1. Module 4 PARTNERS for Mathematics Learning Grade 7 Partners

2. “The Importance of Equal Sign Understanding in the Middle Grades”2
“The Importance of Equal Sign
Understanding in the Middle Grades”
 Read your section of the article by Knuth,
Alibali, Hattikudur, McNeil, and Stephens from
Mathematics Teaching in the Middle School
 Be prepared to share with your group
 Key notes
 A favorite quote
 Questions you have
Partners
for Mathematics Learning

3. Sweet Algebra  Using the Sweet Algebra handout, find3
Meaningful Practice
Sweet Algebra
“ Helping students acquire a view
of the equal sign as a symbol that
represents an equivalence relation
between two quantities…”
 Using the Sweet Algebra handout, find
out how much candy is in each bag
Partners
for Mathematics Learning

4. Sweet Algebra Meaningful Practice “Helping students acquire a view4
Meaningful Practice
Sweet Algebra
“Helping students acquire a view
of the equal sign as a symbol that
represents an equivalence relation
between two quantities…”
 How does this activity help students with
their understanding of the equal sign?
Partners
for Mathematics Learning

5. Sweet Algebra  How is variable used in this problem?5
Meaningful Practice
Sweet Algebra
 How is variable used in this problem?
 As a quantity that varies and changes
 As a specific unknown
 As quantities that vary in relation to one another
 How does this activity help students
communicate relationships with symbols?
 Which clues might pose difficulty for students
to translate into symbols? Why is this?
Partners
for Mathematics Learning

6. Sticks and No Stones  Use toothpicks to build several stages6
Sticks and No Stones
Part One
 Use toothpicks to build several stages
of the pattern
 Complete the handout as you determine
the relationship between the stage number
and the number of sticks
Partners
for Mathematics Learning

7. Sticks and No Stones Part One7
Sticks and No Stones
Part One
 What is the purpose of questions like how many
sticks in Stage 10? Stage 50?
 How can teachers help students translate their
pattern thinking into algebraic symbols?
 Why are tasks like this important for the
development of algebraic reasoning?
Partners
for Mathematics Learning

8. Sticks and No Stones  Complete Sticks and No Stones8
Sticks and No Stones
Part Two
 Complete Sticks and No Stones
Part Two Handout
 Compare and contrast Part One and
 Why might Part Two appear more
challenging to a student?
Partners
for Mathematics Learning

9. Sticks and No Stones  Once students have had these9
Sticks and No Stones
 Once students have had these
hands-on, structured experiences…
 How could we design similar activities
without the scaffolding?
 What other kinds of problems naturally
follow this type of tasks?
 What questions could you ask that
would reveal students’ thinking about
the mathematics in these tasks?
Partners
for Mathematics Learning

10. An Inequality Story  Read the inequality story10
An Inequality Story
 Read the inequality story
 As you are reading, circle, underline, or
highlight phrases that represent inequality
relationships
 On the handout, choose 5 inequality
phrases and translate to numeric and
algebraic symbols
Partners
for Mathematics Learning

11. An Inequality Story  Share and compare your inequalities11
An Inequality Story
 Share and compare your inequalities
with other members of your group
 Complete the story using a minimum
of 8 inequality relationships
Partners
for Mathematics Learning

12. An Inequality Story  How does using inequality relationships12
An Inequality Story
 How does using inequality relationships
in the context of a problem help students
understand the many meanings of
inequality?
Partners
for Mathematics Learning

13. Taco Twister  Pass out the clues to each member13
Taco Twister
 Pass out the clues to each member
of your group
 You may not look at anyone else’s clue
 If you have a question, check with your
group first
 Be sure everyone participates
Partners
for Mathematics Learning

14. Taco Twister  Using the cards, each group is14
Taco Twister
 Using the cards, each group is
to decide how many tacos Nick ate
 Remember you may not look at any card
except for your own
 You must communicate the information
on your card to the other group members
Partners
for Mathematics Learning

15. Taco Twister How many tacos did Nick eat?  Justify your solution15
Taco Twister
How many tacos did Nick eat?
 Justify your solution
Partners
for Mathematics Learning

16. Taco Twister  What challenges did you face finding16
Taco Twister
 What challenges did you face finding
a solution?
 Why is it important for students to
understand and interpret a solution to
an inequality?
 What other real world situations may
have a range of solutions?
Partners
for Mathematics Learning

17. Taco Twister  How would you use this activity17
Taco Twister
 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?
Partners
for Mathematics Learning

18. Reflection  What does this quote say to you regarding18
Reflection
“Algebraic thinking encompasses the set of
understandings that are needed to interpret the
world by translating information or events into the
language of mathematics in order to explain and
predict phenomena.”
( Lessons for Algebraic Thinking , Lawrence and Hennesey)
 What does this quote say to you regarding
the teaching and learning of algebra in
your classroom?
Partners
for Mathematics Learning

19. Renee Cunningham Kitty Rutherford Robin Barbour Mary H. Russell 19
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

20. PML Dissemination Consultants20
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

21. 2009 Writers Partners Staff Kathy Harris Rendy King Tery Gunter21
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

22. Module 4 PARTNERS for Mathematics Learning Grade 7 Partners