Strip Models, Tape Diagrams, Bar Models, Oh My!

NCTM 2015 Boston
NCSM 2015 conference

My session entitled Strip Models, Tape Diagrams, Bar Models, Oh My! has been accepted for both 2015 national conferences of the  National Council of Supervisors of Mathematics (NCSM) and the National Council of Teachers of Mathematics (NCTM). Lauri Susi of Conceptua Math is my co-presenter on these!


Now you can vote for the session to be held at the National Charter Schools Conference (NCSC) as well. We’ll reach a whole new crowd of Charter School administrators, teachers and founders!

The short description of the session:

Strip Models, Tape Diagrams, Bar Models, Oh My!NCSC15-Logo-Round5_1

These visual components sit at the intersection of Common Core, the Singapore Math® approach, and now technology! Learn why visual models for word problems are so powerful, try some problems from the simple to the complex, and investigate web-based programs and iPad apps that will help anyone incorporate this effective strategy into their classrooms.

Participants will learn how to create visual models for word problems and then integrate model drawing into their instruction. Questioning techniques for guiding student understanding of problem solving will be modeled for participants. Attendees will learn how the use of visual models for word problems can help students build a deeper understanding of mathematical concepts. Attendees will see and try online modeling tools used to develop and assess students’ deep understanding of word problems.

Vote by December 19th to get this session on the schedule!

Vote for Cassy’s NCSC Proposal!



Singapore Math Common Core Edition debuts at NCTM Conference

Cassy Turner

Thanks to Pearson for my cool caricature. Looks just like me, doesn’t it?!

I’ve just returned from an invigorating week at the National Council of Supervisors of Mathematics (NCSM) and National Council of Teachers of Mathematics (NCTM) conferences in New Orleans. Expect some posts soon that will share interesting things that I learned.

Common Core Edition of Primary Mathematics

First off, the new Common Core aligned editions of Primary Mathematics were available at the Singapore Math, Inc.® booth and they looked great! If you’re currently using the California Standards Edition of Primary Mathematics, don’t panic! The company will continue to carry the materials. However, once you see the Common Core Edition, you’re probably going to want to switch. [Using the U.S. Edition? You’re good to go with some supplementing, but you’re used to that already.   😉  ]  Copies of the new materials are not available for preview yet, but I’ll be posting some more info and sample lessons as they do become available.

Good news! Looks like there will be a Primary Digital component to the program as well.

I don’t know about anyone else, but I’m a little Common Core-d out. It seems like EVERY session at both conferences had to reference the Common Core to get accepted. Thank goodness that Primary Mathematics is already fairly well aligned  to Common Core. [Don’t believe me? Here’s Achieve’s analysis.] In perusing the new Primary Mathematics Common Core books, I noticed that content was not moved to higher grade levels, just because that’s where it was in the CCSS-M. They’ve kept the integrity of the sequence, added a few review lessons to meet CCSS-M at grade level and provided an unprecedented level of potential student questioning and discourse in the Teacher’s Guides.

I thought I’d leave you with one of the Japanese Puzzles from a fabulous session at NCTM presented by Jeffrey Wanko called Puzzling It Out: Teaching Inductive Reasoning. Have fun!

Use the three examples of Mirror puzzles and their unique solutions shown below to determine both the goal and the rules that govern Mirror puzzles.Mirrors_Puzzles


NCTM 2014 Conference Singapore Math Sessions


The NCTM Conference program book is now online and choosing which workshops and sessions to attend continues to be a challenge.  If you’d like to check out some sessions on Singapore Mathematics, there’s good news and bad.

Good news? There are 12 sessions involving Singapore-style math this year but you need to look at the session descriptions to really know it. The number of overall choices is slightly more than the number offered last year.

Bad news? Anything listed below in pink is an overlapping session.  Below are my thoughts on which session to choose, if you have a conflict.

FYI – Five (!) of the twelve sessions are Exhibitor’s Workshops:

Exhibitor Workshops (60 minutes) are designed to allow exhibitors more time to showcase their products and services away from the Exhibit Hall.

NCTM_2014_SIngapore Math sessions

Thursday, April 10: 8:00 AM-9:00 AM – No conflict

#29.2 Singapore Math: Common Core Connections
Exhibitor Workshop: Marshall Cavendish Education

Problem-solving is central to Singapore’s mathematics education. The first Common Core standard for mathematical practice states: “Make sense of problems and persevere in solving them.”  This talk addresses connections between the Common Core and Singapore Math; with focus on the standards for mathematical practice and numbers and operations.

