Equation Endurance Warm-Ups Equation Endurance
Daily Warm-Ups • Week 1
Name:
Date:
Training Goal
Master multi-step equations with variables on both sides and rational coefficients. Accuracy is key!
Day 1
The Distributive Stretch
1. Solve for \(x\): \(3(x + 5) = 24\)
2. Solve for \(y\): \(-2(4y - 1) = 18\)
Day 2
Variable Cross-Over
Solve for \(m\). Show each balancing step:
\(5m + 12 = 2m - 9\)
Day 3
The Fractional Finisher
1. Solve: \(\frac{1}{2}w + 4 = 10\)
2. Solve: \(\frac{2}{3}(k - 6) = 4\)
Day 4
Heavy Lifting
Solve for \(x\):
\(4(2x - 3) = 2(3x + 1) + 4\)
Day 5
Solution Scouting
Identify the number of solutions:
\(2(x + 5) = 2x + 10\)
Identify the number of solutions:
\(3x - 4 = 3x + 2\)
Equation Endurance Practice Set Equation Endurance
Practice Set • Week 1
Name:
Date:
Directions
Show all steps to earn full credit on open-response problems. Verify your answers by substituting back into the equation!
Section 1: Multiple Choice
1. What is the value of \(x\) in the equation \(4x - 7 = 2x + 13\)?
A) 3
B) 10
C) 15
D) 20
2. Which equation has infinitely many solutions?
A) \(5x + 2 = 5x - 2\)
B) \(3(x - 4) = 3x - 12\)
C) \(2x + 1 = x + 1\)
Section 2: Show Your Work
3. Solve for \(n\): \(\frac{3}{4}n = 12\)
Answer: \(n = \) ________
4. Solve for \(x\): \(2(3x + 4) - 5x = 14\)
Answer: \(x = \) ________
5. Gym A costs $25/month + $50 fee. Gym B costs $35/month (no fee). When are costs equal? Write and solve an equation.
Answer: ________ months
6. Solve. Express as a simplified fraction: \(0.5x + 3 = 1.2x - 0.5\)
Answer: \(x = \) ________
"Distance is just a number. Every equation solved is a mile closer to the finish line."
Equation Endurance Warm-Ups Answer Key Equation Endurance
Answer Key • Warm-Ups
Teacher Reference
Day 1
Distributive Stretch
1. 3(x + 5) = 24
x = 3
Work: 3x+15=24 → 3x=9
2. -2(4y - 1) = 18
y = -2
Work: -8y+2=18 → -8y=16
Day 2
Variable Cross-Over
5m + 12 = 2m - 9
m = -7
Work: 3m + 12 = -9 → 3m = -21
Day 3
Fractional Finisher
1. 1/2 w + 4 = 10
w = 12
Work: 1/2 w = 6
2. 2/3 (k - 6) = 4
k = 12
Work: k-6 = 6
Day 4
Heavy Lifting
4(2x - 3) = 2(3x + 1) + 4
x = 9
Work: 8x - 12 = 6x + 6 → 2x = 18
Day 5
Solution Scouting
2(x + 5) = 2x + 10
Infinitely Many Solutions
3x - 4 = 3x + 2
No Solution
Empire State Math Marathon • Week 1 Equation Endurance Warm-Ups Key
Equation Endurance Practice Set Answer Key Equation Endurance
Answer Key • Practice Set
Teacher Reference
Section 1: Multiple Choice
1. Value of x in 4x - 7 = 2x + 13?
Work: 2x = 20 → x = 10
B
2. Which equation has infinitely many solutions?
Work: 3x - 12 = 3x - 12
B
Section 2: Show Your Work
3. Solve: 3/4 n = 12
n = 16
Multiply by 4/3 → 12 × 4/3 = 16
4. Solve: 2(3x + 4) - 5x = 14
x = 6
Work: 6x + 8 - 5x = 14 → x + 8 = 14
5. Gym Costs Comparison
Equation: 25m + 50 = 35m
5 months
Work: 50 = 10m → m = 5
6. Solve: 0.5x + 3 = 1.2x - 0.5
x = 5
Work: 3.5 = 0.7x → x = 3.5 / 0.7 = 5
Empire State Math Marathon • Week 1 Equation Endurance Practice Key
Linear Landscapes Warm-Ups Linear Landscapes
Daily Warm-Ups • Week 2
Name:
Date:
Training Goal
Master proportional relationships, unit rates, and the slope-intercept form \(y = mx + b\).
