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# Math Journal

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BC: The End

FC: Ashley Stoner ECH 415-03 Fall 2011 | Math Journal

1: August 30, 2011 | Grade Level: 3-4 years and up Topics: Measuring, graphing Standards covered: Measurement, Data analysis and probability General Procedure: To start this activity, give every student a piece of plan white paper and a crayon. Have the students then remove one of their shoes and place it upside down on the table and make a shoe imprint on the paper with the crayon. After all children have made their imprint the possibilities are endless. You can make graphs, sort, measure, etc. Comments and reactions: I really liked this activity. I think it is a simple activity that can be used from preschool even throughout high school. I like that it was interactive to keep the children engaged. It is also way more concrete than having the student draw a bar graph on their paper. Extensions and connections: Instead of having the children make a graph based on left and right foot, you can have the children group the shoe imprints by size before making the graph. This activity can also be used in the older grades to find pounds per square foot using the measurements from their shoe imprints. | Activity: Shoe Prints

2: Septmeber 1, 2011 | Grade Level: First grade and up Topics : Geometry Standards covered: Giving and Listening to directions. Geometry, Communication, representation, problem solving General Procedure: We were first given a set of tangrams. THen we were given time to explore and play with the tangram set. Next, we were asked to make an animal out of shapre presented to us. THen, in pairs, the children sit back to back on the floor. However we sat at the table with a dividied. One of the partners created an animal out of the tangrams. They then gave the other partner step by step directions on how to create an exact replica of their animals. The person receiving the directions was not allowed to ask questions and the person giving directions was not allowed to offer extra help. Then the roles were switched. Comments and reactions: I thought this activity was wonderful for communicating. It allowed chilren to understand how to communicate clear directions. However, with a younger group of children this activity could become very frustrating. The partner receiving the directions may become frustrated with | Activity: Tangram Communication

3: the partner giving the dicrections because they do not understand. The partner giving directions may also become frustrated if their partner does not understand. However, I think that this activity is a good way to build those communication skills. Extensions and connections: This can be extended in many ways. One of the ways would be to only use triangles. You could also give the students only squares or circles. For older children you can even add shapes such as a rhombus or octagon. The tangram set can be used for geometry not only communication skills.

4: September 6, 2011 | Grade Level: Grade 4 and up Topics: probability, communication Standards covered: Data analysis and probability, problem solving, communication General Procedure: First, we were all given a piece of paper with a question on it and were were told not to look at it. We had to go around the room and show 6 different people our question and have them tell us the answer. After we had six answers we had to find the mean, median, more, and range of the data. Using our data, we then had to try to figure out what the questions on our paper was. Comments and reactions: I really enjoyed this activity becuase it showed students it was ok to be wrong. The students would be practicing math skills while communication with other students in the class. The questions can be anything that you want them to be which makes it interesting. I like that you could relate the questions in this acitivty to something you are learning about in social studies or science. | Activity: Statistical Jeopardy

5: Extensions and connections: I think this acitivty could be used in different subject areas. It could be used in social studies, science, even reading. However, for math this can be extended by using a range of different numbers. The answers could be fractions, decimals, degrees, small numbers, large numbers. etc. anything you want them to. This would make the activity suitable for even high school students. Having the student do this would also be a good short activity for a brain break. The students wouldn't necessarily have to find the mean, median, and mode but the could use the data they collected to figure out their questions.

6: September 8, 2011 | Grade Level: 2nd grade and up Topics: Sorting, graphing, probability Standards covered: Data analysis and probability, Number and Operations General Procedure: Each group was asked to predict how many M&Ms were in a single bag. They were then asked to predict how many blue, green, brown, orange, red, and yellow were in each bag. After everyone had their predictions the groups were told to open their bag and count the M&Ms to find the total and how many of each color. The groups were given a paper to make a graph or sort them by color, however they choose. They were then told to compare these numbers to their predictions. Comments and reactions: I think this would be a great activity to use when first introducing data collection. Children learn from concrete to abstract and this is a concrete activity. The activity could include graphing, sorting, counting, probability, etc. It is a good fun way to show the basic concepts of data collection. | Activity: M&M Sorting

7: Extensions and connections: This activity could be used for many other things. After the children find out how many of each color are in the bag, have them find the probability of choosing a green M&M out of the bag. Then repeat this for all of the colors. The students could also compare all of their data as a class and find the average number of M&M's and colors in a bag. THey could also do the same activity for peanut M&Ms or others kinds and compare the amounts per bag using charts and graphs. The students could also weigh the M&M's per bag then each M&M to see the differences in weights. This could teach ounces. There are many things you can do with this activity, therefore I feel that is can be used all the way through high school.

