Getting into Algebra- Relationships between Objects
To get a feel for the idea of mathematical relations between objects, it is helpful to think about actual relationships- relationships between people in a family, for instance. For example, consider a situation where my name is Jen, and my mom's name is Heather. My mom has a sister, Linda, and my mom's sister, Linda, has a daughter, Jackie.
Question: In this case, what is the relationship between me and Jackie?
(Once you’ve tried to work it out yourself, see Answer 1, bottom of page)
To get this answer, you had to think about the relationship between me and my mom, between my mom and her sister, and between my mom's sister and my mom's sister's daughter. Then you had to remember the name that describes 'a person who is my mother's sister's daughter'.
Now, what if I told you that Danny is also my cousin and that Danny is Jackie's brother? Is it possible to use the information I've given you to figure out who Danny's mom is?
Question: Who is Danny's mom?
To answer this question, you need to take all of the information you have been given, and reason from the connections you already know to this new piece of information. This process is called deduction. You can use the strategies discussed in section 3.1 to help you:
Make a diagram or draw a picture
Make a list of facts or known information
Make a table or a chart of know information
Make a list of questions that you want to answer
Make a list of unknowns- facts that you don't yet know.
One way to get to the answer is to reason out loud as follows:
"Okay- I know Danny is Jackie's brother. What else do I know about Jackie. I know that earlier I was told that Jackie is Jen's cousin. That doesn't seem to directly connect to who Danny's mom is though, so I'll put that aside for now. What else do I know? I know that Linda has a daughter, Jackie. Okay, so thinking about it in the other direction, Jackie's mom is Linda. So, Jackie's mom is Linda and Jackie's brother is Danny. Since Jackie and Danny are brother and sister, they have the same mom, so the answer is that Danny's mom is Linda
Another way would be to draw a diagram and use that to help.
Next Question: Refer back to the information at the top of the page. Based on this, what is Linda's relationship to me (Jen)?
(Once you’ve tried to work it out yourself, see Answer 2, bottom of page)
Try writing out your thought process for "What is Linda's relationship to Jen?”
Try writing a diagram or drawing a picture to help you solve the problem.
Answer 1: Jackie is my (Jen's) cousin.
Answer 2: She's my aunt.