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BC: The most difficult thing is to just start the ball rolling. Once it starts, it's actually more difficult to stop it. -- Butch Lovelace

FC: My Math Journal | Gail Erickson

1: Table Of Contents | 1. Shoe Prints 2. Tangram Story Telling 3. Statistics Jeopardy 4. M&M Math 5. Hop to the Pond 6. Frog Pond Game 7. String Games 8. Chip Trading 9. How Much is A Million? 10. Are You A Square? 11. Color Tile Riddles 12. I am/ Who is? 13. Adding & Subtracting Puzzles - Magic Square and Diffy Board 14. HOG 15. Five Square 16. Challenge 24 17. Whats my Unit? 18. Cut a Card

2: Shoe | Grade Level: K - 4 Standards: Number and Operations, Algebra, Measurement, Data Analysis | We began the activity by taking off one of our shoes, and making a rubbing of the bottom of it on a blank piece of paper, using a crayon. We then realized that a shoe print that looked like a right foot, was actually one from our left foot (and vice versa) Our class then made a bar graph, using our shoe prints, to show that we had more people use their right foot for the activity than those who used their left foot.

3: Comments & Reactions: I thought it was interesting how different all of the shoes prints looked, and I found it even more interesting how many people chose their right shoe, versus those who chose their left. It would be interesting to see if it had to deal with being right or left handed. I also liked how concrete our bar graph was, which would be very simple for children first learning the concept of bar graphs. | Extension: like I said in my reflection, the students could look at whether the students were right or left handed. They could also graph the data differently by looking at the size, style, or color of the shoe print for further practice with graphing data. | Prints

4: Tangram | Grade Level: 1 - 6 Standards: geometry and measurement communication, problem solving, connections procedures | We cut out a series of shapes including triangles or different sizes, a square, and a rhombus. After playing with our shapes we were told to try and figure out how to place them to make one, large square. We then had to create a shape and try to describe it to our partner, piece by piece, so that they may create the same shape.

5: Story Telling | Extension: Students could create a solid picture of their creation and then have other students try to figure out what shapes need to be placed where in order to re-create that same image. | Comments & Reactions: I had worked with the tangram shapes before, but I had never used them to make other shapes and then to try and use them to instruct someone else to make the same shape. It was very difficult to be specific with your partner to explain the shape you had created.

6: Statistics | Each one of us was given a piece of paper that had a question that had a number for an answer. The question topics varied from "How many digits are in your Social Security Number?" to "How many shoes do you own?" We had to get at least five people to answer the question, then we tried to figure out what our question was before looking. | Grade Level: 2 - 12 Standards: numbers and operations communication, connections

7: Jeopardy | Comments & Reactions: My question was how many digits are in your social security number, and four people said 9, and the fifth person said 8. It was very difficult to try and think of what could be something that everyone said 9 to and I hate guessing and being wrong. Although I did not have written down who had said 8, I knew who it was, which could be slightly embarrassing for a student. | Extension: Students may use this to help study for tests on conversions in math, or on concrete facts in any subject.

8: Each table was given a small packet of M&Ms and told to guess how many M&Ms were in the packet, and what the most common color is. After much debating, we opened the packets and counted it out. Our professor had created a program on the computer so we could enter our findings as a table to be graphed with the class to find the average number of M&Ms, and the most common color. | Grade Level: K - 3 Standards: number and operations, data analysis and probability, problem solving | M & M

9: Extension: Our class extended this activity by asking why orange and blue were most common. Other classroom activities could be showing the data on different kinds of graphs. | Comments & Reactions: I loved how concrete this example was, and how every table contributed to the class data. Each table even had an outline to create a bar graph on a piece of paper with the actual M&Ms that would make this task much easier for students in the beginning stages of data collection. | Math

10: Each set of partners had a game board that had the numbers 1-12 on it, and one frog in each place. Two number cubes were thrown and whatever the sum of the two numbers was, was the frog that got to move ahead on the board one spot toward the pond on the other side of the page. Before the activity, we guessed what frog we would think would win, and the partners competed so see who would be right. We then looked at the probability of each sum option and realized what the best guess would be for the game. | Grade Level: 3 - 7 Standards: data analysis and probability, problem solving, reasoning and proof | Hop to

11: Extension: Students can record their answers as a graph to see if seven really is the best option since it has the highest probability of being rolled. | the Pond | Comments & Reactions: This activity required simple addition that was repeated with many different examples. This activity also made students realize the probability of each number option, and what guess would give them the best chances of winning.

12: Ten frogs were placed on the board, and the students worked with one other person. On your turn you could take away one, or two frogs from the board. The point of the game was not to be the person who had to pick up the last frog. After playing this game a few times we had to come up with a way to win the game every time, and then we went up against another group in the classroom | Grade Level: 3 - 10 Standards: numbers and operations, algebra, problem solving, reasoning and proof | Frog Pond

13: Extension: Students could play this game with fewer or more pieces to help them find the strategy. Students could also play it with having to take away more pieces to allow them to figure out a new strategy after being told the first one. | Comments & Reactions: When playing the game the first few times I was able to figure out how to win after the first three turns were taken. However, I was not able to figure out the actual strategy until after it was explained to me a few times. It was difficult for me to understand that you did not want to be caught with 3, 6, or 9 frogs on the board when it was your turn | Game

14: Three string circles were placed on the board to create a Venn Diagram and we had squares, triangles, and circles that were large, middle, and small, that were red, yellow, green and blue. Each circle represented one of the characteristics and it was our job to figure out the Venn Diagram by watching our professor place shapes in each of the circle options. We did this with three circles, and then two circle. Then the class broke down into table groups to further practice by being the one to give the directions | Grade Level: 1 - 6 Standards: geometry, data analysis and probability, communication, connections | String

15: Extension: Venn Diagrams may be used in many other subjects, and students may used it to classify in Science, compare stories in Reading, or find trends in famous historic figures. | Comments & Reactions: I liked how we were able to be the ones getting the directions, and then later got to practice giving the directions in this activity. It made it easier to understand the concept of the Venn Diagrams if you had to work with it in both senses. | Game

16: Grade Level: K - 4 Standards: number and operations, algebra, problem solving, communication | We were given tables that had a column for yellow chips, blue chips, green chips and red chips. Each person took turns to roll the number cube and that was how many yellow chips they were allowed to place on the board. However, 3 yellow = 1 blue, 3 blue = 1 green, and 3 green = 1 red. The point of the game was to be the first to get a red chip | Chip

17: Extension: Like we did in class, you could start with a red chip, and work to take away all of your chips first, or add chips on your first turn then take away on your second turn when doing a double roll. The number to exchange chips could be changed. Or you could say that even numbers mean you add that many yellow chips, and odd numbers mean you get to subtract that many yellow chips | Comments & Reactions: This was a quick moving game that could be abstract in thinking, or very concrete by placing yellow chips on the board before replacing them for blue chips. This was a very neat way of showing the beginnings of regrouping that is required for upper levels of mathematics, and can be very difficult for students to learn. | Trading

18: Grade Level: 7 - 10 Standards: number and operations, algebra, measurement, problem solving, reasoning and proof | Students work in pairs to measure any item in the classroom. They then take that item and place one million of them end to end and mathematically determine how far they could go. This works best when you can then convert this measurement into miles or something more useful that they can relate to. | How Much is

19: Extension: Students can really go crazy finding things to compare their measurements to, and they could work on comparing their measurements to other groups as fractions. | Comments & Reactions: This went well since we were able to do the conversions, but younger ages will have lots of trouble with this. It would have also been nice for us to have a conversion table available to look off of to make our findings more concrete rather than us just guessing them. | One Million?

20: We broke off into small groups to help each other find our measurings. There were tape measures put on the walls so that seeing the vertical and horizontal measurements were simple. Then we determined if we were a perfect square (giving ourselves 3 cm handicap), and created a bar graph with post-its to show our data as a class | Grade Level: 2 - 7 Standards: measurement, connections | Are You

21: Extension: Students could go home and measure their family to see if it is a genetic trait. In my family, my dad, brother, sister, and I are all wide squares; while my mom is a perfect square to a T. | Comments & Reactions: I actually did this in 6th grade and this was really neat to see how my class in 6th grade only had 3 perfect squares, and now almost the entire class was a perfect square. | A Square?

22: Students are given a series of hints about what color tiles are in a paper bag, and how many of each tile. The hints are given one at a time until students guess correctly what tiles are in the bag. Students can then make up their own examples and test it on peers. | Grade Level: 3 - 6 Standards: algebra, problem solving, reasoning and proof, communication | Color Tile

23: Extension: This type of activity can continue with the practice of fractions and upper level mathematics because it can be included in the hints that "1/3 of the bag is green". | Comments & Reactions: This activity was really fun when we got to make our own riddles because we got to practice writing the hints like we had seen in the professor's examples. This would be great for students to practice writing instruction skills. | Riddles

24: Students all received index cards that had "I am #" at the top, and "who is (insert math problem)". The cycle started with the teacher saying their who is problem and then it jumped from student to student. The math problems included examples of multiplication and division. | Grade Level: 3 - 6 Standards: numbers and operations, problem solving, connections | I Am/

25: Extension: This activity could be done with states and capitals in social studies, or describing shapes in upper level geometry. | Comments & Reactions: I loved how each person was in charge of their own card and the cycle jumped around the room at random. I also liked how each student had to follow what was being said by their peers and had to do the math in order to determine if they were describing their number. | Who Is?

26: Students place any numbers in the four corners of the diffy board (which is a square). They then take the difference of the two numbers that share each line and place the difference in the middle of the line. The differences then create a diamond inside the square which students can then find the differences to those. This pattern continues and eventually all differences become zero. | Grade Level: 1 - 3 Standards: numbers & operations, connections | Diffy

27: Extension: This activity is pretty basic, but students can practice doing this and see who can make their diffy board require the most squares/diamonds inside the original square to get to zero. | Comments & Reactions: This was the neatest magic trick I have ever seen because it always worked with any set of numbers that we tried. While completing this task we had a lot of practice with subtraction problems even though we thought we may not have realized this. | Board

28: Students were given a sheet of squares with some of the numbers filled in at random. The instructions at the top were that 3x3 sum 15, 4x4 sum 34, 5x5 sum 65. With this you can then figure out what numbers need to go into the squares because every vertical, horizontal, and diagonal is the sum as listed. You can only use each number once in a square | Grade Level Standards: numbers and operations, problem solving, connections | Magic

29: Extension: The larger square puzzles (5x5) are for more advanced levels of students. You can also ask students to create their own puzzle using even numbers 2-18 (3x3 sum of 30) | Comments & Reactions: This reminded me a lot of the sudoku logic puzzles because you have to look at what you know and try to figure out where to go to next. I liked this better though because it is on a much smaller scale and required math skills beyond just knowing your numbers 1-9. | Squares

30: Students are given 10 dice to roll, and each person takes turns rolling the dice, adding them up and racking up their score to try and be the first to hit 100. The students may roll as many of the dice as they want to get their points. The catch is that when you roll a one, your points for that roll don't count and you don't get any points for that turn. | Grade Level: 1 - 3 Standards: numbers and operations, data analysis and probability, reasoning and proof | HOG

31: Extension: Students could change the game rules to whatever they wanted. They could make it be that you had to roll a one for your score to count, or make it so that if you get doubles you get to add the numbers you see on those dice, and the numbers that are on the opposite side. | Comments & Reactions: This game was highly entertaining and was up to luck if you won. We had to do a lot of adding of numbers to come up with a score for that turn, and the overall score of the game.

32: The activity began with students having to create the twelve shapes that you could create with five small squares that touch on their flat sides. We created these shapes using large square graph paper and cut them out. With the shapes completed, we then had to try and piece the shapes together to fit in a rectangle that the professor had given us with the correct measurements. (there was only way to fit them all in. | Grade Level: 2 - 6 Standards: geometry, problem solving, representations | Five Square

33: Extension: There is a board game called "Blokus" where the players use the same shapes as the pentominos against each other. The rules explain how you are allowed to set your pieces on the board, and the goal is to make it so that you have more pieces on the board than your opponent by blocking all of their possible moves | Comments & Reactions: This activity got you to at first think of what shapes were possible, and then creating the rectangle was impossibly difficult. Having squares to move around to create the pieces helped, and then it was great how we could move our pentominos around on the board to make the rectangle. | (Pentominos)

34: A card is set in the middle of a group of students and each person tries to come up with a way to use all four numbers using addition, subtraction, multiplication, and division in order to get a final answer of 24. The cards have various levels of difficulty, including upper levels with double digits and fractions. First person to tap the card and say their solution collects the card points | Grade Level: 5 - 7 Standards: numbers and operations, algebra, communication | Challenge

35: Extension: Even though this is a game for a group of people, students can still be encouraged to solve the cards individually and get the opportunity to write out their work if they need to. | Comments & Reactions: I remember doing this activity in math classes in elementary school and hating it because some of the kids played it all the time and memorized a lot of the cards. Even though playing in class was a lot more fair, you could still see who still remembered their simple math problems. | 24

36: Students were all given bingo cards with letters A-G on them shown at random. They then took turns spinning two spinners, one showing shapes (hexagon, trapezoid, triangle) and the other showing fractions (1/2, 1/3, 1/6). There was a piece of paper showing outlines of shapes, each labeled with a letter. As each student took turns spinning the spinners, they then had to create the shape that would happen for each of the examples, and connect it to an outlined shape. They then could mark that on their bingo card. The first person to get five in a row wins. | Grade Level: 7 - 9 Standards: geometry, algebra, communication, representations | Whats My

37: Extension: This was difficult with the shapes that we had, but it could be used with circles to allow students better chances of understanding the task. | Comments & Reactions: This was a little difficult to figure out at first, but with the examples of all of the shapes on the spinner we were able to manipulate them to create our final answer. | Unit?

38: Students start out with 1/4 of a piece of paper and scissors and shown the professor's example of the final product. They are told not to think, but to simply being cutting and trying things. The example can be touched, but this doesn't immediately give away the answer. | Grade Level: 1 - 6 Standards: geometry, problem solving | Cut A

39: Extension: Students could create their own brain puzzles with the paper and ask peers to try and figure theirs out. | Comments & Reactions: I thought this was an awesome activity (granted I was able to figure out the puzzle). It was interesting to see how we all wanted to touch and look at the example, but elementary students would have started by cutting and trying things. | Card