Week 1 explained answer key

Teacher reference. Record first attempts before giving explanations. Corrections are separate evidence.

Day 1: Percents in everyday decisions

Retrieval

W1: 0.75. 3 ÷ 4 = 0.75.

W2: 8. 0.10 × 80 = 8.

Guided practice

G1: 9. 0.15 × 60 = 9. You can also add 10% (6) and 5% (3).

G2: 40. The discount is 0.20 × 50 = $10. Subtract: 50 − 10 = $40.

Practice

P1: 30. 0.12 × 250 = 30.

P2: 60. Let w be the whole: 0.30w = 18, so w = 18 ÷ 0.30 = 60.

P3: 15. The $6 increase is compared with $40: 6 ÷ 40 × 100 = 15%.

P4: 25.98. Tax = 24 × 0.0825 = $1.98. Total = $25.98.

Exit ticket

E1: 27. 0.18 × 150 = 27.

E2: 15. The decrease is $12; 12 ÷ 80 × 100 = 15%.

Day 2: Solve and check linear equations

Retrieval

W1: 10. Subtracting a negative adds: 6 + 4 = 10.

W2: 18. 3(4 + 2) = 3 × 6 = 18.

Guided practice

G1: 7. Subtract 5: 3x = 21; divide by 3: x = 7. Check: 3(7) + 5 = 26.

G2: 10. Divide by 2: x − 3 = 7; add 3: x = 10. Check: 2(10 − 3) = 14.

Practice

P1: 5. Add 7 to get 5x = 25; divide by 5. Check: 25 − 7 = 18.

P2: 7. 4x + 8 = 3x + 15, so x + 8 = 15 and x = 7. Both sides equal 36.

P3: 15. Subtract 4: x/3 = 5. Multiply by 3: x = 15. Check: 5 + 4 = 9.

P4: 6. 4 + 2.50m = 19; 2.50m = 15; m = 6 miles.

Exit ticket

E1: 4. Subtract 9: −2x = −8; divide by −2: x = 4. Check: −8 + 9 = 1.

E2: 6. 18 + 6w = 54; 6w = 36; w = 6 weeks.

Day 3: Connect slope, tables, and equations

Retrieval

W1: 2. Slope = (13 − 5)/(6 − 2) = 8/4 = 2.

W2: 7. At x = 0, y = 7, so the y-intercept value is 7.

Guided practice

G1: 3. Slope = (16 − 4)/(5 − 1) = 12/4 = 3.

G2: 13. y = 2(4) + 5 = 13.

Practice

P1: 3. From one row to the next, y increases 6 while x increases 2. The rate is 6/2 = 3.

P2: y = -2x + 7. Substitute m = −2 and b = 7 to obtain y = −2x + 7.

P3: undefined. The change in x is 4 − 4 = 0, so the slope would require dividing by zero. It is undefined.

P4: 26. V = 50 − 3t; at t = 8, V = 50 − 24 = 26 liters.

Exit ticket

E1: -2. Slope = (−3 − 5)/(3 − (−1)) = −8/4 = −2.

E2: 12. The initial charge is the value at h = 0: C = 12 dollars.

Day 4: Build and compare linear models

Retrieval

W1: 18. 12 + 3(2) = 18.

W2: 6. Divide both sides by 5 to get x = 6.

Guided practice

G1: 3. 12 + 3h = 6 + 5h gives 6 = 2h, so h = 3. Both cost $21.

G2: B. A costs 12 + 6 = $18; B costs 6 + 10 = $16. B is cheaper.

Practice

P1: 6. 20 + 4h = 8 + 6h gives 12 = 2h, so h = 6. Both cost $44.

P2: 2. A = $26 and B = $28; the cheaper plan A saves $2.

P3: 6. 5 + 1.50m = 2 + 2m gives 3 = 0.50m, so m = 6. Both cost $14.

P4: 100. 15 + 0.10p = 5 + 0.20p gives 10 = 0.10p, so p = 100. Both cost $25.

Exit ticket

E1: 6. 18 + 2h = 6 + 4h gives 12 = 2h, so h = 6. Both cost $30.

E2: 4. A = $27 and B = $31; the cheaper plan A saves $4.

Day 5: Weekly practice check and corrections

Weekly check

Q1: B. 0.15 × 80 = 12.

Distractors: A: Finds only 10%. C: Uses the percent number as the amount. D: Subtracts the percent amount instead of reporting it.

Q2: C. The savings are $12, leaving 48 − 12 = $36.

Distractors: A: Reports savings, not sale price. B: Subtracts 25 dollars rather than 25%. D: Adds the savings instead of subtracting.

Q3: C. The $10 increase is 10/50 = 20% of the original price.

Distractors: A: Confuses dollar change with percent change. B: Divides by the new price. D: Reports the new price as a percent of the original, not the increase.

Q4: B. Add 7, then divide by 4: x = 7.

Distractors: A: Subtracts 7 instead of adding it. C: Does not consistently isolate x. D: Stops before dividing by 4.

Q5: A. Divide by 3: x + 2 = 8. Subtract 2: x = 6.

Distractors: B: Stops at x + 2 = 8. C: Adds 2 instead of subtracting. D: Subtracts 2 before accounting for the factor of 3.

Q6: B. (19 − 7)/(6 − 2) = 12/4 = 3.

Distractors: A: Reverses rise and run. C: Uses only the change in y. D: Adds the y-values.

Q7: A. The rate is 6/2 = 3 and y = 5 at x = 0, so y = 3x + 5.

Distractors: B: Swaps the rate and initial value. C: Uses the y step without dividing by the x step. D: Omits the initial value.

Q8: C. C = 2(4) + 9 = $17.

Distractors: A: Omits the starting charge. B: Adds the rate to the starting charge without multiplying by hours. D: Multiplies both the rate and starting charge by hours.

Q9: B. 14 + 2h = 4 + 4h gives 10 = 2h, so h = 5. Both cost $24.

Distractors: A: Uses only the difference between hourly rates. C: Uses the sum of starting fees divided by the rate difference. D: Stops at 10 = 2h.

Q10: A. A costs $20; B costs $22. Plan A is cheaper by $2.

Distractors: B: May compare only the starting fees. C: May assume all comparisons are at the crossover. D: The supplied input and both models are enough to compare.