Stories to Math

Stories to Math Coverage Packet • Teacher Answer Key Key Page 1 of 5

SECTION 3: FILL IN THE BLANK (PAGE 3) 6 Items

1. Jordan's Account: Blank = 19 ($19).

-12 + 19 = 7

2. Temp Drop: Blank = 5 (\(5^\circ\text{C}\)).

5 - 8 = -3

3. Diver Depth: Blank = 15 (\(15\text{ ft}\)).

-24 + 15 = -9

4. Team Score: Blank = 100 (100 pts).

100 - 150 = -50

5. Company Profit: Q2 Change = +$4,700.

-3500 + 4700 = 1200

6. Desert Canyon: Start = 355 ft.

355 - 420 = -65

SECTION 4: CHOOSE THE EQUATION (PAGE 4) 6 Items

1. Cold Front: Choice B \(t = -7^\circ\text{F}\)

Start at positive 4; dropping 11 means subtracting 11.

2. Debit Card: Choice A \(b = -\$43\)

Start at \(-18\); withdrawing 25 is subtracting 25.

3. Trench Ascent: Choice C \(p = -55\text{ m}\)

Start at \(-90\); climbing 35 means adding \(+35\).

4. Golf Score: Choice A \(s = -1\)

Under par is \(-3\); a bogie adds \(+2\) to the total.

5. Elevator Drop: Choice C \(f = -5\)

Start at \(-2\); going down 3 levels means subtracting 3.

6. Science Lab: Choice C \(T = 6.5^\circ\text{C}\)

Heating increases temperature, so add 22 to \(-15.5\).

SECTION 5: WRITE THE EQUATION YOURSELF (PAGE 5) 6 Items

1. Winter Thaw: Start: \(-9\) | Change: \(+16\)

Eq: \(-9 + 16 = 7\) → Sol: \(7^\circ\text{F}\)

2. Bank Account: Start: \(42\) | Change: \(-65\)

Eq: \(42 - 65 = -23\) → Sol: \(-\$23\)

3. Scuba Diver: Start: \(-28\) | Change: \(-15\)

Eq: \(-28 - 15 = -43\) → Sol: \(-43\text{ ft}\)

4. Board Game: Start: \(-120\) | Change: \(+85\)

Eq: \(-120 + 85 = -35\) → Sol: \(-35\text{ pts}\)

5. Freezer: Start: \(-4.5\) | Change: \(-6.5\)

Eq: \(-4.5 - 6.5 = -11\) → Sol: \(-11^\circ\text{C}\)

6. Balloon: Start: \(450\) | Change: \(-180, +75\)

Eq: \(450 - 180 + 75 = 345\) → Sol: \(345\text{ ft}\)

Stories to Math Coverage Packet • Teacher Answer Key Key Page 2 of 5

SECTION 6: EQUATION + CONTEXT + SOLUTION (PAGE 6) 5 Problems • Rubric: 1pt eq, 1pt calc, 1pt context

1. Bakery Account \(-84.50 + 210.00 = 125.50\) | Solution: \(\$125.50\)

Acceptable Meaning in Context: "The bakery is no longer overdrawn and now has a positive balance of \(\$125.50\) in its bank account."

2. Arctic Weather \(-14 - (5 \times 3) = -29\) | Solution: \(-29^\circ\text{F}\)

Acceptable Meaning in Context: "At 11:00 PM, the outdoor temperature in Fairbanks dropped to \(29^\circ\text{F}\) below zero (\(-29^\circ\text{F}\))."

3. Death Valley Trek \(5475 - (-282) = 5757\) | Solution: \(5,757\text{ ft}\)

Acceptable Meaning in Context: "The team experienced a total elevation increase of \(5,757\) feet from the basin to the viewpoint."

4. Streaming Subscription \(15.00 - (4 \times 6.25) = -10.00\) | Solution: \(-\$10.00\)

Acceptable Meaning in Context: "Mateo has an overdrawn wallet balance and owes \(\$10.00\) (or has a negative balance of \(-\$10.00\))."

5. Fuel Depletion \(12.5 - (4 \times 3.5) = -1.5\) | Solution: \(-1.5\text{ units}\)

Acceptable Meaning in Context: "The airplane exhausted all reserve fuel and is \(1.5\) units below the reserve minimum."

SECTION 7: REVERSE IT — CREATE THE STORY (PAGE 7) 4 Student Items • Sample Responses

Note: Student stories may vary in context (temperature, money, elevation, yardage). Award credit if the starting number, operation, sign, and resulting value all align with the equation.

1. Equation: \(12 - 19 = -7\)

Sample Context: "At noon the temperature was \(12^\circ\text{F}\). A cold front caused the temperature to drop by \(19^\circ\text{F}\). By midnight, the temperature was \(-7^\circ\text{F}\)."

2. Equation: \(-4.5 + 6 = 1.5\)

Sample Context: "Samantha's cafeteria account had a negative balance of \(-\$4.50\). She deposited \(\$6.00\) in cash. Her new balance is \(\$1.50\)."

3. Equation: \(-20 - 15 = -35\)

Sample Context: "A football team lost \(20\) yards on first down. On the next play, they were penalized another \(15\) yards, resulting in a total yardage change of \(-35\) yards."

