2. Middle School Mathematics Tammy L. Jones, Dr. Scott Eddins, & Larry Phillips TammyJones@TLJConsultingGroup.com ScottEddins@TLJConsultingGroup.com LarryPhillips@TLJConsultingGroup.com www.TLJConsultingGroup.com

4. The Mathematician’s Notebook www.TLJConsultingGroup.com

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

6. Student’s 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 mathematician’s/scientist’s/engineer’s thoughts www.TLJConsultingGroup.com

7. Student’s 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

8. Why use the Mathematician’s Notebook? “From Galileo to today’s 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

9. Let’s Begin Materials: – Notebook – Post-it® notes – Post-it® flags – Scissors – Tape, glue – Handouts www.TLJConsultingGroup.com

10. Communication & the Manufacturing Process Embedded Process Standards Variable Thinking Team Building Creating a classroom culture for Problem Solving The Assembly Line www.TLJConsultingGroup.com

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

12. Multiple Representations 7 th : 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

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

14. Multiple Representations Multiple Representation Match Multiple Representation Models www.TLJConsultingGroup.com

15. Vee Numbers Rich Text Problems www.TLJConsultingGroup.com

16. 6 th Grade 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

17. 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

18. Literature Higher-order thinking skills Mathematics www.TLJConsultingGroup.com

19. Geometry 0606.4.1 Identify, define or describe geometric shapes given a visual representation or a written description of its properties. www.TLJConsultingGroup.com

20. Geometry 0606.4.5 Determine the surface area and volume of prisms, pyramids and cylinders.surface area and volume www.TLJConsultingGroup.com

21. 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

22. Tangrams www.TLJConsultingGroup.com

24. 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

25. 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

26. 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

27. Terminating Decimals Draw a 10 x 10 grid. Color ½ of the grid. Share all the different ways people represented ½. Write ½ as 50/100 and.50 or.5. Divide the room in 4 groups. Give group one ¾, group two 17/20, group three 3/5, and group four ¼. Share www.TLJConsultingGroup.com

28. Cooperative Problem Solving…. www.TLJConsultingGroup.com

29. Cooperative Problem Solving Groups of 4 Everyone gets a card Facilitator Questioner Scribe “Computer”, thinker www.TLJConsultingGroup.com

30. 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

31. Debrief Then move to 2 statements with two people Then entire question with two people Then everyone has their own question www.TLJConsultingGroup.com

32. “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

33. A Bell Ringer or Problem of the Week…Find the Number Use as few clues as possible, in the order given 1.It is a five-digit whole number 2.It is divisible by 5 3.It is divisible by 4 4.The sum of its ten- thousands digit and its thousands digit is 14. 5.The sum of its ten- thousands 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

34. Carry out the plan: Are you being systematic 1.ab,cde 2.(and 3) d is even, e = 0 4.a + b = 14 5.a + c = 11 6.b + d = 8 7.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 (yes…even) The number is: www.TLJConsultingGroup.com 86,320

35. Rich Text Problems NAEP www.TLJConsultingGroup.com

36. Resources NCTM Illuminations: http://illuminations.nctm.org/ NSA Lessons: http://www.nsa.gov/academia/early_opportunitie s/math_edu_partnership/collected_learning/inde x.shtml Shodor: http://www.shodor.org/ www.TLJConsultingGroup.com