1.Cynthia, Peter, Nancy, and Kevin arre all carpenters. Last week each built the following number of chairs. Cynthia—36 Peter—45 Nancy—74 Kevin—13 What is the average number of chairs they built? A.39 B.42 C.55 D.59 E.63

How could number sense help you solve this problem?

2. There are 600 school children in the Lakeville district. If 54 of them are high school seniors, what is the percentage of high school seniors in the Lakeville district? A.2.32% B.0.9% C.9% D.11% E.90%

What are the three types of percentage problems your students will see?

3. Susan’s take-home pay is $300 per week, of which she spends $80 on food and $150 on rent. What fraction of her take-home pay does she spend on food? A. B. C. D. E.

What part of this problem will cause students to give a wrong answer?

4. Which of the following expresses the prime factorization of 54? A.9 x 6 B.3 x 3 x 6 C.3 x 3 x 2 D.3 x 3 x 3 x 2 E.5.4 x 10

What are the only two possibilities and why?

5. The number 1134 is divisible by all of the following except A. 3 B. 6 C. 9 D.12 E.14

What are some divisibility rules that help you here?

6. When is an integer? A.Only when a is negative B.Only when a is positive C.Only when a is odd D.Only when a equals 0 E.Only when a is even

A calculator would help students working the last problem. True False

7.On Friday, Jane does one-third of her homework. On Saturday, she does one-sixth of the remainder. What fraction of her homework is still left to be done? A. B. C. D. E.

What is it about this problem that assures lots of incorrect answers?

8.If the ratio of 2x to 5y is 1:20, what is the ratio of x to y? A.1:40 B.1:20 C.1:10 D.1:8 E.1:4

Work this problem three different ways.

9.If the area of circle A is 16π, then what is the circumference of circle B if its radius is one-half that of circle A? A.2π B.4π C.6π D.8π E. 16π

What percentage of your students will correctly answer that geometry problem?

Vocabulary

Introduction: Why Study Vocabulary in Math Class? The thesis of this book is that vocabulary acquisition impacts the learning of mathematics. Confident math students understand and use the specialized vocabulary associated with the math they are doing, where every word...clarifies a given situation

Descriptions of mathematically powerful students Understand the power of mathematics as a tool for making sense of situations, information, and events in their world Are persistent in their search for solutions to complex, messy, or ill-defined tasks

Descriptions of mathematically powerful students (con’t) Enjoy doing mathematics and find the pursuit of solutions to complex problems both challenging and engaging Understand that mathematics is not just arithmetic

Descriptions of mathematically powerful students (con’t) Make connections within and among mathematical ideas and domains Have a disposition to search for patterns and relationships Make conjectures and investigate them

Descriptions of mathematically powerful students (con’t) Have “number sense” and are able to make sense of numerical information Use algorithmic thinking, and are able to estimate and mentally compute

Descriptions of mathematically powerful students (con’t) Work both independently and collaboratively as problem posers and problem solvers Communicate and justify their thinking and ideas both orally and in writing

Descriptions of mathematically powerful students (con’t) Use available tools to solve problems and to examine mathematical ideas

Pick a goal or two (or three) These descriptions are on pages 3 and 4. Discuss them in your group Identify several that you will target this year Write them down!!!!!!!

BIG IDEAS All Students need to be mathematically literate Mathematics vocabulary, studied in context, has a profound effect on performance Vocabulary instruction...supports learning new concepts, deeper conceptual understanding, and more effective communication

Mathematical communication requires more than mastery of numbers and symbols. It requires the development of a common language using vocabulary that is understood by all.

From NCTM’s Curriculum and Evaluation Standards for School Mathematics (1989) Writing and talking about their thinking clarifies students’ ideas and gives the teacher valuable information from which to make instructional decisions.

Emphasizing communication in a mathematics class helps shift the classroom from and environment in which students are totally dependent on the teacher to one in which students are assume more responsibility for validating their own thinking.

Miki Murray lays the groundwork Letter to the parents Day 1: ”Expectations for Mathematics,” Binder Organization and Problem Exploration Day 2: Student Guidelines for Mathematics Journal and Binder, Problem-Solving Write-Up, and Resources Scavenger Hunt Day 3: Math Survey

With a talking partner, discuss the efficacy of the letter and the three days.

Blachowicz and Fisher’s summary on the research on essential elements for robust vocabulary development 1. Immerse students in words 2. Encourage students to be active in making connections between words and experiences 3. Encourage students to personalize word learning 4. Build on multiple sources of information

5. Help students control their learning 6. Aid students in developing independent strategies 7. Assist students in using words in meaningful ways; meaningful use leads to long-lasing learning

…the vocabulary focus...is not an add-on to the curriculum, or more to teach; it is a way to teach mathematics

from Principles and Standards for School Mathematics Beginning in the middle grades, students should understand the role of mathematical definitions and should use them in mathematics work. Doing so should become pervasive in high school.

from Principles and Standards for School Mathematics However, it is important to avoid a premature rush to impose formal mathematical language; students need to develop an appreciation for the need for precise definitions

Some guidelines and hints Begin each unit with an informal assessment of where students are in terms of their math language Vocabulary student is always undertaken in the context of developing mathematical understanding

Some guidelines and hints (con’t) Vocabulary is a tool for communicating and demonstrating understanding Students need to hear, see, and use terminology in mathematical contexts first

One strategy Miki Murray uses a combination of a personal vocabulary list (add five words— not necessarily new ones—each week) Keep a personal word wall to keep track of words

Multiplication & Division Games

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45 Format of the Educational Planning Assessment System (EPAS)…

The EXPLORE Purpose: Help 8 th graders plan for their high school coursework as well as career choices. Score Range: 1 – 25 Testing Window: September 46

The PLAN Purpose: Helps students measure their academic development and make plans for remaining high school years and beyond. Score Range: 1 – 32 Testing Window: September 47

The ACT Purpose: Assess general educational development and their ability to successfully complete freshmen level college courses Score Range: Testing Window: Administration - March 9 ACT Make-up Day - March 23 ACT Accommodations Window - March

Kentucky and the ACT Why is Kentucky administering? What is the law surrounding this mandate? Senate Bill Related to the bill is KRS

The Math Test ACT There are sixty multiple choice questions in sixty minutes It’s the mathematics needed for college mathematics courses 50

Math Content 55% 40% of which is pre and elementary algebra Algebra 38% Geometry 7% These questions won’t make or break a score! Trigonometry 51

Math Content 23% 14 Questions Pre-Algebra 17% 10 Questions Elementary Algebra 15% 9 Questions Intermediate Algebra 15% 9 Questions Coordinate Geometry 23% 14 Questions Plane Geometry 7% 4 Questions Trigonometry 52

53 Subject Number of Questions How Long It Takes English4030 minutes Math3030 minutes Reading3030 minutes Science2830 minutes

ACT’s College Readiness Benchmarks College Course or Course Area Test EXPLORE Score PLAN Score ACT Score English Comp. English Social Sciences Reading AlgebraMathematics BiologyScience

What does College Readiness mean, and what does it have to do with me? 55

What do the benchmarks mean? According to the ACT site, a benchmark of 22 on the mathematics section means a student has approximately a 50% chance of earning a B or better and 75% chance of earning a C or better in an equivalent college course. 56

57

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59

Look at 2008 state results… 60

EXPLORE (N=49,518) (N=48,194) (N=48,653) National* Composite Science Reading Mathematics English

PLAN (N=49,631) (N=50,097) (N= 50,531) National* Composite Science Reading Mathematics English

Chapter 7 Pipes, Tubes, and Beakers: New Approaches to Teaching the Rational- Number System

Additive vs. Multiplicative Reasoning Relative vs. Absolute Reasoning Take a look at the box on pg Discuss with a talking partner the difference between the reasoning above. Which of the types of reasoning results in the correct answer to who grew the most, String Bean, or Slim.

As stated in the book, “Students cannot succeed in algebra if they do not understand rational numbers.” What factors inhibit student understanding of rational numbers?

Rational numbers can take on may forms.  0.8 = 1/8 (Really??!!)  Part over whole…3 parts out of 4 Quotient Interpretation…3 divided by 4 A ratio…3 boys to 4 girls What is the unit?

Let’s Eat

Geogebra Share experiences Geometry  Help  Geogebra Wiki  English  Middle School Geometry Formulas

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TI-73 APPS Area Forms Number Line