Thursday, April 10: 9:45 AM-11:00 AM – No conflict

#92 Putting Students on the Fast Track to Better Problem Solving
Lead Speaker: Darlyne de Haan

Come and discover how to efficiently and effectively teach students how to solve and model word problems using simple brain-based strategies and bar modeling. These strategies will transform your students into excited, motivated and successful problem-solving pros. You and your students will never see or solve word problems the same again!

Not sure on this one, but thought that if it includes some bar modeling, it might be worth checking into.

Thursday, April 10: 11:00 AM – 12:00 PM – Two sessions conflict

#121 Ratio and Proportion: A Common Core Progression for Grades 6–7
Lead Speakers: Duane Habecker
Co-Speaker: Mary Anne Freitas

This session presents a two-year, flipped sixth- and seventh-grade ratio and proportion unit using instructional videos viewed at home and Common Core lessons in the classroom. Participants will be shown how to effectively use ratio tables and bar models to develop their students’ proportional thinking.

131.4 It’s here! Singapore Math® presents Primary Mathematics Common Core Edition!
Exhibitor Workshop: Singapore Math, Inc.

We will introduce our newest Singapore Math® program, Primary Mathematics Common Core Edition! Learn about the highly successful Singapore Math® elementary math series and the recent changes that have been made for the CCSS. This will be beneficial to those currently using Primary Mathematics and those considering implementing for the first time.

-> Interested in bar modeling and ratios? Looks like they may be using bar models in the Ratio & Proportion session.  (Or head to Richard Bisk’s session on Ratios on Friday; #452 at 12:30)
-> Interested in learning more about Singapore Math and how the Common Core Edition was developed? I’d go to session 131.4 and check that out. 

Thursday, April 10: 12:30 PM – 1:30 PM – Three sessions conflict

#170 Representation and Visualization in Middle School: Lessons from Singapore
Lead Speaker: Andy Clark

The Common Core State Standards emphasize the importance of representation in learning mathematics. In this session, we will share strategies for developing deeper understanding of rational numbers, ratio and rate, proportion, and algebraic expressions and equations with visual models from Singapore, with the goal of helping students make the challenging transition from arithmetic to algebra.

#182.2 Reaching and Teaching all Levels of Learners with Singapore Math
Exhibitor Workshop: Marshall Cavendish Education

This session will focus on strategies to reach the struggling student. Specifically, we will explore use of the CPA cycle, transition materials, and the analysis of student assessments in meeting the needs of underachieving students.

#182.3 Singapore Math® program for Middle School. Crossing the bridge to algebra!
Exhibitor Workshop: Singapore Math, Inc.

Middle school math often takes a backseat to elementary and high school mathematics. Dimensions Math Common Core Edition is a new series that is changing that trend. Picking up where our elementary series leaves off, this Singapore Math® middle school program fully prepares students for success in advanced high school math.

-> Looking for secondary materials? Head to the Exhibitor session 182.3 and check out the Dimensions Math Common Core Edition.
-> Head to see Andy Clark, one of the authors of  the Math in Focus series for a look at specific middle school concepts.

Thursday, April 10: 2:00 PM – 3:00 PM – Conflicts with session starting at 2:45 PM

#220 Reasoning in the Middle Grades: It’s Easier Than You Think
Lead Speaker: Berinderjeet Kaur
Co-Speaker: Denisse R. Thompson

Mathematical reasoning is not only one of the NCTM process standards, but it is also an important practice in the Common Core. This session will share several strategies from both the Singapore and U.S. perspectives on modifying non-geometrical textbook tasks and questions to bring reasoning to the instructional forefront.

Thursday, April 10: 2:45 PM – 4:00 PM

#239 Fraction Fun: Games That Cement Critical Concepts
Lead Speaker: Ricky Mikelman

Frustrated that your students don’t retain fraction concepts? Do they make common errors? Singapore teaches us the importance of the consolidation phase of learning—playing games! When students play, they move learning into long-term memory. We’ll use dice, cards, and commonly found materials to reinforce concepts that align to the Common Core State Standards.

Tough call – either way you’ll be well-informed.
->Ms. Kaur works with Singapore’s National Institute of Education and is always fascinating – I’ll probably be here.
->Ms. Mikelman works with Staff Development for Educators. She’s a great presenter and you’ll walk away with plenty of fraction games.

