1. Module 3 PARTNERS for Mathematics Learning Grade 6 Partners

2. Equation Talks  Is there more  In what ways do number (equation)2
Equation Talks
x + 7 = 28
x – 4 = 16
 Is there more
than one way to solve
these?
 In what ways do
number (equation)
talks encourage
students to think x 5
+ 4 = 6
flexibly about number
and operation
relationships?
Partners
for Mathematics Learning
2 x – 3 = 17

3. It’s All in the Translation3
It’s All in the Translation
 Recognizing symbolic relationships is
important in developing algebraic reasoning
 According to NCTM’s PSSM , students should
 Explore symbolic expressions
 Use symbolic algebra to represent situations and
solve problems
 Recognize and generate equivalent forms for
simple algebraic expressions
Partners
for Mathematics Learning

4. It’s All in the Translation4
It’s All in the Translation
 In your group, read the directions for
playing It’s All in the Translation
 Play at least one game with your group
Partners
for Mathematics Learning

5. It’s All in the Translation5
It’s All in the Translation
 How would you use this activity
in your classroom?
 How could you modify this activity to meet the
needs of struggling learners?
 How could you make this activity more
challenging?
 Which Big Idea was the focus of this activity?
 How does this relate to the Essential
Standards?
Partners
for Mathematics Learning

6.  Explain to your neighbor if this is or is not 6
Equation Talk
3/8 + 4/8 = 3(1/8) + 4(1/8) =
(3 + 4)(1/8) = 7(1/8) = 7/8
 Explain to your neighbor if this is or is not
correct
 Are the expressions equivalent?
 How does this illustrate the relationship
between addition and multiplication?
Partners
for Mathematics Learning

7. Translation to Translation7
Translation to Translation
 Mathematical Vocabulary Challenges
 Words are shared with everyday English
language and other disciplines
 Some words are homonyms
 Some words are found only in mathematics
 Some words are learned in pairs and often
confuse students
Focused Strategies for Middle-Grades Mathematics Vocabulary
Development by Rheta N. Rubenstein
From Mathematics Teaching in the Middle School
Partners
for Mathematics Learning

8. Translation to Translation8
Translation to Translation
 We’ve spent time translating words into
symbols
 Now we are going to translate geometric
figures in the coordinate plane
What do airplanes
have to do with
geometric figures?
Partners
for Mathematics Learning

9. Rigid Transformations9
Rigid Transformations
 Translation: points in a figure
are slid across a translation vector the
same distance along parallel paths
 Rotation: turns a set of points about the
center of rotation an identical number of
degrees
 Reflection: points in a figure are reflected
across a line (mirror image)
Partners
for Mathematics Learning 9

10.  Using the Follow the Path10
Follow the Path
 Using the Follow the Path
activity sheet, transform the start arrow to
the stop arrow
 You must use at least one reflection, one
rotation, and one translation
 List the steps you take so that a partner
can follow your directions
Partners
for Mathematics Learning

11. Follow the Path  Exchange your directions11
Follow the Path
 Exchange your directions
with a partner
 Now transform the start arrow using your
partner’s directions
 Were you able to successfully transform
the start arrow to the stop arrow using your
partner’s directions? Explain
Partners
for Mathematics Learning

12. Follow the Path  Which Big Idea was the12
Follow the Path
 Which Big Idea was the
focus of this activity?
 How could you modify this activity to meet
the needs of struggling learners?
 How could you make this activity more
challenging?
Special note about 2009
Essential Standards
Partners
for Mathematics Learning

13. Making Cents 1. Take out some coins 2.13
Making Cents 1. 2. 3. 4. 5. 6. 7.
Take out some coins
Multiply the value of the coins in cents by 4
Add 10 to the product
Multiply your answer by 25
Add 115 to your answer
Add your age in years (truth!!)
Subtract the number of days in a normal year
What did you get?
Partners
for Mathematics Learning

14. Practice vs Problems  We’ve practiced translating14
Practice vs Problems
 We’ve practiced translating
English into mathematics
 Let’s apply this skill to a problem
 Why does “Making Cents” work?
 Will it work if you are over 100 or under 10?
Partners
for Mathematics Learning

15. They Knew Calculus When They Left…15
They Knew Calculus When
They Left…
 Read the article, They Knew Calculus When
They Left…, by Kevin St. Jarre
 Highlight, underline key points, favorite quotes,
and questions you may have
 What implications does this article have for
middle school teachers and students?
They Knew Calculus When They Left…The Thinking Disconnect Between High
School and University By Kevin St. Jarre from the Phi Delta Kappan
Partners
for Mathematics Learning

16. They Knew Calculus When They Left…16
They Knew Calculus When
They Left…
“[Universities] only want students who have been
taught how to learn and think. Students who,
when faced with problems in a new context can
self-correct their own thinking, adapt, and
succeed.”
Partners
for Mathematics Learning

17. Reflection  How can the activities in the Partners17
Reflection
 How can the activities in the Partners
Professional Development encourage
student thinking?
Partners
for Mathematics Learning

18. Renee Cunningham Kitty Rutherford Robin Barbour Mary H. Russell 18
DPI Mathematics Staff
Everly Broadway, Chief Consultant
Renee Cunningham Kitty Rutherford
Robin Barbour Mary H. Russell
Carmella Fair Johannah Maynor
Amy Smith
Partners for Mathematics Learning is a Mathematics-Science
Partnership Project funded by the NC Department of Public Instruction.
Permission is granted for the use of these materials in professional
development in North Carolina Partners school districts.
Partners
for Mathematics Learning

19. PML Dissemination Consultants19
PML Dissemination Consultants
Susan Allman
Julia Cazin
Ruafika Cobb
Anna Corbett
Gail Cotton
Jeanette Cox
Leanne Daughtry
Lisa Davis
Ryan Dougherty
Shakila Faqih
Patricia Essick
Donna Godley
Cara Gordon
Tery Gunter
Barbara Hardy
Kathy Harris
Julie Kolb
Renee Matney
Tina McSwain
Marilyn Michue
Amanda Northrup
Kayonna Pitchford
Ron Powell
Susan Riddle
Judith Rucker
Shana Runge
Yolanda Sawyer
Penny Shockley
Pat Sickles
Nancy Teague
Michelle Tucker
Kaneka Turner
Bob Vorbroker
Jan Wessell
Daniel Wicks
Carol Williams
Stacy Wozny
Partners
for Mathematics Learning

20. 2009 Writers Partners Staff Kathy Harris Rendy King Tery Gunter
Judy Rucker
Penny Shockley
Nancy Teague
Jan Wessell
Stacy Wozny
Amanda Baucom
Julie Kolb
Freda Ballard, Webmaster
Anita Bowman, Outside Evaluator
Ana Floyd, Reviewer
Meghan Griffith, Administrative Assistant
Tim Hendrix, Co-PI and Higher Ed
Ben Klein , Higher Education
Katie Mawhinney, Co-PI and Higher Ed
Wendy Rich, Reviewer
Catherine Stein, Higher Education
Please give appropriate credit to the Partners
for Mathematics Learning project when using the
materials.
Jeane Joyner, Co-PI a nd Project Director
Partners
for Mathematics Learning

21. Module 3 PARTNERS for Mathematics Learning Grade 6 Partners