Calculating Area (1512)

I have really been hoping to replace the carpet in my basement for quite some time and I’m debating on spending the money now or not. What does this have to do with math you might ask? EVERYTHING! I have to take the materials and labor into account, along with my monthly family budget.

 

One option would be to replace only the spare bedroom; the other option would be to include the whole basement hallway, family room and bedroom. While trying to figure out if it was a justified expense I first need to calculate the area to be covered. The bedroom is rather small with a closet that should be included.

To determine the area of carpet needed, I first had to decide if my room was a square or rectangle to use the appropriate formulas. I quickly realized that the room is longer than it is wide just be estimation, so I concluded that this room is a rectangle.

The formula to find the area of a rectangle is: Area = length x width 

The formula to find the area of a square is: Area = s x s where s is the length of each side

The measurements of the room are 14 feet long x 12 feet wide = 168 square feet. I also need to have matching carpet in the closet as well or it wouldn’t look too good if we ever decide to sell. The closet is essentially another long skinny rectangle that is 12 feet long and 3 feet wide = 36 feet. The total area needed is 204 feet (36 feet for closet + 168 feet for the main bedroom). You can imagine this as needing 204 of those squares that are 12” x 12” and putting them end-to-end for the whole room. Of course there will need to be some cuts made when they put the closet portion in for the door, so there will be a waste factor that I will include about 10%, or another 20 square feet. The total square footage I would buy is 225.

I shopped around, and for a decent carpet pad underneath and the actual carpet, I’m looking at about $3.50 per square foot x 225 square feet = $787.50 for the entire bedroom. I have a friend who would install it with my husband so it would only cost me the food and beverage while he was there. I know that I could go a cheaper route and spend less on materials, but I’d rather buy something that will last. Unfortunately after doing all of the computations, I think I will just have to shut that bedroom door and pretend like it doesn’t bother me. I’m an unemployed non-traditional student who has a pretty strict budget right now. My accounting background tells me that I should focus my funds on paying off debt and creating a savings until I land that great elementary teaching position in another 3 years!

Here is a link to a website, Math is Fun, that can help with calculating the area of different objects.

I'm in My Prime, How About You? (1510)

Prime Numbers

This is one of those math topics that I honestly don’t use in my daily life, and have likewise forgotten the basics to what makes a number a prime number. I vaguely remembered that 5 and 7 were some of the first ones on the list, but I obviously needed a refresher when looking at the difference between a prime and composite number.

Here is a great interactive game that really gets the heart thumping and brain moving. Prime Shooter requires a person to have a quick reaction time. I found myself at the edge of my seat trying to shoot the prime numbers!

Dictionary.com defines our numbers as follows:

Prime number:

A positive integer that is not divisible without remainder by any integer except itself and 1, with 1 often excluded: For example, the integers 2, 3, 5, and 7 are prime numbers.

Composite Number:

A number that is a multiple of at least two numbers other than itself and 1.

To give a few examples of these types of numbers you can look at the list of numbers 2-10 as the number 1 is only divisible by itself.

2 - This is divisible only by the numbers 1 and 2, so it is a prime number

3 – This is divisible only by the numbers 1 and 3, so it is a prime number

4 – This is divisible by the numbers 1, 2, and 4 so it is a composite number

5 – This is divisible only by the numbers 1 and 5, so it is a prime number

6 – This is divisible by the numbers 1, 2, 3, and 6 so it is a composite number

7 – This is divisible only by the numbers 1 and 7, so it is a prime number

8 – This is divisible by the numbers 1, 2, 4, and 8 so it is a composite number

9 – This is divisible by the numbers 1, 3, and 9 so it is a composite number

10 – This is divisible by the numbers 1, 2, 5, and 10 so it is a composite number

Off of the top of my head, I use a shortcut to decide if a number is prime by seeing if it is an even number, which is obviously divisible by 2. I also think to myself on whether the number is easily divisible by 3, 5, and 7. (This obviously gets a little more difficult as the numbers get higher.) When your brain fails you, it is easy to do a quick search for a table online. I’m including a link that is helpful for this. 

Prime Numbers List

Don't be afraid of the math items that you haven't used for years. Embrace the challenge, do a little research and refresh that part of your brain!

Snowflakes, in July?? (1512)

Abby's first attempt

Abby's Snowflake

My 6 year old daughter asked for help to make snowflakes over the 4^th of July weekend when it was 90 degrees outside! We were on a camping trip and had a little downtime this past weekend, and my artistic daughter wanted to make something fun. We got out her paper and markers and decided to make some snowflakes. I started showing her how the paper needed to be folded from a square, then into a triangle and then another small triangle. She has made them before of course, but it seemed to be a good math lesson for this camping trip. My 4-year-old son was interested too, but he couldn’t quite get the cutting down for such a small area with his little fingers. The first attempt on her own ended up in a piece of paper crumbled into many pieces because she had cut through the edges too far. She soon got the hang of how deep she could cut in, which edges corresponded to the outside and which were the middle of the snowflake. The symmetry when it is done is what she loves the most! She practiced making tiny slits, diamonds, circles and even hearts while cutting through the layers.

