Homework With Meaning!

You may enlarge the thumbnail image by clicking on it.

These two homework problems may seem too easy for a 5th grade student, but on examination of the thinking displayed, it is clear that a deep understanding of important concepts, like place value, are well understood by this student.

The first problem was quickly identified as a "subtraction" problem, but it was solved using simple addition. This young mathematician added up from 267 to 323 on an open number line. This is kind of like what folks did in the good old days before cash registers had built in electronic calculators. They would count back the change using landmarks along the way. This student also used landmarks (easily recognized and "easy to work with numbers"), as she first "jumped from 267 to 270. This allowed her to easily add on to 270 in order to get to 300. From 300, the jump to 323 was a piece of cake. Finally, all of the jumps were totalled, and the distance between $267 and $323 was found correctly.

Also of note are the sentence restating the prompt (question) and the matching equation, These also signify a real sense of math understanding.

On the second problem, the student added from left to right, and to me that is great! Adding the largest place values first makes it less likely to make a mistake of great magnitude. Using the traditional algorithm makes it more likely to make a mistake in the larger place values, and that's a real drawback to sticking with traditional algorithmic thinking, unless you REALLY understand the method well.

EDC and More!

Please click on the thumbnails to enlarge the pictures.

Today we spent time completing another day of our EDC curriculum, and we began to diagnose the needs of students. It was great to see that many students do remember the strategies that they have learned over the last five years. It was so great to see students paying such close attention to detail on our fourth day of EDC. I wrote, in black pen, some of the important concepts that we discussed during today's session on one student's awesome work :-}

Simple Beginnings Have Powerful Meaning

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These are pictures of the first couple of days work in a our calendar math series, "Every Day Counts". All of these examples show student work that is remarkably complete and detailed. The concepts may seem simple, but in reality all of this work involved very deep conversations about place value and other important concepts that relate to number sense.

A big "Booooyyyaaahhhh" goes out to the three students that produced this work.

2009-2010 School Year Approaches!

Well if you are reading this, you have found my "famous" math blog. This year, I plan to include, dare I say this, almost daily pictures of the work that is being produced in our math classes. I think that by doing this, students and parents will get a very clear picture of just what is really going on in class. There will be way less writing by me (stop clapping), and way more for you to DISCUSS.

To do this, I really need parents to sign and turn in all of the Internet permission slips. I will never post a child's name. I might call Suzy "Student S." :-}, or I might just leave it at "This student". You guys please tell me what you are OK with. I will never embarrass a student by leaving a negative comment about work.

Oh, just another note about the photos of work that I attach. What you will see first is a small "thumb nail" image at the top of the blog. By clicking on the thumb nail, you will see the full size piece of work. Sometimes, I forget to select the correct size for the image, and the work will be too large to view. If I do this, please let me know.

I am blessed and honored to have your kids in my class. They WILL create remarkable work!

Line Plots, Cats, and 5th Graders

If you were presented with this data about cat height, what could state about what was typical of the cats in this group. Could you find the mean, the mode, the range, and the median? Could you tell what fraction and percent of the cats were taller than 5.5 inches but less than 8 inches? (Click on the picture if you need a full-size view.)

I just measured my cat and she is 10 inches tall at the shoulder. She is a smallish seven-year-old female cat. Does that make you think anything about what kind of sample this might have been?

If you have a cat, could you measure their height and reply? We'll stick to inches since the chart was created in that unit:-}

Spinner Games and Probability

If the above picture was a spinner game, and you were given the choice of "two scoring options" to choose (you would get a point if you landed on a number that met the requirements of either of your two options chosen), what would you choose?

A. a prime number
B. an odd number
C. a multiple of 5
D. an even number

Many students would look at choice A, and state that it has a 4:8 or 50% probability, as 4 of the 8 numbers are prime.

B would have a 5:8 or 62.5% probability, as there are 5 odd numbers

C would have a 4:8 or 50% probability, as there are 4 multiples of 5

D would have a 3:8 or 37.5% probability, as there are 3 even numbers


Man students would just look for the highest probabilities. Perhaps, they would choose A and B, but if you study those choices closely, you may see that several sections would be possible "losers". So, what two options would you choose?

Hints for Taking the FCAT Test!

1. Your teachers, principal, family, friends, and classmates have faith in you!

2. You have all the tools you need in order to be successful. I've taught a bunch of kids, and you guys have the goods!

3. Do not stress out. This is a time to show off.

4. If a question is too difficult, skip it! It is far better to miss one item than the 23 items that come after it :-}

5. Read each question carefully. Be sure to read with "a voice" that you can hear in your head. Rereading with a voice has helped me solve so many problems over the years.

6. Make some notes to back up your mental math strategies. If you show some work, your chances of being correct go up a bunch. I have seen that most errors occur through rushed simple operations like adding or subtracting. So, don not rush (you know who I am talking to ;-} )However, please remember that you do not have time to "write a book" about each problem (again, you know who I am talking to ;-} ) .

7. Look at your final answer and see if it makes sense. Elephants do not weight 17 pounds!

PEACE!