Fraction Krypto

Krypto is a game I learned about at the conference where Dr. Lola May presented. I didn't realize until recently that it was a commercial game that could be purchased :-)   I had simply used the game idea from time to time, following the rules as laid out in the book. Krypto can be played with whole numbers or fractions (and with positive and negative integers as well, I'm sure!), but for today, I'm going to talk about the use of it with fractions.

The rules are simple (kind of like the "24" game):
1. Choose 5 common fractions, with denominators of halves, thirds, fourths, sixths, eighths, tenths and twelfths.
2. Students add, subtract, multiply, and/or divide the fractions to make the 5 fractions equal the target number of 1.
3. Students can receive points for meeting the target number of 1. If they do so using only 3 numbers, they get 300 pts; 4 numbers = 400 pts; all 5 numbers = 1,000 pts....you can set up the point system any way you'd like.

We're going to try it a few days next week, after we finish all the operations, and since I have my fraction cards, I'll just hang them on the board:

For this particular set of fractions, I found that 3/4 x 2/3 = 1/2 + /2 = 1; that uses only 3 fractions, so I'd get 300 points.

 2/3 + 2/6 = 1, but that's only 2 fractions. I may consider giving points for using just 2 fractions though, until they get the hang of the game.

Can you make the 5 fractions equal 1?

"Casting Out Nines"

I was a very new teacher (in my second year, I believe), when I was lucky enough to go to a conference and hear Dr. Lola May speak. She was a great presenter, and certainly made an impression on me. I still (20 years later) have the book that was given at the conference and refer to it now and again.

It was at this conference that I first learned how to use "casting out nines" to check the answers to multiplication and division problems. I had never heard of this method when I was a student, but being a new teacher, I kind of assumed it was a method well-known to other teachers.....until I talked about it during a meeting at which our Curriculum and Instruction director was present. He overheard me explaining it to another teacher; he had never heard of it, was quite surprised and interested in how it worked, and asked me to show him a few more examples.

Over the years, I have taught it to some classes (and not to others...I haven't taught it yet this year, but plan to...though the school year will be over before we know it!), and I don't think any students have ever told me that they had already learned it. So, I supposed it isn't as well-known as I had thought (at least not around here...)

The kids really like it because it's a "trick" to check their work.  I made this little video explanation explaining how to check a multiplication problem...it's very basic and amateur, I know, (and I apologize for the blurriness at the end), but hopefully it provides clear enough directions for you to get the idea:)

The steps of casting out nines to check multiplication:
1. Going across the rows of the multiplication problem, "cast out" any 9s or combinations of numbers that add up to 9.
2. Add the remaining digits across each row, until the result is a single digit.
3. Multiply the single digits, and if the result is a 2-digit number, add the digits to get a single digit.
4. Follow the same steps in the product, until you arrive at a single-digit number.
5. If the results match, the answer to the problem is most likely correct (not 100% certain, but most likely); if the results do not match, the product is not correct.

I'll post another short video with an example or two of checking the answer to a division problem in a day or two.

Have you used casting out nines?

Word Challenge

I love to play thinking games with my students (especially when they don't see it as really thinking)!

Quite a few years ago (at least 15) I went to a make 'n take workshop, and whoever was running it had quite a few activities made from cardboard circles. For this particular activity, a hole had to be made in the center of the circle, and a shoestring was secured to the bottom of the circle and threaded through the hole. The circle was divided into 32 sections, and each section was labeled with a letter of the alphabet (using some letters, like vowels, twice). As you can see, the sections can be colored so the circle is more attractive:)

The rules of the game were conveniently written on the back (otherwise I might have forgotten them!) Here they are:

1. Divide into 2 teams (sometimes I divide the class into 3 or 4 teams)
2. Spin the wheel for Team 1 (hold onto the shoestring and spin wheel).
3.  A member of Team 1 stops the wheel with thumb and forefinger (so the thumb lands on only one letter).
4. The team must think of a word using that letter, in order to earn 1 point (they have 10 seconds to think of the word...I don't let them use proper nouns).
5. The team may spin again. They must use the new letter and the previous letter in a word, to earn a total of 2 points. If they think of a word within 20 seconds, their point total is 2. If they can't think of a word, they go back to 0 points and the next team gets a turn.
6. If Team 1 gets to 2 points, they may choose to spin again to earn 3 points (using all 3 letters in a word in 30 seconds), then 4 points, (using all 4 letters in a word in 40 seconds) and so on. If, on any turn, the team can't think of a word, they lose ALL points, and play goes to the other team.
7. The first team to reach 6 points wins.....(doesn't sound hard to the kids, but once they get to 4 letters, they often end up losing their points. It's tough to get to 6 points because of the combination of letters they end up with.)

8. The time limit is 10 seconds per letter, so as a team attempts to earn more points, the time limit increases. (3 letters = 30 seconds, 4 letters = 40 seconds, etc.)



Students really do enjoy this game and work hard to think of words....it's FUN thinking!

Playing Footloose

Free Order of Operations Footloose!

I realized that I have mentioned the activity called Footloose in my blog before, but have never really explained it. It's an activity that is enjoyed by kids of all ages, and can certainly be varied according to the topic that is being studied. I use it mostly for math, because that's what I teach; but in the past, when I taught different grade levels, I used it as a review activity in other subject areas as well.

It is amazing how quiet and engaged students are when doing this activity. They are up and down, out of their seats, and you'd think they'd be very distracted...but no matter what the grade level (I've used it with 2nd, 4th, 5th, and 6th), they work hard to complete the questions!  

