FAL’Problem’Solving’Lesson’ - Silicon Valley …MARS$taskpossibili9es :6 th$2001$Area$and$ Perimeter,$6 th$2002$Tank,$6 2004Parallelograms Ending$MARS$taskpossibili9es :6 th2007BuildingBlocks,

FAL Problem Solving Lesson

InstrucJonal ImplicaJons

•  Have students develop their own measurements and gather data to check for possible correlaJons by making their own scacerplots

•  Look further into the Standards to ask quesJons about 2-‐way tables and bivariate data

One Approach to Unit Development

Overarching Statement or Essen9al Ques9on: A.  Two quanJJes in bivariate data can be associated to predict

posiJve, negaJve, or no correlaJon by using a line of best fit in a scaPerplot or using a 2-‐way table. These two quanJJes being related can represent conJnuous situaJons which appear to be independent of each other, but may have some associaJon or relaJonship. Students interpret these associaJons in order to understand and make decisions about real world situaJons.

B.  Bivariate data is the graphical representaJon of the comparison of two quanJJes. By comparing quanJJes, relaJonships, paPerns, and trends are revealed. The use of a scaPer plot may prove a possible posiJve, negaJve, or even no correlaJon at all. A line through the data can be analyzed to show specific mathemaJcal effect one quanJty has on the other, if any.

Beginning MARS task possibili9es: 6th 2001 Area and Perimeter, 6th 2002 Tank, 6th 2004 Parallelograms Ending MARS task possibili9es: 6th 2007 Building Blocks, 6th 2008 Area and Perimeter, 6th 2012 Unfolding a Box, 2013 Xiomara’s Triangles, 2013 Expressions, 7th 2007 Parallelogram Problem of the Month: Surrounded and Covered, Between the Lines, Infinite Windows, Polly Gone Forma9ve Assessment Lessons: Describing Quadrilaterals, Designing Candy Cartons, Security Cameras Number Talks: use number talks on number line and dealing with integers to build skill levels, develop talks around geometric proper9es, finding areas on and off grid paper, drawing geometric shapes, review adding and subtrac9ng frac9ons . . . Resources: Dr. Takeshashi lesson study video on Area and Perimeter

Danger of Two-‐Page Spread

•  ObservaJons of FAL lessons in classrooms •  Change in understanding the next day •  Allowing enough Jme for ideas to grow and develop when doing unit planning

•  Time for reflecJon about what is learned-‐How is it similar to things in the past? How is it different?

How Students Learn

•  Are students learning ideas in ways that can be built upon at later grades or just learning answer-‐geing tricks?

Place-‐value Understanding


This is an idea quickly dealt with using Strategic number talks.



Bucerfly Method

ProporJonal Reasoning

•  About mulJplicaJve reasoning. •  Sliding door example

•  TradiJonal approach

a/b=c/d


“In general, the research indicates that instrucJon can have an effect, especially if rules and algorithms for fracJon computaJon, for comparing raJos, and for solving proporJons are delayed. Students may need as much as three years’ worth of opportuniJes to reason in mulJplicaJve situaJons in order to adequately develop proporJonal reasoning. Premature use of rules encourages students to apply rules without think and, thus the ability to reason proporJonally ojen does not develop.”

John Van de Walle


Number Talks

•  Helps students develop flexible thinking •  Develop jusJficaJon and explanatory skills •  Focuses on place-‐value •  Prepares students for wriJng number sentences and algebraic notaJon

•  One way to work on skills without starJng each year from the beginning

•  Biggest bang for your buck!

Number Talks

•  If used at later grade, for what further purpose? Thinking about what is the purpose different at different grade levels. What further quesJons help students to develop or make connecJons to grade appropriate strategies?

•  Lay ground work for new ideas.

Re-‐engagement Lessons

•  Everyone makes sense of problems from their comfort zone.

•  Re-‐engagement then allows us to move students to more grade-‐appropriate strategies and helps students make connecJons from ideas they understand to new ideas.

•  Also, I think an idea that can be applied to presenJng new ideas or concepts.

Number Talks & Re-‐engagement Lessons

•  Build a community of good explainers •  Students will always be at different levels on different days, but in a rich environment there are whole groups of students available and capable of explaining ideas

Cut Score Process

Look at Grade Level Standards

Professional Judgment: Looking at Rubric

Process Repeated for all Tasks

Task Level 2 Level 3 Level 4

Banquet Tables 3 4 6

DuplicaJng Dollars 2 4 6

Is It ProporJonal? 2 3 5

A Drink Carton 3 4 6

Playoff Party 3 4 6

13 19 29

Read Student Work Around Targets

Task Level 2 Level 3 Level 4

Banquet Tables 3 4 6

DuplicaJng Dollars 2 4 6

Is It ProporJonal? 2 3 5

A Drink Carton 3 4 6

Playoff Party 3 4 6

13/12 19/18 29/27

Would we feel bad if student wasn’t at level? Ajer reading papers and discussing them, adjustments made to totals.

Reading Cut Scores

Individual Student Reports

Parent Lecer with district ediJng available:

Making Sense of Test

Programming InformaJon For Parent Lecer

SuggesJons for Improvement

How do you share informaJon?

•  Talk in groups about ways to share thinking with teachers. – What to share? – Format or seing? – Techniques that work?

To log in to MARS and POMs– username: svmimember2 and password: lucky13

To access POMs -‐ password: member00 To access MARS/MAC materials 1999-‐2009: password-‐sweet16 To access MARS/MAC materials 2010-‐2013: password – lucky13 To access MAC 2014: username – macadmin and password – secure16

Documents

FAL’Problem’Solving’Lesson’ - Silicon Valley …MARS$taskpossibili9es :6 th$2001$Area$and$ Perimeter,$6 th$2002$Tank,$6 2004Parallelograms Ending$MARS$taskpossibili9es :6 th2007BuildingBlocks,