Day 1
Unit Rate Sprint
A train travels 150 miles in 3 hours. What is the unit rate in miles per hour? Show work.
Day 2
Slope Scout
Find slope between \((2, 5)\) and \((4, 11)\):
Properties of \(y = -3x + 7\):
Slope (\(m\)): ___________
\(y\)-intercept (\(b\)): ___________
Day 3
Graphing the Route
Graph \(y = \frac{2}{3}x - 1\):
0 x y
1. \(y\)-intercept from graph: ________
2. Slope from graph: ________
Day 4
Equation Builder
<table class="w-full text-center border-collapse border border-slate-400 mb-4 text-sm"><tbody><tr class="bg-slate-100"><th class="border p-2">\(x\)</th><td class="border p-2">0</td><td class="border p-2">1</td><td class="border p-2">2</td><td class="border p-2">3</td></tr><tr><th class="border p-2">\(y\)</th><td class="border p-2">4</td><td class="border p-2">6</td><td class="border p-2">8</td><td class="border p-2">10</td></tr></tbody></table>
Write an equation for the table:
\(y =\) ____________________
Day 5
Comparing Courses
Company A: \(y = 5x\). Company B passes through \((0,0)\) and \((2, 12)\). Which rate is greater?
Linear Landscapes Practice Set Linear Landscapes
Practice Set • Week 2
Name:
Date:
Trail Map
Slope (\(m\)) is change in \(y\) over change in \(x\). Proportional lines MUST pass through \((0,0)\).
Section 1: Rate Check
1. Which equation represents a proportional relationship?
A) \(y = 3x + 2\)
B) \(y = \frac{1}{2}x - 4\)
C) \(y = 5x\)
D) \(y = x^2\)
2. A line passes through \((0,0)\) and \((3, 9)\). Its equation is:
A) \(y = 3x\)
B) \(y = \frac{1}{3}x\)
C) \(y = x + 6\)
D) \(y = 9x\)
Section 2: The Ascent
3. Which function has a steeper slope? Justify with calculations.
Function A
\(y = 4x + 10\)
Function B
<table class="w-full text-center border-collapse border border-slate-300 text-xs bg-white"><tbody><tr><th class="border p-1">\(x\)</th><td class="border p-1">0</td><td class="border p-1">2</td></tr><tr><th class="border p-1">\(y\)</th><td class="border p-1">5</td><td class="border p-1">17</td></tr></tbody></table>
Steeper: __________
4. A plumber charges $40 fee + $30 per hour. Write the equation for total cost \(C\) for \(h\) hours. Find cost for 4 hours.
Equation: \(C =\) __________________
Total Cost: $__________
5. Graph a line with slope \(m = -1/2\) and \(y\)-intercept \(b = 3\). Label with equation.
123 123
Equation: \(y =\) ____________________
Linear Landscapes Warm-Ups Answer Key Linear Landscapes
Answer Key • Warm-Ups
Teacher reference
Day 1
UNIT RATE
50 miles per hour
Calculation: 150 miles / 3 hours = 50 mph
Day 2
SLOPE SCOUT
Slope Between (2,5), (4,11):
3
Work: (11 - 5) / (4 - 2) = 6/2
y = -3x + 7:
Slope (m): -3
y-intercept (b): 7
Day 3
GRAPHING ROUTE
y-intercept: -1
Slope: 2/3 (Rise 2, Run 3)
Day 4
EQUATION BUILDER
y = 2x + 4
Check: Starts at 4, increases by 2 each unit.
Day 5
COMPARISON
Company B is faster (6 mph vs 5 mph).
Empire State Math Marathon • Week 2 Linear Landscapes Warm-Ups Key
Linear Landscapes Practice Set Answer Key Linear Landscapes
Answer Key • Practice Set
Teacher Reference
Section 1: Rate Check
1. Proportional Relationship?
C (y = 5x)
2. Origin and (3, 9)?
A (y = 3x)
Section 2: The Ascent
3. Slope Comparison
Function B is steeper (m = 6) than Function A (m = 4).
