Math Awareness Month

I'm getting ready for Math Awareness Month (MAM) by putting together 30 days of every day math. I hope to make these real world examples of math that we are doing on a daily basis. Some of these examples apply to everyone, some are more targeted towards students while others are more "adult" types of math (think taxes!). I tried my best to pull from lots of aspects of life, but I think I found a decent amount of math that I personally deal with on a day to day basis.


Check in on the 1st of April for my first posts and expect new ones to come out every day for Math Awareness Month! It's my goal to get people to realize how much math we are surrounded by, how much we participate in math, and how much we depend on math to live.

Think you aren't good at math? Think you don't like it? Think again! It's everywhere!


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Math Awareness Month is coming!

Did you know that Math Awareness Month has been held in April for the last 24 years? I sure didn't!

Math Awareness Month was started in April 1986 by President Ronald Regean who emphasized that a good math education is crucial for highly skilled professions in the sciences such as "medicine, computer sciences, space exploration, the skilled trades, business, defense, and government." We may forget about how much math we do on a daily basis, but I'm making it my duty to remind you all about how and when we're doing math daily. Suggestions and any ideas are helpful and very appreciated!

This year's Math Awareness Month's theme is Math and Sports! I learned today that a soccer ball is a spherical truncated icosahedron, which has 20 hexagonal sides, and 12 pentagonal sides. Well if a soccer ball is spherical, it doesn't have "sides" but you get what I mean.


Although I don't play sports, I can appreciate the amount of math that goes into sports games. I'll attempt to use my knowledge of math to show you how much math is involved in tennis, basketball, or ice skating. More to come!


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Opposite day?

I like to blame things on the weather because it doesn't make logical sense. I should probably do more research into weather and how it affects human behavior, but the flip flop weather change from yesterday's 65 degrees to today's snow flurries and wind chill are to blame for the odd student behaviors I saw today at tutoring.

In my 5th grade class today, we worked on an assessment work packet with multi-digit division and multiplication problems. The kids were supposed to do most if not all of the work by themselves. After a lot of stalling and seating changes, we finally got down to the work.

As usual, my two more self-motivated students breezed through the packet and only needed to review what factors were. Surprisingly, the other girl in my group wasn't being distracting and worked very hard on her packet. She managed to get ahead of me in our worksheets! Usually it takes a lot of pleading and bargaining to get her to focus enough to work, but she was a superstar today.

My other two students in the group usually have lots of attention issues. The newest addition to our group is very capable of doing work, but he really like distractions and being the distraction for other students in the group. I used a much more serious tone with him today in getting him to stop messing around and to do his work. My last student spent a lot of time goofing off in the beginning of the session and finished last today. It's so frustrating to know that all of these kids are very capable of doing their work, but when put together in a small group, they lose all focus.

On a more positive note: I got a welcome to class hug and teased during my time with the 5th graders.

The 3rd graders were working on patterns, counting color cubes, and deriving an easy way to count certain numbers of cubes. I was working with a few students, but one student in particular just didn't get it. I got pretty frustrated with her, but we slogged through and did our best. One moment she understood and the next she completely regressed and started guessing randomly. I'll work on being more patient next time.

My 3rd grade positive note: the 3rd grade teacher said that I was a big help during math because I could help some of the students while she was focusing on the other students in the class.
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P.S. I finally beat the computer on Ker-Splash! After a few dozen games, I finally won.

x = 7
y = 10

Calculation Nation: 61x + 17y + 15 = 612
Math Rules: 32x + 52y + 39 = 783


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Computer math games

Calculation Nation a website our ED sent to the office. It has eight math games that are pretty challenging. I'd say it's targeted towards middle schoolers because some games involve fractions, factors, multiplication, strategic thinking, and some luck. I've been trying to beat the computer on Ker-Splash, and I haven't even gotten close!

Good luck and may the math be with you!

