Welcome Back! 1. Grab some food. 2. Say hello to old and ... · 6-12 MATH CONFERENCE DAY Thursday,...

6-12 MATH

CONFERENCE DAY Thursday, August 28, 2014

Welcome Back!

1. Grab some food.

2. Say hello to old and new

friends.

3. Sit at a group with at

least two other people

from a different building.

We’ll start around 8:15AM

AGENDA

Goals for 2014-2015

What does the ideal math student look like?

Student Engagement/Learning Targets

Looking to Geometry

Some tools from the Modules

Other Business

GOALS

2014-2015

GOALS Professional Development

Support

Vertical and horizontal teams

Curriculum

Comprehensive, usable curriculum maps

Continue to lead the transition to CCLS and the modules

Data

Formative data with learning targets

Leadership

Fair, open, and reasonable

Provide clear communication

Advocate as we transition into consolidation

“Only sustained conversation will make us

successful.”

- Ken Wagner, Deputy Education Commissioner

WHERE ARE YOU NOW?

Use the self-assessment chart to identify where

you are now

WHAT DOES YOUR IDEAL

STUDENT LOOK LIKE?

Activity

DRAW YOUR IDEAL STUDENT

Think about the ideal Ken-Ton math graduate as they cross the

stage at Kleinhans in June 2014.

1. Each person in the group grabs a marker.

2. One person at a time draw a piece of your student

without talking to each other in the group.

3. Add words or phrases around your student to indicate

what qualities (particularly in math) you want this student

to have.

CHECK OUT OTHER GROUPS

4. Take 10 minutes and walk around to see the other groups’

students

5. Add phrases you feel are important that you may have

missed

OUR IDEAL STUDENT

What are the common themes

among our ideal students?

The urgency for our kids now leads to frustration.

STUDENT ENGAGEMENT

AND RUBRICS

Like two peas in a pod

MAKING CONNECTIONS:

TRI-STATE, DANIELSON, DTSDE

DTSDE

(System-wide check)

Danielson

(All aspects of us as Professionals)

Tri-State

(Daily Lessons)

MAKING CONNECTIONS What do each of the documents say about the expectations

for student ownership?

1. Using each of the documents (Tri-State, Danielson, Math

Practice Standards) – select words/phrases from the

Effective/Highly Effective sections that reveal the

expectations for student ownership of learning in

each of these documents

2. Put words, phrases around your student drawing – what

would our student be doing?

3. Discuss and indicate the phrases that most reflect current

practices, and identify areas of weakness

STUDENT ENGAGEMENT IN 11TH GRADE

LEARNING TARGETS

What makes them effective?

WHAT’S IN THE BAG?

Take out the slip of paper in your bag that has a

learning target on it

Decide with your group if it is a good learning

target or not

Discuss why

FACTS IN FIVE

1. Your group will read one of the four readings on

Learning Targets

2. After reading, individually record 3-5 facts from

the article

3. Come to a consensus on the five important facts

as a group and record on poster paper

4. Gallery Walk to view what others have said

LEARNING TARGETS

What qualities makes a learning

target effective?

STUDENTS DISCUSS LEARNING TARGETS

WHAT MAKES A GOOD LEARNING

TARGET?

November,2012

LearningTargetsRubric

Accomplished Developing Beginning

Standards-based and rigorous

They are derived from national or state standards and school or district documents such as curriculum maps and adopted program materials. Targets fall across multiple categories in a cognitive rigor matrix.

They are derived from general academic tasks but not grade-specific standards, or they describe learning or tasks that do not meet proficiency standards. Targets fall across limited categories in a cognitive rigor matrix.

They are not derived from standards and do not clearly reference academic tasks. Targets fall primarily in one or two columns/rows of a cognitive rigor matrix, or learning targets are not rigorous enough.

Student- friendly

They are written in student-friendly language (accessible vocabulary and from a student perspective) and begin with the stem “I can”.

They begin with the stem “I can” but may not use student-friendly language; i.e., they sound like “objectives.”

They do not begin with “I can” and/or are simply reiterations of state objectives.

Measurable They are measurable and use concrete, assessable verbs (e.g., identify, compare, analyze). The verb suggests the way in which the target will be assessed (e.g., “analyze” suggests a writing or problem-solving assessment, not a multiple choice quiz).

They are measurable but may contain two verbs or have too broad a scope in content (e.g., I can draw a raccoon and describe its habitat).

They are not measurable (e.g., I can understand, or I can commit).

Specific and contextualized

They are specific, often referring to the particular context of a lesson, project, or case study.

They articulate only long-term targets that can be generalized for any similar academic task (e.g., I can write a persuasive essay).

They are too broad for students to see progress (e.g., I can read) or too narrow for students to own their learning (e.g. I can put my name on my paper).

Learning-centered

The verb following the "I can" stem clearly identifies the intended learning, articulating what the students will learn rather than how they will demonstrate their learning.

They verb following the “I can” stem focuses on the academic tasks students will do rather than what students will learn (e.g., I can complete a graphic organizer).

The targets are focused only on compliance and completion (e.g., I can retake my test).

WHAT’S IN THE BAG?

Go back to your learning target

Rewrite it (if necessary) and prepare to share with

the whole group

WARM-UP WITH THIS EXERCISE:

94 children are in a reading club. One-third of the

boys and three-sevenths of the girls prefer fiction. If

36 students prefer fiction, how many girls prefer

fiction?

GEOMETRY

The Road to

WHY 6TH GRADE TEACHERS

SHOULD GIVE A SHIFT…

Geometry

WHY ALL TEACHERS SHOULD

GIVE A SHIFT

Geometry

CAPSTONE – GRADE 12 MODULE 2

Grade 9 -- Algebra I Grade 10 -- Geometry Grade 11 -- Algebra II Grade 12 -- Precalculus

State Examinations State Examinations State Examinations State Examinations

M3: Functions

(45 days)

(35 days)

M2:

Vectors and Matrices

(40 days)

M3:

Rational and Exponential

Functions

(25 days)

M4: Trigonometry

(20 days)

20 days

20 days 20 days

20 days

M1:

Polynomial, Rational, and

Radical Relationships

(45 days)

M2:

Trigonometric Functions

(20 days)

20 days

20 days

M1:

Congruence, Proof, and

Constructions

(45 days)

M2:

Similarity, Proof, and

Trigonometry

(45 days)M3:

Linear and Exponential

Functions

M2: Descriptive Statistics

(25 days)

M1:

Relationships Between

Quantities and Reasoning

with Equations and Their

Graphs

(40 days)

M1:

Complex Numbers and

Transformations

(40 days)

20 days

20 days

20 days

20 days 20 days

20 days

M4:

Inferences and Conclusions

from Data

(40 days)

20 days

20 days 20 days

Review and Examinations

M3: Extending to Three

Dimensions (10 days)

M4: Connecting Algebra

and Geometry through

Coordinates (25 days)

Review and Examinations20 days 20 days

20 days

M5:

Circles with and Without

Coordinates

(25 days)


M5:

A Synthesis of Modeling

with Equations and

Functions (20 days)

M4:

Polynomial and Quadratic

Expressions, Equations and

Functions

(30 days)


M5:

Probability and Statistics

(25 days)

HOW DO 3D FIRST PERSON SHOOTER

GAMES PROJECT A 3D WORLD ONTO A 2D

SCREEN?

The Road to Geometry

DESIGNERS USE PERSPECTIVE

FOUNDATIONS RATIOS, RATES AND LINEAR EQUATIONS

• Grade 6, Module 1, Lessons 14-15, 20

• Grade 7, Module 1, Lessons 9, 10, 15, 16.

Lesson 14: From Ratio Tables, Equations, and Double Number Line Diagrams to Plots on the Coordinate Plane

Date: 8/5/13

110

© 2013 Common Core, Inc. Some rights reserved. commoncore.org This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

NYS COMMON CORE MATHEMATICS CURRICULUM 6 Lesson 14

Lesson Summary

A ratio table, equation, or double number line diagram can be used to create ordered pairs. These ordered pairs

can then be graphed on a coordinate plane as a representation of the ratio.

Example:

Equation: =

0 0

1 3

2 6

3 9

What do you notice? It takes 2 hours to travel 100 miles.

What would happen if I drew a horizontal line from 200 miles on the -axis to the line representing the

relationship between hours and miles and then drew a vertical line down to the -axis?

We will intersect the -axis at 4 hours.

Draw a horizontal line from 250 miles on the -axis to the line representing the relationship between hours and miles.

Draw a vertical line down to the -axis.

What do you notice?

We intersect the -axis halfway between 4 hours and 6 hours.

What is the midpoint of the intervals between 4 hours and 6 hours?

5 hours

How many hours will the team have to wait to be served dinner?

5 hours

Check with the table and the following equation:

= 50 ×

= 50 × 5

250 = 250

Closing (5 minutes)

Why would you choose to use a graph to represent a ratio?

Answers will vary but should include consideration that reading a graph can be more efficient than

creating a table to determine missing values.

Exit Ticket (5 minutes)

Ordered Pairs

( , )

(0, 0)

(1, 3)

(2, 6)

(3, 9)

Lesson 15: Equations of Graphs of Proportional Relationships Involving Fractions

Date: 8/8/13

137



Exit Ticket Sample Solutions

The following solutions indicate an understanding of the objectives of this lesson:

1. Describe the relationship that the graph depicts.

The graph shows that in 3 days the water was at 4 inches high. The water has

risen at a constant rate. Therefore the water has risen inches per day.

2. Identify two points on the line and explain what they mean in the context of the

problem.

(6, 8) means that by the 6th day, the water had risen 8 inches; (9, 12) means that by

the 9th day the water had risen 12 inches.

3. What is the unit rate?

The unit rate in inches per day is 4/3.

4. What point represents the unit rate?

The point that shows the unit rate is (1, 1 )

Problem Set Sample Solutions

1. Students are responsible for providing snacks and drinks for the Junior Beta Club Induction Reception. Susan and

Myra were asked to provide the punch for the 100 students and family members who will attend the event. The

chart below will help Susan and Myra determine the proportion of cranberry juice to sparkling water that will be

needed to make the punch. Complete the chart, graph the data, and write the equation that models this

proportional relationship.

Sparkling water

(cups)

Cranberry juice

(cups)

1 4/5

5 4

8 6 2/5

12 9 3/5

50 40

100 80

= , where = Cups of Cranberry Juice and = Cups of Sparkling water

2. Jenny is a member of a summer swim team.

a. How many calories does she burn in one minute?

Jenny burns 100 calories every 15 minutes, so she burns 6 2/3 calories

each minute.

b. Use the graph below to determine the equation that models how many

calories Jenny burns within a certain number of minutes.

= , where =calories and = time in minutes

FOUNDATIONS RATIOS, RATES AND LINEAR EQUATIONS

Grade 8 Module 4 Lessons 15, 16 and 17

Lesson 17: The Line Joining Two Distinct Points of the Graph = + has Slope

Date: 11/8/13



Discussion (12 minutes)

Recall the goal from Lesson 15: We want to prove that the graph of a linear equation is a line. To do so, we needed

some tools, specifically two related to slope. Now that facts are known about slope, we will focus on showing that the

line that joins two distinct points is a linear equation with slope .

We know from our previous work with slope that when the horizontal distance between two points is fixed at

one, then the slope of the line is the difference in the -coordinates. We also know that when the horizontal

distance is not fixed at one, we can find the slope of the line using any two points because the ratio of

corresponding sides of similar triangles will be equal. We can put these two facts together to prove that the

graph of the line = has slope . Consider the diagram below:

Examine the diagram and think of how we could prove that = .

Provide students time to work independently, then time for them to discuss in pairs a possible proof of = . If

necessary, use the four bullet points below to guide students’ thinking.

Do we have similar triangles? Explain.

Yes. Each of the triangles has a common angle at the origin, and each triangle has a right angle. By the

AA criterion these triangles are similar.

What is the slope of the line? Explain.

The slope of the line is . By our definition of slope and the information in the diagram, when the

horizontal distance between two points is fixed at one, the slope is .

Write the ratio of the corresponding sides. Then solve for .

= , =

Therefore, the slope of the graph of = is .

