Problem of the Week – June 8, 2010

Grade 1 to 3
#1 Question :
Sally has to be at school at 8:15 am. If it takes her 25 minutes to get ready, 10 minutes to eat breakfast, and 15 minutes to get to school, what time should Sally wake up in the morning to make sure she gets to school on time?

Grade 3 to 5
#2. Question
: Every Friday the students in Mrs. Hull class get a chance to win a homework pass using a spinner. The spinner contains the letters F, I, J, Q, S, and the numbers 2, 6, 9, 11, 15. To win a homework pass a student must spin either a vowel or a prime number. What is the probability of a student winning a homework pass each week?

6 – 8th Grade
#3 Question
: If two monkeys can eat two bananas in two minutes, how many monkeys will it take to eat 18 bananas in six minutes?

Algebra and Higher
#4 Question:
A square has a side length of 8″ . An isosceles right triangle with legs that are 8″ has its vertex at the center of the square. What is the area of overlap of the triangle and the square?

#1 Answer: 7:25 am
Note: We assume that the time that Sally should wake up gives her the minimum amount of time she needs to get ready.
#2. Answer: 3/10 or 30%
#3 Answer: 6 monkeys
Note: Since it takes two monkeys to eat two bananas in two minutes, it takes one money two minutes to eat one banana. So in six minutes one monkey can eat 3 bananas. That means it will take 6 monkeys to eat 18 bananas in six minutes.
#4 Answer: 16 inches2
Note: Because the vertex angle is a right angle at the center of the square the legs of the triangle iintersect adjacent corners of the square. This means the overlap is a fourth of the area of the square. 64 / 4 = 16.

I Demand a Recount!

It’s Math MCAS prep time here at my house and a 4th grader friend of my daughter’s was tackling this problem:

Bar Chart

Bar Chart

The multiple-choice question asks the student to select a reasonable conclusion based on the data above.

The student studied the question, then said, “I don’t like this. It makes boys look bad. I demand a recount!” My initial reaction, as his instructor, is to get him to focus on the question and answer it, not turn it into a debate. I got more flustered when he proceeded to take a pencil and extend the dark bars:

But thankfully, I stopped short to appreciate what’s actually happening. This kid really understands this graph. In fact, he internalizes the data from the graph to the point of getting upset about what it’s saying. That is true understanding. That’s more precious than the ability to pick the right multiple choice answer.

When math becomes relevant, when math makes you mad, when math is more than symbols and digits, when math talks to kids, that’s so awesome!

Guess-and-Check vs. Algebra

I have a 5th and 7th grader.  At the dinner table last night, I asked:  If Tom takes 2 years from his age and gives it to Mary, Mary’s new age is twice Tom’s new age.  If Tom takes 3 years from his age and gives it to Mary, Mary’s new age is three times Tom’s new age.  How old are they?

My husband immediately said, ‘classic algebra’.  The 5th grader went, ‘I don’t know Algebra, I’m going to use Guess and Check’.  My 7th grader has started algebra so he started setting it up with variables T and M.

I just sat there and continued eating my dessert.

Would you know it, the guess-and-checker got the answer first.  The algebra solver plodded along, got a negative answer, changed his setup, rechecked the negative and positive signs and eventually arrived at same answer.

Start doing ‘algebra’-type problems with your kids before they learn algebra.  Simple problems like: Tom has $10 more than Joe.  Together they have $120.  How much does Tom have?  Problems like that prompt non-algebra students to use their number sense.  Ok, $10 is not a lot, so they have close to the same.  Half of $120 is $60.  Let me try $50 for Joe.  Tom has $10 more, that would make it $60.  Total’s only $110.  So Joe must have a little more to  total up to $120.  That kind of mental exercise for your child’s ind is like what going to the gym is for your body.

Here’s another algebra problem a 3rd grader should be able to do: The sum of 2 numbers is 20.  The difference of those same 2 numbers is 10.  What are those 2 numbers?

When your child starts algebra, his math muscles will be primed and ready to use unknown variable to help him do what he has been doing, just a lot more efficiently.  x, the Unknown, will be a very good friend indeed, instead of an intimidating stranger.