How to Help with Math Homework
Many math curricula, such as the Interactive Math Program (IMP) and Connected Math Program (CMP), emphasize problem-solving and do not provide answers in the back of the book or worked out examples. So how are parents supposed to help?
Two Initial Points to Keep in Mind
- Don't panic! You don't have to know the answer to help. Students need to learn how to be good problem solvers, not how to memorize one way of solving a problem. This pamphlet tells how you can help middle and high school students become good problem solvers.
- Be encouraging! Even if you had a bad experience in math class, don't give a student an excuse to quit. Math is not about memorizing rules and procedures. It is about making sense out of the world. Give a consistent message: "I believe in you! You can do it!"
Following guides by William Blatner
The Hows and Whys of Homework for Students
Effort is everything!
All in good time...
There's more than one way to be right!
Show your work!
Keep your work!
Make a time and place to do math every day.
A Sample Problem: The Broken Eggs
A farmer is carying her eggs to market, but she hits a pothole and knocks over all the containers of eggs. Every egg is broken.
She goes to her insturance agent who asks her how many eggs she had. She says she doesn't know but she does remember some things from the various ways she tried packing the eggs.
When she put the eggs in groups of two, she had one egg left over. When she put the eggs in groups of three, she had also had one left over. The same thing happened when she put the eggs in groups of four, five and six. But when she put the eggs in groups of seven, she had complete groups of seven with no eggs left over.
What can the farmer figure out from this information about how many eggs she had? Is there more than one possibility?
From Interactive Mathematics Program Year I, by Fendel, Resek, Alper and Fraser, copyright 1997 by Interactive Mathematics Program.
A sample discussion between a student and parent:
Parent: What is this question asking us to find?
Student: I think we're supposed to figure out how many eggs she had.
Parent: That sounds right to me. What have you tried so far?
Student: Seven has to go evenly into the number of eggs. I tried some multiples of seven, but none of them worked.
Parent: Show me what you tried.
Student: Seven doesn't work because four times one is four and that makes three left over, but there has to be only one left over. Fourteen doesn't work because two goes evenly. There has to be one left over when you use two's. Next is 21. That doesn't work because three goes evenly. This could go on forever.
Parent: Well, let's try a few more and see what happens. What's next after 21?
Student: 28 is next. That won't work because two goes evenly...wait...it has to be an odd number or else two goes evenly.
Parent: Good observation. What's next?
Student: Let's see...28 plus seven is...35. It's odd so two works. What about three?
Parent: How can we tell if three works?
Student: Let's see...three times ten is thirty, three more makes thirty-three - no good. It has two left over. This is impossible.
Parent: Let's not give up yet. What's next?
Student: 35 plus seven is 42. No good - it's even. See, this could go on forever.
Parent: Ok, let's make a list of what we've tried so far and see if that helps.
Student: All right...7, 14, 21, 28, 35, 42...hey, every other one is even. We can skip every other one. Ok, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112. I can cross out the even ones.
Parent: Good. What about 49?
Student: I'm going to use the calculator. 49 divided by 3 is...16.3333. I don't get it. Oh, three isn't supposed to go into 49, it's supposed to go into 48. Sixteen times three is 48. It works for three. Let's see...4 times 10 is 40, 44, 48...so 4 works.
Parent: Does five work?
Student: Five's...I mean multiples of five, always end in zero or five. So to have one left it has to end in one or six. So the number has to end in one or six. what about 56? Wait...that can't work because it's even. So it has to end in one!
Parent: Wow. You're way ahead of me.
Student: The next one to try is 91. I can check if numbers go evenly into one less - 90. Two is ok because it's even. Three times thirty is ninety - that works. What about four? Ninety divided by four is 22.5. No good. What's next? I can use the calculator to add sevens - 91, 98, 105, 112, 119, 126, 133, 140, 147, 154, 161 - 160 divided by three is 53.333 - no good.
Parent: You're going a little fast for me.
Student: What's the next one that ends with a one? ...231. 230 divided by 3 is...76.66...no good. What's next? ...301. 300 divided by three works. 300 divided by four is 75 - that's ok. Five works because it ends with zero. 300 divided by 6 is...50...is that it? Is that the answer?
Parent: Can you check it?
Student: Two, three, four, five and six all have one left over and seven goes...43 times. That's it! I did it!
Parent: Wow, you really narrowed that down. Let's go back and make sure we answered everything.
Student: Oh no! It asks if there are other possibilities!
Parent: Ok, let's get a snack and then think about that one...