Distributive Express Task Cards The Distributive Express
ACTIVITY TYPE: WARM-UP TASK CARDS
Set 1: Basic Variables
Cut along dashed lines to separate into 4 individual desk warm-up cards
ID: #01-ALPHA Level 1
Logistics Diagram
CARGO 4
(x+6)
Express Delivery Mission
\( 4(x + 6) \)
Driver's Manifest:
Deliver 4 to the term x
Deliver 4 to the term 6
ID: #02-BETA Level 1
Logistics Diagram
CARGO -3
(a-7)
Express Delivery Mission
\( -3(a - 7) \)
Driver's Manifest:
Deliver -3 to the term a
Watch out! Negative times negative equals?
ID: #03-GAMMA Level 1
Logistics Diagram
CARGO 5
(2y+3)
Express Delivery Mission
\( 5(2y + 3) \)
Driver's Manifest:
Deliver 5 to the term 2y (multiply coefficients!)
Deliver 5 to the term 3
ID: #04-DELTA Level 1
Logistics Diagram
CARGO -6
(3b-2)
Express Delivery Mission
\( -6(3b - 2) \)
Driver's Manifest:
Deliver -6 to the term 3b
Deliver -6 to the term -2
THE DISTRIBUTIVE EXPRESS PROJECT PAGE 1 of 4
The Distributive Express
ACTIVITY TYPE: WARM-UP TASK CARDS
Set 2: Power Up Exponents
Cut along dashed lines to separate into 4 individual desk warm-up cards
ID: #05-EPSILON Level 2
Logistics Diagram
CARGO 2x
(x²+4x)
Express Delivery Mission
\( 2x(x^2 + 4x) \)
Driver's Manifest:
Deliver 2x to x² (remember: \(x^1 \cdot x^2 = x^3\))
Deliver 2x to 4x (add the exponents!)
ID: #06-ZETA Level 2
Logistics Diagram
CARGO -4y²
(3y-5)
Express Delivery Mission
\( -4y^2(3y - 5) \)
Driver's Manifest:
Deliver -4y² to 3y (multiply coefficients, add exponents)
Watch the negatives: \(-4y^2 \cdot -5\) is positive!
ID: #07-ETA Level 2
Logistics Diagram
CARGO 3a³
(2a²-4a+1)
Express Delivery Mission
\( 3a^3(2a^2 - 4a + 1) \)
Driver's Manifest:
Triple Delivery! Distribute 3a³ to all 3 terms.
Exponent check: \(a^3 \cdot a^2 = a^5\) and \(a^3 \cdot a^1 = a^4\).
ID: #08-THETA Level 2
Logistics Diagram
CARGO -x²
(5x²-3x-8)
Express Delivery Mission
\( -x^2(5x^2 - 3x - 8) \)
Driver's Manifest:
Double Negative Alert! Watch the signs for the middle and end cargo.
Keep variables aligned and powers added neatly.
THE DISTRIBUTIVE EXPRESS PROJECT PAGE 2 of 4
Distributive Express
OFFICIAL CARGO MANIFEST (RECORDING SHEET)
SCORE / 8 Missions
CONDUCTOR:
DEPOT DATE:
CLASS RUN:
Conductor Mission: Pick up a cargo task card. Show your distribution pathways, write your step-by-step calculations in the blank workspace, and record your simplified expression in the final cargo container!
MISSION #01 (ALPHA) \( 4(x + 6) \)
Final Cargo:
MISSION #02 (BETA) \( -3(a - 7) \)
Final Cargo:
MISSION #03 (GAMMA) \( 5(2y + 3) \)
Final Cargo:
MISSION #04 (DELTA) \( -6(3b - 2) \)
Final Cargo:
MISSION #05 (EPSILON) \( 2x(x^2 + 4x) \)
Final Cargo:
MISSION #06 (ZETA) \( -4y^2(3y - 5) \)
Final Cargo:
MISSION #07 (ETA) \( 3a^3(2a^2 - 4a + 1) \)
Final Cargo:
MISSION #08 (THETA) \( -x^2(5x^2 - 3x - 8) \)
Final Cargo:
THE DISTRIBUTIVE EXPRESS PROJECT PAGE 3 of 4
Distributive Express
DISPATCH CONTROL MASTER KEY (ANSWER KEY)
TEACHER USE ONLY
Evaluation Guide: Fully worked-out distribution steps are shown below. Final simplified expressions are enclosed in highlighted high-visibility containers. Watch for correct variable power additions!
MISSION #01 (ALPHA) \( 4(x + 6) \)
Distribution step:
\( 4 \cdot (x) + 4 \cdot (6) \)
\( = 4x + 24 \)
Final Cargo:
\( 4x + 24 \)
MISSION #02 (BETA) \( -3(a - 7) \)
Distribution step:
\( -3 \cdot (a) - (-3) \cdot (7) \)
\( = -3a + 21 \)
Final Cargo:
\( -3a + 21 \)
MISSION #03 (GAMMA) \( 5(2y + 3) \)
Distribution step:
\( 5 \cdot (2y) + 5 \cdot (3) \)
\( = 10y + 15 \)
Final Cargo:
\( 10y + 15 \)
MISSION #04 (DELTA) \( -6(3b - 2) \)
Distribution step:
\( -6 \cdot (3b) - (-6) \cdot (2) \)
\( = -18b + 12 \)
Final Cargo:
\( -18b + 12 \)
MISSION #05 (EPSILON) \( 2x(x^2 + 4x) \)
Distribution step:
\( 2x \cdot (x^2) + 2x \cdot (4x) \)
\( = 2x^3 + 8x^2 \)
Final Cargo:
\( 2x^3 + 8x^2 \)
MISSION #06 (ZETA) \( -4y^2(3y - 5) \)
Distribution step:
\( -4y^2 \cdot (3y) - (-4y^2) \cdot (5) \)
\( = -12y^3 + 20y^2 \)
Final Cargo:
\( -12y^3 + 20y^2 \)
MISSION #07 (ETA) \( 3a^3(2a^2 - 4a + 1) \)
Distribution step:
\( 3a^3 \cdot (2a^2) - 3a^3 \cdot (4a) + 3a^3 \cdot (1) \)
\( = 6a^5 - 12a^4 + 3a^3 \)
Final Cargo:
\( 6a^5 - 12a^4 + 3a^3 \)
MISSION #08 (THETA) \( -x^2(5x^2 - 3x - 8) \)
Distribution step:
\( -x^2 \cdot (5x^2) - (-x^2) \cdot (3x) - (-x^2) \cdot (8) \)
\( = -5x^4 + 3x^3 + 8x^2 \)
Final Cargo:
\( -5x^4 + 3x^3 + 8x^2 \)
THE DISTRIBUTIVE EXPRESS PROJECT PAGE 4 of 4
Distributive Express Worksheet The Distributive Express
CLASSROOM WORKSHEET: DELIVERING TERMS
Warm-Up Run
CONDUCTOR:
DEPOT DATE:
CLASS PERIOD:
Standard Delivery Regulations
To distribute a cargo term, you must multiply the outside factor by every inside term inside the parentheses. Use the visual branching schematic to route your multiplication correctly!