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Compounded mentoring moments

I guess the school year has gotten into that slump where there isn't anything drastically new to report from my volunteer/tutor sessions, so today I'll be talking about how I've developed mentor relationships that start from "mentoring moments" as our Executive Director calls them.

This came up for a number of reasons. Yesterday I went to an info session about my AmeriCorps program, the Massachusetts Promise Fellowship, a service program that partners with Northeastern University and focuses on serving youth across the Commonwealth of Massachusetts. The Fellow projects range from developing after-school programs, providing educational support, developing youth leadership and work-related skills, training youth workers, to free college financial aid guidance, and other youth related projects.

One of my fellow Fellows asked the question, "After our year of service, how do we let go of our youth?" I almost started crying right then and there because I thought about the youth I had grown to love and care for; having to say goodbye would kill me. It's interesting because there are certain students that I would not (and could not) say goodbye to, while there have been other individuals in my life who did not evoke the same upswell of emotions and tears as these students. Some of these kids I've known for a little over a year, and others I've only met this year. But as a collective, I've really come to enjoy working with and seeing these different groups of kids weekly.

For the new students I've only met this year, it was tough to start off a year not knowing what to expect and knowing very little about their situations that led them to our tutoring partnerships. But as time goes on, we've built relationships slowly from week to week. At first the students were wary of me being in the classroom at all, but I notice a little excitement when I come for tutoring. The students jump out of their seats and say hi to me. The other students I don't work with look towards our group questioningly, and in some cases, they come right over and ask to work with us.

I'm pretty sure it's the consistency that really helps tutoring and mentoring relationships. Sometimes it's a matter of personality matching as well, but for me, I've had good relationships with the students I'm working with. The kids (myself included) really look foward to working together every week on our scheduled day. There was a point where I had to switch my schedule around, and the kids questioned me "Don't you come on X day?" I've also gotten to a place where the students work so well that we have extra time to chat and get to know each other beyond the math, or their schoolwork.

The "mentoring moments" were originally used in the context of the Big Cheese Reads (BCR) program at Boston Partners in Education. The BCR program asks for community, government, corporate, and public figures to come into a middle school classroom and read an inspirational and student relevant short story or excerpt. Afterwards, the Big Cheese Readers talk about their experiences growing up, getting work experience, and how they got to where they are now. The BCReaders also field questions from students taht range from "How do you get an internship?" to "What's your favorite TV show?" The Big Cheese Reads program is a mentoring moment where students are exposed to a life they may not get to glimpse into, and hopefully learn and grow from it.

I've taken the phrase to apply to my weekly meetings with my different students. There are weeks where we don't have a chance to talk about subjects other than math. And there are weeks where the students don't really feel like talking at all. On some level, I don't really feel like a true mentor who guides young people through difficult lifestages and turning points. Sometimes I feel more like just an academic tutor, however, there are those moments when I feel like I've really made a difference, or that I've expanded their world a little bit just by talking frankly about something. I notice these passing moments when it's significant to me, but I wouldn't be surprised if my students have many more of these significant moments when they learn something about me, the world, or themselves.

And to be honest, I don't have enough time to get to know these young people enough. I always want more! Last year, I was fortunate to go to MathSTARS twice a week, but this year I only have time for once a week. If things were up to me, I would go all four days a week. Every week, I only manage to speak one-on-one with a handful of the kids, but it's the little things and the short conversations that add up to make me so darn emotional!

Sometimes I think, "Did I really help these kids today with their work?" but sometimes it doesn't matter so much. It matters that I was there when they were expecting me. At the meeting yesterday, one of my fellow Fellows said that she got an email from a youth she had worked with years before and she didn't realize how much of an impact she had made until she got the email. In the now, it's hard to gauge how much your presence is making a difference, but in the long run, I hope these kids will remember me and our time together. I know I'll look back fondly on this year of service, and the students I worked with.


