TCPS Math

I recently asked 6th graders in homeroom to write one word to summarize their year. Some of their words included: different, freedom, enlightening, challenging, exciting, and groovy. I have to agree!

The middle schoolers have already had a chance to think about and solve the following problem. Maybe alumni, parents, or younger students would like to give it a go too. Post your answer and share how you came up with the solution!

This number is the Kaprekar constant, after its discoverer, Dattaraya Kaprekar, an Indian mathematician. Kaprekar was a school teacher in a small town in India, Devlali, yet he discovered many interesting properties in the field of number theory.

So, explore this number. Take any four-digit number (not all digits the same like 1111 and 2222) then construct the greatest and smallest numbers that can be formed from the four-digit number. Repeat the same process with the difference. Repeat this many times. Eventually you will reach the Kaprekar constant.

What is the value of the Kaprekar constant??

Hey Parents-

Here’s an article that might help answer a few questions from the National Council of Teachers of Mathematics (www.nctm.org).

Click here!

Fifth graders have spent the past couple weeks exploring some ideas of geometry and really getting into their work! They have been developing understanding about what area actually is, as well as coming up with efficient ways to find the area of different geometric shapes.

We started by finding the area of different polygons on geoboards and then creating our own polygons given a specific area.

Alek LOVES geoboards!

Sammy shows off his creative way to make 6 square units.

We also explored the area of rectangles, squares, parallelograms, and triangles. Students created their own understanding by using graph paper to discover different ways to form area.

Max and Sammy's parallelogram turns into a rectangle!

Sophie and Greer match up partial square units to make whole ones.

They justified their strategies to the class and discussed efficient ways to find the area of any type of shape. As a class, students discovered the formula for area of squares, rectangles, and parallelograms. Next up…triangles!

This question was posed on the March Math Olympiad for 5th and 6th graders. Can you figure it out?? Leave  a comment with your strategy!

A toll bridge charges $4 for a car and $6 for a truck. One day 200 of these vehicles crossed the bridge and paid a total of $860 in tolls. How many of these vehicles were trucks?

Allie, 6th grade, shows off her geometry skills.

Go Allie!!

Coming soon to a math room near you…

PI Day!!!

π is the symbol for the ratio of the circumference of a circle to its diameter. Pi = 3.1415926535… Pi Day is celebrated by math enthusiasts around the world on 3/14. TCPS 7^th grade math enthusiasts will be celebrating this week on Tuesday.

Update:

This is what one student, Nathan, said about our celebration…

“Today in math class, we did many educational, interesting, and fun activities relating to pi, 3.14159265 and so forth. On top of eating circular treats and trying to memorize pi to the best of our abilities, we also learned all about pi and its importance to mathematics and circles. Pi is the number of times the diameter of any given circle can fit in the measure of the circle’s circumference. The amount of times is always 3 and a little bit more, hence 3.14159265 etc. This is so important because without it we wouldn’t be able to find circles’ circumferences or areas or really any complex information about a circle.”

Recently, 7th graders brought a lesson to life when learning about similar figures. We went outside armed with yard sticks to determine the height of the tether ball pole.

Students were unable to measure the pole but instead had to use the known height of a classmate and the shadows of the pole and the classmate.

Because the shadows created were proportional, students were able to work together to find the missing height of the tether ball pole…about 9 feet!

Well done, 7th graders!

How few times can you weigh 9 identical cookies on a balance scale to find the one with a gold ring inside?

In a recent Algebra lesson, 8th graders had the opportunity to solve a real-world problem faced by an architectural engineer at a firm in Ohio. Students were given office blueprints along with an actual email saying:

“I did notice that the ramp to the raised computer room floor is shown to be 4′ long with a 1:12 slope. It was my understanding that the raised floor was 6″ high. The slope given dictates a 4″ raised floor.”

Students then worked to understand why the slope given dictated a 4″ floor, and had to problem solve to create a solution that would work for the company, just like the actual engineer. Some worked to create a model of the floor and ramp, while others drew a scale drawing to aid in planning.

The class discovered that with a 4′ ramp, moving up 1″ and over 12″, given that slope, only allowed for raising up 4″ and over 48″ total. They decided they needed to move up 6″, over 48″ to reach the raised floor, making the slope 6:48 or 1:8.

As a check, students applied the Pythagorean Theorem to ensure the 4′ ramp would still fit with that slope. They saw that the ramp would need to be just over 4′ long. Well done 8th grade!!