Missing whole problems

12 students in Grade 7 play football. If 20% of Grade 7 students play football, how many students are there in Grade 7?

Although this is the difficult missing 100% problem, this question is not much harder with the use of the dual number line to organise the work.
Solution 1. Noticing relationship between 100 and 20



Step 1: Draw the dual number line
Step 2: Notice the × 5 relationship
Step 3: Use on other side
Dual number line: 20% = 12 of ?
Dual number line: 20% = 12 of ?

Dual number line: 20% x 5 = 100%
Dual number line: 20% x 5 = 100%

Dual number line: 5 x 12 = 60
Dual number line: 5 x 12 = 60

There are some students in a class and 12 of them play football.
If 20% of the students in the class play football, how many students
are there in the class?
5 times 20% is 100%
5 times 12 is 60
There are 60 students.

Solution 2. Using proportional reasoning



Step 1: Draw the dual number line
Step 2: Write down the relationship
Step 3: Solve
Dual number line: 20% = 12 of ?
Dual number line: 20% = 12 of ?

Dual number line: 100/20 = x/12
Dual number line: 100/20 = x/12

20% of 12 = 60
20% of 12 = 60

There are some students in a class and 12 of them play football.
If 20% of the students in the class play football, how many students
are there in the class?
100/20 = x/12
100/20 = x/12

x/12 = 100/20
x/12 = 100/20
There are 60 students.
Now have a look at the percentage wheel.

Source:

http://www.education.vic.gov.au/studentlearning/teachingresources/maths/mathscontinuum/number/N55003P.htm