## Workshop Schedule

**$215** for one workshop; **$195** each when two or more registrations are received at the same time.

Registration fee includes extensive coursebook with blacklines, full breakfast, and a delicious lunch.

Call today for reduced group rates: (847) 722-8690

#### Latest Workshops

Strategies for Teaching Fractions -- July 14Strategies for Teaching Algebra I -- July 15

*Coming this Fall:*Financial Literacy, Grades 6-12## Workshop #261: Strategies for Teaching Fractions

** No matter how you slice it, fractions are foundational.** This workshop engages participants in research-based instructional strategies that promote deep student understanding of fraction concepts and operations addressed by the Common Core State Standards. Each topic is aligned to specific

**.**

*Common Core State Standards*A comprehensive collection of student error patterns will be examined. Participants explore student misconceptions that result in those errors — and learn how to use error patterns to inform instruction, pinpoint intervention, and stimulate student thinking. The workshop addresses the use of estimation, alternative algorithms, instructional games, hands-on activities, comics, and guided discovery lessons.

Explore connections between fractions and decimals, probability, and statistics. The strategies support instruction of both regular and special-needs students.

**Overview of Academic Research:**We will examine academic research on these topics: Accessing language for English learners, Error analysis, Multiple representations, Teaching estimation strategies*prior*to formal instruction on algorithms, Alternative algorithms, Differentiating instruction, and Instructional games to provide practice and reinforcement.**Big Ideas in Fraction Concepts and Computation:**Explore ways to teach the big ideas about fractions: What is a fraction? How can they be represented? How do benchmarks facilitate estimation? How can fractions be compared*without*finding a common denominator?**Big Ideas in Problem Solving:**Key actions and problem structures will be explored for each of the operations to provide insight as to why a particular operation is appropriate to use to solve a given problem. Participants will write and share their own word problems for given actions and problem structures for fraction word problems.**Multiple Representations for Fractions:**Explore models for part-whole (circle and length), parts of a collection (sets), location and distance from 0 on a number line, and symbolic (fraction as an indicated division).**Guided Discovery Lessons:**Engage in lessons promoting the discovery of computational algorithms: Making*Sum Difference*Using Strips (addition / subtraction), It’s*in the Fold*(paperfolding for multiplication), and How Many Strips Will Fit? (using “fraction lines” for division). Learn how to help students make the transition from the models to paper-pencil algorithms. Explore how fraction multiplication leads to the discovery of a rule for multiplying**decimals**.**A Model of Diagnosis, Item Analysis, and Targeted Intervention:**Diagnostic tests, provided in the book*Strategies for Teaching Fractions*, will be examined. The power of using item analysis to pinpoint student misconceptions as a way to form a basis for meaningful step-by-step interventions will be explored. To aid the teacher in this process, the interventions revolve around the same problems that appear on the diagnostic tests—targeting the error patterns

revealed by student misconceptions on those problems. The interventions are based on an instructional model of starting with a tactile, hands-on representation, moving to the use of drawings, and finally moving to a symbolic algorithm (Concrete → Semi-concrete → Abstract).**Instructional Games and Activities:**Engage in exciting activities and games such as Paper-Folding to Find Fraction/Decimal Equivalents, Equivalent Fractions Cover-All, Fractions on My Plate (for addition and subtraction — with a connection to**probability**), and Rolling*a-Plot*of Fractions (game that integrates fractions and**statistics**).**Editor Error Search:**Students find and correct errors that appear in specially prepared lessons that are full of mathematical and grammatical errors. This is an excellent way for students to review concepts: In order to correct the errors, students must understand the concepts.**A Walk in the PARCC:**Survey and discuss sample fraction PARCC Assessment items.**Mathematical Humor Via “Cartoon Corner”:**David is co-editor of “Cartoon Corner” (a regular feature in*Mathematics Teaching in the Middle School*) — so you can expect some humor in this workshop. The following “Cartoon Corner” activities will be explored:**Let’s Be**(fun overview of whole numbers, integers, rational numbers, and irrational numbers)*Rational*about Numbers**Earplugs Might Help Retain What’s Inside**(connects the concept of half-life to “mathematical decay”)**A Seating Chart Would Help**(applies fraction concepts and operations to**probability**)

All teachers, including those teaching developmental curricula or math education teachers, should benefit from this workshop.

