Middle School Mathematics

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

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

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

5. 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

6. 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

7. 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

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

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

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

11. 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

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

13. Multiple Representations • Multiple Representation Match • Multiple Representation Models www.TLJConsultingGroup.com

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

15. 6th Grade • 0606.4.1 Identify, define or describe geometric shapes given a visual representation or a writtendescription 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

16. 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

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

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

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

20. 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

21. Tangrams www.TLJConsultingGroup.com

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23. 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

24. 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

25. 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

26. 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

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

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

29. 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

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

31. “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

32. A Bell Ringer or Problem of the Week…Find the NumberUse as few clues as possible, in the order given • It is a five-digit whole number • It is divisible by 5 • It is divisible by 4 • The 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

33. Carry out the plan: Are you being systematic • 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 (yes…even) The number is: 86,320 www.TLJConsultingGroup.com

34. Rich Text Problems • NAEP www.TLJConsultingGroup.com

35. Resources • NCTM 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