4. Plumber Word Problem
Equation: C = 30h + 40
Total Cost for 4 hours: $160
5. Graphing Task Check
Checklist for Question 5:
Y-intercept at 3 (Red dot).
Negative slope.
Down 1 unit for every 2 right.
Equation: y = -1/2 x + 3
Empire State Math Marathon • Week 2 Linear Landscapes Practice Key
Function Fuel Warm-Ups Function Fuel
Daily Warm-Ups • Week 3
Name:
Date:
Training Goal
Identify functions from sets of ordered pairs, tables, and graphs. Master linear vs. non-linear patterns.
Day 1
The Function Test
Is this set of ordered pairs a function? Explain.
{(1, 2), (2, 4), (3, 6), (2, 8)}
Day 2
Vertical Line Drill
A
B
Which is a function? Explain:
Day 3
Linear or Non-Linear?
Eq A: \(y = 2x^2 + 5\)
Eq B: \(y = 4x - 1\)
Which is linear? Explain by checking exponents.
Day 4
Output Check
1. Find \(y\) for \(y = 3x - 5\) if \(x = 4\).
2. Find \(y\) for \(y = x^2 + 2\) if \(x = -3\).
Day 5
Function Comparison
Func 1: \(y = 3x + 1\). Func 2 passes through \((0, 4)\) and \((1, 6)\). Greater rate?
Answer: __________
Function Fuel Practice Set Function Fuel
Practice Set • Week 3
Name:
Date:
Fuel Gauge
Functions map each input to exactly ONE output. Linear functions have a constant rate of change.
Section 1: Identification
1. Which set of ordered pairs represents a function?
A) {(1,5), (2,5), (3,5)}
B) {(1,2), (1,3), (1,4)}
C) {(5,1), (5,2), (5,3)}
D) {(0,2), (0,4), (0,6)}
2. Which equation represents a non-linear function?
A) \(y = \frac{x}{4} + 2\)
B) \(y = 3 - 2x\)
C) \(y = x^2 - 1\)
D) \(y = x\)
Section 2: Analysis
3. Complete the table and graph for \(y = -2x + 6\).
\(x\) \(y\) -1 ________ 0 ________ 2 ________ 4 ________
246 246
4. Plan X: $20 flat + $0.05/text. Plan Y: \(y = 0.10x + 10\). Cheaper at 300 texts?
Equation Plan X: \(y =\) __________________
Work:
Cheaper Plan: __________
Function Fuel Warm-Ups Answer Key Function Fuel
Answer Key • Warm-Ups
Teacher Copy
Day 1
Function Test
Not a Function.
Reason: Input 2 has two outputs (4 and 8).
Day 2
Vertical Line Test
Graph B is a function.
Reason: Vertical lines hit B once. Lines would hit circle A twice.
Day 3
Linearity
Equation B is linear.
Reason: x exponent is 1. Equation A is squared (non-linear).
Day 4
Output Check
1. Input 4
y = 7
2. Input -3
y = 11
Day 5
Comparison
Function 1 is greater.
Rates: F1 = 3, F2 = 2.
Empire State Math Marathon • Week 3 Function Fuel Warm-Ups Key
Function Fuel Practice Set Answer Key Function Fuel
Answer Key • Practice Set
Teacher copy
Section 1: Identification
1. Set representing a function?
A
2. Non-linear function equation?
C (y = x² - 1)
Section 2: Analysis
3. Table Completion for y = -2x + 6
Graph Check:
Line should pass through (0, 6) on the y-axis and have a steady downward trend of 2 units for every 1 unit right.
4. Cell Phone Plan Comparison
Part A Equation: y = 0.05x + 20
Part B Answer: Plan X is cheaper.
Supporting Work:
Plan X (300 texts): 0.05(300) + 20 = 15 + 20 = $35
Plan Y (300 texts): 0.10(300) + 10 = 30 + 10 = $40
Empire State Math Marathon • Week 3 Function Fuel Practice Key
Power Play Warm-Ups Power Play
Daily Warm-Ups • Week 4
Name:
Date:
Training Goal
Master integer exponents, square and cube roots, and distinguishing between rational and irrational numbers.