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Tricky students

Today's volunteer sessions went pretty much the same as usual. My 5th graders worked on division problems. It was asking two ways to divide and I was stumped to help them with their worksheets. The long division or the standard algorithm we got through very quickly. The second way to solve a division problem, we used partial sums to get back to the answer. If anyone has any other solutions for division problems please let me know!

The last part of working with the 5th graders was a pop quiz division question that the students were supposed to do by themselves. I asked the kids to spread out and work on the problems. Two of my students whipped through the problem and two had a very hard time focusing. Once I asked one of the slower students to move, he finished the problem by himself pretty quickly. I think he has trouble focusing when others are distracting him. My last student sat for a long time and didn't work on her problem. When I asked her what's up, she told me "I'm thinking" which is code for "I don't know what I'm doing." She then made up excuses that the other kids knew what they were doing, and that she forgot everything, but when I nudged her and sat down next to her, she got it done. I sometimes wonder if she needs extra attention to be able to work. I know she knows her math, but she doesn't think so and gets distracted, then she distracts the other students.


My 3rd grade students were working on line graphs of different cities and their monthly temperatures. Ms. Ph later commented that the line graphs were too complex to start with, and the workbook has much simpler graphs after this first one. The three students I was working with were a bit behind on their workbooks so I was trying to help them get through the last few pages. A student aid told me not to help one of the students and I got confused - I was there to help that specific student. The student aid later told me that some of the students are tricky and want you to give them the answer instead of making them work for their own answers.

I didn't want to let her know that I already know this trick, and since I started tutoring last year, I haven't given away answers. I've gotten tutor training that has trained me to stop doing the work for the students and leading them towards the right answer by asking follow up questions that get the students to reread the question, firmly understand what the question is asking, and then figuring out how to get the answer.


Please disregard this line graph, it's a joke.
Haha! I'm smarter than 3rd and 5th graders and won't fall for their tricks. I still have to reward/bribe my 5th graders because I owe them from a few weeks back...More updates next week, have a great weekend!

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Student juggling

I managed to work with three different students on Tuesday at MathSTARS and all three students got a significant amount of work done, which is amazing! I don't really know how it happened, but I started on a physics lab with C and we got halfway through before she got bored with it and moved on to other homework.



In the meantime, I switched and worked with V on his math packet. He's a very sharp boy and knows his math fairly well, but he has serious focus issues. We worked through it, I think he's warming up to me pretty well because it took a lot less effort to get him to focus. We also had a very nice and lengthy conversation about tattoos, family, his friends, and his future career (he wants to fix cars and planes and eventually buy a $15 million plane someday).

C came back over and gave me a hard time saying that I had "abandoned-ed" her to work with V. We have an interesting relationship where she teases me endlessly. C and I then worked on her Romeo and Juliet homework which basically meant I sat and watched her do her homework. These kids are so smart that sometimes they just want and need extra attention from the MathSTARS tutors.

The last student I worked with was J. He has consistently had attention difficulties and gives us all a run for our money. It's really hard to get him to focus, and he ended reading National Geographic magazines for the Tuesday session. The afterschool director Ms. D gave him a two question assignment to summarize and explain an article in the NatGeo. He hadn't started writing at all, so Ms. D suggested I write while he dictates. It was somewhat frustrating to get him to sit still and talk to me about the article, but once he got started, it was tough to keep up with him.


Then we played Apples to Apples. It was a good day at MathSTARS.

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Pi Day + 1

Pi day celebrated on 3/14 (sometimes at Pi time at 1:59:26 p.m) celebrates the unique irrational number pi. I remember in grade school celebrating with pies, possibly pizza, and other round foods that embody pi.


A dino comic about pi
Pi is approximated as 3.1415926535..., this website has calculated it to the millionth digit. My calculus teacher in high school had memorized a thousand digits the last time I remember. Why anyone would need to know a thousand digits of pi, I'll never know.


You can search for certain number strings in pi (my birthdate occurs after the millionth digits of pi). And even listen to the pi rap or do Pi day activities.

This article summarizes the superiority and geekiness of pi.