#### THIS WORKSHOP INCLUDES

- An extensive coursebook with blacklines to use directly with your students
- A complimentary full breakfast and a delicious lunch
- A copy of David’s book,
—a $38.95 value!*Strategies for Teaching Fractions*

- A certificate of participation suitable for framing and a fascinating puzzle

*There will be an opportunity to examine and purchase supplemental math materials. Bring your school Tax ID to the workshop.*

**One hour of graduate level professional development credit**, for an additional $65 fee paid at the workshop, available through

**Brandman University Extended Education – EDDU 9046**

*A reflection paper is required for graduate level professional development.*

**CPDU Provider: National-Louis University — 7 Illinois CPDUs are available for this workshop**

*No outside assignments are required to receive CPDUs.*

## Workshop #262: Strategies for Teaching Algebra I

This workshop, an extension of our “Preparing to Use Common Core Algebra,” is designed to strengthen teachers’ conceptual understanding of key algebraic concepts and skills while examining how teaching and learning may be enhanced through hands-on, motivating activities. Algebraic topics from the algebra domains of the **Common Core State Standards **(Operations and Algebraic Thinking, The Number System, Expressions and Equations, Arithmetic with Polynomials, and Rational Expressions) will be explored. Come away with a collection of proven instructional strategies that will ** take the unknowns out of algebra** — while motivating both regular and special needs students to gain deeper understandings.

**Warm-up Exercises — Let’s Get Physical:**You will literally be*up in arms*representing linear and quadratic equations.**Algebra Representation Match:**Cut out slips for equations, rules, tables of values, and graphs — and then try to match the four representations that form a “family” for the same relationship.**Conjecture Rather than Lecture:**Discover relationships about linear equations and their graphs by examining the slope, y-intercept, and x-intercept of graphs.**It’s Not Magic, It’s ALGEBRA!**Participate in a variety of card and number “tricks” that not only motivate students, but also reinforce key concepts involving variables, expressions, equations, and factoring.**Take Real-World Applications of Algebra Back to Your Class:**Use airline data and health statistics to discover concepts about slope. Make connections between algebra and statistics by finding the equation for a line of best fit and making predictions based on real-world data. Use inequalities and their graphs to describe real-world situations. With these activities, your students will likely never ask, “**When am I going to use algebra?**”Engage in a series of guided discovery lessons with algebra tiles that lead students to develop their own rules for adding and subtracting polynomials, multiplying binomials, and factoring polynomials.*Cover*and*Uncover*Important Concepts with Algebra Tiles:**Paper-Folding to**Cut out a small square from a large square to see why a*Unfold*the Mystery Behind Factoring the Difference of Two Squares:^{2}– b^{2}= (a + b)(a – b).**What’s My**Functions become more understandable when you approach them through rules, mappings, sets of ordered pairs, graphs, and equations. Learn how to use a calculator as a function machine. Make connections between the symbols “y = ” and “f(x) = ”.*Function*?**Is Pythagoras**Use triangles and area relationships to discover this relationship and its converse. Explore Pythagorean triples.*in the Area*:**Gain Power**Explore multiplication/division properties of powers with positive and negative exponents as an*Exponentially*with Generalized Arithmetic:*extension of arithmetic to algebra.***Are You**Examine three aspects of justification: Find a counterexample; Investigate a conjecture; and Evaluate an argument.*Justified*?**Instructional Games:**Play “Put Your Cards on the Table” (explores algebraic expressions and their possible values), “The Social Function Game” (explores functions), “Celebrity Challenge: Guess My Age” (explores ordered pairs, line of best fit, and residual values).**Algebra Error Alert!**Find and correct errors on a page riddled with common Algebra I mistakes made by students. Discuss possible underlying reasons behind those algebraic misconceptions.**A Walk in the PARCC:**Survey and discuss sample algebra PARCC assessment items.**Mathematical Humor via “Cartoon Corner”:**David is co-editor of “Cartoon Corner” (a regular feature in NCTM’s*Mathematics Teaching in the Middle School*) — so you can expect some humor in this workshop. The following “Cartoon Corner” activities will be explored:**Find x**(student “wise-cracks” based on strategies for solving simple equations)**Throw in the Towel**(writing equations to solve consumer problems)**Math Warm-ups on a Cold Day**(JUMBLE using temperature formulas in a fun way)**Calendar Conundrums**(exploring algebraic patterns on a calendar)**Pythagorean Football Pattern**(applying the Pythagorean Theorem and its converse)

**How to Have the “Last Word” on**Did David*Just About Anything*:*really*memorize the last word on EVERY page of his algebra book? Find out what “trick” he has up his sleeve.

All teachers, including those teaching developmental curricula or math education teachers, should benefit from this workshop.

#### THIS WORKSHOP INCLUDES

- An extensive coursebook with blacklines to use directly with your

students - A complimentary full breakfast and a delicious lunch
- A certificate of participation suitable for framing and a fascinating puzzle

*There will be an opportunity to examine and purchase supplemental math materials. Bring your school Tax ID to the workshop.*

**One hour of graduate level professional development credit**, for an additional $65 fee paid at the workshop, available through

**Brandman University Extended Education – EDTU 9001**

*A reflection paper is required for graduate level professional development.*

**CPDU Provider: National-Louis University — 7 Illinois CPDUs are available for this workshop**

*No outside assignments are required to receive CPDUs.*