Day 1
Exponent Rules Sprint
1. Simplify: \(4^3 \cdot 4^5\)
2. Simplify: \(\frac{7^{10}}{7^4}\)
Day 2
Negative Power Lift
1. Evaluate: \(5^{-2}\)
2. Simplify: \((x^3)^4\)
Day 3
Roots and Power
1. Solve for \(x\): \(x^2 = 64\)
2. Solve for \(y\): \(y^3 = 27\)
Day 4
Rational vs. Irrational
Circle the irrational numbers. Explain why one of them is irrational.
\(\frac{1}{2}\)
\(\pi\)
\(\sqrt{16}\)
\(\sqrt{2}\)
0.75
\(0.\overline{3}\)
\(\sqrt{10}\)
-5
Day 5
Repeating Decimal Challenge
Convert \(0.\overline{5}\) to a fraction. Show all steps using an equation.
Power Play Practice Set Power Play
Practice Set • Week 4
Name:
Date:
Coach's Playbook
Negative exponents represent the reciprocal. Remember: \(\sqrt{12}\) is between 3 and 4.
Section 1: Multiple Choice
1. Which is equivalent to \(5^2 \cdot 5^{-4}\)?
A) \(5^6\)
B) \(5^{-2}\)
C) \(5^{-8}\)
D) \(25^{-2}\)
2. Solve for \(n\) in the equation \(n^3 = 64\).
A) 4
B) 8
C) 16
D) 21.3
Section 2: Show Your Work
3. Simplify the expression below. Final answer must have only positive exponents.
\( \frac{(2^3)^4}{2^6 \cdot 2^2} \)
Answer: __________
4. Convert \(0.\overline{7}\) into a fraction. Show all steps (setting \(x = 0.777...\)).
Answer: __________
5. Plot \(\sqrt{12}\). Between which two integers does it fall? Justify.
01 23 45 6
Justify: __________________________________________________
Between: ____ & ____
Power Play Warm-Ups Answer Key Power Play
Answer Key • Warm-Ups
Teacher Reference
Day 1
EXPONENT RULES
1. 43 · 45
48
2. 710 / 74
76
Day 2
NEGATIVE POWERS
1. Evaluate 5−2
1/25
2. Simplify (x3)4
x12
Day 3
ROOTS & EQUATIONS
1. x2 = 64
x = ±8
2. y3 = 27
y = 3
Day 4
IRRATIONAL NUMBERS
π, √2, √10
Reason: Non-repeating, non-terminating decimals.
Day 5
REPEATING DECIMALS
5/9
Work: 10x − x = 5.55... − 0.55... → 9x = 5
Empire State Math Marathon • Week 4 Power Play Warm-Ups Key
Power Play Practice Set Answer Key Power Play
Answer Key • Practice Set
TEACHER REFERENCE
Section 1: Multiple Choice
1. Equivalent to 5^2 * 5^-4?
B (5^-2)
2. Solve n^3 = 64?
A (4)
Section 2: Show Your Work
3. Simplify: (2^3)^4 / (2^6 * 2^2)
16 (or 2^4)
Work: 2^12 / 2^8 = 2^4
4. Decimal to Fraction: 0.777...
7/9
Work: 10x - x = 7 -> 9x = 7
5. Plot sqrt(12)
Between 3 and 4
Justification: 3^2 = 9 and 4^2 = 16. Since 12 is between 9 and 16, sqrt(12) is between 3 and 4.
Location: ~3.46 (Slightly before halfway mark).
Empire State Math Marathon • Week 4 Power Play Practice Key
Geometry Gaps Warm-Ups Geometry Gaps
Daily Warm-Ups • Week 5
Name:
Date:
Training Goal
Apply the Pythagorean Theorem (\(a^2 + b^2 = c^2\)) and calculate volume of 3D shapes.
Day 1
Pythagorean Theorem
1. Find \(c\) if \(a = 3\) and \(b = 4\).
34
2. Find \(a\) if \(b = 12\) and \(c = 13\).
Day 2
Cylinder Volume
Cylinder: radius = 5 cm, height = 10 cm. Find Volume (\(\pi \approx 3.14\)).
\(V = \pi r^2 h\)
Day 3
Distance Drills
Find distance between \((1, 2)\) and \((4, 6)\). (Hint: \(a=3, b=4\)).
Day 4
The Cone Connection
Cone: radius = 3 in, height = 6 in. Volume? (\(\pi \approx 3.14\)).