4. Equation: \(3 \times (-8) = -24\)

Sample Context: "For \(3\) consecutive months, an automatic service charge of \(\$8\) was deducted from a bank account, resulting in a total change of \(-\$24\)."

Stories to Math Coverage Packet • Teacher Answer Key Key Page 3 of 5

SECTION 8: ERROR DETECTIVE (PAGE 8) 4 Cases • Diagnose & Correct

Case 1: Carlos's Bank Account

Mistake: Carlos added \(15\) instead of subtracting it (or adding a negative fee). An overdraft fee increases debt, so it should be subtracted from an already negative balance.

Correct: \(-25 - 15 = -40\) (or \(-25 + (-15) = -40\)). Balance is \(-\$40\).

Case 2: Priya's Temperature Drop

Mistake: Priya treated \(-4 - 9\) as \(9 - 4\) or made a sign error resulting in positive \(5\). Dropping from a negative number moves further left on the number line into greater negatives.

Correct: \(-4 - 9 = -13^\circ\text{C}\).

Case 3: Dev's Context Interpretation

Mistake: Dev calculated the number correctly (\(-70\)) but misinterpreted the negative sign in context, claiming the miner was "above ground level."

Correct: The miner is \(70\) feet below ground level (depth of \(-70\text{ ft}\)).

Case 4: Sarah's Football Field Goal

Mistake: Sarah wrote \(-8 - 15 = -23\), which subtracts the penalty from the end result instead of setting up a start value \(y\) minus \(15\) equals \(-8\).

Correct: \(y - 15 = -8 \implies y = -8 + 15 = 7\text{ yards}\).

SECTION 9: INDEPENDENT CHALLENGE (PAGE 9) 3 Rigorous Multi-Step Problems

1. Mount Washington Weather Station

Equation: \(-18 + (5 \times 3.5) - 22 = T\)

Steps: \(5 \times 3.5 = 17.5\) → \(-18 + 17.5 = -0.5\) → \(-0.5 - 22 = -22.5^\circ\text{F}\).

Sentence: The evening temperature on Mount Washington was \(-22.5^\circ\text{F}\) (\(22.5^\circ\text{F}\) below zero).

2. School Club Ledger

Equation: \(145 - (3 \times 68) + 120 - 35 = B\)

Steps: \(3 \times 68 = 204\) → \(145 - 204 = -59\) → \(-59 + 120 = 61\) → \(61 - 35 = 26\).

Sentence: The club's final account balance is \(\$26.00\).

3. Drone Flight Survey

Equation: \(0 - 135 + 80 - 25 + 110 = E\)

Steps: \(-135 + 80 = -55\) → \(-55 - 25 = -80\) → \(-80 + 110 = +30\text{ ft}\).

Sentence: The drone is currently \(30\) feet above sea level.

Stories to Math Coverage Packet • Teacher Answer Key Key Page 4 of 5

EXIT TICKET ANSWER KEY & REFLECTION (PAGE 10) 5 Total Points

Q1: Diver Equation Match → Choice B (\(-32 + 14 = -18\text{ m}\)).

Q2: Lunch Account Balance

Equation: \(18 - 24.50 = -6.50\) | Solution: \(-\$6.50\)

Context Meaning: "Kai's lunch account is overdrawn by \(\$6.50\) (he owes the cafeteria \(\$6.50\))."

Q3: Story for \(-5 - 8 = -13\)

Sample Context: "The temperature at dawn was \(-5^\circ\text{F}\). By mid-morning, it dropped another \(8^\circ\text{F}\), bringing the temperature to \(-13^\circ\text{F}\)." (Also accept bank debt, submarine depth, golf score).

Today I Learned... (Model Student Responses):

• "When I read a word problem, the first thing I should identify is the starting amount and whether it is positive or negative."
• "One thing I need to pay attention to when writing an equation is the direction of change (whether words like 'drop', 'withdraw', or 'descend' mean subtraction)."

EARLY FINISHER: THE VAULT MYSTERY KEY (PAGE 11) Complete Puzzle Solution

Clue 1 (Anchor) \(-12 - 38 + 15 =\) \(K_1 = -35\)

Clue 2 (Cryo) \(-8.5 - 14.5 + 31 =\) \(K_2 = 8\)

Clue 3 (Debt) \(-64 + 150 - 84 =\) \(K_3 = 2\)

Clue 4 (Order of Ops) \(6 + (-35) + 24 =\) \(K_4 = -5\)

Clue 5 (Lift) \(-14 + 9 - 12 + 23 =\) \(K_5 = 6\)

Clue 6 (Fractions) \(\left(\frac{7}{4}\right) \times (-8) =\) \(K_6 = -14\)

Passcode Decoder Calculations:

Digit 1: \(K_2 - K_5 + 3\) \(8 - 6 + 3 =\) 5

Digit 2: \(|K_4| - 2\) \(|-5| - 2 = 5 - 2 =\) 3

Digit 3: \(K_3 + K_6 + 18\) \(2 + (-14) + 18 =\) 6

Digit 4: \(|K_1| - 31\) \(|-35| - 31 = 35 - 31 =\) 4

Master Vault Passcode: 5 3 6 4

Stories to Math Coverage Packet • Teacher Answer Key Key Page 5 of 5