COMPASS « 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.
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.
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 « 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 In simplest radical form, ﬁnd the demonstrated: distance between: 7! 9!5 = 7!9 !5 ( ) ( ) (1, !3), ( 7, 2) Simplify (posi2ve exponents): Sketch the graph of: !3 2 6x y ( ) y = 2sin x 7 x Find the remainder when Evaluate the determinant: 3 2 " 1 !4 % 3x + 2x ! 5x ! 2 $ is divided by ( x + 2 ) # 3 !2 &
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.
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
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.