\(V = \frac{1}{3} \pi r^2 h\)
Day 5
Sphere Size
Sphere: radius = 3 ft. Find Volume in terms of \(\pi\).
\(V = \frac{4}{3} \pi r^3\)
Geometry Gaps Practice Set Geometry Gaps
Practice Set • Week 5
Name:
Date:
Blueprint Checklist
Hypotenuse is always across from the right angle. Volume requires radius, not diameter!
Section 1: Quick Stats
1. Which set of side lengths could form a right triangle?
A) 2, 3, 4
B) 5, 12, 13
C) 6, 8, 12
D) 1, 1, 2
2. Cylinder volume is \(100\pi\) units\(^3\). If height = 4, radius is:
A) 5 units
B) 10 units
C) 25 units
D) 20 units
Section 2: Show Your Work
3. A ladder base is 6 ft from a wall and reaches 8 ft up. How long is the ladder?
Answer: __________ ft
4. Find volume of sphere with diameter 12 inches (\(\pi \approx 3.14\)). Round to nearest tenth.
Answer: __________ in\(^3\)
5. Compare Volumes: Cone (\(r=4, h=9\)) vs Cylinder (\(r=4, h=3\)).
Cone:
Cylinder:
Result: __________________________________________________
Geometry Gaps Warm-Ups Answer Key Geometry Gaps
Answer Key • Warm-Ups
Teacher Reference
Day 1
PYTHAGOREAN THEOREM
1. a=3, b=4
c = 5
2. b=12, c=13
a = 5
Day 2
CYLINDER VOLUME
785 cm³ (or 250π)
Calculation: 3.14 × 5² × 10 = 3.14 × 250 = 785
Day 3
Grid Distance
5 units
Legs of triangle are 3 and 4 → Hypotenuse √(3² + 4²) = 5.
Day 4
CONE VOLUME
56.52 in³ (or 18π)
Calculation: (1/3) × 3.14 × 3² × 6 = 2 × 3.14 × 9 = 56.52
Day 5
Sphere Size
36π ft³ (or ~113.04)
Calculation: (4/3) × π × 3³ = 4 × π × 9 = 36π
Empire State Math Marathon • Week 5 Geometry Warm-Ups Key
Geometry Gaps Practice Set Answer Key Geometry Gaps
Answer Key • Practice Set
Teacher Reference
Section 1: Quick Stats
1. Set forming a right triangle?
B (5, 12, 13)
2. Cylinder V=100π, H=4. Radius?
5 units
Section 2: Show Your Work
3. Ladder (6ft from wall, 8ft up wall)
10 feet
Work: 6² + 8² = c² → 36 + 64 = 100 → √100 = 10
4. Sphere Volume (Diameter 12, radius 6)
904.3 in³
Work: V = (4/3) × 3.14 × 6³ → 4.18 × 216 ≈ 904.32
5. Comparison (Cone r=4 h=9 vs Cyl r=4 h=3)
CONE:
(1/3)π · 16 · 9 = 48π cm³
CYLINDER:
π · 16 · 3 = 48π cm³
The volumes are exactly equal.
Empire State Math Marathon • Week 5 Geometry Practice Key
Shape Shifters Warm-Ups Shape Shifters
Daily Warm-Ups • Week 6
Name:
Date:
Training Goal
Master translations, reflections, rotations, and dilations. Congruence vs. Similarity.
Day 1
Translation Slide
\(A(2, -3)\). Translate 4 units left and 5 units up.
\(A'\): ( ____ , ____ )
0
Day 2
Reflection Mirror
Reflect \((4, 5)\) across \(x\)-axis:
\(A'\): ( ____ , ____ )
Reflect \((4, 5)\) across \(y\)-axis:
\(A''\): ( ____ , ____ )
Day 3
Rotation Spin
Rotate \((1, 3)\) \(90^{\circ}\) counter-clockwise. Rule: \((x, y) \to (-y, x)\).
Result: ( ____ , ____ )
Day 4
Dilation Stretch
Vertices: \((0, 0)\), \((2, 4)\), \((6, 0)\). Dilate by \(k = 0.5\).
( ____ , ____ )
( ____ , ____ )
( ____ , ____ )
Day 5
Rigid vs. Non-Rigid
Label as Rigid or Non-Rigid :
1. Translation:
2. Dilation:
3. Rotation:
Shape Shifters Practice Set Shape Shifters
Practice Set • Week 6
Name:
Date:
Observation Deck
Dilations change size but keep shape (similar). Translations, reflections, and rotations preserve size (congruent).
