Math Ideas

Individualized Math
~ Renee Goularte

For several years I incorporated into my classroom a very individualized, manipulative-based process that I called "math card." I had lots and lots of manipulatives in my classroom, on open shelves, which this absolutely required. This was when I was teaching third grade. At the beginning of the year I gave my students a "diagnostic" test which covered (in a basic way) most of the major concepts for the year. From this, I found each students' strengths and needs. From that, I created for each student a "math card" which was basically an index card with math activities listed on it. I started out with about six things listed. When we did "math card" the students took these out, did the first activity on the list (that had not been crossed out). When they finished, they showed me their work, we discussed it, I asked questions, etc. and sometimes I gave an extension. When the work was complete, I crossed it out and added something to the bottom of the list. I kept a good amount of their written math work in portfolios. This worked very well for me. I know you are going to ask what was on the card, so here's a **very small** list of examples of things I might write:

pattern blocks
blue story problem
stump the adult
play "Battleship" with (name of another student)
fraction tiles (see me first)
pg 42 math book
geometric solids
multiplication challenge
yellow story problem

These are just off the top of my head and every one of them would need an explanation, but understand that all these activities would have been presented to the students in a fishbowl-type demonstration. If not, then the note would say "see me" so I could explain to the student what to do. All my story problems are in boxes cut up into single story problems, categorized by color: red=add or subtract, no regrouping; blue=add or subtract, regrouping; green=multiplication and division, single digit; yellow=multiplication and division, multidigit; orange=fractions; purple=two-step and other challenge problems, including problems with unknowns.

I LOVED doing math card. I could stretch out one story problem for a week with extensions and additional questions. My students were required to draw a picture that showed the solution, solve it with numbers/math, and write a complete, grammatical sentence which answered the question in the problems (i.e., How many sandwiches did they have altogether?" they would write something like "They had six sandwiches altogether" or "Altogether they ate six sandwiches" or "The four girls had six sandwiches.") You can see what I required on story problems by reading about giant story problems on my website (in later years this process was introduced by doing whole-class and small group giant story problems): The process is
pretty much the same, just imagine that it is being done by an individual student after this whole group process.

 Math Journals
~ Sandy Elsasser

I use "Math Journals" with my students to improve problem solving skills, develop thought processes, and practice math concepts. They involve writing equations and drawing to prove the solution.

Each student has a spiral notebook that they use for their Math Journal. Each time we use the journal I hand out the 'Problem of the Day' and they glue it to the top of the next blank page in thier journal. (I model 2-3 similar problems before I give them thier actual problem, that we read together as a class.) The student then writes an equation, solves it, and draws a picture to prove their work.

For more detailed information about these Math Journals, and to access sample problems, go to and look for April and May 2006.

 100 Facts About 100
~ Alice Pickel

1.      100 pennies equals one dollar.
2.      100 years are a century.
3.      100 centimeters are one meter.
4.      100% means all your answers are correct....

There are way too many to list here! Click on the 100 to see the whole list. Have fun on the one hundredth day of school!

 Cupcake Combinations
~ Lori Jackson

One day we had a mathematical party to say good-bye to one of our students who is going away to boarding school. I brought in unfrosted cupcakes, yellow and chocolate, and icing in two colors, green and blue. We worked together to figure out what combinations we could make then each picked and frosted a cupcake. We used paper cupcakes to color to match and created a graph showing our choices. We discussed the graph in depth, then ate our cupcakes and toasted the guest of honor with bubbly (soda). As one boy went out the door (we were pressed for time due to last minute early dismissal), he reminded me that our graph wasn't done because we hadn't finished labeling it (we did on Wednesday, once we finally got back to school). So today two of my kids were writing in their journals about this very popular party and went out in the hallway to find the word cupcake in our labeling. Along came our principal and asked the two boys about the graph. They talked her ear off, explaining the whole lesson and making nice comparisons and observations. But here's the kicker, they began their discourse with this statement, "Last Wednesday we didn't have math 'cuz we were having this party..." It absolutely made her day!

Note: This activity works lots and lots of ways - sandwishes with two jelly choices and two bread colors, bugs with two body colors and two wing colors, etc.

Race to 100 - a place-value game for three or four people
~ Renee Goularte

Materials Needed: a pair of dice and Base Ten Blocks, or, if not available, use dry lima or kidney beans for ones; popsicle sticks or straws for tens; one index card with the number "100" written on it.
Directions: The players consist of one banker and two or three players. At the start of the game, the banker has all the ones, tens, and the hundred card. The first player rolls the dice and adds the numbers. The banker gives the player the number shown on the dice, represented with beans. For example, if the player rolls a 3 and a 4, the banker gives him or her 7 beans. The next player rolls the dice and the play continues. At any point in the game, when a player has more than ten "ones" (beans), he must trade them in for a "ten" (a straw). For example, if a player has 8 beans and rolls a 4 and a 2, the banker gives the player six more beans, so the player will have 14 beans. At that point, the player must trade in ten of the beans for one straw. The game continues until one player reaches 100 and wins the 100 card. If players wish to play again, the banker becomes a player and the winner becomes the banker.

Facts Patterns - Students work individually to learn addition facts
~ Ruby Clayton

Each student works with manipulatives to build all the combinations of a number. For 7, there are eight combinations. When they build with two colors of manipulatives, they would have groups of say five red and two blue. Then they take a scrap piece of paper, 1 inch by 4, and write the equation on the paper next to what they built. They keep building and writing the equations until they have found all eight. When they think they really know all the combinations of 7, I give them a "test" on seven. They get a quarter sheet of paper with the numbers from 0 to 7 written down the side in random order. They then go to a quiet place in the room and complete the test by themselves. If they are able to complete the test with 100% they move on to the next number. Students that need more practice can choose a different set of manipulatives to work through the building and writing again. Unifix cubes, tiles, pattern blocks, ceramic tiles, toothpicks, and other manipulatives work well. All I have to keep track of is the number each child is working on, and when they pass each number. Every child can work at their own level.

Click here to see a Sample Test

Facts Challenge - a simple partner game for practicing math facts

Materials Needed: One standard deck of cards.
Directions: Divide a standard deck of cards equally between two people. Players hold the cards so they can't see the numbers. At the count of three, both players put a card face up on the table at the same time. The first player to add, subtract, or multiply the numbers correctly gets both cards and puts them aside. The game is over when one player runs out of cards. With three people, the third person can play the role of the judge, or the game can be played with three people adding up three numbers. Note: Face cards are worth 10, and Jokers are worth zero.

Money Rap - Try this one when you are teaching about money!
Thanks to Suzanne Nayback!

Five pennies make a nickel,
Two nickels make a dime.
Two dimes and a nickel make a quarter every time.
Four quarters make a dollar
And that is quite a lot.
And a dollar in my pocket
Is exactly what I've got.

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