Middle School Mathematics Tammy L. Jones, Dr. Scott Eddins, & Larry Phillips

The Mathematician’s Notebook

What is it? An adaptation of the Scientist’s Notebook – East Bay Educational Collaborative

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

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%)

Multiple Representations 8 th : 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

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

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

Literature Higher-order thinking skills Mathematics

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

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

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 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 The sum of its ten- thousands digit and its hundreds digit is 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 Its thousands digit is 6.

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: 86,320

Rich Text Problems NAEP

Resources NCTM Illuminations: NSA Lessons: s/math_edu_partnership/collected_learning/inde x.shtml Shodor: