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Consecutive Integers
Linear Problems
Objective: Students will be able to solve consecutive integers 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,
…• x, x + 2, x + 4, x + 6, …
– Consecutive even numbers like –4, –2, 0, 2, 4, …• x, x + 2, x + 4, x + 6, …
• The sum of two consecutive even numbers is -14. What are the two numbers.
Read and solve
Step 1:
• Define the unknown.–Let x = 1st consecutive number.–Let x + 2 = 2nd consecutive
number.
Step 2:
• Setup the Equation.–(x) + (x + 2) = -14
Step 3:• Solve the equation.
(x) + (x + 2) = -14
x + x + 2 = -14
2x + 2 = - 14
- 2 - 2
2x = -16
2 2
x = - 8
Step 4
• Answer the question
x = –8
x + 2 =
• Check
–8 + (–6) = –14
-6
Speed, Distance & Time
Speed, Distance, Time Calculations
The aim of this lesson is to be able to use the correct formulas to
calculate speed, distance or time
15 mins = 0•25 hourSo: 3 hours 15 mins = 3•25 hours
30 mins = 0•5 hourSo: 7 hours 30 mins = 7•5 hours
45 mins = 0•75 hourSo: 2 hours 45 mins = 2•75 hours
Reminder: How to change minutes into a decimal
The 3 formulas for Speed, Time & Distance:
Speed = Distance
TimeTime =
Distance
SpeedDistance =Speed x Time
Remember them from
this triangle:
D
S T
Solving for Speed Solving for Time Solving for Distance
D
S T
A windsurfer travelled 28 km in 1 hour 45 mins.
Calculate his speed.
Speed =
DistanceTime
28
1•75=
= 16 km/h
1 hour 45 mins
Answer: His speed was 16 km / hour
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
S TDistance = Speed x Time
= 50 x 2•5
= 125 km
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
S TTime =
DistanceSpeed
55560=
= 9•25 hours
= 9 hours 15 mins
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