math step out loud to your opponent. If validated, place your token!
Opponent verifies work on sheet!
Invalid math results in a Turn Forfeit . Check your signs! 2 to 4 Players per Arena Board
02
Tiered Power Decks
Balanced Matchmaking
TIER 1: ROOKIE
Foundational Flow
2-card combinations, integer addition and subtraction, and visual number-line jumps.
Special Ability:
Free sign-flip once per match. Number line tracker enabled.
TIER 2: PRO
Target Standard
Full 4 operations across positive and negative integers using 3 cards and PEMDAS.
Special Ability:
Absolute Value Shield: Convert any negative total into positive.
TIER 3: ELITE
Master Gauntlet
Exponents \((-2)^3\), target-lock constraints, and 4-number nested expressions.
Special Ability:
Grid Steal: Capture enemy cells if you match their value with 4 cards!
Players can choose their tier at the start of each match or be matched by their teacher.
03
Mental Math Blitz: Rapid Fire
Showdown Warm-Up
Call out the value and justify your shortcut before your partner!
Duel 1
\(-15 - (-23) = \ ?\)
Shortcut \(-15 + 23 = +8\)
Duel 2
\((-6 \times 7) \div (-2) = \ ?\)
Shortcut \(-42 \div -2 = +21\)
Duel 3
\(|-8 + 14| \times (-3) = \ ?\)
Shortcut \(6 \times -3 = -18\)
Duel 4
\((-4)^2 - (-10) = \ ?\)
Shortcut \(16 + 10 = 26\)
Fastest correct justification gets First Turn Advantage ! 30 Seconds per Duel
04
Winning Strategy: Matrix Control
Tactical Guide
1. Target The Center (0)
Worth 50 pts! Look for additive inverses: \((-7) + (+7) = 0\) or any integer multiplied by zero.
2. Connect 4 for Surge
Connect 4 adjacent cells in any direction to earn an instant +100 pt Grid Surge.
3. Challenge Sign Errors
If an opponent miscalculates their integer sign, call a challenge to claim their coordinate!
Sample 5x5 Matrix Targets
-24
-15
-8
-4
+1
-18
-10
-5
-1
+3
-12
-6
0
+6
+12
-3
+2
+5
+10
+18
-2
+4
+8
+16
+24
Write all calculations on your official Score Tracker Sheet as you play.
05
Mission Debrief: Arena Tactics
Reflection Protocol
Mental Shortcuts
What strategy did you use to quickly predict whether a product would be positive or negative?
Hardest Target
Which board numbers were the hardest to construct? Why are prime numbers or large magnitudes trickier?
Next Up: Day 2
Get ready for Rational Clash : fractions, repeating decimals, and percent conversions join the battlefield!
Submit your Score Tracker to your instructor for round audit. Arena Session 01 Complete
Integer Gridlock Game Kit Arena Board 01 • Ink-Saver Edition
INTEGER GRIDLOCK
Players: 2–4 Players / Pairs
Objective: Most Territory Points
COL A
COL B
COL C
COL D
COL E
ROW 1
ROW 2
ROW 3
ROW 4
ROW 5
A1 • 20pt -24 CORNER
B1 • 15pt -15 EDGE
C1 • 15pt -8 EDGE
D1 • 15pt -4 EDGE
E1 • 20pt +1 CORNER
A2 • 15pt -18 EDGE
B2 • 10pt -10 INNER
C2 • 10pt -5 INNER
D2 • 10pt -1 INNER
E2 • 15pt +3 EDGE
A3 • 15pt -12 EDGE
B3 • 10pt -6 INNER
C3 • 50pt 0 NEXUS CORE
D3 • 10pt +6 INNER
E3 • 15pt +12 EDGE
A4 • 15pt -3 EDGE
B4 • 10pt +2 INNER
C4 • 10pt +5 INNER
D4 • 10pt +10 INNER
E4 • 15pt +18 EDGE
A5 • 20pt -2 CORNER
B5 • 15pt +4 EDGE
C5 • 15pt +8 EDGE
D5 • 15pt +16 EDGE
E5 • 20pt +24 CORNER
Turn Procedure
1. Draw 3 cards from your tiered battle deck.
2. Use any operations (\(+, -, \times, \div\)) to hit an open matrix target number.
3. State equation clearly & record in Score Tracker. Place counter on coordinate.
Bonus Scoring
Center Nexus (0): +50 pts
Corners: +20 pts each
Grid Surge (4 in a line): +100 pts bonus
Challenge Win (catch error): +15 pts & steal
Place counters/tokens on claimed cells • Ink-Saver Printable Integer Gridlock • Game Sheet Page 1 of 2
Cut-Out Game Components • 24 Playing Cards
TIERED BATTLE CARDS DECK
Cut along dashed lines • Distribute by tier
TIER 1 • ROOKIE +3 Add / Sub Focus
TIER 1 • ROOKIE -5 Add / Sub Focus
TIER 1 • ROOKIE +8 Add / Sub Focus
TIER 1 • ROOKIE -2 Add / Sub Focus
TIER 1 • ROOKIE +6 Add / Sub Focus
TIER 1 • ROOKIE -7 Add / Sub Focus
TIER 1 • ROOKIE +10 Add / Sub Focus
TIER 1 • ROOKIE -4 Add / Sub Focus
TIER 2 • PRO -6 4 Operations
TIER 2 • PRO +9 4 Operations
TIER 2 • PRO -12 4 Operations
TIER 2 • PRO +4 4 Operations
TIER 2 • PRO -3 4 Operations
TIER 2 • PRO +12 4 Operations
Integer Gridlock Score Tracker Arena Mission 01 • Player Log
INTEGER GRIDLOCK SCORE TRACKER
Ink-Saver Edition
Player Name
Opponent Name
Date
Power Tier
T1 T2 T3
Round-by-Round Battle Equations
Every calculation must be verified by opponent before claiming coordinate
Rnd Cards Drawn Cell Equation Constructed & Order of Operations Opponent Verified Round Pts R1 R2
| |
| R3 | | | |
| |
| R4 | | | |
| |
| R5 | | | |
| |
| R6 | | | |
| |
Mental Math Strategy Note
Explain one mental shortcut or benchmark rule you used to compute quickly during play:
Final Score Summary
Cell Points:
Bonus Surge (+100):
Total Arena Pts:
Integer Gridlock • Match Tracker Page 1 of 2
Analysis & Mastery
ARENA DEFENSE & TARGET LOCK
Post-Game Skills Check
A
Opponent Error Analysis (Catch the Glitch)
Analyze the two claims made by opposing players below. Determine whether the math is valid or invalid. If invalid, explain the sign error and calculate the correct result.
Claim #1 Target Claimed: -18
\(-3 \times (-4) - 30 = -18\)
Is this claim correct?
Valid Invalid
Explain the error and provide the correct calculation:
Claim #2 Target Claimed: +5
\(-20 \div (-4) - (+10) = +5\)
Is this claim correct?
Valid Invalid
Explain the error and provide the correct calculation:
B
Boss Challenge: Reverse Target Lock
You are dealt the following four locked cards: [-6] [+3] [-4] [+8] . You may use any operations (\(+, -, \times, \div\)) and parentheses. Use at least 3 cards to create equations reaching each goal:
Goal: Center Nexus 0
Construct an equation equal to 0:
Goal: Negative Edge -10
Construct an equation equal to -10:
Goal: Positive Corner +24
Rational Clash Slides Session 02 Grade 7 Number Sense Arena
Rational Clash
RATIONAL CLASH
Master the triangle of numbers: convert freely between fractions, decimals, and percents to unlock high-multiplier matrix zones.
FDP Conversions
Target Estimation
3x Combo Multipliers
Prerequisite: Integer mastery • Equip your Rational Score Tracker Arena Level: EXPANDED
01
The F-D-P Triangle System
Match Protocol
Fractions
Parts of a whole. Look for friendly denominators: halves, fourths, fifths, eighths, and tenths.
\(\frac{3}{4} \ = \ \frac{75}{100}\)
Decimals
Place value precision. Think tenths and hundredths to convert instantly without long division!
\(0.75 \ = \ 75\text{ hundredths}\)
Percents
Per hundred. Move decimal point two places right, or scale denominator to 100.
\(0.75 \times 100\% \ = \ 75\%\)
Combo Multiplier: State all 3 equivalent forms when claiming a cell for a 2x Point Bonus ! Equivalency Power
02
Benchmark Mental Shortcuts
Speed Memorization
Halves & Fourths
\(\frac{1}{2} = 0.5 = 50\%\)
\(\frac{1}{4} = 0.25 = 25\%\)
\(\frac{3}{4} = 0.75 = 75\%\)
Fifths & Tenths
\(\frac{1}{5} = 0.2 = 20\%\)
\(\frac{2}{5} = 0.4 = 40\%\)
\(\frac{1}{10} = 0.1 = 10\%\)
Eighths Family
\(\frac{1}{8} = 0.125 = 12.5\%\)
\(\frac{3}{8} = 0.375 = 37.5\%\)
\(\frac{5}{8} = 0.625 = 62.5\%\)
Thirds & Repeaters
\(\frac{1}{3} \approx 0.\overline{3} = 33\frac{1}{3}\%\)
\(\frac{2}{3} \approx 0.\overline{6} = 66\frac{2}{3}\%\)
\(\frac{1}{6} \approx 0.1\overline{6} = 16\frac{2}{3}\%\)
Memorizing these 12 benchmarks allows you to calculate 90% of rational challenges mentally!
03
Rational Blitz: Conversion Duel
Fast-Draw Duel
Face your opponent! Solve the missing equivalent form before they can blink!