Section 1: The Identity Check
1. Which transformation results in a figure similar but NOT congruent?
A) Reflection
B) Rotation
C) Dilation
D) Translation
2. Rectangle rotated \(180^{\circ}\). Which is true?
A) Area changes
B) Side lengths remain congruent
Section 2: Mapping the Shift
3. Triangle \(PQR\): \(P(-2, 1), Q(-2, 4), R(3, 1)\). Reflect over \(y\)-axis, then translate 3 down.
2424
P'': (____, ____)
Q'': (____, ____)
R'': (____, ____)
4. Describe the specific transformation mapping T1 to T2.
T1T2 123
Description: __________________________________________________
5. Are shapes A and B congruent or similar? Justify.
A: (0,0), (2,0), (0,2)
B: (0,0), (6,0), (0,6)
Shape Shifters Warm-Ups Answer Key Shape Shifters
Answer Key • Warm-Ups
Teacher Copy
Day 1
Translation
A'(-2, 2)
Rule: (x - 4, y + 5)
Day 2
Reflection
Over x-axis:
(4, -5)
Over y-axis:
(-4, 5)
Day 3
Rotation
(-3, 1)
Rule: (x, y) → (-y, x)
Day 4
Dilation
(0, 0), (1, 2), (3, 0)
Rule: Multiply all coordinates by k = 0.5
Day 5
Rigid Check
1. Rigid
2. Non-Rigid
3. Rigid
Empire State Math Marathon • Week 6 Shape Shifters Warm-Ups Key
Shape Shifters Practice Set Answer Key Shape Shifters
Answer Key • Practice Set
Teacher reference
Section 1: Identity Check
1. Transformation resulting in similar NOT congruent?
C (Dilation)
2. Rectangle rotated 180 deg? True statement:
B (Side lengths congruent)
Section 2: Mapping the Shift
3. Triangle PQR Sequence (-2,1), (-2,4), (3,1)
Final: P''(2, -2), Q''(2, 1), R''(-3, -2)
Work: Reflect y-axis -> (2,1), (2,4), (-3,1). Translate 3 down -> subtract 3 from y-coords.
4. Transformation mapping T1 to T2
Dilation with a scale factor of 2 centered at the origin.
Proof: Coords double from (1,1) to (2,2), (1,2) to (2,4), etc.
5. Congruent or Similar?
Similar, but not congruent.
Justification: Shape B is a dilation of Shape A (scale factor 3). All angles are congruent and sides are proportional (6/2 = 3), meeting requirements for similarity.
Empire State Math Marathon • Week 6 Shape Shifters Practice Key
Data Dash Warm-Ups Data Dash
Daily Warm-Ups • Week 7
Name:
Date:
Training Goal
Analyze scatter plots for association patterns and interpret lines of best fit in real-world contexts.
Day 1
Association Identification
1. ____________
2. ____________
3. ____________
Label as Positive, Negative, or No Association.
Day 2
Outlier Alert
Define "outlier" and explain its impact on the line of best fit.
Day 3
Trend Line Context
A line of best fit is y = 3x - 100 (x=height, y=weight). What does the slope of 3 mean?
Day 4
Best Fit Prediction
A line of best fit is y = -0.05x + 12 (x=miles, y=gas). Predict gas after 100 miles.
Day 5
Drawing the Trend
Draw a line of best fit for the scatter plot:
Estimate the y-intercept: ________
Identify the association: ________________
Data Dash Practice Set Data Dash
Practice Set • Week 7
Name:
Date:
Finishing Kick
Scatter plots show trends. Use the y-intercept and slope of the best-fit line to model relationships accurately.
