Lower Elementary
Question: Together Jeremy, Molly, and Billy have 16 pencils. If Jeremy has 4 pencils and Molly has 9 pencils, how many pencils does Billy have?
Answer: 3 pencils
Solution: Because a part is the whole minus the other parts we subtract the 4 pencils Jeremy has (a part) and the 9 pencils Molly has (another part) from the 16 pencils (the whole).
Whole – a part – another part = the part we’re looking for
16 pencils – 4 pencils – 9 pencils = 3 pencils
Upper Elementary
Question: Emily made 1 dozen chocolate chip cookies. If the recipe calls for ¾ a cup of chocolate chips, how many chocolate chips does she need for 3 dozen cookies?
Answer: 2¼ cups
Solution: A dozen cookies require ¾ cup of chocolate chips, so 3 dozen cookies require 3 half cups of chocolate chips.
¾ + ¾ + ¾ = 9/4 = 2¼ cups
Middle School
Question: A basketball tournament has 11 teams. Every team has to play every other team twice. Then the top 4 teams go on to single elimination play-offs. If you went to every game, how many games will you attend?
Answer: 113 games
Solution: If each of the 11 teams play the other 10 teams once, there will be (11 • 10)/2 games played in order to avoid double counting because team A playing team B = team B playing team A. Since each team plays the other twice, the answer is just 11 • 10 = 110. Lastly, because there are play-offs, 4 teams go against each other. In the semi-finals there are 2 games where the winners play one last time in the finals totaling 3 games. Adding together the 2 parts together we find our answer which is the whole.
110 + 3 = 113
Algebra and Up
Question: In a classroom of students, 17 of the students have brown eyes. 7 of the students have blonde hair, and 9 do not have brown eyes or blonde hair. If 4 of those students are brown-eyed blondes, how many students are in the classroom?
Answer: 29 Students
Solution: While trying to solve this problem keep in mind “wholes and parts.” Looking at the students with brown eyes and/or blonde hair, these students can be separated into parts. 17 students would belong to the brown eyed part, 7 students would belong to the blonde haired part, but 4 students belong to both the brown eyed group and the blonde haired part. So by subtracting those students who have both brown eyes and blonde hair from both parts we see that 13 students in class have brown eyes and not blonde hair and 3 students in class have blonde hair and not brown eyes.
Now by adding all the groups together, including the group that does not have brown eyes or blonde hair we can find how many students are in the class, the whole.
# just brown eyed students + # just blonde students + # brown eyed/blonde hair students + # students with neither blonde hair nor brown eyes = # students are in the class
13 students + 3 Students + 4 Students + 9 Students = 29 Students
A way to model this would be to use Venn Diagrams.