Here is a quick video on tips to make the perfect snowflake.

It is never too early to introduce children to the names of shapes and where we find them in our every day life. There also has been many times where we are sitting down with the Magna Doodle and draw shapes and pictures. My son likes to say, “Build a house Mommy”! Obviously in our brains we usually start with the outside square or rectangle, then the triangle for a roof, then the square windows, rectangle vertical door, circle doorknob and any other details we might be imagining at the time. By introducing kids to these images early in life, it puts it in their head to be on the lookout for them. For instance, a sailboat on the lake looks like it has triangles that make up the sail reaching up high above the rest of the boat. If a teacher can get the kids involved with fun projects and they are much more willing to spend the time on learning about math!

 

Standard Devi-what? (1512)

As a “non-traditional” student, it is hard to remember how and when I learned some of the basic information in math class. I might have some visions of a chalkboard and a teacher lecturing, others might have memories of endless sheets of problems to be solved. The methods we learned many years ago might have changed for the current generation of students, and we must adjust and learn how to teach these children.

I have not used standard deviation in years and struggled while recently trying to calculate it. I started with things that I could do well, like calculating the mean of the items. After finding the mean in the set of numbers, I then subtracted the mean from each number in the set. This gave me the deviation of the specific numbers from the mean. The next steps are to square all of those deviations (differences) and add them together and then divide by the count to get the variance. (Is anyone else tired and confused by this point already?) Once you have the variance you are so close!! Keep going!! The standard deviation is computed by taking the square root of the variance.

The standard deviation is a way of knowing what is normal, and what is extra large or extra small. The standard deviation can either be negative or positive depending on whether it is smaller or greater than the mean. It is a difficult concept to understand, to say the least. I could have used this knowledge more this past year when the preschool screeners were trying to tell me where my son was compared to others who had tested. I was quite confused and couldn’t remember the reasoning behind the term and was too afraid to ask in fear of looking like an idiot. I’m glad that I can now understand the concept and inform future parents on the explanations behind the scores they might see.

Here is a website that walks you through the steps to compute the standard deviation.

 Math is Fun

What is a map, and why do I need to know how to read it? (1512)

With our current technology wants/needs and endless electronic devices, will road maps become a thing of the past? When I was reviewing information on proportions and scale drawings I became more interested in this age old concept of how to determine “are we there yet?” that every child will probably ask at some point this summer. Sure, it is easy to look at our Garmin, Tom-Tom or iPhone and read what it has to say, but does that really cause us to think about how far it is?

I can remember as a child opening up the dusty 2 foot high atlas with all of the states listed in alphabetical order and find it quite interesting to see different points within our state, and other states I dreamed about visiting. I’m sure that most elementary students would not know what the little legend words and symbols mean and how to transfer that 1 inch equals 50 miles, for example. Would they know what the list of cities and numbers also means? I loved looking at how many miles Minneapolis was from Brainerd and thinking about how far it really meant by comparing to the miles between St. Cloud and Brainerd.

I don’t remember how we ever got so interested or consumed in just dreaming of things within that atlas, but with 4 kids in the family, there were many times we were fighting over this neat treasure. I hope to continue this with my own children and within the classroom. I think that a teacher would need to adjust things to the age level information that they can follow. For instance, when we drive to Montana next year to see my sister, I will place a big cow on the map near New Salem, North Dakota so they can see it on the map and on the horizon!

Fractions and proportions might seem scary to most of us, but when you look at the relevance it has to our every day life it should seem worth the effort to learn it before reaching for an electronic toy to solve our problems!

Here is a good website that walks through the age appropriate levels with using a map. 

 Teach your child to read a map

Is it a union or intersection? (1510)

I was having some issues with getting my symbols to show up when I pasted from word, so I found a way to embed a pdf file at the link below. So please clink on this information to view my blog, and let me know if you have any great ideas on how to insert symbols for union and intersection of two sets!

Union and Intersect

Here is a YouTube video that also explained the differences quite well.

If-Then (Week 1, 1510)

After a 10-year break from college courses, high school calculus, geometry, algebra and basic elementary math, I'm back at it! What I have realized while diving back into the content is that I remember bits and pieces of the information. I was not able to complete any of the questions without referencing my textbook, at first. I wonder if this is what young children feel like after returning from summer break and staring at their math homework that they had mastered only 90 days prior? 

Part of the difficulty I experienced was due to the terminology being something that I don't use in my every day life. There are not many people I know that analyze a conditional statement for "fun". I have noticed that my 4-year-old son often has troubles with if-then scenarios, but I guess I can't blame him when I struggle at times too! He doesn’t always understand the phrase, “If you go to the bathroom and wash your hands, then we can go to the park.” He immediately rushes out the door without thinking twice about any of the steps in between that might need to happen. Sometimes we just need to stop and think about whether a statement makes sense or whether it has any instances where the answer would disprove the statement.

A friend who was struggling with the terms and explanations related to reasoning mathematically was directed to this link (and shared it with me) and it is a wonderful video to engage anyone who wants to learn about this topic! If-then statements are everywhere and it is nice to have a real world explanation versus a textbook for examples.