MP.2

Lesson 16: The Computation of the Slope of a Non-Vertical Line Date: 11/8/13

218



Discussion (10 minutes)

In the last lesson, we found a number that described the slope or rate of change of a line. In each case, we

were looking at a special case of slope because the horizontal distance between the two points used to

determine the slope, and , was always 1. Since the horizontal distance was 1, the difference between the

- coordinates of points and is equal to the slope or rate of change. For example, in the following graph

we thought of point as zero on a vertical number line and noted how many units point was from point .

Also in the last lesson we found that the unit rate of a problem was equal to the slope. Using that knowledge

we can say that the slope or rate of change of a line = .

Now the task is to determine the rate of change of a non-vertical line when the distance between points and

is a number other than 1. We can use what we know already to guide our thinking.

PERSPECTIVE SCALING ACROSS THE

GRADES

Grade 6 Grade 7 Grade 8

20 days

20 days

M1:

Ratios and Unit Rates

(35 days)

M2:

Arithmetic Operations Including

Division of Fractions

(25 days)

M3:

Rational Numbers

(25 days)

M4:

Expressions and Equations

(45 days)

M5:

Area, Surface Area, and Volume

Problems

(25 days)

20 days

20 days

20 days

M6:

Statistics

(25 days)

20 days

M1: Integer Exponents and the

Scientific Notation

(20 days)

20 days

20 days 20 days

20 days

M2:

The Concept of Congruence

(25 days)

M3:

Similarity

(25 days)

M4:

Linear Equations

(40 days)

20 daysM5: Examples of Functions from

Geometry (15 days)

20 daysM1:

Ratios and Proportional

Relationships

(30 days)

20 days

20 days 20 days

M6:

Geometry

(35 days)

M5:

Statistics and Probability

(25 days)

M4:

Percent and Proportional

Relationships

(25 days)

M3:


(35 days)

M2:

Rational Numbers

(30 days)

Approx. test

date for

Grades 6-8

M6:

Linear Functions

(20 days)

20 days

20 daysM7:

Introduction to Irrational Numbers

Using Geometry

(35 days) 20 days



M3: Functions

(45 days)

(35 days)

M2:


(40 days)

M3:


Functions

(25 days)

M4: Trigonometry

(20 days)

20 days

20 days 20 days

20 days

M1:



(45 days)

M2:


(20 days)

20 days

20 days

M1:


Constructions

(45 days)

M2:


Trigonometry

(45 days)M3:


Functions


(25 days)

M1:




Graphs

(40 days)

M1:

Complex Numbers and

Transformations

(40 days)

20 days

20 days

20 days

20 days 20 days

20 days

M4:


from Data

(40 days)

20 days

20 days 20 days








20 days

M5:


Coordinates

(25 days)


M5:


with Equations and

Functions (20 days)

M4:



Functions

(30 days)


M5:


(25 days)

RIGID MOTIONS, DILATIONS,

PERSPECTIVE PROJECTION, AND SCALING

ARE A THEME OF… Grade 6 Grade 7 Grade 8

20 days

20 days

M1:


(35 days)

M2:



(25 days)

M3:

Rational Numbers

(25 days)

M4:


(45 days)

M5:


Problems

(25 days)

20 days

20 days

20 days

M6:

Statistics

(25 days)

20 days


Scientific Notation

(20 days)

20 days

20 days 20 days

20 days

M2:


(25 days)

M3:

Similarity

(25 days)

M4:

Linear Equations

(40 days)


Geometry (15 days)

20 daysM1:


Relationships

(30 days)

20 days

20 days 20 days

M6:

Geometry

(35 days)

M5:


(25 days)

M4:


Relationships

(25 days)

M3:


(35 days)

M2:

Rational Numbers

(30 days)

Approx. test

date for

Grades 6-8

M6:

Linear Functions

(20 days)

20 days

20 daysM7:


Using Geometry

(35 days) 20 days



M3: Functions

(45 days)

(35 days)

M2:


(40 days)

M3:


Functions

(25 days)

M4: Trigonometry

(20 days)

20 days

20 days 20 days

20 days

M1:



(45 days)

M2:


(20 days)

20 days

20 days

M1:


Constructions

(45 days)

M2:


Trigonometry

(45 days)M3:


Functions


(25 days)

M1:




Graphs

(40 days)

M1:

Complex Numbers and

Transformations

(40 days)

20 days

20 days

20 days

20 days 20 days

20 days

M4:


from Data

(40 days)

20 days

20 days 20 days








20 days

M5:


Coordinates

(25 days)


M5:


with Equations and

Functions (20 days)

M4:



Functions

(30 days)


M5:


(25 days)

INCLUDING ANGLE PREPARATION

Grade 6 Grade 7 Grade 8

20 days

20 days

M1:


(35 days)

M2:



(25 days)

M3:

Rational Numbers

(25 days)

M4:


(45 days)

M5:


Problems

(25 days)

20 days

20 days

20 days

M6:

Statistics

(25 days)

20 days


Scientific Notation

(20 days)

20 days

20 days 20 days

20 days

M2:


(25 days)

M3:

Similarity

(25 days)

M4:

Linear Equations

(40 days)


Geometry (15 days)

20 daysM1:


Relationships

(30 days)

20 days

20 days 20 days

M6:

Geometry

(35 days)

M5:


(25 days)

M4:


Relationships

(25 days)

M3:


(35 days)

M2:

Rational Numbers

(30 days)

Approx. test

date for

Grades 6-8

M6:

Linear Functions

(20 days)

20 days

20 daysM7:


Using Geometry

(35 days) 20 days



M3: Functions

(45 days)

(35 days)

M2:


(40 days)

M3:


Functions

(25 days)

M4: Trigonometry

(20 days)

20 days

20 days 20 days

20 days

M1:



(45 days)

M2:


(20 days)

20 days

20 days

M1:


Constructions

(45 days)

M2:


Trigonometry

(45 days)M3:


Functions


(25 days)

M1:




Graphs

(40 days)

M1:

Complex Numbers and

Transformations

(40 days)

20 days

20 days

20 days

20 days 20 days

20 days

M4:


from Data

(40 days)

20 days

20 days 20 days








20 days

M5:


Coordinates

(25 days)


M5:


with Equations and

Functions (20 days)

M4:



Functions

(30 days)


M5:


(25 days)

FUNCTION TRANSFORMATIONS

All function transformations are represented through

translations, reflections, and directional scalings of the

graphs of functions:

y=f(x)+k

y=f(x+k)

y=kf(x)

y=f(k x)

These function transformations help students better

understand the properties of functions.

MAJOR TAKE AWAY

Our work is more interconnected vertically

than ever before

Details are in the Modules

TAPE DIAGRAMS

What is this crazy math I keep seeing on Facebook?

Concrete Pictorial Abstract

?

5 2

FORMS OF THE TAPE DIAGRAM

Part – Whole Model Fraction Model

Part Part

Additive Comparison Model Models for Ratios & Mutiplicative Comparison

5 pieces of size one-fifth

Difference

5 times as much as; 1:5 ratio

EARLY BASIC EXAMPLES

1. Rose has a vase with 13 flowers. She puts 7 more

in the vase. How many flowers are in the vase?

1. Nine dogs were playing at the park. Some more

dogs came to the park. Then there were 11 dogs.

How many more dogs came to the park?

G1 M4 L20

EARLY BASIC EXAMPLES

3. Rose wrote 8 letters. Nikii wrote 12 letters.

How many more letters did Nikii write than

Rose?

4. Peter has 8 more green crayons than yellow

crayons. Peter has 10 green crayons. How many

yellow crayons does Peter have?

G1 M6

TRY USING A TAPE DIAGRAM TO SOLVE

THE FOLLOWING PROBLEM:

5. The total weight of a football and 10 tennis balls

is 1 kg. If the weight of each tennis ball is 60g,

find the weight of the football.

G3

A MULTIPLICATION/RATIO COMPARISON

PROBLEM:

6. There are 400 children at Park Elementary

School. Park High School has 4 times as many

students. How many students in all attend both

schools?

G4 M3

OUR FRIENDS…FRACTIONS

7. David spent 2/5 of his money on a storybook.

The storybook cost $20. How much did he have

at first?

Your turn:

8. Max spent 3/5 of his money in a shop and ¼ of

the remainder in another shop. What fraction of

his money was left? If he had $90 left, how much

did he have first?

