Middle School Mathematics Tammy L. Jones, Dr. Scott Eddins, & Larry Phillips [email protected] [email protected] [email protected] www.TLJConsultingGroup.com www.TLJConsultingGroup.com The Mathematicians Notebook

www.TLJConsultingGroup.com What is it? An adaptation of the Scientists Notebook East Bay Educational Collaborative http://www.ebecri.org/custom/toolkit.html www.TLJConsultingGroup.com

Students Model the Way Mathematicians Work Each notebook is unique to that person, that problem, that situation The notebook is a collection of thoughts, ideas, sketches, data, equations a running record of the mathematicians/scientists/engineers thoughts www.TLJConsultingGroup.com

Students Model the Way M/S/E Work It is not necessarily organized or neat There is no right way or format Dr. Jennifer Anderson, Brown University www.TLJConsultingGroup.com Why 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. www.TLJConsultingGroup.com

Lets Begin Materials: Notebook Post-it notes Post-it flags Scissors Tape, glue Handouts www.TLJConsultingGroup.com

Communication & the Manufacturing Process Embedded Process Standards Variable Thinking Team Building Creating a classroom culture for Problem

Solving The Assembly Line www.TLJConsultingGroup.com Multiple Representations 6th: Decimals & Fractions: Representations, Operations, Problem Solving (22%) Algebraic Expressions, Patterns, and Equations: Multiple representations (22%)

www.TLJConsultingGroup.com Multiple Representations 7th: 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 Representations 8th: Linear Functions & Inequalities: Multiple representations of and working with and distinguishing from non-linear forms (41%) www.TLJConsultingGroup.com Multiple Representations

Multiple Representation Match Multiple Representation Models www.TLJConsultingGroup.com Rich Text Problems Vee Numbers www.TLJConsultingGroup.com 6 Grade

th 0606.4.1 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. www.TLJConsultingGroup.com

Geometry 0606.4.1 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. www.TLJConsultingGroup.com

Higher-order thinking skills Literature Mathematics www.TLJConsultingGroup.com Geometry 0606.4.1 Identify, define or describe

geometric shapes given a visual representation or a written description of its properties. www.TLJConsultingGroup.com Geometry 0606.4.5 Determine the surface area and volume of prisms, pyramids and cylinders.

www.TLJConsultingGroup.com 0606.2.4 Solve multi-step arithmetic problems using fractions, mixed numbers, and decimals. Fractions

Mixed Numbers Decimals Co-operative Problem Solving www.TLJConsultingGroup.com Tangrams www.TLJConsultingGroup.com www.TLJConsultingGroup.com

Fractions with Tangrams If 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 card Compare 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 Hundredths Draw 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 Terminating 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 .

Share www.TLJConsultingGroup.com Cooperative Problem Solving. www.TLJConsultingGroup.com Cooperative Problem Solving

Groups of 4 Everyone gets a card Facilitator Questioner Scribe Computer, thinker

www.TLJConsultingGroup.com Debrief Advantages 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

Debrief Then move to 2 statements with two people Then entire question with two people Then everyone has their own question www.TLJConsultingGroup.com Free Math Free Math can integrate it on the fly Rich Discussions Creates the culture for doing math and

having grand conversations about math Open-ended Quick and easy pre-assessment Helps develop number fluency www.TLJConsultingGroup.com A Bell Ringer or Problem of the Week Find the Number Use as few clues as possible, in the order given 1. 2.

3. 4. 5. It is a five-digit whole number It is divisible by 5 It is divisible by 4 The sum of its tenthousands digit and its thousands digit is 14.

The sum of its tenthousands digit and its hundreds digit is 11. 6. The sum of its thousands digit and its tens digit is 8. 7. The sum of its hundreds digit and its ones digit is 3. 8. The sum of its tens digit and its ones digit is 2. 9. It is greater than 80000. 10. Its thousands digit is 6.

www.TLJConsultingGroup.com Carry out the plan: Are you being systematic 1. 2. 4. 5. 6. 7.

ab,cde (and 3) d is even, e = 0 a + b = 14 a + c = 11 b+d=8 c+e=3 Looks like I have enough info to continue. If e = 0 and c + e = 3, then

c=3 So..a = 8 Then b = 6 And d = 2 (yeseven) The number is: 86,320 www.TLJConsultingGroup.com Rich Text Problems NAEP

www.TLJConsultingGroup.com Resources NCTM Illuminations: http://illuminations.nctm.org/ NSA Lessons: http://www.nsa.gov/academia/early_opportunities/ math_edu_partnership/collected_learning/index.sht ml

Shodor: http://www.shodor.org/ www.TLJConsultingGroup.com