MISSION #1 (ALPHA) Level 1
ROUTE: 4 → (x + 6)
\( 4(x + 6) \)
Final Cargo:
MISSION #2 (BETA) Level 1
ROUTE: -3 → (a - 7)
\( -3(a - 7) \)
Final Cargo:
MISSION #3 (GAMMA) Level 1
ROUTE: 5 → (2y + 3)
\( 5(2y + 3) \)
Final Cargo:
MISSION #4 (DELTA) Level 1
ROUTE: -6 → (3b - 2)
\( -6(3b - 2) \)
Final Cargo:
MISSION #5 (EPSILON) - POWER UP CHALLENGE Level 2
Logistics Route
2x → (x² + 4x)
\( 2x(x^2 + 4x) \)
Tip: Don't forget to add exponent powers! \( x^1 \cdot x^2 = x^3 \)
Work Space (Add exponents)
Final Cargo:
THE DISTRIBUTIVE EXPRESS PROJECT STUDENT RUN SHEET
Distributive Express Answer Key The Distributive Express
DISPATCH CONTROL MASTER KEY (ANSWER KEY)
Teacher Key
EVALUATOR:
Control Dispatcher
DEPOT STATUS:
Approved Key
TOTAL CAPACITY:
100% Score (5/5)
Grading Regulations
Evaluate student worksheets against the detailed mathematical distributions below. Ensure steps demonstrate proper sign combinations and appropriate variable exponent addition.
MISSION #1 (ALPHA) Level 1 Solution
ROUTE: 4 → (x + 6) 4(x) + 4(6)
\( 4(x + 6) \)
Distribution path:
\( = 4 \cdot x + 4 \cdot 6 \)
\( = 4x + 24 \)
Final Cargo:
\( 4x + 24 \)
MISSION #2 (BETA) Level 1 Solution
ROUTE: -3 → (a - 7) -3(a) - (-3)(7)
\( -3(a - 7) \)
Distribution path:
\( = -3 \cdot a - (-3) \cdot 7 \)
\( = -3a + 21 \)
Final Cargo:
\( -3a + 21 \)
MISSION #3 (GAMMA) Level 1 Solution
ROUTE: 5 → (2y + 3) 5(2y) + 5(3)
\( 5(2y + 3) \)
Distribution path:
\( = 5 \cdot 2y + 5 \cdot 3 \)
\( = 10y + 15 \)
Final Cargo:
\( 10y + 15 \)
MISSION #4 (DELTA) Level 1 Solution
ROUTE: -6 → (3b - 2) -6(3b) - (-6)(2)
\( -6(3b - 2) \)
Distribution path:
\( = -6 \cdot 3b - (-6) \cdot 2 \)
\( = -18b + 12 \)
Final Cargo:
\( -18b + 12 \)
MISSION #5 (EPSILON) - POWER UP CHALLENGE SOLUTION Level 2 Solution
Logistics Route
2x → (x² + 4x)
\( 2x(x^2 + 4x) \)
Check: Multiplying exponents adds powers. \( 2x^1 \cdot x^2 = 2x^3 \) and \( 2x^1 \cdot 4x^1 = 8x^2 \)
Work Space Solutions (Add exponents)
Distribution path:
\( = 2x \cdot (x^2) + 2x \cdot (4x) \)
\( = 2x^3 + 8x^2 \)
Final Cargo:
\( 2x^3 + 8x^2 \)
THE DISTRIBUTIVE EXPRESS PROJECT TEACHER DISPATCH KEY
Fraction Express Worksheet The Fraction Express
CLASSROOM WORKSHEET: COMBINING LIKE TERMS
Combine Cargo
CONDUCTOR:
DEPOT DATE:
CLASS PERIOD:
Like Terms Regulations
Combine fractional terms directly by finding a common denominator . Remember, you can only combine terms that share the exact same variable (like bases)! There are no exponents on this run.
ROUTE #1: SAME BASES (3 TERMS) 3 Cargo Stops
\[ \frac{1}{4}x + \frac{1}{3}x + \frac{2}{3}x \]
Final Cargo:
ROUTE #2: SAME VARIABLE BASES (3 TERMS) 3 Cargo Stops
\[ \frac{1}{2}y - \frac{2}{5}y + \frac{4}{5}y \]
Final Cargo:
ROUTE #3: MIXED VARIABLE BASES (4 TERMS) 4 Cargo Stops
\[ \frac{1}{3}a + \frac{1}{4}b + \frac{2}{3}a - \frac{3}{4}b \]
Final Cargo:
ROUTE #4: MIXED VARIABLE BASES (4 TERMS) 4 Cargo Stops
\[ \frac{3}{4}m + \frac{1}{2}n - \frac{1}{4}m + \frac{1}{3}n \]
Final Cargo:
ROUTE #5: MIXED CARGO BASES & CONSTA-INTEGERS (4 TERMS) - MAXIMUM CAPACITY RUN 4 Cargo Stops
Logistics Route
Combine same bases: k-terms with k-terms, and constant numbers together. No exponents!
\[ \frac{5}{6}k - \frac{1}{2} + \frac{1}{6}k + \frac{2}{3} \]
Check: Find common denominators for the constant fractions (\(2\) and \(3\)) and combine neatly!
