Engaging Students in Learning CPSB High School Mathema2cs Inservice, 2012
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ì Engaging Students in Learning CPSB High School Mathema2cs Inservice, 2012
Organized Chaos
« Se#ng Instruc-onal Outcomes (1c): Establishing clear, rigorous objec2ves that describe what students will learn.
« Managing Classroom Procedures (2c): Establishing a smoothly func2oning classroom through the management of instruc2on and transi2ons to allow for maximum learning for all students.
« Using Ques-oning and Discussion (3b): Strategically using a varied set of ques2ons to engage all students in discussion around rigorous content.
« Engaging Students in Learning (3c): Asking all students to do work that is rigorous an intellectually challenging.
« Using Assessment in Instruc-on (3d): Using clear assessment criteria to drive instruc2onal choices throughout the lesson and at the end.
COMPASS
Standards of Mathematical Practice
« Make sense of problems and persevere in solving them.
« Reason abstractly and quan2ta2vely.
« Construct viable arguments and cri2que the reasoning of others.
« Model with mathema2cs.
« Use appropriate tools strategically.
« ALend to precision.
« Look for and make use of structure.
« Look for and express regularity in repeated reasoning.
Attention Getter
Marshmallow Challenge
« 20 s2cks of spagheN
« 1 yard of tape
« 1 yard of string
« 1 marshmallow
Marshmallow Challenge
« The winning team is the one that has the tallest structure measured from the table top surface to the top of the marshmallow.
« The en2re marshmallow must be on top.
« Use as much or as liLle of the kit.
« Break up the spagheN, string, or tape.
« The challenge lasts for 18 minutes.
Marshmallow Challenge
Marshmallow Challenge
0
10
20
30
40
50
Height (Inches)
Marshmallow Challenge
Marshmallow Challenge
« Why do kindergarteners create taller and more interes2ng structures than business graduates?
« The marshmallow is a metaphor for the hidden assump2ons of a project.
« What are your assump2ons this school year?
Mix-‐N-‐Match
« Each student is given a card with some type of problem or informa2on on it.
« Students ‘mix’ and find the person with a card that ‘matches’ theirs.
« As students pair up, they move to the outside perimeter of the classroom and stand together as a pair.
« Once everyone has found their match, students confer with another nearby pair to double check that they do indeed make a match.
« Redistribute if desired.
Mix-‐N-‐Match
Name the property demonstrated:
In simplest radical form, find the distance between:
Simplify (posi2ve exponents):
Sketch the graph of:
Find the remainder when
is divided by
Evaluate the determinant:
7! 9!5( ) = 7!9( )!5 1,!3( ), 7, 2( )
6x y!3( )2
x7y = 2sin x
3x3 + 2x2 ! 5x ! 2x + 2( )
1 !43 !2
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Line-‐Ups
« Each student is given a card with some type of problem on it.
« Students evaluate the answer to their problem and then line up in order from least to greatest.
« Once students are lined up, they then discuss their card and posi2on with a nearby partner.
« Partners may be formed by pairing up or by ‘folding’ the line in half.
Line-‐Ups
« Line up in order from the teacher who has taught the most years to the teacher who has taught the fewest.
« Fold the line.
« The more experienced teacher tells the less experienced about their most embarrassing teaching moment.
« The less experienced teacher then shares with the more experienced how that situa2on could have been avoided.
Line-‐Ups
« Frac2ons, Decimals, & Percents
« Sta2s2cs
« Order of Opera2ons
« Algebraic Expressions
« Angle Measures
« Radian and Degree Measures
« Arithme2c and Geometric Sequences
Inside-‐Outside Circle
« Students form two concentric circles, with equal numbers of students in each circle. Students stand face-‐to-‐face with a partner, one person from the inside circle and one from the outside.
« The circles rotate according to the teacher’s instruc2ons.
« Partners take turn asking each other ques2ons, quizzing each other with flashcards, sharing some informa2on, or answering ques2ons.
Inside-‐Outside Circle
« Structure works best when the problems being solved do not require lengthy paper-‐pencil solu2ons.
« Structure is more conducive to short-‐answer or higher level thinking ques2ons that can be answered verbally.
« Any ideas?
Rally Coach
« Students pair up and decide who is Person A and who is Person B. There is only one sheet of paper and one pencil for each student pair.
« Teacher poses a problem, verbally or on paper.
« Person A begins contribu2ng to the solu2on of the problem in wri2ng and states aloud what (s)he is doing.
« Meanwhile, Person B watches, listens, and coaches. If necessary, Person B reteaches.
« Reverse roles.
Rally Coach
« Mul2-‐Step problems
« Comple2ng worksheets
« Genera2ng lists
« Constructed response items
Round Table
« Similar to Rally Coach but involves four students instead of two.
« Students take turns passing the paper and pencil, each wri2ng one answer or making a contribu2on.
Round Table
« Given three points, A (4, -‐7), B (3, 1), and C (-‐2, 0)…
« Person 1 finds the slope of the line passing through A and B.
« Person 2 writes the equa2on of line AB.
« Person 3 writes the equa2on of the line parallel to AB and passing through C.
« Person 4 writes the equa2on of the line perpendicular to AB and passing through C.
Mix Pair Rally Coach
« Each student is given a card containing some informa2on.
« Students ‘mix’ around the room and find a partner, Person A and Person B.
« Person A solves the problem on his/her card while Person B watches, checks, and praises.
« Person B then solve the problem on his/her card while Person A watches, checks, and praises.
« Partners reteach as necessary.
Showdown
« Teacher selects one student from each group to be the Showdown Captain.
« The Showdown Captain draws the first card, reads the ques2on, and provides think 2me.
« Working alone, all students, including the Showdown Captain, write their answers.
« ‘Showdown’ is called and teammates share and discuss their answers.
Showdown
« The Showdown Captain leads the checking.
« If correct, the team celebrates; if not, teammates tutor, then celebrate.
« Repeat with a new captain.
« Modifica2ons—oral ques2ons, ques2ons from a handout, or ques2ons displayed by a projector
Classroom Setup
Stations
« Sta2on 1: Students will be given eight index cards with func2ons and func2on answers on them. They will match the func2ons with the appropriate func2on answers. Then, they will evaluate func2ons.
« Sta2on 2: Students will use a ruler to perform the ver2cal line test on graphs of rela2ons. They will determine if the rela2on is a func2on. They will construct a graph that is a func2on. Then, they will determine if a rela2on is a func2on by analyzing coordinate points.
Stations
« Sta2on 3: Students will be given a calculator to help them solve a real-‐world linear func2on. They will write and solve a linear func2on based on two data points.
« Sta2on 4: Students will be given a number cube. They roll the number cube to populate a rela2on. They find the domain and range of the rela2on and determine if it is a func2on. Then for given rela2ons, they determine the domain, range, and whether or not it is a func2on.
Questions
References
« Kushnir, Dina. (2001). Coopera*ve learning and mathema*cs: High school ac*vi*es. San Clemente, CA: Kagan Publishing.
« The Marshmallow Challenge: hLp://marshmallowchallenge.com
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