middle school mathematics

www.TLJConsultingGroup.com

Middle School Mathematics

Tammy L. Jones, Dr. Scott Eddins, & Larry PhillipsTammyJones@TLJConsultingGroup.comScottEddins@TLJConsultingGroup.com

LarryPhillips@TLJConsultingGroup.com

The Mathematician’s Notebook

What is it?

• An adaptation of the Scientist’s Notebook– East Bay Educational Collaborative

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

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

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

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.”

Let’s Begin

• Materials:– Notebook– Post-it® notes– Post-it® flags– Scissors– Tape, glue– Handouts

Communication & the Manufacturing Process

• Embedded Process Standards• Variable Thinking• Team Building• Creating a classroom culture for Problem

Solving

The Assembly Line

Multiple Representations6th:

Decimals & Fractions: Representations, Operations, Problem Solving (22%)

Algebraic Expressions, Patterns, and Equations: Multiple representations (22%)

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%)

Multiple Representations8th: Linear Functions & Inequalities: Multiple

representations of and working with and distinguishing from non-linear forms (41%)

Multiple Representations

• Multiple Representation Match• Multiple Representation Models

Vee Numbers

Rich Text Problems

6th 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.

Geometry

Literature Higher-order thinking skills

Mathematics

Geometry

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

and decimals.

• Fractions• Mixed Numbers• Decimals• Co-operative Problem Solving

Tangrams

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.

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.

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?

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

Cooperative Problem Solving….

Cooperative Problem Solving

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

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?

Debrief

• Then move to 2 statements with two people• Then entire question with two people• Then everyone has their own question

“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

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

number2. It is divisible by 53. It is divisible by 44. 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.

Carry out the plan: Are you being systematic

1. ab,cde2. (and 3) d is even, e = 04. a + b = 145. a + c = 116. b + d = 87. c + e = 3

Looks like I have enough info to continue.

If e = 0 and c + e = 3, then c = 3

So..a = 8Then b = 6And d = 2 (yes…even)The number is:

86,320

Rich Text Problems

• NAEP

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/

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