Different types of pi

And I found this somewhere on the internet:

The formula for volume of a cylinder:
V(cylinder) = pi * radius^2 * height

For a pizza of radius "z" and height "a".
V (pizza) = pi zz a

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Vacation week

Apologies for the lack of posts last week, I was on a retreat with the Massachusetts Promise Fellows up in New Hampshire. We had a few trainings, workshops, and lots of Fellow bonding time. I taught a workshop on making eggrolls and managed to smell up the resort hallway for a few days. I also helped teach some Fellows how to ski for the first time. Lots of good fun!

I'll update this afternoon because yesterday was Pi Day; missing it was some sort of math blashphemy, but I hope to make it up to everyone!

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Multiplication approaches

When I started volunteering in my fifth grade class, we had an exercise that says "Solve this equation in two different ways." I panicked because I had ever only learned one way - the standard algorithm for multiplication.


Luckily, I've been working on enough multiplication tables now that I have a variety of ways to solve multiplication problems! It's great, my students have taught me a thing or two. I'll go over some different ways of multiplying that don't require a good knowledge of DDR.

1) Adding
Yes, it's not the preferred method of multiplication at the 5th grade level, but every once in a while, it may work. I would suggest you convince your students that it's not the most efficient way to do multiplication, especially if you're doing anything higher than one digit multiplication.

2) Partial sums
I've touched on this in my Greg Tang posts, but we can work through this method here. I actually really like this method and I think it works well for smaller two digit multiplication.

To do partial sums, you use several "easy" products and sum them all up to get to the answer. In the case of 83 x 24:

83 x 10 = 830
83 x 10 = 830
83 x 4 = 332

830 + 830 + 332 = 1992

Easy, no?

3) The array
I actually really enjoy this method as well. It's a more involved method of partial sums, but the visual aspect of it helps some students more than others.


You set up by making a box and separating the tens and ones. Multiply through and put your answers in the boxes. Then add everything up.


Make sure you get your students to check their zeros when multiplying the tens. Ask them how many zeros you start with and how many are in the answer. It will help with their self checking later on.

So there you have it, four methods to solving a multiplication problem!

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On a side note: leave it to the fifth graders to call me out on my doofy haircut. And I got the most adorable chorus of "Hi Ms. Minh" again when I came into the 3rd grade class. They. are. so. cute. I don't think it'll wear off anytime soon. I hope it doesn't.


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Plus or minus

Yesterday while I was signing myself out for lunch and a quick run to the bank, I noticed that many of my co-workers use the plus or minus sign to indicate an approximation of when they would be coming back to the office. I've always kind of enjoyed the symbol and even considered getting a pretentious plus or minus tattoo somewhere. Luckily for me, I decided against it.


For me, the plus or minus symbol can be used in everyday life as an approximation of time. Back in grade school, the symbol represents possible solutions to algebra equations that can be either negative or positive.

For example the solution to: y = | x | allows solutions of x to be either negative or postive, because of the absolute value function. Another example: 4 = x squared. The solutions for this very simple equation are plus or minus two, because squaring either will give you an answer of positive 4.

The simplicity of the symbol, what it represents, and the way it looks are some of the reasons why I love the plus or minus symbol and mathematical symbols in general.


I searched online to see what kinds of things I would come up with. There are is a myspace group called plus/minus, a techno music forum, and an avant-garde octet from Belgium.

The more interesting links that come up on Google are a decision making tool that I might actually use in the future, and finally the plus or minus game.


Try it out! The plus or minus game is very simple to play, but I have yet to figure out how to win the game consistently. There is a cryptic solution/hint to winning, but I need some more practice to figure out the hint and start winning. I can win with just five digits, but seven is more tough. *edit* I figured it out. I can't mathematically figure it out right now, but I'm so nerdy that I am almost tempted to spend the rest of my day trying to figure it out.


All links and pictures are from Google.

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Greg Tang: Place Values

Part two of the workshop is place values and Greg making us compute in different bases. Place values boiled down are groupings of different size units. Although many students learn about place values in elementary school, we don't spend enough time teaching students to really understand place values enough so when they get to adding and most importantly subtracting, that they understand regrouping or borrowing and why they need to borrow from the next place value.

In the number 43, the 3 represents 3 ones, and the 4 represents 4 tens. Our number system is in base 10, which is also called the decimal system.

Base 10 means grouping place values by 10s. A group of 10 ones can be grouped into one group of tens. A group of 10 tens can be grouped into one group of hundreds, etc. Greg simplified it by saying, 10 is too many, so we group things into groups of ten.

We had to switch to a different base, where place values are different depending on different size groups. We did some exercises in base 5, and changing it back to base 10 where we understand the numbers better. Changing bases helped me understand place value a lot better and even helped me understand enough to be able to explain to my students.

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Even in "real life" math, we do deal with different bases, and a firm understanding of place values. For example, in dealing with time, we have to switch to base 60 to figure out elapsed time. Greg's example was finding the total elapsed time for:

1 hour 45 minutes and 30 seconds
1 hour 19 minutes and 50 seconds

When we're adding up the seconds, you get 80 seconds, but of course, no one would leave 80 seconds in the final answer, you have to regroup for a group of 60 seconds, or one minute, and have the remaining 20 seconds.

With our regrouped minute, we add to 45 minutes and 19 minutes, which equals 65 minutes. Again regrouping into 60 minutes (1 hour) and remaining 5 minutes, we add to the hours place value.

Ending up with:

3 hours 5 minutes and 20 seconds

instead of:

2 hours 64 minutes and 80 seconds

Which mathematically makes sense, but no one in the real world would be comfortable leaving an answer like such. It goes to show that anyone who understand time and time conversions have an understanding of base 60, but very few people talk about changing bases.

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Having a firm understanding of place values is incredibly important for doing fraction and decimal equations.

4 and 5/7ths + 3 and 5/7ths = 7 and 10/7ths, but improper fractions are usually frowned upon, so students have to understand that in this case, 7 is too much and you have to regroup to get a proper fraction. Regrouping the 10/7ths into 1 whole and 3/7ths gets us to the "proper" answer:

4 and 5/7ths + 3 and 5/7ths = 8 and 3/7ths

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Where this comes most handy in most Math Rules! math is subtraction and fractions & decimals. Helping students with regrouping in subtraction can be easier for this problem:

800
-347

Instead of regrouping twice for both zeros, thinking of 80 tens, and 0 ones and regrouping once to get 79 tens and 10 ones. Which is much easier and doesn't involve regrouping twice.

79 tens | 10 ones
- 34 tens | 7 ones

It also works for bigger numbers, to see that
1000
-458

Can also be seen as:

100 tens | 0 ones
-45 tens | 8 ones

And regrouped once to get:

90 tens | 10 ones
-45 tens | 8 ones

Making this problem a lot easier to solve with less work.

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I'm looking forward to the third workshop with Greg because like I said yesterday, it's a revolutionary way (for me) of looking at math problems that will help me help my students. Not only do I feel better at math, I have a firm grasp of number sense and Greg's two main concepts of partial sums and place values which will be useful for working with 3rd - 5th graders.

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Greg Tang math workshop

I got an incredible opportunity to attend a math support session/workshop with children's math book author Greg Tang today. This post is pretty numbers heavy, but if you skip to the end (where the other picture is), I've put in my two cents on the first half of what we covered today.


We started with a refresher course from Greg's 1st session back in December which covered breaking numbers down into partial sums to make addition, subtraction, multiplication, and division easier.

12 - 5 is an example of breaking a number down into partial sums.
12 - 5 can also be seen as
12 - (2 + 3) or
12 - 2 = 10
then 10 - 3 = 7.

