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Middle School Mathematics. Tammy L. Jones, Dr. Scott Eddins, & Larry Phillips TammyJones@TLJConsultingGroup.com ScottEddins@TLJConsultingGroup.com LarryPhillips@TLJConsultingGroup.com. The Mathematicians Notebook. What is it?. An adaptation of the Scientists Notebook - PowerPoint PPT Presentation

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Middle School Mathematics

Middle School MathematicsTammy L. Jones, Dr. Scott Eddins, & Larry PhillipsTammyJones@TLJConsultingGroup.comScottEddins@TLJConsultingGroup.comLarryPhillips@TLJConsultingGroup.com

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The Mathematicians Notebook

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3What is it?An adaptation of the Scientists NotebookEast Bay Educational Collaborative

http://www.ebecri.org/custom/toolkit.html

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Students Model the Way Mathematicians WorkEach notebook is unique to that person, that problem, that situationThe notebook is a collection of thoughts, ideas, sketches, data, equations a running record of the mathematicians/scientists/engineers thoughtswww.TLJConsultingGroup.com

5Students Model the Way M/S/E WorkIt is not necessarily organized or neatThere is no right way or formatDr. Jennifer Anderson, Brown Universitywww.TLJConsultingGroup.com

6Why use the Mathematicians Notebook?From Galileo to todays scientists and mathematicians , notebooks have been used to document discovery. Notebooks are also effective tools in the classroom. They make science and mathematics experiences more meaningful and authentic for students as they observe, record, and reflect on what they've learned.

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7Lets BeginMaterials:NotebookPost-it notesPost-it flagsScissorsTape, glueHandouts

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Communication & the Manufacturing ProcessEmbedded Process StandardsVariable ThinkingTeam BuildingCreating a classroom culture for Problem Solving

The Assembly Line

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Multiple Representations6th: Decimals & Fractions: Representations, Operations, Problem Solving (22%)Algebraic Expressions, Patterns, and Equations: Multiple representations (22%)www.TLJConsultingGroup.com

Multiple Representations7th: Evaluating Expressions Multiple Representations roots, radicals, classification of numbers, and comparisons. (19%)Relations, Equations & Inequalities: Multiple representations of and working with (16%)Problem Solving: Representations & Proportions (11%)www.TLJConsultingGroup.com

Multiple Representations8th: Linear Functions & Inequalities: Multiple representations of and working with and distinguishing from non-linear forms (41%)www.TLJConsultingGroup.com

Multiple RepresentationsMultiple Representation MatchMultiple Representation Modelswww.TLJConsultingGroup.com Vee NumbersRich Text Problemswww.TLJConsultingGroup.com

6th Grade0606.4.1 Identify, define or describe geometric shapes given a visual representation or a written description of its properties.0606.4.5 Determine the surface area and volume of prisms, pyramids and cylinders.0606.2.4 Solve multi-step arithmetic problems using fractions, mixed numbers, and decimals.

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Geometry0606.4.1 Identify, define or describe geometric shapes given a visual representation or a written description of its properties.0606.4.5 Determine the surface area and volume of prisms, pyramids and cylinders.

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LiteratureHigher-order thinking skillsMathematicswww.TLJConsultingGroup.com

Geometry0606.4.1 Identify, define or describe geometric shapes given a visual representation or a written description of its properties.

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Geometry0606.4.5 Determine the surface area and volume of prisms, pyramids and cylinders.

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0606.2.4 Solve multi-step arithmetic problems using fractions, mixed numbers, and decimals.

FractionsMixed NumbersDecimalsCo-operative Problem Solvingwww.TLJConsultingGroup.com

Tangrams

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Fractions with TangramsIf the completed square is the UNIT, name each piece with its fractional representation of the completed square.Write the fractions on half of an index cardCompare the fractions on the number line.www.TLJConsultingGroup.com

Tenths Today we are going to use graph paper. Draw four 10 x 10 grids on your sheet.Divide the first grid into 10 equal parts. Shade 3/10 of the box. Can you write this fraction as a decimal?Divide the second grid into 5 equal parts. Write the fraction and the decimal.The third grid should show 7/10 and the fourth will show 9/10.www.TLJConsultingGroup.com

This is on page 43 in the book. Remind them of the puffs lesson. Brainstorm manipulatives you could use to teach tenths. 24HundredthsDraw two 10 x 10 grids on your graph paper. Notice that each of the squares has 100 small squares inside. Explore showing 3/10 and 3/100 on the two grids. How can we represent these two fractions?How would we write these 2 fractions as decimals?www.TLJConsultingGroup.com

Pg 4325Terminating Decimals Draw a 10 x 10 grid. Color of the grid. Share all the different ways people represented .Write as 50/100 and .50 or .5.Divide the room in 4 groups. Give group one , group two 17/20, group three 3/5, and group four .Sharewww.TLJConsultingGroup.com

Cooperative Problem Solving.www.TLJConsultingGroup.com

Cooperative Problem SolvingGroups of 4Everyone gets a cardFacilitatorQuestionerScribeComputer, thinkerwww.TLJConsultingGroup.com

Lead participants in modeling this problem as their students would. Have everyone choose a role to play. Debrief carefully. Follow next slide.

28DebriefAdvantages of only having to read one statement?Forming groups: who should be the questioner to begin, the facilitator, the scribe?How often to be beneficial?www.TLJConsultingGroup.com

DebriefThen move to 2 statements with two peopleThen entire question with two peopleThen everyone has their own question

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Free MathFree Math can integrate it on the flyRich DiscussionsCreates the culture for doing math and having grand conversations about mathOpen-endedQuick and easy pre-assessmentHelps develop number fluency www.TLJConsultingGroup.com

A Bell Ringer or Problem of the WeekFind the NumberUse as few clues as possible, in the order given It is a five-digit whole numberIt is divisible by 5It is divisible by 4The sum of its ten-thousands digit and its thousands digit is 14.The sum of its ten-thousands digit and its hundreds digit is 11.The sum of its thousands digit and its tens digit is 8.The sum of its hundreds digit and its ones digit is 3.The sum of its tens digit and its ones digit is 2.It is greater than 80000.Its thousands digit is 6.www.TLJConsultingGroup.com

Carry out the plan: Are you being systematicab,cde(and 3) d is even, e = 0a + b = 14a + c = 11b + d = 8c + e = 3Looks like I have enough info to continue.If e = 0 and c + e = 3, then c = 3So..a = 8Then b = 6And d = 2 (yeseven)The number is:www.TLJConsultingGroup.com 86,320

Rich Text ProblemsNAEPwww.TLJConsultingGroup.com

ResourcesNCTM Illuminations: http://illuminations.nctm.org/ NSA Lessons:http://www.nsa.gov/academia/early_opportunities/math_edu_partnership/collected_learning/index.shtml Shodor: http://www.shodor.org/ www.TLJConsultingGroup.com

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