Work Space (Group like terms, find common denominators)
Final Cargo:
THE DISTRIBUTIVE EXPRESS PROJECT FRACTION EXPRESS RUN
Fraction Express Answer Key The Fraction Express
DISPATCH CONTROL MASTER KEY (ANSWER KEY)
Teacher Key
EVALUATOR:
Control Dispatcher
DEPOT STATUS:
Approved Key
TOTAL CAPACITY:
100% Score (5/5)
Grading Regulations
Evaluate student worksheets against the detailed fraction-combining steps below. Watch for correct common denominator grouping, signs, and simplified fraction representations. Exponents are not present in this run.
ROUTE #1: SAME BASES (3 TERMS) 3 Cargo Stops
\( \frac{1}{4}x + \frac{1}{3}x + \frac{2}{3}x \)
Finding common denominator (12):
\( = \frac{3}{12}x + \frac{4}{12}x + \frac{8}{12}x \)
\( = \frac{15}{12}x = \frac{5}{4}x \)
Final Cargo:
\( \frac{5}{4}x \)
ROUTE #2: SAME VARIABLE BASES (3 TERMS) 3 Cargo Stops
\( \frac{1}{2}y - \frac{2}{5}y + \frac{4}{5}y \)
Finding common denominator (10):
\( = \frac{5}{10}y - \frac{4}{10}y + \frac{8}{10}y \)
\( = \frac{9}{10}y \)
Final Cargo:
\( \frac{9}{10}y \)
ROUTE #3: MIXED VARIABLE BASES (4 TERMS) 4 Cargo Stops
\( \frac{1}{3}a + \frac{1}{4}b + \frac{2}{3}a - \frac{3}{4}b \)
Group and combine like bases:
\( = (\frac{1}{3} + \frac{2}{3})a + (\frac{1}{4} - \frac{3}{4})b \)
\( = \frac{3}{3}a - \frac{2}{4}b = a - \frac{1}{2}b \)
Final Cargo:
\( a - \frac{1}{2}b \)
ROUTE #4: MIXED VARIABLE BASES (4 TERMS) 4 Cargo Stops
\( \frac{3}{4}m + \frac{1}{2}n - \frac{1}{4}m + \frac{1}{3}n \)
Group \(m\) terms and \(n\) terms (LCD 6):
\( = (\frac{3}{4} - \frac{1}{4})m + (\frac{3}{6} + \frac{2}{6})n \)
\( = \frac{2}{4}m + \frac{5}{6}n = \frac{1}{2}m + \frac{5}{6}n \)
Final Cargo:
\( \frac{1}{2}m + \frac{5}{6}n \)
ROUTE #5: MIXED CARGO BASES & CONSTA-INTEGERS (4 TERMS) - MASTER SOLUTION 4 Cargo Stops Solution
Logistics Route
Group k-terms and group constant fractions together. No exponents!
\[ \frac{5}{6}k - \frac{1}{2} + \frac{1}{6}k + \frac{2}{3} \]
Check: Constant fractions LCD is 6. \(-\frac{1}{2} = -\frac{3}{6}\) and \(\frac{2}{3} = \frac{4}{6}\).
Work Space Solutions
Grouping and calculations:
\( = (\frac{5}{6}k + \frac{1}{6}k) + (-\frac{3}{6} + \frac{4}{6}) \)
\( = \frac{6}{6}k + \frac{1}{6} = k + \frac{1}{6} \)