Section 1: Data Patterns
1. As outdoor temperature increases, hot chocolate sales decrease. Association?
A) Positive
B) Negative
C) No Association
D) Non-linear
2. Positive association model with a y-intercept of 5?
A) y = -2x + 5
B) y = 2x + 5
C) y = 5x
D) y = 2x - 5
Section 2: The Final Analysis
3. Construct a scatter plot from the table. Then, draw a line of best fit by eye.
Hours (x) Score (y) 1 60 2 70 3 80 4 90
Study Hours Test Score 0 1 2 3 4 5 0 20 40 60 80 100
4. Predict the score for 6 hours. Explain your reasoning using your trend line.
Prediction: __________
5. Original data starts at y = 12 when x = 0. Which line is a better fit?y = 2x + 10 | Line B: y = 2x + 50
Choice: Line _______
Data Dash Warm-Ups Answer Key Data Dash
Answer Key • Warm-Ups
Teacher Reference
Day 1
ASSOCIATION
1. NEGATIVE
2. POSITIVE
3. NONE
Day 2
OUTLIERS
Outlier Definition:
A data point that falls significantly far from the overall trend. It can "pull" the line of best fit towards itself, making the prediction less accurate for the bulk of the data.
Day 3
SLOPE MEANING
"For every 1-inch increase in height, the predicted weight increases by 3 pounds."
Day 4
PREDICTION
7 gallons
Work: y = -0.05(100) + 12 = -5 + 12 = 7
Day 5
Drawing Trend
Y-Intercept: ~95-100
Association: NEGATIVE
The line should start high on the y-axis and slope downward through the middle of the cluster.
Empire State Math Marathon • Week 7 Data Dash Warm-Ups Key
Data Dash Practice Set Answer Key Data Dash
Answer Key • Practice Set
Teacher Copy
Section 1: Data Patterns
1. Temp vs. hot chocolate sales?
B (Negative)
2. Positive model (y-int 5)?
B (y = 2x + 5)
Section 2: The Final Analysis
3. Scatter Plot / Best Fit Line Thumbnail
Hours (x) Score (y)
Plot Points Check:
(1, 60), (2, 70), (3, 80), (4, 90)
Equation Check:
Straight line through all points. Equation: y = 10x + 50
4. Prediction for 6 Hours
110%
Work: y = 10(6) + 50. Slope of 10 means 10 score points per 1 hour studied.
5. Line Selection (y-int check)
Line A is better fit.
Justification: Data starts near y=12. Line A's intercept of 10 is much closer than Line B's 50.
Empire State Math Marathon • Week 7 Data Dash Practice Key
Championship Milestone Assessment Student Copy Milestone Assessment
RIT RANGE: 221 - 230 • GRADE 6 PROFICIENCY
Athlete:
Date:
Final Qualifying Round
This assessment measures foundational Grade 6 standards. Show your strategies clearly!
1
Ratios and Rates
1. A marathon runner covers 12 miles in 2 hours. At this same constant rate, how many miles will the runner cover in 5 hours?
Total Distance:
2. A pack of 8 headbands costs $12.00. What is the unit price per headband?
A) $0.67
B) $1.25
C) $1.50
D) $4.00
2
Expressions and Equations
3. Evaluate the numerical expression below using the order of operations:
\( 4^2 + (10 \div 2) - 3 \)
Final Value:
4. Solve for \(x\). Show your inverse operation steps below:
\( x + 7.4 = 15.1 \)
\( x = \) ________
3
Geometry and Data
5. Calculate the area of the triangular flag shown below.
12 cm 8 cm
Formula: A = ½bh
Final Area:
6. A training group has athletes with ages: 12, 15, 12, 18, 13. Find the mean age.
Mean Age:
Empire State Math Marathon Milestone Assessment
Championship Milestone Assessment Answer Key Milestone Key
GRADE 6 PROFICIENCY • RIT 221-230
TEACHER KEY
1
Distance Ratio
Work: 12 mi / 2 hrs = 6 mph → 6 × 5 = 30 miles
Final Answer: 30 miles
2
Unit Price
Work: $12.00 / 8 = $1.50 per headband
Final Answer: C ($1.50)
3
Order of Operations
4² + (10 ÷ 2) − 3 → 16 + 5 − 3 = 18
Final Answer: 18
4
Linear Equation
Work: Subtract 7.4 from 15.1 → 15.1 − 7.4 = 7.7
Final Answer: x = 7.7
5
Triangle Area
Work: A = ½ × 12 × 8 = 6 × 8 = 48
Final Answer: 48 cm²
6
Mean Age
Work: Sum = 70. Mean = 70 / 5 = 14
Final Answer: 14 years old
Empire State Math Marathon Milestone Key • Grade 6 Proficiency • RIT 221-230
