Large Numbers and Famous Paintings

I was having an interesting discussion with a few teachers about getting students to understand the value of large numbers. At 3rd grade, any number beyond 4 digits becomes an exercise in abstract art. They have tens, hundreds, and thousands pretty well, but really haven't had a lot of experience with more and unless you can count it, even by 100,000's, you really can't quantify it.

I began to think about my own experiences with this. My family played a lot of board games when we were youngsters and one I remember vividly was called "Masterpiece". It was a game that involved selling and buying famous paintings. There would be auctions where you could purchase paintings, hoping to secure the one worth $1,000,000. Some were worth as little as $150,000, some more. The money came in denominations of $50,000/$100,000/$500,00 and $1,000,000. We had to make change and I think this is where I became familiar with 5 and 6-digit numbers-easily, without thinking about it.

Many fond memories of buying and selling famous paintings

It was that great juxtaposition where math meets necessity. It is what we try to give children in the classroom. Effortlessly using math to do, to create, to solve, to communicate, to advance.

Not only did I gain experience with large numbers, but who can forget Edward Hopper's Night Hawks, Edgar Degas' The Dance Class, or Grant Wood's American Gothic?

The "What is and What Isn't" Game

I recently chatted with a college math professor. He mentioned that there was one thing elementary teachers could do that would help secondary teachers out tremendously. My ears perked up and I waited in anticipation to what we could do better, faster, higher, or harder  to help our students prepare for college.

It turns out, that in a standardized math test given to secondary students, one question that many students "bombed" was a quite simple question about pentagons. When shown many different examples of pentagons, students were asked to identify which ones were, indeed, pentagons. So many students answered incorrectly that it came to the attention of college professors.

It would seem that somewhere along the line, students learned that a pentagon has five sides and looks like a house. Relying on a past visual experience, students began to correlate a pentagon to a familiar shape instead of using the properties of a pentagon to identify it.

A 3rd grade activity I use to make sure students are focusing on the properties of shapes and not just the memorizing the visual picture.

Obviously we need to spend more time and bring out more examples while focusing on the properties of these shapes, but it got me to think about other instances in which students need more exposure to concepts and properties so they can reason more effectively.

This was the beginning of the "What is and What Isn't" game we do in the classroom. I have extended it beyond geometric shapes. Here are some areas that students have to identify and explain their thinking:

"What is and What Isn't" an improper fraction?
"What is and What Isn't" a mixed number?
"What is and What Isn't" an obtuse/acute/right angle?
"What is and What Isn't" a ruler?
"What is and What Isn't" a quadrilateral?
"What is and What Isn't" a 2-D and 3-D shape?
"What is and What Isn't" subtraction and multiplications strategies that work?
"What is and What Isn't" an equivalent fraction?
 

A Rich Problem For Third Graders

8 pieces

8 pieces

4 pieces

Last week I wrote a story problem on the board for morning work. I am always looking for ways to stretch my students' thinking, to develop their conceptual knowledge and to get them actively problem solving as much as possible.

The problem read like this: Henry had 4 pizzas. They were all the same size. He cut each one into eight pieces. He ate 20 pieces. How much of the four pizzas did he eat?

Students dutifully drew the pizzas out and divided them into eighths. They carefully shaded in 2 pizzas (16 pieces) and 4 pieces of the next pizza.

Here is where is got interesting. When asked how much of the four pizzas Henry ate, a student answered: 2 1/2. Another student answered 20/32.

Students began to look at me with the "O.K. so what is the right answer?" look. This was tricky, since the question wasn't how much pizza did Henry eat (2 1/2) but how much of the total pizza did he eat?

I wanted students to do the math thinking and to really use everything they knew about fractions to help them understand the different answers and the difference between the two questions.

We made some assumptions "Yes, there are 2 1/2 pizzas shaded in. Yes, Henry started with 4 pizzas, or 32 pieces. Yes, the question is asking how much of the all four pizzas did he eat."

I began asking questions. When we want to show the fraction of something shaded in, what does the denominator represent?  Lets do that. I also stopped at this point and drew 4 rectangles side by side, divided into eighths. I shaded in 20 parts. We formulated a fraction for this picture. We went back to the pizza problem.
Suddenly a light bulb went on: A student raised her hand. "OHHHHHHH, when we said 2 1/2, we were only looking at the pizzas shaded in. We didn't count the unshaded pizza.

We went on to have a great discussion about what the question was really asking. These opportunities for rich discussions don't come up every day, but I love it when they happen!

New Toy

A new I-Pad. Yippee! It is almost permanently glued to my hand by now. What a fun toy. Just another example of how the tech world anticipates our "needs" before we realize what they are.

I'm always on the lookout for new apps that would benefit students and teachers. I really like the app Little Monkey Apps. There are different modules that include: place value, teaching graphs, missing numbers, fractions, coordinates, mystery number, number lines, early division, ten frames and subitizing. They cost money but may be worth it if you use the I-Pad for centers.

 

Mine is white and silver



Summer Review

I can already feel summer coming on in spite of the cool, wet days we have been having lately in the Northwest. Once spring break is done with, it seems like we arrive back to school ready for the final "home stretch" before testing. Once testing is done, it's not long before the final day arrives and the classroom empties out for the last time.

