Missing part problems

There are 60 students in Grade 7 and 20% play football. How many students play football?

Solution 1. Unitary method – finding 1% first
Step 1: Draw the dual number line
Step 2: Find 1%
Step 3: Find 20%
Dual number line: 20% = ? of 60
Dual number line: 20% = ? of 60

Dual number line: find 1% of 60
Dual number line: find 1% of 60

Dual number line: Find 20% of 60
Dual number line: Find 20% of 60

There are 60 students and 20% play football.
How many students play football?
1% is 0.6 students
20% is 20 × 0.6 = 12
There are 12 students who play football
NOTE: A variation, particularly useful in this case, is to find 10% first and then find 20%.

Solution 2. Noticing 100 = 5 × 20




Step 1: Draw the dual number line
Step 2: Notice link between percents
Step 3: Use link on quantities
Dual number line: 20% = ? of 60
Dual number line: 20% = ? of 60

Dual number line: One fifth of 100% = 20%
Dual number line: One fifth of 100% = 20%

Dual number line: One fifth of 60 is 12
Dual number line: One fifth of 60 is 12


One fifth of 100% is 20%
One fifth of 60 is 12
There are 12 students
who play football


Solution 3. Using the ratio between 100 and 60



Step 1: Draw the dual number line
Step 2: Notice link from percent to quantity
Step 3: Use link from percent to quantity
Dual number line: 20% = ? of 60
Dual number line: 20% = ? of 60

Dual number line: 6/10 of 100 = 60
Dual number line: 6/10 of 100 = 60

Dual number line: 6/10 of 20 = 12
Dual number line: 6/10 of 20 = 12

There are 60 students and 20% are play football. How many students play football?
60% of 100 = 60
60% of 100 = 60

6/10 of 20 = 12
6/10 of 20 = 12

There are 12 students who play football

Solution 4. Identifying equivalent proportions



Step 1: Draw the dual number line
Step 2: State that both sides ofthe line are in the same proportion
Step 3: Solve algebraically
Dual number line: 20% = ? of 60
Dual number line: 20% = ? of 60

Dual number line: 20/100 = x/60
Dual number line: 20/100 = x/60

Dual number line: 20/100 = x/60
Dual number line: 20/100 = x/60

There are 60 students, and 20% play football. How many
students play football?
20/100 = x/60
20/100 = x/60

20/100 = x/60
20/100 = x/60

There are 12 students who play football



Now go to
Dual number lines - missing whole problems


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