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At the little country college that I went to, I was never really taught “how” to teach the different concepts in math. I’m not sure how other colleges’ math education programs are, but for me it was all about the “math” and very little about how to teach any math concepts. I learned a lot of general information about behavior, how to run a copy machine, how to make tests, blah, blah, blah. There were so many things that I still had to figure out on my own. I learned all of the different ways to differentiate equations and all other concepts that jr high students won’t be learning for years. By the time I finished college, I had totally forgotten all of the basic math that I would be teaching. I had forgotten how I had actually learned it as well. Either way, I can promise you that I never learned the “why’s” of what I was learning for sure. It took me several years to finally figure out all of this teaching business. Once I got out of the “traditional” teaching methods, teaching became so much more fun. Over the last few years, I have learned that if you teach students concepts starting from scratch….. they understand it without frustration and without confusion. Almost all of my lessons start with a concrete hands-on activity, a pictorial activity, and then a fun game to play. By the time we get to the pictorial representation of whatever concept we are learning, I have several students asking for “hard” questions. It always makes me smile when I am able to tell them that they don’t get any harder.
The same goes with how I teach students how to change mixed numbers to improper fractions and vice versa. I use fraction strips. We use the fraction strips, then we draw the representations, and then we play a game. I see so many lessons for fractions that use circles. I use rectangles. Maybe I’m not as talented as some, but I have a difficult time dividing circles into larger, odd numbers. I can easily divide a rectangle into any number of pieces with little difficulty. I have written up the way I teach this lesson, I made printable fraction strips, and an extremely cool file folder game for sale in my Teachers Pay Teachers store and here on my blog. Here are a few pictures and explanations of the things I did this last week.
We’ll start with the super cool fraction strips I made to use for my whiteboard. Here is a picture of the final product.
I printed, laminated, and cut out the pieces. At the beginning of school, I found an amazing product…….. magnet tape. I found it at Lakeshore Learning Center and at Mardel’s. I’m sure they probably have it at Hobby Lobby as well. I put a small piece of that magnet tape on the back of each of the pieces. I wrote numbers on the board and had students come up and model it with the pieces. Students, especially in my co-taught class, absolutely loved doing this! Click on the picture below to download these fraction strips for your magnetized board for FREE!!
Here are some pictures of my process……..
Magnet tape and the backs of the pieces
To prepare my students to learn about fractions, I printed out fraction strips. I totally meant to print them on colored card stock, but forgot to go buy some. I didn’t have enough colored paper to copy all of the pages I needed (over a hundred students, and three pages a student is a lot). I bought quart size baggies and double-sided tape.
Before class, I put a piece of double-sided tape down the sides of each of the baggies. I left the white strips on until I was ready to put them in the back of my students’ spiral notebooks.
As my students were cutting out their fraction strips, I had them bring me their spirals and I taped them onto the back cover.
Here are a couple of pictures of what one of my students put in her spiral notebook for the lesson.
Here is a link to buy my lesson for teaching students how to change mixed numbers to improper fractions and vice versa. It also includes a super cute and fun file folder “board game” to help reinforce the concept.
This is a picture of the game that is included in the pack. You can buy it from my Teachers Pay Teachers store, or here on my blog for only $3.00!
I hope your students enjoy learning about mixed numbers and improper fractions as much as mine did!!
One of my most searched for and read posts is my foldable for divisibilty rules. The foldable was just a flap book that I had students write the rules under the flaps. I decided that since it was such a big hit, that I needed to “outdo” that post this year.
This year, I used the same fold as my “Back to School Foldable.” I made a printable for the different numbers that I wanted the students to know the rules over. I totally meant to print these out on colored paper for my students. I even took the colored paper down to the copy machine, and completely forgot to put the paper in the machine. For my class, I used the numbers; 2, 3, 4, 5, 6, 9, and 10.
Here are the following rules I used for each of the numbers:
A number is divisible by 2 if: it is even. If it ends with 0, 2, 4, 6, 8
A number is divisible by 3 if: the sum of its digits is divisible by 3
A number is divisible by 4 if: the number formed by the last two digits is divisible by 4
A number is divisible by 5 if: it ends with 0 or 5
A number is divisible by 6 if: it is divisible by 2 and 3
A number is divisible by 9 if: the sum of the digits is divisible by 9
A number is divisible by 10 if: it ends with 0
Click on the picture below to download the free foldable template.
This is a little bit of a tricky fold. I have a great “Back to School” post in which I have a video that explains how to fold it, and it also includes pictures of each step. Click here for a link to that post.
We went through each of these divisibility rules together and gave examples. After we finished, we taped the foldable to the bottom of a page in their math spiral notebooks. We titled the page “Divisibility Rules.”
To give my students practice, I put the students in groups of two. I gave them three ten-sided die per group. I had them take turns rolling the dice to form a three digit number. After they got the number, they went through each of the divisibility rules and circled which of those that number was divisible by. Here is an example of their spiral notebook page.
