1. Consecutive Integers Linear Problems Objective: Students will be able to solve consecutive integers problems.

2. Two Cases for Consecutive Numbers Case one: –Consecutive numbers like 4, 5, 6,7, … x, x + 1, x + 2, x + 3, … Case Two: –Consecutive odd numbers like –5, –3, –1, 1, 3, … x, x + 2, x + 4, x + 6, … –Consecutive even numbers like –4, –2, 0, 2, 4, … x, x + 2, x + 4, x + 6, …

3. The sum of two consecutive even numbers is -14. What are the two numbers. Read and solve

4. Step 1: Define the unknown. –Let x = 1st consecutive number. –Let x + 2 = 2 nd consecutive number.

5. Step 2: Setup the Equation. –(x) + (x + 2) = -14

6. Step 3: Solve the equation. (x) + (x + 2) = -14 x + x + 2 = -14 2x + 2 = - 14 - 2 - 2 2x = -16 2 2 x = - 8

7. Step 4 Answer the question x = –8 x + 2 = Check –8 + (–6) = –14 -6

8. Speed, Distance & Time Speed, Distance, Time Calculations

9. The aim of this lesson is to be able to use the correct formulas to calculate speed, distance or time

10. 15 mins = 025 hour So: 3 hours 15 mins = 325 hours 30 mins = 05 hour So: 7 hours 30 mins = 75 hours 45 mins = 075 hour So: 2 hours 45 mins = 275 hours Reminder: How to change minutes into a decimal

11. The 3 formulas for Speed, Time & Distance: Speed = Distance Time Time = Distance Speed Distance =Speed xTime Remember them from this triangle: D ST Solving for SpeedSolving for TimeSolving for Distance

12. D ST A windsurfer travelled 28 km in 1 hour 45 mins. Calculate his speed. Speed = Distance Time 28 175 = = 16 km/h 1 hour 45 mins Answer: His speed was 16 km / hour

13. 2 hour 30 mins Answer: He travelled 125 km A salesman travelled at an average speed of 50 km/h for 2 hours 30 mins. How far did he travel? D ST Distance = Speed x Time = 50 x 25 = 125 km

14. Answer: It took 9 hours 15 minutes A train travelled 555 miles at an average speed of 60 mph. How long did the journey take? D ST Time = Distance Speed 555 60 = = 925 hours= 9 hours 15 mins