Here's how it works:

1. There are 30 cards, with a question on each card. Each card is numbered, from 1-30. I do laminate the cards so that they don't get ruined after one use:)
2. Students receive a Footloose grid (there's one on the desk in the picture).
3. Each student is given a card to start with, and the  extras are placed around the room. I typically put
them on the chalk/white boards ledges (cards are on the ledge in the picture).
4. Students find the answer to each question, writing their work on the grid or on separate paper. They
then record the answer to each question on the grid, in the box with the corresponding number.
5. When students finish with a card, they place it on the chalk ledge and get a new card.
6. This continues until students have answered all questions.

Free Single-Digit Addition Footloose!

A few times I have taped the cards around the room instead of using the ledges, because when students are looking for the last couple of cards, they have trouble finding them. When they are posted, it's a little easier to find them all.

Sometimes I make it a competition, and the student with the most answers correct is the winner; other times I use it as a graded review.

I haven't used the activity much lately, which is good, because I don't want them to get tired of it!

What math review activities do you use? (I need some more variety!)

  

"Remove One" - Probability Game

Remove One is one of my favorite games! It's a great way to teach probability and the students love it. I've been using it nearly every year since I was introduced to it through a program called the Mathline Middle School Math Project, sponsored by PBS (back in 1997?). I was involved in the program through my graduate studies at Allentown College of Saint Francis DeSales (now DeSales University). Anyway, this year, my student teacher is teaching our probability lessons; so she is the one who taught this lesson.

This is how the lesson works:
1. Students use a piece of paper as their "game board" and number the paper from 12-2 (or 2-12) . They then place 15 chips next to the numbers. They are told that they can place one chip next to every number and then place the extras next to any number they want. Or, they can leave some numbers with no chips and put several on others. Usually, they place the chips like those in the picture to the right.
2. Once students have their chips set up, the teacher rolls 2 dice and finds the sum of the numbers that are rolled.
3. If students have a chip next to that sum, the students may remove ONE chip from their paper (thus the name of the game -Remove One).
4. Play continues, with the teacher rolling the dice and the students removing one chip each time the corresponding sum is rolled.
The "winner" is the student who removes all of the chips first.

Without much class discussion, we play the game a second time. Normally, I just ask them to make some quiet observations to themselves before placing their chips again. Students typically notice that the sums of 6, 7, and 8 are rolled the most often and that 2 and 12 are usually rolled the least often, so they arrange their chips differently.

After the second game, we have a discussion about all of the possible outcomes (sums) one can get when rolling 2 dice. We also discuss how many ways there are to roll each of those outcomes, and what the probability is of rolling each sum. We find this probability in fraction form, and then often convert them to decimals and percents.

After this discussion, we play the game for a third time, and students' "game boards" often look like this:

This year, since I was observing rather than teaching, I was better able to hear some of the students' quiet comments to each other...   "There's a better chance of getting a seven."  "I'm not going to put any on 2, because it still hasn't come up."

 When I started discussing this lesson with my student teacher, I searched for the lesson online, just in case it was around, and I found it right away. Click HERE to see the full lesson plan from PBS.

Have any of you played this game?
What other probability games do your students enjoy?

New Probability Footloose game, to review probability:

Integer Ideas

I haven't had the opportunity to teach much about integers, or about how to add or subtract positive and negative integers, but I might get the chance this year. It isn't in our current curriculum, so it's an extra topic that we don't normally get to spend time on. However, we will be teaching integer concepts next year, as we work on Common Core implementation....and maybe, just maybe, we'll get to work on some integer concepts at the end of this year.

Even though I don't get to teach this topic, I do have a large number line with positive and negative numbers posted in my room, with the hope that the kids will observe it and think about it. And, from time to time, when we talk about the idea that the Commutative Property does NOT work for subtraction, we will refer to the number line (that I have to be on tiptoe to reach!) to see that a problem like 7-2 = 5, but 2-7 = -5. So, we do have that visual to discuss from time to time.

In preparation for next year (and this year, just in case), I created an Integer Operations Footloose activity, and as I was searching for hands-on activities,
I also found this great number line idea on Pinterest, shown here. Students can walk on the number line - I would think this would help students get a better understanding of moving in the positive and negative directions. I really hope I get to use it! If I can't use it at school, maybe I can use it with my daughter this summer.....she still struggles with adding and subtracting negatives and positives.

What are some good memory tricks to help students learn the rules of adding, subtracting, multiplying and dividing integers?

Trying to Make Triangles

Although we're trying to get through quite a bit of material before our state testing, we took some time today to explore triangles. I'm sure many of you may have done this exploration, but it was quick and fun, so I thought I'd share:) We explored the idea that the sum of the two smaller sides of a triangle must be greater than the longest side. I cut straws of three different lengths, and asked students (in groups) to use the straws to make a triangle.

In my first math class, I used straws that were cut to 2 inches, 3 inches, and 5 inches. These lengths, using straws, made it almost possible to make a triangle, even though it shouldn't have been possible. So, I had to insist that their straw ends be lined up perfectly. I wanted to use 3, 5 and 2 inches to show that even these dimensions won't make a triangle, because the sum is equal to the longest side, not longer than it. So, after understanding how precise they had to be and that they couldn't leave segment parts sticking out of the end of the triangle, they came to the conclusion that it couldn't be done. Next I gave the groups a new set of straws that were cut to 3 inches, 3 inches, 5 inches. In this case, they were excited to make their triangles in about 30 seconds! We then discussed why the 3, 2, 5 didn't work and worked our way to "creating" the rule.

For my next classes, I trimmed the 3 inch straws to 2 inches, so that my next classes would have more difficulty getting the ends to meet. It was so funny to hear their comments - "This doesn't work," "Is this a trick question?"  "This is impossible!" And then, their excitement when they made the 3, 3, 5 triangle  - "We did it first!"

I think (hope!) that they understood the concept....we'll see tomorrow when we go over their homework:)