Category Archives: math problems

Horse Math Problem: Solved!

This problem recently went viral.

horses

My first reaction was “Hooray! Another math problem went viral.” But beyond that I found it really interesting to troll through the thousands of comments. And this problem illustrates an important issue. People were all able to correctly figure out what a horse, pair of boots, and horseshoe had to equal. Their mistake came when they substituted in the last step.

Horse=10

Pair of Horseshoes=4

One Horseshoe=2

Pair of boots=2

One boot=1

So what does 1 + 10 x  2 equal?

21

Why? Because you multiply first and then add. PEMDAS, or the order of operations guides us hear. So it is not a matter of opinion or debate. In math we have a prescribed way of doing things just so we can avoid massive internet confusion like what we have witnessed with this problem.

MATHCOUNTS Problem of the Week

Lately I’ve been doing a lot of research on prealgebra. Most of us don’t think about it as much as the high school math subjects but I’m starting to think a strong foundation in the content covered in prealgebra would eliminate so much of the stress many students experience in high school.

MATHCOUNTS is a middle school math competition that produces lots of great resources if you’re working on prealgebra concepts. One that I recently discovered is their problem of the week. Here is this week’s problem:

MATHCOUNTS

So many great skills are covered here. It is a great resource for a co-op or as a supplement. I’d try doing them on Fridays with your 7th or 8th grader.

Probability and Punxsutawney Phil

From the archives…

Here are a few math problems to keep your math skills warmed up on this cold February 2nd 🙂

groundhog

1. A groundhog is a true hibernator. When it hibernates, its heart rate can drop from seventy-five beats per minute to five beats per minute. In four hours, how many fewer heartbeats will a hibernating groundhog have than a groundhog not hibernating?

2.When Phil came out of his burrow in 1971, it was negative fourteen degrees Fahrenheit. If the temperature this year is thirty-five degrees Fahrenheit, how much warmer will it be than it was in 1971?

3. If Punxsutawney Phil sees his shadow on the first Monday in February, then legend says that winter will last 6 more weeks. In 118 years, Phil has seen his shadow 104 times. (a) What is the probability that Phil will see his shadow on a randomly chosen Groundhog Day? (b) What kind of probability is this?

The answers are here.

 

*Problems 1 and 2 taken from edhelper

*Problem 3 taken from algebra.com

Photo Credit: PoliticsPA

Problem Solving in Algebra 1

In my Algebra 1 class problem solving is a main emphasis. Each week the students have a special problem to complete on Fridays. It normally involves several steps and some creative thinking. Here is one from last week:

sample POW

This problem was taken from Drexel University’s problems of the week.

When students respond their written explanation is just as important as the mathematical methods they used. Here is an excellent response I received last week:

First I made t = time in hours that has passed by since 8:15 { so at 8:15, t=0} 
then I have
(0,50) and (1.5, 62) 

for (time, temperature in Fahrenheit). Forming a linear equation here. I first had to determine the slope. That will be 
m = (62 – 50) / (1.5 – 0) 
m = 8 

Since the y-intercept (50), then I wrote the linear equation through slope-intercept form. I came up with
y = mx + b 

I replaced y with F for temperature in Fahrenheit, and x with t for time and ended up with

F = 8t + 50 

in order to answer the second question I did this

104 = 8t + 50 
54 = 8t 
t = 6.75 hrs 

6.75 hrs after 8:15AM is 3PM. 

At 5PM, t=8.75. Thus 

F = 8(8.75) + 50 
F = 70 + 50 
F = 120 

So by 5PM, the water in the tub will have a temperature of 120 degrees F. 

The water in the tub won’t be heated in a linear fashion. It will be heated in a logarithmic fashion. Because the wood-burning stove has a maximum temperature, then eventually the water can only be heated until that temperature. If  i assumed that the water follows a linear trend, then it can go beyond the wood-burning stove’s maximum temperature. Another reason why it cannot follow a linear trend is that the particles would begin to heat faster during the first few moments, but eventually slowdown in heating up.

Look all the excellent vocabulary that was included and how clearly you can follow each step. Being able to explain a problem like that in writing means a student fully understands the concepts.

Squaring Off

Can you create a square that is exactly 5 square inches in area? This activity will show you how.

Gather a ruler, a piece of paper, a pair of scissors, and something to write with.

squaring off 1

Use the ruler to draw 5 squares in a row that are 1 in by 1 in.

IMG_0440

Cut them out.

IMG_0441

Cut off two squares and draw a line diagonally across them.

IMG_0443

Do this again with a second pair of squares. Cut along the diagonals so that you have 1 square and 4 triangles.

IMG_0446

Using these five shapes see if you can create a square. I’ll post the answer in a few days 🙂 You can also leave your answer in the comments.

The idea for this came from Shapes in Math, Science and Nature.

Tricky SAT Problem

tricky SAT problem

This problem from Khan Academy earned my respect this morning. Although the numbers and math are quite simple it contains several details that might trip you up. First they wrote the binomials with the constant first and then the variable which always kind of annoys me (and sometimes leads to me making mistakes!).

Why does x+2 look so much better than 2+x?  I don’t know but whenever I see it written the second way I tell myself to slow down and proceed with caution. That is of course after I sigh and wonder why’d they have to write it like that?

Next, they’ve mixed order of operations and polynomials. Do I FOIL or subtract first?

And then there is that pesky subtraction sign to be distributed…so many math students have died in that battle 🙂

Finally, the answer choices are written differently than the question. So when you finish you have to see if you can rearrange your answer to match theirs.

Phew! Not bad for a practice problem.

Post your answers and explanations below 🙂

Varsity Math Revisited

This week my algebra students are going to be tacking some of the Varsity Math problems from the weekend edition of the Wall Street Journal. The problems are a great resource for building your problem solving skills and they are sponsored by the Museum of Mathematics. Here’s an engaging video that walks your through one of the easier problems. The idea is to work your way up to playing on varsity.

Codes

We’ve been working on problem solving skills in my algebra 1 class and lately that has meant creating and breaking codes. One of my students created this one and it was trickier than I expected.  Give it a try and post your comment below.

Using these 4 equation can you find x and y? In class we also did this where instead of variables we solved for shapes or even the operations themselves.

james code