Consecutive integers
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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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Consecutive integers

Objective: Students will be able to solve consecutive integers problems.

Consecutive Integers

Linear Problems


Two cases for consecutive numbers

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, …


Read and solve

Read and solve

  • The sum of two consecutive even numbers is -14. What are the two numbers.


Step 1

Step 1:

  • Define the unknown.

    • Let x = 1st consecutive number.

    • Let x + 2 = 2nd consecutive number.


Step 2

Step 2:

  • Setup the Equation.

    • (x) + (x + 2) = -14


Step 3

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

Step 4

  • Answer the question

    x = –8

    x + 2 =

  • Check

    –8 + (–6) = –14

-6


Speed distance time

Speed, Distance & Time

Speed, Distance, Time Calculations


Consecutive integers

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


Consecutive integers

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


Consecutive integers

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:


Consecutive integers

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


Consecutive integers

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


Consecutive integers

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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