But not so fast.... what about those students you worry about? You know - the ones that struggle throughout the year, and finally get it (tentatively). Then summer comes and they enter the world of I'M PLAYING AND SPENDING TIME WITH MY FAMILY AND I'M NOT THINKING ABOUT SCHOOL, OR THINGS LIKE MULTIPLICATION, HOW TO FIND AREA, OR THE ATTRIBUTES OF A TRAPEZOID.

With the new Common Core standards, we just don't have time to spend the first 4 weeks in Sept reviewing.  It's pretty much hang onto your hats and go!

A couple of parents requested some resources that they could spend time with their children at home over summer break so I decided to put together a "fun" book of most things learned in 3rd grade math. I designed the pages to take 20 minutes a day and to be visually pleasing. Here is a finished pic.

Something New For Spring

My husband and I were celebrating our anniversary at the Skamania Lodge in the Columbia Gorge last weekend. We were enjoying the view when suddenly my cell phone started making noises. A lot of noises. I was curious and checked it. I saw about 8 notices that I had feedback for a "freebie" product I have on Teachers Pay Teachers. Wow! I realized at that moment I had made it into the weekly newsletter and many people were downloading it and leaving feedback.

A week later, and 15,000 people (yes, that is fifteen thousand) have downloaded it. It was a wake-up call for me about the power of the Internet. I was very energized to start working on a follow-up product for 2nd grade since so many teachers had commented that they really needed activities that reinforce number sense and place value.

I just posted my latest series of 4 activities that will get students playing, learning and becoming adept with numbers.

Racing Into Spring
Link to Racing Into Spring on Teachers Pay Teachers

What I Look Like By Friday Afternoon

Looking at my class on Friday afternoon and trying to figure out why they didn't do well on the measurement test.


 

Well, it is Friday afternoon. I quickly corrected the measurement test that had my students using a ruler to measure lines to the nearest quarter inch, drawing lines, and using a pre-printed ruler to determine length. The other half of the test was converting inches, feet and yards. It wasn't what my son would call an Epic Fail, but it was close.

Somehow, I thought by teaching measurement right after fractions, students would make the obvious connection of dividing an inch into four equal sections and being able to label and name them. Wrong! They just didn't seem to make the jump and connect the two concepts. When the line measured 2 and a half inches, they wrote down one half. When the line started at 1 inch and ended at 3 inches, they wrote that the line was 3 inches long. Uggghh.

I've decided that I need to add a separate unit to my fractions unit that is called "Beyond One, Improper Fractions". Hopefully, that will better prepare students for using a ruler, which I feel is truly a valuable skill to have as they will be using a ruler, tape measure,  the rest of their lives.

We will be revisiting measuring with a ruler in the near future!

Just Don't Do It!

Just returned from a timely conference. We spent a whole day discussing Common Core Math and sequencing learning for children in elementary mathematics instruction. One issue being discussed caught my attention since it has been a thorny, ongoing "problem" at our school. Subtraction with re-grouping. Need I say more? Second grade teachers would teach it. Students wouldn't be able to do it in third grade. Third grade teachers would teach it. Students wouldn't be able to do it. Fourth grade teachers would teach it and so on.

What is going on here? Why weren't our children learning to subtract? The concept didn't seem that difficult. The regrouping seemed insurmountable. What's up?

One thing suggested was that first grade teachers  not teach double digit subraction at all. Leave subtraction to second grade. That way, students can start with an understanding that students are taking a group away from another group. Their strategy was to circle the top number, regroup every column where needed and then subtract (at this point, students can move left to right or right to left).
Also important was the use of counter, or manipulatives to reinforce the concept of subtaction and place value. This makes sense and hopefully will avoid students subtracting the smaller number from the larger number, no matter where is lies.

So, first grade teachers, Just Don't Do It!

                                                                 

Remember the Candy Bar?

Today was "kick-off" day for fractions. Yahoo! It is probably one of my favorite days in math since I know we are embarking on a six to eight week trip learning all there is to know (in third grade) about fractions. We start off with a bang - that is ... a chocolate bang.

I pass out a notecard to each student. I show them a stack of Hershey's candy bars and tell them they get to "order" the size they want. They get very excited and the anticipation is like static electricity. They can almost taste the chocolate already! This is a rare treat since I don't believe in giving students any kind of candy as a reward. However, the benefits of this one activity outweigh the cons.

I write two fractions on the board- 1/12 and 1/4. I tell them they must write one down without sharing with their neighbor. Hersheys are already divided into 12 mini squares, or you can break them into 4 larger squares. I go around the room and hold up each piece requested before I set them on the card and read off the fraction.

When the realization hits, there are many ohhhs and ahhhs. Some students are grinning and some look quite unhappy. As they eat, we talk about what 1/12 and 1/4 mean as far as the numerator and the denominator. We also talk about the fact that fractions are kind of backwards, the larger the denominator, the smaller the fraction, or piece is. This is an experience we will refer back to over the next six to eight weeks.

We began a discussion about 1/3 and 1/6. When talking about the size of  each piece, a student became confused. Another another student suddenly chirped, "Well, would you rather have a piece of candy bar cut into three pieces, or one cut into six pieces?" Suddely everyone nodded in agreement.


Materials I will be using to teach and assess this unit:Fraction Frenzy and 3rd Grade Common Core Fractions Assessment