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Consecutive Integers

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

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Consecutive Integers

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  1. Objective: Students will be able to solve consecutive integers problems. Consecutive Integers Linear 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. Read and solve • The sum of two consecutive even numbers is -14. What are the two numbers.

  4. Step 1: • Define the unknown. • Let x = 1st consecutive number. • Let x + 2 = 2nd 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. Reminder: How to change minutes into a decimal 15 mins = 0•25 hour So: 3 hours 15 mins = 3•25hours 30 mins = 0•5 hour So: 7 hours 30 mins = 7•5hours 45 mins = 0•75 hour So: 2 hours 45 mins = 2•75hours

  11. Distance Distance = Speed x Time Speed = Time Distance Time = Speed D S T The 3 formulas for Speed, Time & Distance: Solving for Speed Solving for Time Solving for Distance Remember them from this triangle:

  12. Distance Time 28 = 1•75 D S T A windsurfer travelled 28 km in 1 hour 45 mins. Calculate his speed. Speed = 1 hour 45 mins = 16 km/h Answer: His speed was 16 km / hour

  13. D S T A salesman travelled at an average speed of 50 km/h for 2 hours 30 mins. How far did he travel? Distance = Speed x Time = 50 x 2•5 2 hour 30 mins = 125 km Answer: He travelled 125 km

  14. Distance Speed 555 = 60 D S T A train travelled 555 miles at an average speed of 60 mph. How long did the journey take? Time = = 9•25 hours = 9 hours 15 mins Answer: It took 9 hours 15 minutes

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