8: September 13, 2011 | Grade Level: 2nd and up Topics: Probability Standards covered: Data analysis and probability, Communication General Procedure: Each pair was given frogs and a frog pond game board. One frog was placed on each number 1-12. Each person predicted which frog they think will reach the other end of the paper first when rolling two die. After the predictions are made, the pair rolls both dice. Whichever number shows up, that frog is moved on space. The students will repeat this two times. The students will then find the probability of rolling a 1,2,3,4,5,6,7,8,9,10,11, or 12. Comments and reactions: I think this is a great way to teach probability and prediction. As mentioned before, children learn concrete to abstract. Therefore, when trying to help children understand probability; this is a good way to start. I also feel that this is a good game to promote communication and team work because the children have to work in groups of two. | Activity: Frogs hop to the Pond

9: Extensions and connections: I think that this game can be used for other things rather than only numbers. You can used a die with colors, shapes, letters, etc. Not only will you be teaching probability but other content such as letters shapes, and colors. This game can also be used when talking about fractions because the probability of the numbers is a fraction. You can teach students how to reduce fractions to the smallest unit. You can also teach how to add fractions if you ask questions such as, "What is the probability of rolling a 7 or an 8?"

10: September 13, 2011 | Grade Level: 2nd grade and up Topics: Probability Standards covered: Problem solving, Probability General Procedure: Each pair of students is given a game board consisting of 10 lily pads. One frog is placed on each lily pad. The partners take turns removing one or two frogs from the pond at a time. The goal of the game is to be able to remove the last frog from the pond. The students are asked to think about the game and try to figure out the strategy of a way to win every time. Comments and reactions: I think this is a challenging game to use with students that will incorporate problem solving and probability. I really like that it is math but also a fun game. However, I do feel that if a student looses constantly to their partner they will become frustrated and not understand the math concept of the game. | Activity: Frog Pond Game

11: Extensions and connections: I think this game could extended by having the student figure out the probability of taking the last frog after each turn. It could also be turned around so that you want your partner to take the last frog, not you. This could also be connected to prediction. After playing the game one time, have the students predict what they think the strategy is. Then have them predict their strategy in the next game.

12: September 15, 2011 | Grade Level: Topics: Geometry, Venn Diagrams Standards covered: Geometry, data analysis and probablity General Procedure: Start by placing a set of attribute blocks out that includes large circles, squares, and triangles of blue, red, and yellow. Also small circles, squares and triangles of the same colors. Then place two strings in the form of a venn diagram. As the teacher, decide what you want to be placed in the middle, for example blue squares. The students will then guess which shapes or colors go into the left circle, the right circle, or the middle. The students will be prompted to use their correct and wrong guesses to try to figure out the answer. For example, the left circle will be all blue shapes, and the right circle will be all squares. However, the blue squares are placed in the middle. Once the students can do this, place another circle on the board so there is three. You can now use shape, size, and color. After a few, have the students create their own with a small group. | Activity: String game

13: Comments and reactions: This was my favorite activity so far. I really enjoyed that the activity can be simple with two circles or challenging with three. This activity also requires your students to pay very close attention to their peers so they can hear their responses. However, If you are completing this on the board as a whole class activity it is important to make sure all students stay actively involved. Extensions and connections: This activity can be done with many other subjects. For example you can use famous people in history. One circle can be presidents, the other circle can be famous people from history from Pa, and the middle would be presidents from PA. I feel that this activity could be related to almost any subject or topic being taught in any grade level.

14: September 22, 2011 | Grade Level: 2nd grade and up Topics: Data analysis, addition, subtraction, multiplication Standards covered: Data analysis and probability, Number and Operations General Procedure: To begin this activity each pair had to pick an object in the room. I chose a pencil. Then, you needed to measure it in inches and figure out how many inches one million would be. After you figure out how many inches, you then had to put that number into a simplier idea for people to understand. For example, how many laps around a track, how many miles, etc. If I laid out 1 million of the pencils i chose end to end it would extend 110 miles or 440 laps around a track or 2 hours driving at 55mph. | Activity: How much is 1 million?

15: Comments and reactions: I really enjoyed this activity. It is a good way to show children how much 1 million really is. A lot of children either have an idea that 1 million is about the same as infinite or other children believe it is a lot less than what it really is. I also liked that the children would be using items that they see in everyday life so it is easier to relate to. Extensions and connections: This can be extended when working with addition, subtraction, and multiplication. There was a lot of math involved when figuring out exactly how far the item would reach. It could also be used when talking about miles. The activity could be changed to "How much is one mile". The students could then figure out how many pencils or other items it would take to reach one mile. | One milion pennies in a clear boz the size of a refrigerator.