G5

TRY THIS ONE:

9. Henry bought 280 blue and red paper cups. He

used 1/3 of the blue ones and 1/2 of the red ones

at a party. If he had an equal number of blue cups

and red cups left, how many did he use

altogether?

6TH GRADE:

10. The ratio of the length of Tom’s rope to the

length of Jan’s rope was 3:1. The ratio of the

length of Maxwell’s rope to the length of Jan’s

rope was 4:1. If Tom, Maxwell, and Jan have 80

feet of rope altogether, how many feet of rope

does Tom have?

G6

TRY THIS ONE:

11. Jack and Matteo had an equal amount of money

each. After Jack spent $38 and Matteo spent $32,

the ratio of Jack’s money to Matteo’s money was

3:5. How much did each boy have at first?

G6

BACK TO OUR WARM UP 94 children are in a reading club. One-third of the boys and three-

sevenths of the girls prefer fiction. If 36 students prefer fiction, how many

girls prefer fiction? 94

36

22

Boys Girls

Prefers fiction

Children in Reading Club

Prefers non-fiction

58

36

Prefers fiction

14

22

HOW DO WE MAKE THE MOVE TO

ABSTRACT?

Max had x brownies. He ate 4 brownies and shared

the remaining brownies among his 6 friends equally.

How many brownies did each friend receive?

Express your answer in terms of x.

G7

HOW DO WE MAKE THE MOVE TO

ABSTRACT?

The ages of three sisters are consecutive integers.

The sum of their ages is 45. Find their ages.

G7 M3 L7

PICTORIAL TOOLS

Enable students to persevere in problem solving

Use appropriate tools strategically

Develop students’ independence in asking themselves:

“Can I draw something?”

“What can I label?”

“What do I see?”

“What can I learn from my drawing?”

WHERE ARE YOU NOW?

Use the self-assessment chart to mark where you

think you are now with a

Answer the questions at the bottom of the sheet:

Connect

Extend

Challenge

Roll up your sheet and put it in your bag

BUSINESS

Math

MODULES UPDATE

EngageNY got a facelift

Re-visit EngageNY for updates to the Modules

Link under “Common Core”

New Modules posted (as of 8/27/14):

Geometry Module 4

Algebra 2/Trig Module 1 & 2

Pre-Calculus Module 1

EXAMS

Algebra B – Common Core Algebra Exam

Geometry – Common Core Geometry Exam

Local Exams will be revised at Secondary Math

Meetings

Students’ best scores are vital

PERFORMANCE LEVELS

Performance Levels on Common Core Regents Exams

Level 5: Exceeds Common Core expectations

Level 4: Meets Common Core expectations

(First required for Regents Diploma purposes with the Class of 2022)

Level 3: Partially meets Common Core expectations

(Required for current Regents Diploma purposes. We expect comparable

percentages of students to attain Level 3 or above as do students who pass current

Regents Exams (2005 Standards) with a score of 65 or above)

Level 2 (Safety Net): Partially meets Common Core expectations

(Required for Local Diploma purposes. We expect comparable percentages of

students to attain Level 2 or above as do students who pass current Regents Exams

(2005 Standards) with a score of 55 or above)

Level 1: Does not demonstrate Knowledge and Skills for Level 2

SLO

All HS SLOs are secured in Castle Learning

Otherwise scanned at building (ZipGrade)

Less pretty

BUDGET INFORMATION

Books

Supplies

Transition to consolidation

CURRICULUM MAPS

NYLearns cleaned up

Added a Common Core Geometry map

Algebra/ Algebra B maps updated – added additional

resources

Updated?

Grade 7

Grade 7 Accelerated

Grade 8

Change format to be more user-friendly

TECHNOLOGY

Access

www.desmos.com

http://www.geogebra.org

Minitab/Minitab Express update (HS computer labs)

Carnegie Learning Cognitive Tutor

Calculators

http://www.desmos.com



SECONDARY MATH CURRICULUM

COMMITTEE

Schedule forthcoming

Review Final Exams

Update Curriculum Maps

Disseminate important information

HAVE A GREAT SCHOOL YEAR!

I look forward to working with you this year.

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