Strengthen Your CoreOne Activity at a Time The CCSS-M are designed around coherent progressions from grade to grade. Each standard is not a new event, but an extension of previous learning. Learning is carefully connected across grades so that students can build new understanding onto foundations built in previous years. But what do teachers do when that foundation is not there? In this session we will share engaging teacher tested games, tasks, and stations designed to help students build and strengthen their mathematical foundation. The activities from our session will help to build students’ procedural fluency and conceptual understanding. Jane Lewis & Danielle Pierro Greenfield Middle School School district of Greenfield [email protected] 414-281-3450 [email protected] 414-281-3439 Learning Intentions Strengthen the level of student engagement in common core aligned activities that promote student centered learning. Learn how to apply stations, games, and tasks to build student’s procedural and conceptual understanding. Strengthen Your Core-One Activity at a Time Game Ideas “Never “Bored” Game Wheel of Mathematics (Spinner) Magnet Darts Tic-Tac-Toe Tasks Bowl-a-Fact Add it Up Zip it (Modeling on Number Lines) Hexagon Trains Express the Perimeter Line it Up Tangram Task Biggest Bang for Your Buck (from a 2nd grade Investigations, but modified for use in 2-7th grades) Stations Hit the Trail (Math Maze) Lost Your Marbles (It’s in the Bag) Math Journals Two of Kind Top Three Game Changers: 1) 2) 3) Math Talking Stems (bookmarks) My Favorite “NO” For 7th grade teachers: What Stuck With You? Probability 1) Roller Derby 2) Playing Fair 3) Use Your Head Never “Bored” Game Directions 1) On your white board or chalk board trace a sheet of paper over and over going up and down again creating a game board type pattern. 2) On the board game write movement directions for students. Examples: You got it correct, move up 2. Switch places with another group. Going too fast, move back 5. 3) Place students on teams of 2-4 people. Each team will have a magnet that they will move across the game board. (You can make each magnet a famous mathematician, for example on group could be Einstein, or Pythagoras) 4) Have groups write their names on notecards or if you already use popsicle sticks or notecards to call on students you can use those. You might want to only have a single notecard for each team though. 5) All groups must work together and try all of the problems. 6) I give the class a problem to solve. Each group works together to solve the problem. Groups can do their work on white boards or in their notebooks. 7) After some time, I tell the groups to put their markers down. I pick a few teams to show me their answers. If they are correct, they roll one of my giant foam cubes (or any dice would work) and then that groups moves their magnet the correct number of spaces. Tips 1) I make sure the students know that they must follow what the game board says, so if they land on switch places and they are actually in the lead, they still must switch with someone. 2) I usually make the end square say something about them doing so great but that they must go back to the beginning and start again. The students will ask when the game will end then and I just tell them it ends when I’m ready for it to end (based on time and if we finished the review) 3) Sometimes groups keep track of how Benefits 1) Every student is engaged and solving every problem 2) Students are working together and are able to help each other 3) Great formative assessment. I tell which students need help and which type of problems are giving the class difficulty 4) Great review before tests or quizzes 5) Kids have fun moving along the game board and they think it is fun to be the “magnets” 6) Teacher prep can be very easy; you can just pick random questions from many times they go through the board to “determine the winner,” but we usually don’t worry about who wins. Of course you can give a small treat to the winners if you want, but I really try to emphasis the effort and not who won. 4) I pick multiple groups for each question to keep all groups engaged. I also keep every groups card in the pile. Students never know if they will get picked or not, so they must all try every problem. I also keep the number of groups picked random; sometimes I pick 2 groups or 4 groups. I think this randomness keeps all groups on track. It can make the game “unfair” in that some groups get called on more than others, but since “winning” isn’t our focus it is fine. 5) I have played were every group that gets the answer correct gets to roll the dice and move, but that can get a little crazy, but it does then keep the game “fair” and then every group shares their answer every time. your book and ask those. If for some questions though the students need to see the problem or problems I just cut and paste some review problems from the book and put into a Smart doc, still very quick prep. Wheel-Of-Mathematics Directions: Teacher creates teams of students. Teams can be two large teams or smaller groups of 4-5 students each. Teacher asks a question, students answer, and teacher randomly picks a student’s name to see if they have the answer correct for their team. If student is correct, they get to spin. If student is incorrect, the next team steals the question and the teacher picks students from another team. Rules: 1. All students must try each problem even if it is no their turn in order to be ready for the steal. If a team member is not trying, the team forfeits their turn. 2. Poor sportsmanship results in a loss of points. For example, if a team teasing that the spinning team only earned one point on their spin then the team may double the points earn. 3. In the case that a student gets a question wrong, the teacher will never say who. Benefits: *The game can be mixed up each time you play so the game has new twists and turns *Can be used for any subject and unit-we have played created spinner game in Language Arts and Math *Can be differentiated by separating team in multiple ways *Position struggling students by choosing their name when they have a question correct. *Students like digital spinners on Smart Boards but they LOVE spinners they can actually feel *Students do not see who answers the question correct and who does not *Students walk away with several review questions *Encourages sportsmanship Other Game Ideas: Anything pretty much can be turned into a board game. I’m sure most of us have played trash can basketball or Smartboards are great for “Jeopardy” and “Koosh ball” games. My students love playing all sorts of games. Some of our favorites are: Magnet Darts: Years ago I found a magnet dart board at a dollar store and it has been a classroom favorite ever since. I usually just put the class into two teams, usually boys against girls, but you can do whatever. I explain that our darts are magnets, so they don’t have that exact point like darts, so we don’t play with the doubles and triples on the dart board and if we really can’t tell what number it landed on, we will always pick the larger number. I have notecards with each student’s name written on it and I divide those cards into the two teams. (Again I usually sort boys and girls but you can just “deal” the cards into the two teams.) I give the class a problem to solve. They can solve on white boards or in their notebooks. (They tend to love the white boards, but sometimes I have them do in their notebooks so that they can use this to review or study for a test.) After some time, I pull a notecard and have that student share their answer. If correct they get 10 points just for being correct and then they get to throw the dart to add to their points. Students mark the points on the board. Every student must try every problem, since they never know whose card will get picked. If a student answers incorrectly, the other team gets to “steal” and try to answer. Even once a card is picked; it still goes back in my pile, so that every student knows they could get picked. (I still control whose card gets picked so I can determine how to best “help” students with special needs. Since I’m walking around as they work, I will often pick a student who struggles only after I saw that they have it correct on their sheet. Tic-Tac-Toe Another game the students love is tic-tac-toe. We play this game a few different ways. I have an old “Toss Across” game that has students toss bean bags at a game board that spins to reveal either a “X” or an “O.” I also bought a tic-tac-toe beach towel game from Oriental Trade. This is just a towel with the game board on it and students toss either their “X” or an “O” at the towel after answering. The fun part of both of these is that sometimes they can’t control were their “X” or an “O” lands or if a “X” or an “O” will flip over in Toss Across. This really puts an interesting twist to tic-tac-toe and then if often won’t end in a “cats” game. We also sometimes play the traditional way and just draw the game board and place our “X” or an “O” on the board. (This is the best way when we don’t have much time.) Benefits: Again every student is involved Great formative assessment Easy teacher prep Bowl-A-Fact Start by rolling three dice. This is your first “throw” down the lane. 1) The students must use all three and only those three numbers rolled to try to knock down as many “pins” as possible. To knock down a pin, the pin number needs to be the answer to the problem the students create. I put the pin sheet on the Smartboard and as we knock down the pins, we cross them out. 2) To knock down a pin students can add, subtract, multiply, divide, use fractions, exponents, etc. BUT again they must use all 3 and only those 3, so you can’t have 32 unless you rolled both a 3 and a 2. 3) Goal: to work together as a class to try to get a strike. 4) After a few minutes of work time, students can come up to board and share their work for a pin that they knocked down. Students will discuss if they agree with the work and if they “knocked” down that pin a different way. (Often as they are working, they will say aloud, “I got the 4 pin.” Or “I can’t get 8, did anyone get the 8?” etc. I encourage this type of talk. I often work on it too and will tell them if I got a number they need, but I don’t tell them how. Since all totals are not possible with three numbers I don’t want them to try forever to get something they can’t get, but I also don’t want them giving up with something can be knocked down.) 5) If we don’t get a strike, we throw again looking for the spare. A throw is rolling the three dice. Now, we only have to try to get the pins that are still standing. If we knocked down the five on our first roll, we don’t have to get that answer again. EXAMPLE Roll #1 4–2–3 Possible work: 32 – 4= 9-4 = 5, knocked down the 5 pin 24 ÷ 3 = 8, knocked down the 8 pin 4 + 3 +2 = 9, knock down 9 4 – 3 + 2 = 3, got the three etc. Great for working on order of operations. Often students get a pin, but without ( ) it might not be correct, so we work on that. Roll #1 Roll #2 Add It UP Directions Create four problems for each team of four students. Each student is assigned a number and will complete the matching problem. When all students have finished their problem, their team adds up all four answers, writes the sum in the center, and raises their hand. If the team’s sum is incorrect the teacher will simply let the team know to rotate the board. Students rotate the board and work together to find the error. Students pose questions about their peer’s work to better understand where their final answer came from and share if they have a critique. In the rare case that no errors are found, students can rotate the board until the error is found. Students add their new answers together, place the new sum in the center, and raise their hand to signal they are ready for the teacher to review their work. If the team’s sum is correct, the teacher asks the team to cover their answer and “teach” their group their problem if they haven’t rotated the board yet. Another option is to send one student from the finished group to each of the unfinished groups as “coaches”. Once a stopping point presents itself, have different groups share out their solutions one problem at a time. Tips *Before sending “coaches”, students need to practice asking questions to guide their peers to the answer and not just tell struggling students the final answer. *Require students to be able to explain their own problem so no one student can take over. *When appropriate, try to require all four students to understand all problems in the group. Interview students on questions that they were not assigned to before telling a group if they are correct or not. *When playing multiple rounds, rotate the type of question that each student receives. Benefits *Create leveled problems to meet the needs of all students *Each student has a critical piece in the activity- all students have equal value as a member of the team *Individual work and team work in one activity *Students work together to critique and understand all problems *Students’ perseverance in problem solving is strengthened Person #1 Person #2 Sum of all four answers Person #3 Person #4 Person #1 Person #2 4.26 + 17 – 9.23 = SUM Person #3 84.56 – (12.3 + 65) = 27–15.43 – 2.8 = of all four answers Person #4 71 – 33.6 + 18.23 = Person #1 Person #2 You are cooking a turkey. The turkey must reach a temperature of at least 165 degrees to be considered fully cooked. The temperature of the turkey is currently 165 degrees. Write and solve an inequality to represent the number of degrees the temperature must increase for the turkey to be done. Write the word sentence as an inequality. Then solve the inequality. The difference between a number b and 4.5 is greater than 8. Sum of all four answers Person #3 Write the word sentence as an inequality. Then solve the inequality. The quotient of a number z and 7 is at most 12. Person #4 Three friends decide to share the rent of an apartment equally. The apartment they are renting costs at least $1200 per month. Write and solve an inequality to represent each person’s share of the rental cost. Person #1 How many Edges does this solid have? Person #2 Find the Surface Area of this Rectangular Prism Sum of all four answers Person #3 Find the Surface Area of the following solid Person #4 How many Faces does this solid have? Zip It! Directions: Students are in groups of two. Partner 1 is the only one that can write for the team and needs to ZIP IT! Partner 2 is the only one that can speak. Partner two explains what partner 1 should write. No erasing can be done unless the speaker requests it. The student writing cannot write an assumption but must wait for specific directions. Example: A student cannot say write the number in order from least to greatest. They must say “first write 10, now write 11” etc. The partner writing can use the Zip It cards as a way to communicate. The writer can point to either “Can you repeat that?”, “Why?”, or “How do you know?” as a way to move the speaker along or slow them down if needed. tips: Practice! This takes lots and lots of practice. Model this activity with examples and non-examples. Highlight moments when this really helped students develop a stronger understanding and soon enough students will request this when they know they need to work breaking down content. benefits: This allows teachers to hear all voices and allows students to explain EXACTLY what they’re thinking. Students can see the importance of precise math language This helps students to slow down their thinking and gives students practice on giving their peers the “think time” needed. Can you repeat that? Why? How do you know? Can you repeat that? Why? How do you know? Can you repeat that? Why? How do you know? Can you repeat that? Why? How do you know? Grade 2 Zip It! Round 1: Using an open number line, model 32 + = 70 Speaker explains how to solve while scribe follows directions given. Scribe should use their question cards as much as needed. Once done- scribe can explain how they would have solved if differently, if they agree/disagree and why. Round 2: Using an open number line, model 42 + = 82 Don’t forget to switch roles and follow the steps above ! Name: _________________________ Block: ________________ Hexagon Pattern Train Task The first train in this pattern consists of one regular hexagon. For each subsequent train, one additional hexagon is added. The first three trains in the pattern are shown below. train 1 train 2 train 3 1) Find the perimeter for the first four trains. Train Number (number of hexagons to make the train) Perimeter ONE TWO THREE FOUR 2) Find the perimeter of the tenth train (try to do without constructing the train.) Express the Perimeter Boaler, J., & Staples, M. (2008). Create mathematical futures through an equitable teaching approach: The case of Railside School. The Teachers College Record, 110(3), 608-645. Line it Up Your group will get a set of notecards (white and a color.) The white cards will be your “benchmark” fractions, place them out in front of the group leaving room in between (think of your spacing) 0, 1 2 , 1, 1 1 , 2 2 The colored notecards will have the fractions from the first box on them. You will then take turns picking and then placing your notecard down in the correct place based on your benchmarks on the number line you are creating. When you place your notecard, you must explain why you chose that location. If your group can not decide if you are correct based on your reasoning, discuss and see if you can all agree on the correct placement. If you still are not sure use your calculator and make it into a decimal, does that help? If not, ask me. When your group finishes the first box, write the correct answers below. Then come up to get another set of colored cards and work on the second box, etc. Answers 0 1 1 1 2 𝟏 𝟏 𝟗 𝟗 𝟏 𝟏 𝟗 𝟗 1 1 𝟖 𝟏𝟔 𝟖 𝟓 𝟖 𝟏𝟔 𝟖 𝟓 𝟏𝟒 𝟏 𝟏 𝟏𝟒 𝟏 𝟏 0 1𝟏 𝟐 𝟏𝟓 𝟒 𝟐𝟎 𝟏𝟓 𝟒 𝟐𝟎 𝟏 𝟔 𝟑 𝟓 𝟏 𝟔 𝟑 𝟓 2 2 𝟐 𝟏𝟐 𝟒 𝟐 𝟐 𝟏𝟐 𝟒 𝟐 0 𝟏 1 𝟐 Tangram Task TASK: You will be demonstrating your ability to write and reason in math. If all seven tangram pieces equal one whole-you need to figure out what fractional part each piece represents. Your answer must be complete! YOU NEED TO EXPLAIN YOUR REASONING. (You only get one point for having the correct answer-the rest is based on your explanation of how you got that answer.) I should be able to tell exactly what you did to solve the problem and what you know. You should also prove that your answer is correct. You can use diagrams, phrases, equations, or sentence. Tangram task-student direction sheet It doesn’t have to be in complete sentences though. Jane Lewis Tangram Fractions Task Find the fractional part of each Tangram piece in the whole (All seven pieces). Be sure to explain your reasoning Purpose This task allows the teacher to plan for future units on fractions. This task also involves a whole that is divided into pieces that are not the same size. The more students play around with different concepts of “whole” and “parts,” the better their understanding of fractions will be. Context This is one of the first tasks that I give to my students. I start by giving them a sheet that has them making their own Tangram pieces by folding and cutting paper. Once they make their Tangram pieces they keep them in their folders throughout the school year. They need their pieces because sometimes as a warm-up for class we will do Tangoes puzzles. I also like doing this one first because most of the students can do this. The students start off confused and want more direction, but with time, most can figure it out for themselves. This helps them to feel more positive about problem solving. I know the students have studied fractions in previous grades and I want to get a feel for how many had a conceptual understanding of a fraction and how it relates to the whole. The task itself does not name any of the shapes. I used to create a table for the students and had them just put in the answer, but I decided to let them use their mathematics language and name the shapes themselves. I also like that they need to decide how best to represent their answers than just filling in my table. Solutions Large triangles (#’s 1 & 2) = 1/4 Medium triangle, square, parallelogram (#’s 3, 5, & 7) = 1/8 Small triangles (#’s 4 & 6) = 1/16 Tangram task-teacher page Name______________________ Hour___________________ Biggest Bang for Your Buck You have decided to give your math teacher a little treat to show her how much you appreciate her. You have decided to buy her a candy bar as a small token of thanks (a bigger gift will come later on in the school year ) The cafeteria sells 7 different candy bars all of which are the same thickness. You want to show your math teacher how much you have learned in math class by purchasing the candy bar that is the best value. If all the candy bars are $.50 each, how can you show that you picked the candy bar that is the most chocolate for the smallest price? Explain two ways that show that you got the “biggest bang for your buck.” Name_______________________________ How Should I Rate Myself? 0: I needed help with each step in order to solve the problem. 1: I can do some steps in the problem on my own but am not yet independent. 2: I can successfully complete each problem by referring back to my notes/resources. 3: I can independently and successfully complete each problem. 4: I can solve the problems in multiple ways. I can explain how and why the problem works. Question # Question and How I Solved It How comfortable was I solving this independently? # 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 # # # Question # Question and How I Solved It How comfortable was I solving this independently? # 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 # # # # # Hit the Trail How to: 1.) Fold 10 (or more-as many sheets as you want questions) pieces of construction paper in half (hamburger style) and staple a plastic page protector sheet to the inside of your folded paper. (I used brown for a “trail” type of look and created a cover page that I glued to the front of the construction paper, and then I laminated, so I just write on a new answer any time I play.) 2.) Write questions and slip them in the page protectors (a different question for each folder) 3.) Write Answer to NON-matching problem on the outside 4.) Also number the papers on the outside as in #1-10 *I just used questions from our book so I didn't have to take time to make new questions/answers. 5.) Hang problems up around the room so only the answer/outside shows 6.) Hand students *a problem to start with* (a number 1-10 that would work as their starting place. this keeps all the goofballs from picking the same starting area and you can level the questions to have struggling students at the easier problems) Students start at their problem assigned. Once they complete the problem, they find the matching answer to the problem they just solved and then complete the problem that it led them to. If their answer is nowhere to be found- it means they did something wrong. Students can work independently or with the people who are at the same question. I didn't really think that kids would like this because it really is just answering problems...but they loved being able to navigate their way through the room. When I stopped and listened to them- they really were all working and talking about the problems. I did this for equations and changed all variables to "a" so students couldn't just figure out what the answer was by matching up the variable. Math Maze: Directions Directions: Create review problems for students. Place one problem on each page towards the bottom of the page so you can fold over the front to “hide” the problem. On the front of each problem, write the answer to the problem before it. In order to not have students caught in a “loop” or be sent to the same problem more than once; make sure you only have each answer listed once and create a rotation with your answers as modeled below. Create as many or as few problems as needed! Math Maze: Tips *Assign students a starting place. *Require students to show their thinking for each problem. *Mix the problems up so the answers do not go in order...this creates more of a scavenger type feel to the game! *Spread out problems that require more time to prevent “traffic jams”. Math Maze: Benefits *Students self-check their work by instantly knowing if they are correct and retry problems. *Students can practice at their own pace. *Students work in independently or in partners. *You are free to help students. Math Maze Question # Question-work-solution Question # Name_________________________________________ Question-work-solution Lost Your Marbles Directions: Create practice problems to have at each station. Each station has an answer folder and a cup for marble. Each pair of students is given as many marbles as you have stations/questions. (You can do as many or as few of stations as you want. I usually do this as a review and then my number of stations is the same as my number of learning targets.) Students work in partners and put a marble in each cup when they answer correctly. Students travel throughout the stations in numerical order. Students answer each problem before checking their work. When they check their work, they use the following KEY: Put an X through problems you got correct (don’t have to study what you know) and place your marble in that cup Put a ? by the problems that you needed some help with but if you got it correct, you can still put in the marble Put an ! by the problems that you HAVE TO STUDY. Don’t put your marble in this cup then! Tips: * Assign students a number to start at and have them travel around the room. This elminates having chatty students from picking the same questions to start at. *Make sure students show all their work on their sheets. This creates a great study guide for them. *If you only have a few questions you want the students to do, just create multiples of that answer folder to keep students from all gathering at one station. (So for example, if I only have 6 different questions, I only have 6 stations, but I might have 4 of the same folders at each station.) Station 1 Station 4 Station 7 Simplify the expression Are the two expression equivalent? Explain Find the sum 8a 2 4b 7a 2 53a 2 2b 6b 6 x 3 2 x 9 Station 2 Station 5 Station 8 Simplify the expression Find the difference 8k 24 3k 10 j Solve the equation. Check your solution 19a 7 3a 12a 7 9 j 2 3 1 3 r 4 8 Put an X through problems you got correct (don’t have to study what you know) and place your marble in the cup Put a ? by the problems that you needed some help with, but you can put your marble in the cup. Put an ! by the problems that you HAVE TO STUDY. Don’t put your marble in cup. Directions: Create practice problems to have at each station. Students travel throughout the stations in numerical order. Students answer each problem before checking their work. If students have the correct answer, then they put the question/slip of paper in the bag since they have it “in the bag”! If students have the incorrect answer, they take the question with them to study or re-try. If students need to check the answer key before solving (because they are stuck), then they take the problem with them. Tips: * Assign students a number to start at and have them travel around the room. This elminates having chatty students from picking the same questions to start at. *Make sure students put their names on each problem that they put in the bag. The first time you play, remind students throughout the activity to do this so you know what each student acomplished. *At the end, have students walk around to any station that they didn’t get to so they practice all problems. *Have students write the answer to the problems that they had incorrect or didn’t complete so they can self check later on as well. Benefits : * You instantly see just how many students are on track * Each question is a quick snapshot of student’s thinking *Bags/questions that are empty or have few correct answers need more attention *Students work at their own pace *Students take problems home that were incorrect and know what they need to study *Peers do not see who gets the questions right. Two of a Kind: Directions Create two problems that have the same answer and give one to each partner. Students solve their own problem and wait until their partner finished. Once both partners are done, students compare their answers. Students cannot continue onto the next problem without their partner. Students share their problem and discuss how they solved it. Students should discuss similarities between the two problems. If students have different answers, they help each other find the error(s). Two of a Kind: Benefits *Can be used for a partner station, game, or parent-student homework. *Can be leveled to meet each student’s need-You can pair like ability together or different abilities together and match ability with the correct problems *Students practice giving their peers the “think time” needed. *Students critiques the work of others. *Students compare differently representations and see multiple problem solving methods Two of a Kind Partner A Partner B Name __________________________ Name __________________________ 1. Write and simplify the expression for the area and perimeter of the rectangle 15.5 1. Write and simplify the expression for the area and perimeter of the rectangle 9 7 m 5 5.5+ m 2. Find the area of the parallelogram 2. A wildlife conservation group buys a plot of land represented by the triangle. How much land does it buy? Top 3 Game Changers Of all of the new things we have tired or worked on over the years, the three that have had the greatest impact have been: 1) Math Talking Stems (the bookmarks) 2) My Favorite No (see sheet and check out the video link) 3) What Stuck With You? If you try anything from our presentation, we strongly recommend these three things! Math Talking Stems (bookmarks) Working on classroom discourse is huge. We know that we need to get students talking about math. We found that the talking stems help the students know how to start discussions and how to keep the talking more focused on the math. We make the bookmarks on card stock, laminate, and give to the students early on in the school year. We have found that you need to teach the students how to talk like mathematicians and the talking stems seem to help. What Stuck With You? 1) I create a display with numbered squares for each student in my class. I used “library pockets.” I glued them to poster board and then laminated the board. I used an exacto knife cut back open the pockets. 2) Each student is given a math number. This number is used when they use my calculators and it is their number for “What stuck with you?” (I used just have students put their names on it and some students said they didn’t like having their name it. They wanted it to be more confidential. 3) I often use this as a type of warm-up or as an exit question. I give the students a problem. They solve it either on notecards that they tuck in the pocket or on post-its that they stick to their number. 4) The great part with the numbers, I can easily check that all students did the problem. 5) I then can use their answers to form my instruction. I can use it to help group the students, use it to know which students need to work with me, see if there are any misconceptions that I need to clear up, use as example work that I can have the students discuss (see My Favorite No), etc. 6) Also, students use it to just write thoughts, questions, or ideas that they might have on a lesson that day. Students can grab a post-it and write anything that “stuck with them” from that day’s lesson. My Favorite No (by Leah Alcala) One of the biggest changes we have added to our classroom this year has been our work on discourse. We want students to talk about their math. (CCSS.Math.Practice.MP3 Construct viable arguments and critique the reasoning of others.) One idea that we used came from watching this video on “My Favorite No.” https://www.teachingchannel.org/videos/class-warm-up-routine The teacher featured in this video link is Leah Alcala, an eighth grade teacher at Martin Luther King Middle School in Berkeley, CA. She gives her students a warm-up problem at the beginning of every class, which they solve on index cards. She quickly sorts through them, and from the wrong answers chooses her "favorite no." She and her kids then analyze what's right about the solution before delving in to what the writer doesn't do correctly. We don’t use it daily, but both of us have done this with our students and they love it. They have commented that they learn so much more from going over incorrect answers than from looking at correct solutions. Roller Derby Objective: The students will explore experimental and theoretical probability. Supplies: Roller Derby overhead, homework overhead, Roller Derby sheets for each student, 15 cubes for each student, and a pair of dice Vocabulary: probability: the chance of an event occurring theoretical probability: the probability of an event is equal to the number of favorable outcomes divided by number of possible outcomes experimental probability: a statement of probability base on the results of a series of outcomes Procedure: The teacher will put the overhead of Roller Derby on the projector. The teacher will read through the overhead with the students and will explain to the students how to play the game. The teacher will make sure that all of the students understand the rules and will give them some time to place their 15 cubes. The teacher will explain that once the game starts the students can NOT change the placement of the cubes. The teacher will then either roll the dice, or pick a student to role the dice, or pass the dice around the room and allow all the students a chance to roll the dice. The two dice will be announced and the students will then find the sum. Any student who has a cube on that sum will “remove” their cube. Play will continue in this manner until someone removes all 15 of their cubes. The first student to remove all their cubes is the winner. The teacher can then give the winner a small piece of candy if they chose. You will then have all the students clear off their cards and play again! (if time, you can play again and again .) The teacher can then lead a discussion about what strategies the students chose. Homework: The students will then complete the Roller Derby reflection sheet. They need to use complete sentences. Roller Derby # 2 3 4 5 6 7 8 9 10 11 12 Place 15 cubes wherever you would like Once you place them, they can’t be moved Roller Derby Reflection Using complete sentences answer the following questions. 1. Did it seem like “some of the sums” were rolled more than others? Why? Explain the probability of rolling each of the sums. 2. When you played the game a second time, did you change where you placed your cubes? Why or why not? 3. Do you think this is a game of luck or strategy? Explain. Playing Fair Parker Brothers, makers of such great board games as Monopoly, Sorry, and Clue, have enlisted your help. They are in the process of developing a new board game and they need for you to use your math skills and check it out. First you should play the game a few times with a partner and then you should develop a report to present to the company. How to play the game: First get with your partner Then decide which player will be who. One player will be Even Steven and the other player will be The Odd Ball. Each of you will have a six sided number cube. You will each roll your die. Write down the number you both got, then you need to multiply the numbers on the dice, and record the product. [product: is the answer you get when you multiply the two dice] If the product is even-Even Steven gets a point. If the product is odd-The Odd Ball gets a point Do this twenty times and then total up the points. The player with the most points after twenty rolls WINS! Record your results. Repeat the experiment and play again to determine if your results are the same. Finally prepare your report for Parker Brothers. Is this a fair game? Are you “Playing Fair?” Playing Fair Game One PRODUCT Game Two Even’s Point Odd’s Point POINTS Game One Game PRODUCT Even Steven Even’s Point Odd’s Point The Odd Ball Two Report for Parker brothers Did you feel that this game was “playing fair?” Please explain. What is your mathematical reasoning behind your decision? Fill in the multiplication chart below and highlight all of the even products. rolls 1 2 3 4 5 6 1 1 2 3 4 5 6 2 2 4 6 3 3 6 9 4 4 5 5 6 6 20 36 Find the probability of rolling an even product._____ Find the probability of rolling an odd product.______ Is the game fair? USE YOUR HEAD Instructions: Put both coins in the cup. Cover the cup and shake. Turn cup upside-down to toss the coins. Toss the coins 50 times. The winner is the person with the most points. Game Rules: Player A receives 1 point if two heads (HH) are tossed. Player B receives 1 point if two tails (TT) are tossed. Player C receives 1 point if one head and one tail (HT) are tossed. Scoring Chart: Game 1 Name of Player Player A (HH) Player B (TT) Player C (HT) ________________ _________________ __________________ Tally of points Total points Game 2 Name of Player Tally of points Total points Player A (HH) Player B (TT) Player C (HT) ________________ _________________ __________________ Reflection: Is a game with these rules fair? ______________________ Explain why or why not. __________________________________________________________________________ __________________________________________________________________________________________________ __________________________________________________________________________________________________ How might you change the rules to make the game fair? ___________________________________________ __________________________________________________________________________________________________ __________________________________________________________________________________________________ Conduct an experiment to test your new game. New Revised Game Name of Player Player 1 Player 2 Player 3 ________________ _________________ __________________ Tally of points Total points Do you still think your game is fair? _____________________ Why or why not? _________________________________________________________________________________ __________________________________________________________________________________________________ __________________________________________________________________________________________________ Create a fair game with 2 dice. Explain your rules:____________________________________________________________________________________________ __________________________________________________________________________________________________

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