Instead of using 5 as a concrete aboslute number, it can be seen differently in different situations. Greg also put up these equations to show this concept:
13 - 6
12 - 6
11 - 6
Sure, the 6 is the same in all cases, but if you conceptually think of 6 as different sums, it makes addition or subtraction much easier.

13 - 3 (10) - 3 = 7
12 - 2 (10) - 4 = 6
11 - 1 (10) - 5 = 5

Greg also said that building on a student's number sense will allow them to apply similar ideas on harder equations. If a student can use partial sums to do 12 - 5, they can apply it to 82 - 5 using the same ideas. Unfortunately, math education is cumulative building off the basics of addition which carries to subtraction. Addition also carries to multiplication. Multiplication then to division.

Another take away point of Greg Tang's workshop are the "easy" numbers to learn. The math world according to Greg says that multiplication should be taught in a different order. Memorization is detrimental because then children don't grasp number sense and what numbers actually represent. If children memorize the multiplication table, they'll only ever be able to do problems that involve 0x0 through 12x12. Developing methods to figure out answers is what Greg taught us. It also will lead to higher level math when factoring comes into the equation (pardon the pun). Students who have memorized the multiplication table don't have an understanding of factors. Factoring 56 becomes a much harder problem when you memorize instead of build from the basics up.

Greg told us children should learn their multiplication facts for the 0s first, then 1s, 10s, and 2s. The zero and one families are self explanatory. The 10s should be taught in terms of place value instead of "the trick to add a zero to the end." 5 x 10 should be thought as five tens. 345 x 10 should be thought as 345 tens. 2s are double what you started with.

Then to 3s, which is a double + one more:
24 x 3 =
double 24 = 48
48 + one more = 72.

4s are two sets of doubles:
15 x 4 =
double 15 = 30
doubled again 60.

5s and 9s depend on a solid understanding of 10s. 5s are really just half of 10s. Easy numbers to halve:
5 x 86 =
10 x 86 = 860
half of 860 = 430

And not so easy numbers to halve:
5 x 39 =
10 x 39 = 390
half of 390 isn't as "off the top of your head", but it can be easier if you see it as 300 + 90
half of 300 = 150
half of 90 = 45
150 + 45 = 195 = 5 x 39

9s are 10 subtracting one:
16 x 9 =
16 x 10 = 160 minus one
160 - 16 =
160 - 10 = 150
150 - 6 = 144
16 x 9 = 144

6s are double groups of 3s.
8s are double groups of 4s.
7s are no fun and make life hard.
But you can still use the idea and use a group of 5 and a group of 2s to get to your answer.

Finally division. Greg noted that division also uses these concepts of breaking down numbers into easier groupings to make math easier:
192 / 16 =
can be seen as 160 (which is an easy group to spot and understand) + 32 (which should also be apparent if you've got a firm understanding of your multiplication groups)
160 / 16 = 10
32 / 16 = 2
10 + 2 = 12
192 / 16 = 12

A not so easy division problem:
128 / 16 =
The process for this one is reducing the division problem. Greg said that teachers encourage students to reduce fractions, but not division problems.
Dividing both by 2 gives you 64 / 8, which is much easier to deal with.


And all of this in about 45 minutes! I apologize for the number heavy post today, but it was so incredible to see math in this way. It's so easy to grasp now as an adult, but I think it's also much easier for children to get a solid understanding of number sense this way.

It's unfortunate when you come in and a student is counting to do his/her multiplication problems. In most situations you don't have time to go back to addition (which is where multiplication really starts) to show them breaking down numbers. I still think there are opportunities for tutors and educators to work these ideas into learning situations. Sure, you can't reteach a student a completely different approach to math, but if your student asks: what's 6 x 8? You can come back with, what's 3 x 8? Can you double that? Isn't six 3 x 2? And if you do it often enough, students will stop depending on multiplication tables and charts that teachers put up in their classrooms and work out these more difficult multiplication problems themselves.

I'll post again tomorrow about the second half of the workshop (yeah, we covered a lot in a very short amount of time) on place values and thinking about grouping in a different way.


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