Integer Showdown Worksheet Name:
Date:
Period:
7th Grade Math
Integer Showdown
Conquer the order of operations as you climb from Base Camp to the Summit!
The Expedition Rules (G-E-M-D-A-S)
1. Grouping (G)
Parentheses (), brackets [], and fraction bars. Simplify inside-out!
2. Exponents (E)
Evaluate powers. Keep track of negative signs: \((-3)^2 = 9\), but \(-3^2 = -9\).
3. Mult / Div (M/D)
Left to right! Same signs positive \((+)\), different signs negative \((-)\).
4. Add / Sub (A/S)
Left to right! Think of temperature or money to keep signs straight.
LEVEL 1
Base Camp: Two Operations
(Warm up your brain with simple steps)
\( -6 \times 4 + 10 \)
Answer:
\( 15 \div (-3) - 7 \)
Answer:
\( -8 - (-12) \div 2 \)
Answer:
\( (-4)^2 + (-9) \)
Answer:
LEVEL 2
Rocky Path: Three Operations
(Watch your steps with parentheses & exponents)
\( -3 \times (8 - 12) + 5 \)
Answer:
\( 24 \div (-2)^3 - (-6) \)
Answer:
\( -5 - 4 \times (-3) \div 2 \)
Answer:
\( (-10 + 4) \times (-2) - 15 \)
Answer:
Page 1 of 2
Integer Showdown: Climbing Higher
Name: ______________________
LEVEL 3
The Gorge: Nested Grouping Symbols
(Simplify from the innermost parentheses outward)
\( -4 \times [18 + (-2 \times 5)] \div (-8) \)
Answer:
\( 25 - [(-3)^2 \times (14 - 16)] \)
Answer:
\( -12 \div [3 \times (-5 + 7)] - (-14) \)
Answer:
\( [(-2)^3 - 4] \times (-3) + 10 \)
Answer:
LEVEL 4
The Summit: Fraction Bars as Grouping
(Simplify numerator & denominator completely first!)
\[ \frac{-18 - 4 \times (-3)}{-5 + 2} \]
Answer:
\[ \frac{-2 \times [15 \div (-3) + (-2)]}{(-1)^5 - 1} \]
Answer:
Summit Reflection
How confident do you feel after completing this expedition? What strategy helped you conquer the multi-bracket nested groupings or the fraction bars?
Page 2 of 2
Integer Showdown Key Name: TEACHER KEY
Date: CLASS KEY
Period: ALL
Answer Key
Integer Showdown Answer Key
Conquer the order of operations as you climb from Base Camp to the Summit!
Teacher Reference Guide: GEMDAS Rules are active.
G (Grouping) → E (Exponents) → M/D (Left-to-Right) → A/S (Left-to-Right)
LEVEL 1
Base Camp: Two Operations
\( -6 \times 4 + 10 \)
\( = -24 + 10 \)
\( = -14 \)
Answer:
-14
\( 15 \div (-3) - 7 \)
\( = -5 - 7 \)
\( = -12 \)
Answer:
-12
\( -8 - (-12) \div 2 \)
\( = -8 - (-6) \)
\( = -2 \)
Answer:
-2
\( (-4)^2 + (-9) \)
\( = 16 - 9 \)
\( = 7 \)
Answer:
7
LEVEL 2
Rocky Path: Three Operations
\( -3 \times (8 - 12) + 5 \)
\( = -3 \times (-4) + 5 \)
\( = 17 \)
Answer:
17
\( 24 \div (-2)^3 - (-6) \)
\( = 24 \div (-8) + 6 \)
\( = 3 \)
Answer:
3
\( -5 - 4 \times (-3) \div 2 \)
\( = -5 - (-12) \div 2 \)
\( = 1 \)
Answer:
1
\( (-10 + 4) \times (-2) - 15 \)
\( = -6 \times (-2) - 15 \)
\( = -3 \)
Answer:
-3
Page 1 of 2
Integer Showdown: Climbing Higher (Key)
TEACHER KEY
LEVEL 3
The Gorge: Nested Grouping Symbols
\( -4 \times [18 + (-2 \times 5)] \div (-8) \)
\( = -4 \times [18 + (-10)] \div (-8) \)
\( = -4 \times 8 \div (-8) \)
\( = -32 \div (-8) = 4 \)
Answer:
4
\( 25 - [(-3)^2 \times (14 - 16)] \)
\( = 25 - [9 \times (-2)] \)
\( = 25 - [-18] \)
Integer Showdown Exit Ticket Integer Showdown: Exit Ticket
Show your steps clearly before leaving camp!
Name:
Date:
\( -2 \times (10 - 15) - 3^2 \)
Answer:
\[ \frac{-12 + 6 \times (-2)}{-3 - (-1)^3} \]
Answer:
Rate your summit confidence today:
🧗 Stuck at base camp 🚶 Climbing the path 🏔️ Mastered the summit!
Cut along line to save paper
Integer Showdown: Exit Ticket
Show your steps clearly before leaving camp!
Name:
Date:
\( -2 \times (10 - 15) - 3^2 \)
Answer:
\[ \frac{-12 + 6 \times (-2)}{-3 - (-1)^3} \]
Answer:
Rate your summit confidence today:
🧗 Stuck at base camp 🚶 Climbing the path 🏔️ Mastered the summit!
Integer Showdown Ticket Key Integer Showdown: Exit Ticket Key
Show your steps clearly before leaving camp!
Name: TEACHER KEY
Date: CLASS KEY
\( -2 \times (10 - 15) - 3^2 \)
\( = -2 \times (-5) - 9 \)
\( = 10 - 9 = 1 \)
Answer:
1
\[ \frac{-12 + 6 \times (-2)}{-3 - (-1)^3} \]
Num: \( -12 + (-12) = -24 \)
Den: \( -3 - (-1) = -2 \)
Value: \( \frac{-24}{-2} = 12 \)
Answer:
12
Teacher Tip: Common error for #1 is calculating \(-3^2\) as \(+9\) instead of \(-9\).
Teacher Answer Key Cut Line
Integer Showdown: Exit Ticket Key
Show your steps clearly before leaving camp!
Name: TEACHER KEY
Date: CLASS KEY
\( -2 \times (10 - 15) - 3^2 \)
\( = -2 \times (-5) - 9 \)
\( = 10 - 9 = 1 \)
Answer:
1
\[ \frac{-12 + 6 \times (-2)}{-3 - (-1)^3} \]
Num: \( -12 + (-12) = -24 \)
Den: \( -3 - (-1) = -2 \)
Value: \( \frac{-24}{-2} = 12 \)
Answer:
12
Teacher Tip: Common error for #1 is calculating \(-3^2\) as \(+9\) instead of \(-9\).