I hope your students enjoy this lesson as much as mine did! After downloading this great freebie, please head over to my Teachers Pay Teachers store and “follow” me. You can also go “like” my facebook fan page. Here are the links to those places. Thank you so much for your support!
We’ve learned comparing and ordering integers as well as adding and subtracting integers, so we’re on to multiplying integers. I teach multiplying and dividing integers in the same fashion as I do adding and subtracting integers. I didn’t actually hand out the counters, but I used the counter magnets on my white board to demonstrate. Here is a picture of those.
For multiplying integers, here is how I show them:
1. 1(3) means one group of three positives. I show them one group of three yellow counters on the board. You are left with three positives.
2. 1(-3) means one group of three negatives. I show them one group of three red counters on the board. You are left with three negatives.
3. 2(3) means two groups of three positives. I show them two groups of three yellow counters. You are left with six positives.
4. 2(-3) means two groups of three negatives. I show them two groups of three red counters. You are left with six negatives.
5. -1(3) means the opposite of one group of three positives. It is important to explain that negative actually means “the opposite of.” Even in the second problem 1(-3), you could say that means one group of the opposite of three positives. With this one, I say “the opposite of one group of three positives.” One group of three positives is three, so the opposite of that is three negatives.
6. -1(-3) means the opposite of one group of three negatives. Again, you would thing of one group of three negatives, and then the opposite of that which is three positives.
7. -2(3) means the opposite of two groups of three positives. Two groups of three positives is six positives, so the opposite is six negatives.
8. -2(-3) means the opposite of two groups of three negatives. Two groups of three negatives is six negatives, so the opposite is six positives.
I tried to keep from teaching them my integer song, but my Pre-AP students were still having a hard time of remembering how it went, so I went ahead and broke down, and taught them the song.
The second verse of the integer song is to the tune of “Row, Row, Row Your Boat.” It goes like this:
Multiply or divide
It’s an easy thought.
Same signs are positive,
Different signs are not.
The next thing we did was play “I Have/ Who Has.” My students LOVE this game. I make sure that all of my students work each problem as we go. I make sure that they are given a few seconds to work the problem before the “answer person” stands up and reads their card. I have them record the problem and answers if their math spiral notebook. If someone doesn’t stand up and answer within a good little bit of time, I start slowly kind of explaining the answer. It would go something like this, “are the signs the same or different? So the answer would be positive or negative? __ times__ is ? So your answer would be?” I go about it slowly in the hope that someone will stand up before I get to the end. My students will do thirty-one integer expression without one bit of disgruntle. Try giving them an assignment to take home and see if you get 100% participation and return like you do when you play this game.
The “I Have/ Who Has” set that I made for integers is a bundle of all operations. It costs $4.00, and can be bought here on my blog or in my Teachers Pay Teachers store.
Notice the cute “fish eye” lens on some of my pictures? I think it gives the pictures a little character. It was a great Iphone app.
Buy this set of adding, subtracting, multiplying, and dividing integers I Have/ Who Has cards for only $4.00. I promise, your students will thank you. Buy them here or in my Teachers Pay Teachers store.
Playing the “I Have/ Who Has” game first gives students the confidence to play any additional games with partners. One game that I let the students play is “Integer War” with a deck of playing cards. I have them find a partner and give them a deck of playing cards. I write the following on the board:
red = negative
yellow = positive
Ace = 1
Jack = 10
Queen = 11
King = 12
In their math spiral notebooks, I have them put the title “Integer Multiplication War.” They make two columns down their paper and head one column with their name, and the other column with their partner’s name. At the same time, both students will flip over two cards each. They work both their problem and their partners problem. The problem is formed by their two cards. For example: if player A flips over a red nine and a black six, the problem is -9(6). They write both problems in the appropriate columns in their notebook, and find the answer. The student with the highest value wins that round. Play continues until the teacher calls time, or until they have run out of all their cards.
In one of my classes, I had more students than I had decks of cards. Because of this, I modified the rules. I placed them in groups of three. Points were assigned to greatest value down to least value. If the students answer was the greatest value, that student was awarded three points. Second highest was awarded two points, and the least was awarded one point. The student with the most points at the end of game wins.
To give them additional practice, and to give them some independent practice, I also have them “make” their own problems using a spinner I made and a twelve-sided dice. They spin the spinner to decide the sign of the first number and then roll the dice to get the actual number. They do this twice in order to form two numbers, then they multiply those numbers together. I have them work twenty problems (or however many you see necessary). Students get a kick out of getting to role the dice. Throw some dice into anything, and they’ll love it, especially if they’re not the normal six-sided dice. I printed them out, laminated them, and cut them out. Students use a paper clip with a pencil through the center to spin the spinner.
Click on the picture below to download the pdf of the spinner to be able to make your own. You could also use them for adding and subtracting integers as well.