16: September 27, 2011 | Grade Level: 1st grade and up Topics: Measuring, estimating Standards covered: Measurement, data analysis and probability, communication General Procedure: To begin, students estimate their height and wingspan in centimeters. They then stand against the wall were there is a horizontal and vertical tape measure. Their partner measures their height in centimeters. After they are measured, they need to decide if they are a square or not. If their height and wingspan are no more than 3 centimeters apart they are a square. If their height is greater they are a tall rectangle and if their span is greater they are a short rectangle. We then placed a post it note on the board in the correct category to indicate whether or not you were a square, short rectangle, or tall rectangle to compare out data. | Activity: Are you a square?

17: Comments and reactions: I really enjoyed this activity. I think it is a fun interactive way to get children involved in estimation, measuring, and data analysis. The only thing I would change if i was to do this with a classroom, would be to have more tape measures around the room. If you are only using two the children are likely to become impatient and you will have behavior issues. Extensions and connections: This could be extended by having the students collect data throughout the entire school and compare it. This activity could also be done at the beginning of the school year and the end of the school year to see how the children have grown. The children will love doing the activity again to compare themselves to the first time. I also think this could be used when introducing inches not only centimeters.

18: September 28, 2011 | Grade Level: 3rd grade and up Topics : Problem solving Standards covered: Communication, Problem solving, General Procedure: To begin, students are given red, green, blue, and yellow tiles. They are then instructed that they are going to be given a set of clues and they are supposed to figure out how many of each color are in the bag. The clues involve things such as, there are fewer than ten tiles, there are 2 coors, twice as many blue as yellow, 2 yellow tiles, etc. After the children have practice with solving the problems, they can make their own clues to make their own riddle. Comments and reactions: I enjoyed this activity but it may be difficult for some young students to complete. However, I think it is a good activity to help students develop problem solving skills. | Activity: Color tile riddles

19: Extensions and connections: Extensions and connections: I think this could be extended by having the children think of a number and give clues to what number it is. I also think this activity can be used a good way to build students math skills by using clues such as 3x as many green than blue or 3x less green than blue. The more difficult the clues the more advanced students can participate without it being too easy.

20: October 6, 2011 | Grade Level: 1st grade and up Topics: Multiplication Standards covered: Number and operations General Procedure: Pass out a I am who is card to every student. The cards will say something like I am 30. Who is 4 x 7? Whoever has the card with the answer to 4 x 7 will say I am 28 who is .... and so on. The tricky part to this game is that with multiplication there can be more than one to get your answer. For example if your card says I am 20 you may have to listen for 1 x 20, 2 x 10, or 4 x 5. This way the children have to pay attention to what is being sad. However, the cards need to be created carefully because you should not have two cards with the same answer because that may mess up the flow and it will not end correctly. When students have made it al the way through the cards it should end with the first person saying I am.... | Activity: I am, Who is?

21: Comments and reactions: I think this is a wonderful activity. It helps children practice math facts but it also teaches them the importance of paying attention. However, the idea of this game in gerenal is wonderful. It can be used in so many different ways in classrooms of all ages. Extensions and connections: This activity can be used for states and capitols, presidents, vocabulary, adding coins, geometry such as WHo is 4 right angles, I am a square. This game be used in almost every subject is every grade level from 1st grade on. I am 20 Who is 5 x 9

22: October 11, 2011 | Grade Level: 2nd and 3rd Topics: Addition and subtraction Standards covered: Data analysis and probability, Number and Operations General Procedure: The students start with the numbers 2,4,6,8,10,12,14,16,18. The students are given a 3 by 3 square. They are told to fit the numbers into the squares so the sum of each row is 30. The students will be using addition skills and problem solving skills to try to solve the puzzle. Second graders may struggle with this because from experience, they may not be good with double digit addition. After about five minutes, start giving the students a few hints. Make sure the students are writing down their addition problems. At this age, mental math is not encouraged for double digit math because of the regrouping and larger numbers. | Activity: Addition and Subtraction puzzles?

23: Comments and reactions: I enjoyed this activity and it was easy for me. However, from experience teaching second graders this may be more difficult for them. The second graders that I taught did not know regrouping or double digit addition. However, this would be a good activity to do when students are working with regrouping and double digit addition. Extensions and connections: You could use this activity for many different kinds of math. As long as you can figure it out correctly, you may be able to do this with subtraction or multiplication. As long as the total of the rows is possible to get your students can do it. Therefore, this activity can be used in higher grades not just second or third.

24: October 13, 2011 | Grade Level: 2nd to 5th grade Topics: Addition Standards covered: Data analysis and probability, Number and Operations General Procedure: The children split into groups of two. They are given ten dice. They are told they can roll anywhere from 1 to ten dices per turn. The goal of the game is to get a total of 100 faster than your partner. However, if you roll a one you do not get any points for that turn. The goal is to try to figure out the most number of dice you can roll that gives you one the least amount of times. Although roling one die would give you the least probability of rolling a one, it would not get you to 100 very fast. To win this game you must take chances but use problem solving skills. | Activity: Hog

25: Comments and reactions: This is a fun game for students to practice addition. It helps children with their addition skills but it also helps teach self control. If the students just throw all ten dice every turn it is more likely they are going to roll a one. If they realize this and start throwing less dice they may see a difference. Overall, I think it is a good game for addition. Extensions and connections: This game could be used for subtraction also. You can give the students a number to begin with and tell them they must subtract their total to reach zero first. I think this could also be used as a game to teach sportsmanship because students are working against each other.

26: October 18, 2011 | Grade Level: Upper elementary and up Topics: Geometry Standards covered: Geometry, Problem solving General Procedure: First, the students are asked to make as many shapes as possible using five squares. The shapes can not repeat or just be the opposite. After the students have found all of the shapes they need to cut them out. Their next task is to make a small square using the shapes. The hardest task is using all of the shapes to make a large rectangle. There are many ways to complete the task but getting the shapes in the correct spot is difficult. | Activity: Five Square

27: Comments and reactions: I really enjoyed this activity. However, I think using all of the shapes may be difficult for elementary students. Therefore, if I were to use this in an elementary school I would just have the students make the smaller squares and rectangles. However, I do think it is a good activity for them to do because it allows them to practice thinking abstractly. Extensions and connections: I think this can be connected to finding the area in higher levels. The students can find the total area of each square or rectangle. They can then figure out the area of each piece. Using that, they can figure out how many pieces they will need to use to complete the puzzle.

28: October 25, 2011 | Grade Level: 3rd grade and up Topics : Fractions Standards covered: Number and operations, Representations General Procedure: First, give the students manipulatives to use. Then give the students problems such as 2 x 1/2. The students then use their manipulatives to solve the problem. For example, you would have two group of 1/2. ANother problem could be 2/3 X 3. The problem is really asking what is 2/3 of 3. The students make a set of three. They then take 2/3 of 3 resulting in the answer 2. The problems can range from being simple up to problems such as 2 1/3 x 1 1/2. The students will be able touse their manipulative set to complete the problems. The manipulatives will give the students a better understanding of the problem. Most of the time, students do not really understand these types of problems they simply just solve them. | Activity: Whats my unit?

29: Comments and reactions: I really enjoyed this activity. It actually help me with fractions because I was never taught this about solving these kinds of problems. This activity will really help students understand what these kinds of problems are really asking you to solve. Trying to flip and multiply or any other trick being taught is way more difficult to teach than this. I feel that teachers should be teaching fractions this way because it is the really meaning, not just memorizing how to do them. Extensions and connections: This activity can be used for addition, subtraction, and division of fractions. I feel that this is the best way to introduce any kind of math problem with fractions. The students are going to get a more hands on feel while actually learning what the problems are really asking. I feel that this is the best way to teach fractions.

30: October 28, 2011 | Grade Level: Upper elementary Topics: Problem solving Standards covered: Problem solving General Procedure: Students will be shown and example of the card. They will be told not to pick it up from the table but they can touch it. They will then be instructed to make a replica of the card. They can use scissors and folding. If some students get this before others they can try to make one with more than one, continuously on the same sheet of paper. If some students are still struggling after a reasonable amount of time has elapsed. Allow them to pick up the model and manipulate it to see what has been done to the card. Then allow the students to see if they can then replicate it after seeing the card. | Activity: Cut a card

31: Comments and reactions: This activity was really challenging. It takes a lot of concentration and thinking to be able to look at the card and figure out mentally how it will be done. I think that elementary students will just start cutting and have a little more success than we did because they do not think as in depth as we do. Extensions and connections: I think the students can engage in other activities like this. I am sure there are other paper puzzles out there like this. I also think this activity will allow students to work on their communication skills. Students can interact with each other to bounce ideas around. I think this is a good way to encourage cooperate learning and team work.

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