Dots. Boxes. and. xyz. Photo by Kamyar Adl

Transcription

1 Dots and Boes Photo b Kamar Adl

2 Contents.... Standard rules for Dots & Boes (onl for those unfamiliar).... Rules for Dots and Boes Common Core Standards 4 Most of the first class will be spent here. Some students benefit from being creative and designing their own game boards $500 classroom challenge Projectable game for the whole class Printable game-sheets Projectable game with eponents for whole class Printable game-sheets with eponents Make our own game board Sample Game of standard Dots and Boes (not for the class!).... About MathPickle 27 The original idea for using algebra with Dots and Boes game came from Algebra 4 All. You can bu their original product here: Copright 2015 MathPickle - All rights reserved

3 Dots and Boes This is ordinar dots and boes ecept: 1) When ou win a bo, its value is often determined b a variable, or. Eample: a bo labelled 2 is worth 22 if = 11. 2) Once during the game ou ma skip adding a line and change the value of a variable b ±. A variable that has been changed cannot be changed again = 3 = 2 = 1 -=-8 +=11 3) The game is immediatel over once all the boes are filled. Variables cannot be changed after the boes are all filled. 4) The winner is the person with the highest score (or the least negative score.) Score: =19 Score: +2+5=14

4 Standards for Mathematical Practice Common Core State Standards All MathPickle pule designs, including Dots and Boes, are guaranteed to engage a wide spectrum of student abilities while targeting the following Standards for Mathematical Practice: MP1 Toughen up! This is problem solving where our students develop grit and resilienc in the face of nast, thorn problems. It is the most sought after skill for our students. MP3 Work together! This is collaborative problem solving in which students discuss their strategies to solve a problem and identif missteps in a failed solution. MathPickle recommends pairing up students for all its pules. MP6 Be precise! This is where our students learn to communicate using precise terminolog. MathPickle encourages students not onl to use the precise terms of others, but to invent and rigorousl define their own terms. MP7 Be observant! One of the things that the human brain does ver well is identif pattern. We sometimes do this too well and identif patterns that don't reall eist. Dots and Boes targets the following Common Core State Standards from grades 6-: CCSS.MATH.CONTENT.6.EE.A.2 Write, read, and evaluate epressions in which letters stand for numbers. CCSS.MATH.CONTENT.6.EE.A.2.A Write epressions that record operations with numbers and with letters standing for numbers. For eample, epress the calculation "Subtract from 5" as 5 -. CCSS.MATH.CONTENT.6.EE.A.4 Identif when two epressions are equivalent (i.e., when the two epressions name the same number regardless of which value is substituted into them). For eample, the epressions + + and 3 are equivalent because the name the same number regardless of which number stands for. CCSS.MATH.CONTENT.7.EE.B.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems b reasoning about the quantities. CCSS.MATH.CONTENT.HSA.CED.A.2 Create equations in two or more variables to represent relationships between quantities. CCSS.MATH.CONTENT.HSF.BF.A.1 Write a function that describes a relationship between two quantities. (

5 1 1 $500 classroom challenge 1 1 Perhaps our students have created a beautiful Dots and Boes game board or a student who is not usuall ecited about math has become engaged. Perhaps a pair of students discovered that the can guarantee a win for the first or second plaer on one of the ver small boards. Whatever our inspirational eperience with this gem of a game, I d like to know. I'll offer $500 for a photograph and/or stor highlighting Dots and Boes in the classroom. 1 All students featured must have appropriate consent. All photographs and stories submitted ma be used in an updated version of this pdf file and to promote this game elsewhere. Send submissions to gord@mathpickle.com. Use $500 Dots and Boes challenge as the subject of the . The winning classroom will be announced the first March 14th that I have at least submissions from different schools. I hope this will be March 14th,

6 Dots and Boes Photo b darkda

7 2 2 2 = 3 = 2 = Score: Score:

8 Dots and Boes This is ordinar dots and boes ecept: 2 1) When ou win a bo, its value is often determined b a variable, or. Eample: a bo labelled 2 is worth 24 if = 12. = 4 = 4 = 4 5 = 4 2) Once during the game ou ma skip adding a line and change the value of a variable b ±. A variable that has been changed cannot be changed again. = 3 = 2 = 3 = 2 = 3 = 2 = 3 = 2 3) The game is immediatel over once all the boes are filled. Variables cannot be changed after the boes are all filled. 4) The winner is the person with the highest score (or the least negative score.) 1 = 4 = 3 = 2 = 4 = 3 = 2

9 Dots and Boes This is ordinar dots and boes ecept: 1) When ou win a bo, its value is often determined b a variable, or. Eample: a bo labelled 4 is worth 60 if = 15. these edges alread drawn = 7 = 6 = = 7 = 6 = 5 2) Once during the game ou ma skip adding a line and change the value of a variable b ±. A variable that has been changed cannot be changed again. = 7 = 6 = 5 3) The game is immediatel over once all the boes are filled. Variables cannot be changed after the boes are all filled. = 7 = 6 = ) The winner is the person with the highest score (or the least negative score.) 4 4 4

10 = = 9 = = = 9 = Here the boes are triangular or heagonal, but the same rules appl. Whoever adds the last edge of a shape gets that shape and an etra turn. 6

11 = = 0 = = 1 = = -1

12 Dots and Boes = 5 = 5 This is ordinar dots and boes ecept: = 5-1) When ou win a bo, its value is often determined b a variable, or. Eample: a bo labelled 4 is worth 60 if = = 1 = 1 2) Once during the game ou ma skip adding a line and change the value of a variable b ±. A variable that has been changed cannot be changed again. 3) The game is immediatel over once all the boes are filled. Variables cannot be changed after the boes are all filled = 5 = 5 = = 1 4) The winner is the person with the highest score (or the least negative score.)

13 Dots and Boes This is ordinar dots and boes ecept: 3 3 1) When ou win a bo, its value is often determined b a variable, or. Eample: a bo labelled 4 is worth 12 if = 3. 2) Once during the game ou ma skip adding a line and change the value of a variable b ±. A variable that has been changed cannot be changed again = 1 = 0 = ) The game is immediatel over once all the boes are filled. Variables cannot be changed after the boes are all filled. 4) The winner is the person with the highest score (or the least negative score.)

14 0 0 = 2 = 1 = 0 increase or decrease, or b The central square allows the person who completes it to immediatel increase or decrease, or b 5. This cannot be done for a variable that has alread been changed. It cannot be done if this is the last square to be filled. After filling in the square, the plaer still has another turn increase or decrease, or b increase or decrease, or b = 2 = 1 = 0 = 2 = 1 = 0

15 2 2 2 = 3 = 2 = Score: Score:

16 Dots and Boes This is ordinar dots and boes ecept: 1) When ou win a bo, its value is often determined b a variable, or. Eample: a bo labelled 4 is worth 60 if = 15. these edges alread drawn = 0 = 0 = = 0 = 0 = 0 2) Once during the game ou ma skip adding a line and change the value of a variable b ±. A variable that has been changed cannot be changed again. 2 2 = 0 = 0 = 0 3) The game is immediatel over once all the boes are filled. Variables cannot be changed after the boes are all filled = 0 = 0 = ) The winner is the person with the highest score (or the least negative score.)

17 = = 5 = = 5 = 5 =

18 = = 0 = = 1 = 0 2 = -1

19 Dots and Boes = 3 = 4 This is ordinar dots and boes ecept: = 5 2 1) When ou win a bo, its value is often determined b a variable, or. Eample: a bo labelled 4 is worth 60 if = = 3 = 4 2) Once during the game ou ma skip adding a line and change the value of a variable b ±1. A variable that has been changed cannot be changed again. 3) The game is immediatel over once all the boes are filled. Variables cannot be changed after the boes are all filled = 3 = 4 = 5-2 = 5 4) The winner is the person with the highest score (or the least negative score.) This time ou are increasing or decreasing b ±1 instead of ±.

20 Dots and Boes This is ordinar dots and boes ecept: 1 1 1) When ou win a bo, its value is often determined b a variable, or. Eample: a bo labelled 4 is worth 12 if = 3. 2) Once during the game ou ma skip adding a line and change the value of a variable b ±3. A variable that has been changed cannot be changed again. 1 = 1 = 0 = ) The game is immediatel over once all the boes are filled. Variables cannot be changed after the boes are all filled. 4) The winner is the person with the highest score (or the least negative score.) This time ou are increasing or decreasing b ±3 instead of ±.

21 = 2 = 1 = increase or decrease, or b The central square allows the person who completes it to immediatel increase or decrease, or b 4. This cannot be done for a variable that has alread been changed. It cannot be done if this is the last square to be filled. After filling in the square, the plaer still has another turn. This time ou are increasing or decreasing b ±3 instead of ± increase or decrease, or b decrease, or increase or b = 2 = 1 = 0 = 2 = 1 = 0

22 Dots and Boes This is ordinar dots and boes ecept: 1) When ou win a bo, its value is often determined b a variable, or. Eample: a bo labelled 4 is worth 60 if = 15. these edges alread drawn = = = = = = 2) Once during the game ou ma skip adding a line and change the value of a variable b ±. A variable that has been changed cannot be changed again. = = = 3) The game is immediatel over once all the boes are filled. Variables cannot be changed after the boes are all filled. = = = 4) The winner is the person with the highest score (or the least negative score.)

23 = = = = = =

24 In the standard game of dots and boes, plaers take turns joining two horiontall or verticall adjacent dots b a line. A plaer that completes the fourth side of a square (a bo) colors that bo and must pla again. When all boes have been colored,the game ends and the plaer who has colored more boes wins. To pla this game online go to

25 In the standard game of dots and boes, plaers take turns joining two horiontall or verticall adjacent dots b a line. A plaer that completes the fourth side of a square (a bo) colors that bo and must pla again. When all boes have been colored,the game ends and the plaer who has colored more boes wins. To pla this game online go to

26 In the standard game of dots and boes, plaers take turns joining two horiontall or verticall adjacent dots b a line. A plaer that completes the fourth side of a square (a bo) colors that bo and must pla again. When all boes have been colored,the game ends and the plaer who has colored more boes wins. To pla this game online go to red wins 3:6

27 Put Your Students in a Pickle! I m a father of two elementar school children, a mathematician, and designer of pules and board games. Students call me Dr. Pickle. There is nothing I enjo more than stumping students and having them stump me. I founded MathPickle.com in 20 to inject new ideas into the classroom. MathPickle s primar objective is to get thirteen curricular unsolved problems into classrooms worldwide - one for each grade K-12. A conference in November 2013 established the thirteen unsolved problems. To aid with the dissemination of these awesome problems, MathPickle is looking at setting up a $1,000,000 reward for each - the prie mone to be split between the person who solves the problem and their most inspirational K-12 educator. MathPickle is also developing a range of curricular pules like the ones ou ll find at TpT. These help teachers them with their number one challenge: How to engage the spectrum of student abilit? Whenever an elementar school teacher wants to teach addition, she will invariabl face 20% of students who alread know how to add and another 20% who are struggling with last ear s curriculum. How can she engage the top students without losing the bottom students? How can she engage the bottom students without boring the top students? One solution: Parents of top students often ask that their child be allowed to accelerate through the curriculum. This eacerbates the problem for future teachers, and sets up a failure-impoverished education eperience for the bright student. A wiser approach is to use curricular pules, games and minicompetitions to simultaneousl teach curriculum to the students who need it, and to deflect top students into tough problem solving activities. This is never time wasted, because problem solving is the primar reason we teach mathematics. The eperience of mathematics should be profound and beautiful. Too much of the regular K-12 mathematics eperience is trite and true. Children deserve tough, beautiful pules. Gordon Hamilton MMath, PhD