Round 1
\(\frac{4}{5} = \ ?\% = \ ?\text{ dec}\)
Target 80% = 0.80
Round 2
\(0.35 = \ ?\text{ fraction}\)
Target \(\frac{35}{100} = \frac{7}{20}\)
Round 3
\(15\% \text{ of } 80 = \ ?\)
Rational Clash Game Kit Arena Board 02 • Ink-Saver Edition
RATIONAL CLASH
Players: 2–4 Players / Pairs
Mode: F-D-P Triangle Mastery
COL A
COL B
COL C
COL D
COL E
ROW 1
ROW 2
ROW 3
ROW 4
ROW 5
A1 • 20pt \(-\frac{3}{2}\) -1.5
B1 • 15pt -0.75 \(-75\%\)
C1 • 15pt \(-\frac{1}{2}\) -0.50
D1 • 15pt -0.25 \(-\frac{1}{4}\)
E1 • 20pt \(+\frac{1}{10}\) 10%
A2 • 15pt -1.0 \(-100\%\)
B2 • 10pt \(+0.2\) \(\frac{1}{5}\)
C2 • 10pt \(+\frac{1}{4}\) 25%
D2 • 10pt \(+0.5\) \(\frac{1}{2}\)
E2 • 15pt \(+0.75\) 75%
A3 • 15pt \(-\frac{1}{3}\) \(-33.3\%\)
B3 • 10pt \(+0.4\) \(\frac{2}{5}\)
C3 • 50pt \(1.0\) WHOLE CORE
D3 • 10pt \(+\frac{2}{3}\) 66.6%
E3 • 15pt \(+1.25\) \(1\frac{1}{4}\)
A4 • 15pt \(+0.125\) \(\frac{1}{8}\)
B4 • 10pt \(+\frac{3}{5}\) 60%
C4 • 10pt \(+1.5\) \(1\frac{1}{2}\)
D4 • 10pt \(+\frac{7}{4}\) 1.75
E4 • 15pt \(+2.0\) 200%
A5 • 20pt \(+0.375\) \(\frac{3}{8}\)
B5 • 15pt \(+\frac{4}{5}\) 80%
C5 • 15pt \(+2.25\) \(2\frac{1}{4}\)
D5 • 15pt \(+\frac{5}{2}\) 2.50
E5 • 20pt \(+3.0\) 300%
Turn Rules
1. Draw 3 cards from the Rational Battle Deck.
2. Combine cards using \(+, -, \times, \div\) to target any open coordinate value.
3. Stating all 3 forms (Fraction, Decimal, Percent) doubles cell points!
Combo Multipliers
Center Whole Core (1.0): +50 pts
Trifecta Combo (F+D+P): +50 bonus pts
Grid Surge (4 in a line): +100 pts bonus
Conversion Challenge: +20 pts & capture
Place counters/tokens upon claiming cells • Low-Ink Printable Rational Clash • Game Sheet Page 1 of 2
Cut-Out Game Components • 24 Rational Cards
RATIONAL BATTLE CARDS DECK
Cut along dashed lines • Tiered by skill level
TIER 1 • ROOKIE \(\frac{1}{2}\) Benchmark Half
TIER 1 • ROOKIE \(0.25\) Benchmark Quarter
TIER 1 • ROOKIE \(50\%\) Benchmark Half
TIER 1 • ROOKIE \(\frac{3}{4}\) Three Fourths
TIER 1 • ROOKIE \(0.5\) Five Tenths
TIER 1 • ROOKIE \(75\%\) Three Fourths
TIER 1 • ROOKIE \(\frac{1}{10}\) One Tenth
Rational Clash Score Tracker Arena Mission 02 • Championship Log
RATIONAL CLASH SCORE TRACKER
Ink-Saver Edition
Player Name
Opponent Name
Date
Tier Selected
T1 T2 T3
Tournament Round Log & Equivalency Proofs
2x Multiplier: Fill All 3 Forms (F-D-P)
Rnd Cards Used Cell Equation Constructed F-D-P Triangle Equivalency Check Pts R1 F: D: P: R2 F: D: P:
| |
| R3 | | | | F: D: P: |
| |
| R4 | | | | F: D: P: |
| |
| R5 | | | | F: D: P: |
| |
| R6 | | | | F: D: P: |
| |
Mental Conversion Scratchpad
Show mental benchmark steps (e.g. converting fractions to common denominators):
Championship Tally
Base Cell Pts:
Trifecta Combo (+50):
Total Score:
Rational Clash • Tournament Score Tracker Page 1 of 2
Analysis & Strategy
RATIONAL GAUNTLET & BENCHMARKS
Skills Verification
A
Number Line Benchmark Gauntlet
Plot and label the following four rational numbers on the number line below: \(-\frac{3}{2}\) \(+0.75\) \(-0.25\) \(+1\frac{1}{4}\)
◄
►
-2.0
-1.0
0
+1.0
+2.0
Which two plotted numbers have the greatest distance between them? Calculate the exact distance:
B
Mental Math Strategy Challenge
Solve each mental math problem using an efficient shortcut. State your shortcut reasoning:
Problem 1: \(15\% \text{ of } \$60\)
Mental Strategy (Break into \(10\% + 5\%\)):
Problem 2: \(\frac{3}{4} \div \left(-\frac{1}{2}\right)\)
Mental Strategy (Multiply by reciprocal):
C
Grand Championship Reverse Target Lock
Given the cards:
