2015-16 MYCI Session #3Lauren Segedin SHSM Support Initiative Angela Ciarlariello-Bondy Re-engagement & @MathletePearce www.tapintoteenminds.com @JustinLevack TWEET IT OUT! Follow the Math Twitter Blogosphere @MathletePearcewww.tapintoteenminds.com Purpose Promoting cross-panel collaboration Reduce gaps in student achievement Building capacity in collaborative inquiry skills Increase connections among middle years educators @MathletePearce www.tapintoteenminds.com @JustinLevack @MathletePearce www.tapintoteenminds.com @JustinLevack … an iterative process in which teachers collaborate to develop reasonable inquiry questions by implementing research-based strategies and reflecting on how they impact relevant student learning needs in the classroom.Relevant Reflective Collaborative Adaptive Iterative Reasoned @MathletePearce www.tapintoteenminds.com @JustinLevack “There is no prescribed protocol, nor is there a single path.” Capacity Building Series, Collaborative Inquiry Which One Doesn’t Belong? INQUIRY QUESTION What is the impact of introducing topics with 3 act math tasks with an inquiry approach on student confidence, understanding and ability to solve problems in mathematics? @MathletePearcewww.tapintoteenminds.com THEORY OF ACTION If I allow students to discover new learning through contextual tasks, then students will gain a deeper understanding of the learning goal. @MathletePearcewww.tapintoteenminds.com THEORY OF ACTION If I allow students to discover new learning through contextual tasks, then students will gain a deeper understanding of the learning goal. If I wait to introduce algorithms and procedures until students have solved a problem through inquiry, then student confidence and procedural fluency will increase. @MathletePearcewww.tapintoteenminds.com students will gain a deeper understanding of the learning goal. If I wait to introduce algorithms and procedures until students have solved a problem through inquiry, then student confidence and procedural fluency will increase. If curriculum is organized using a spiralled approach, then student understanding and ability to solve problems will increase. @MathletePearcewww.tapintoteenminds.com What is the most urgent student learning @MathletePearcewww.tapintoteenminds.com Is it related to content? Learning skill? Both? What is the most urgent student learning @MathletePearcewww.tapintoteenminds.com Clearly specifies the focus of your inquiry Uses neutral, exploratory language Clearly specifies the focus of your inquiry Uses neutral, exploratory language Clearly specifies the focus of your inquiry Uses neutral, exploratory language What will you do and what are the expected outcomes? @MathletePearcewww.tapintoteenminds.com What will you do and what are the expected outcomes? @MathletePearcewww.tapintoteenminds.com What will you do and what are the expected outcomes? @MathletePearcewww.tapintoteenminds.com return in the stock market and the classroom LEARNING Maximize Reward, Minimize Risk 3. Formula Maximize Reward, Minimize Risk 3. Formula 2. Understanding Maximize Reward, Minimize Risk 3. Formula Ability to formulate, represent & solve mathematical problems using an effective strategy STRATEGIC COMPETENCE PROCEDURAL FLUENCY ADAPTIVE REASONING Capacity for logical thought, reflection, explanation, and justification CONCEPTUAL UNDERSTANDING @MathletePearcewww.tapintoteenminds.com COMPETENCE Learning journey begins at the origin (0, 0) COMPETENCE Learning journey begins at the origin (0, 0) begins at the origin (0, 0) Competence COMPETENCE begins at the origin (0, 0) Competence Consciousness begins at the origin (0, 0) Competence COMPETENCE COMPETENCE Unconsciously Incompetent COMPETENCE Unconsciously Incompetent @MathletePearcewww.tapintoteenminds.com The Four Stages of Mastery COMPETENCE Unconsciously Incompetent COMPETENCE Unconsciously Incompetent Student Might Be Thinking: @MathletePearcewww.tapintoteenminds.com Student Might Be Thinking: COMPETENCE Unconsciously Incompetent @MathletePearcewww.tapintoteenminds.com Student Might Be Thinking: COMPETENCE Unconsciously Incompetent 15 16 17 18 19 20 21 Answer & Justification: “I counted each candy and there are 21 total.” @MathletePearcewww.tapintoteenminds.com COMPETENCE COMPETENCE COMPETENCE COMPETENCE @MathletePearcewww.tapintoteenminds.com COMPETENCE Count how many candies there are. Student Might Be Thinking: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Answer & Justification: “I counted each candy and there are 21 total.” @MathletePearcewww.tapintoteenminds.com COMPETENCE Count how many candies there are. Student Might Be Thinking: COMPETENCE Count how many candies there are. Student Might Be Thinking: “I know I’m supposed to multiply, but I’m not sure how.” @MathletePearcewww.tapintoteenminds.com COMPETENCE Count how many candies there are. Student Might Be Thinking: “I know I’m supposed to multiply, but I’m not sure how.” 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Answer & Justification: “I counted each candy and there are 21 total.” @MathletePearcewww.tapintoteenminds.com COMPETENCE COMPETENCE COMPETENCE COMPETENCE @MathletePearcewww.tapintoteenminds.com COMPETENCE Count how many candies there are. Student Might Be Thinking: “I know I’m supposed to multiply, but I’m not sure how.” 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Answer & Justification: “I counted each candy and there are 21 total.” @MathletePearcewww.tapintoteenminds.com COMPETENCE Count how many candies there are. Student Might Be Thinking: @MathletePearcewww.tapintoteenminds.com COMPETENCE Count how many candies there are. Student Might Be Thinking: “I see 7 groups of 3 candies.” “I added 3 candies, 7 times. There are 21 total candies.” 3 6 9 12 15 18 21 @MathletePearcewww.tapintoteenminds.com COMPETENCE Count how many candies there are. Student Might Be Thinking: “I see 3 groups of 7 candies.” “I added 7 candies, 3 times. There are 21 total candies.” 7 14 21 COMPETENCE COMPETENCE COMPETENCE COMPETENCE @MathletePearcewww.tapintoteenminds.com COMPETENCE Count how many candies there are. Student Might Be Thinking: “I see 3 groups of 7 candies.” “I added 7 candies, 3 times. There are 21 total candies.” 7 14 21 Student Might Be Thinking: Answer & Justification: “There are 21 candies because 7 times 3 is 21. The Four Stages of Mastery COMPETENCE 7 3 @MathletePearcewww.tapintoteenminds.com @MathletePearcewww.tapintoteenminds.com @MathletePearcewww.tapintoteenminds.com @MathletePearcewww.tapintoteenminds.com @MathletePearcewww.tapintoteenminds.com @MathletePearcewww.tapintoteenminds.com Fairly share a minimum of one cube of each colour with as many friends as possible. @MathletePearcewww.tapintoteenminds.com Fairly share a minimum of one cube of each colour with as many friends as possible. @MathletePearcewww.tapintoteenminds.com Fairly share a minimum of one cube of each colour with as many friends as possible. 16 red and 12 green 1 Friend @MathletePearcewww.tapintoteenminds.com Fairly share a minimum of one cube of each colour with as many friends as possible. @MathletePearcewww.tapintoteenminds.com Fairly share a minimum of one cube of each colour with as many friends as possible. 8 red and 6 green 8 red and 6 green Two Friends @MathletePearcewww.tapintoteenminds.com Fairly share a minimum of one cube of each colour with as many friends as possible. @MathletePearcewww.tapintoteenminds.com Fairly share a minimum of one cube of each colour with as many friends as possible. Friends @MathletePearcewww.tapintoteenminds.com Fairly share a minimum of one cube of each colour with as many friends as possible. 4 red and 3 green 4 red and 3 green 4 red and 3 green 4 red and 3 green Four Friends @MathletePearcewww.tapintoteenminds.com @MathletePearcewww.tapintoteenminds.com @MathletePearcewww.tapintoteenminds.com Fairly share a minimum of one cube of each colour with as many friends as possible. @MathletePearcewww.tapintoteenminds.com Fairly share a minimum of one cube of each colour with as many friends as possible. @MathletePearcewww.tapintoteenminds.com Fairly share a minimum of one cube of each colour with as many friends as possible. @MathletePearcewww.tapintoteenminds.com Fairly share a minimum of one cube of each colour with as many friends as possible. @MathletePearcewww.tapintoteenminds.com YOUR TURN! YOUR TURN! Sample Extension Questions If there are 25 red and 30 blue candies, how many of each colour could you fairly share to as many friends as possible? YOUR TURN! If there are 36 green and 18 blue candies, what is the ratio of green to blue candies in lowest terms? @MathletePearcewww.tapintoteenminds.com Kyle's Candy Kyle is preparing candy bags for the upcoming MYCI Participants. James from Kingsville Public requests that for every 7 candies his team receives, 3 are blue and 4 are red. If the Kingsville candy bag has a total of 140 candies, how many of each colour are there? YOUR TURN! YOUR TURN! Paul's Quilt EQAO Winter Assessment Grade 9 Applied 2005-2006, Question 2b [Adapted] Paul’s grandmother asks him to cut red and white pieces. Every 5 pieces in the quilt consist of 2 red pieces and 3 white pieces. If the quilt has a total of 60 pieces, how many pieces are there of each colour? Show your work. Paul’s grandmother is sewing a quilt for him. A quilt consists of pieces of fabric of different shapes sewn together. @MathletePearcewww.tapintoteenminds.com YOUR TURN! Paul's Quilt EQAO Winter Assessment Grade 9 Applied 2005-2006, Question 2b [Adapted] @MathletePearcewww.tapintoteenminds.com Paul’s grandmother asks him to cut red and white pieces. Every 5 pieces in the quilt consist of 2 red pieces and 3 white pieces. If the quilt has a total of 60 pieces, how many pieces are there of each colour? Show your work. Paul’s grandmother is sewing a quilt for him. A quilt consists of pieces of fabric of different shapes sewn together. YOUR TURN! Paul's Quilt YOUR TURN! Paul's Quilt YOUR TURN! Paul's Quilt YOUR TURN! Paul's Quilt YOUR TURN! 0 are 0 white.” pieces” Change r are 0 white.” pieces” 2 QUESTION Make the smallest difference by filling in the boxes below using the whole numbers 1 through 9, no more than one time each. - Shared by openmiddle.com WHAT IF… WHAT IF… x 3 = ? WHAT IF… x 3 = ?1 2 x 3 = ?1 2 LOOK THERE ARE = 2 @MathletePearcewww.tapintoteenminds.com = 2 Two thirds can be split up into two groups of one third groups @MathletePearcewww.tapintoteenminds.com = 3 2 = 1 21 = 1 21 Three quarters can be divided into one and a half groups of two quarters. @MathletePearcewww.tapintoteenminds.com 4 5 3 5÷ = 4 3 4 3= = 1 31 = 1 31 Four fifths can be divided into one and a third groups of three fifths. @MathletePearcewww.tapintoteenminds.com 4= @MathletePearcewww.tapintoteenminds.com 4= @MathletePearcewww.tapintoteenminds.com 4= @MathletePearcewww.tapintoteenminds.com 4= @MathletePearcewww.tapintoteenminds.com 4= @MathletePearcewww.tapintoteenminds.com 4= @MathletePearcewww.tapintoteenminds.com 4= = 3 42 4= = 3 42 Three and two-thirds can be divided by one and one-third into two and three-quarter groups. @MathletePearcewww.tapintoteenminds.com @MathletePearcewww.tapintoteenminds.com