Friday, April 11: 8:00 AM-9:00 AM – No conflict

#310.2 Singapore Math and the Rigor of Common Core: Exploring Assessments
Exhibitor Workshop: Houghton Mifflin Harcourt

In this session, participants will examine the requirements of the Common Core and the types of assessments that students will be asked to complete. The presenter will share how Math in Focus helps students to prepare for the rigor required in both Smarter Balance and PARCC assessments.

HMH is the publisher of Math in Focus. I get oodles of emails about the MiF assessments from teachers and parents. I’ll probably check this out and see what they are doing to address these issues.

Friday, April 11: 12:30 PM – 1:30 PM – No conflict

Lead Speaker: Richard Bisk
Many students struggle when asked to solve word problems involving fractions, ratio, & percent. Model drawing helps students visualize, understand, and solve complex word problems, and provide a bridge to algebraic techniques. Experience sample solutions and learn how to use this effective technique for helping students develop deep understanding
-> Go.

Friday, April 11: 3:30 PM- 4:30 PM – No conflict

#549 Math Talk: Teaching Concepts and Skills through Stories and Illustrations
Lead Speaker: Char Forsten

A young child’s understanding of the world is enlightened and expanded through stories and illustrations so it makes sense to use these resources when learning mathematics. Based on a method used in Singapore, you will learn to use “math talk” as a powerful way to provide purposeful practice through stories and illustrations.

->Char is a very engaging presenter. She already has her handout on the NCTM web site, so you can preview her topics!  


NCTM 2013 Conference Singapore Math Sessions

It’s conference time again. No not parent conferences, Mathematics conferences!

2013 Annual Meeting and Exposition

The NCTM Conference program book is now online and choosing which workshops and sessions to attend continues to be a challenge.  If you’d like to check out some sessions on Singapore Mathematics, there’s good news and bad.

Good news? There are 10 sessions involving Singapore-style math this year and while there’s plenty of bar modeling, there are two that focus on implementations. (The number of overall choices is down again from the number offered last year)

Bad news? Anything listed below in pink is an overlapping session.  Below are my thoughts on which session to choose, if you have a conflict.

FYI – Three of the ten sessions are Exhibitor’s Workshops:

Exhibitor Workshops (60 minutes) are designed to allow exhibitors more time to showcase their products and services away from the Exhibit Hall.


Thursday, April 18: 9:30 AM-10:30 AM – No conflict

#61 – Getting Number Bonds to Stick Like Glue
Lead Speaker: Catherine Kuhns

Inspired by the highly successful strategies from Singapore, this session will focus on high-interest and engaging concrete, pictorial, and abstract tasks that lead to genuine understanding and recall of the critical number combinations up to ten. These activities are appropriate for whole groups, small groups, and centers—and they are kid approved. Suitable for educators teaching Grades prek-2.

Thursday, April 18: 12:30 PM-1:30 PM – No conflict

#173 – Reasoning in the Elementary Classroom: It’s Easier Than You Think
Lead Speaker: Berinderjeet Kaur
Co-Speaker: Denisse R. Thompson

Mathematical reasoning is not only one of the NCTM Process Standards but also an important practice in the Common Core. We will share several simple strategies from both the Singapore and U.S. perspectives on modifying tasks and questions to bring reasoning to the instructional forefront. Suitable for educators teaching Grades 3-5

Thursday, April 18 4:00 PM – 5:00 PM – No conflict

#301.3 – Math Buddies: The Digital Singapore Math Solution in Action
Exhibitor Workshop: Marshall Cavendish Education

The latest K–5 digital curriculum from Marshall Cavendish Education, Math Buddies aligns with the Common Core State Standards and integrates multimedia with instructional pedagogy from Singapore Math texts.

Friday, April 19 8:00 AM- 9:00AM – Some conflict

#306 – Adopting Singapore Math: A Case Study
Lead Speaker: Kathleen Jalalpour
Co-Speaker: Corrinne Lieu

Six years ago, Keys School in Palo Alto, California (K–8), adopted Singapore Math. We will present data, experiences, and film clips of math classes. We will summarize the overwhelming benefits of Singapore Math, the obstacles we had to overcome, and the best methods of implementing this acclaimed math curriculum. Suitable for educators teaching Grades preK-5.

Friday, April 19 8:00 AM- 9:15AM – Some conflict

#337 – Exploring Reasoning and Communication with Problems from Singapore Classrooms
Lead Speaker: Ban Har Yeap

Experience mathematical reasoning and communication by solving problems taken from Singapore classrooms. Learn three strategies to enhance reasoning and communication: the use of questions, concrete materials, and visuals. We will use geometry and measurement problems across grade levels. Designed for teachers working with grades 3 – 8.

The first session will provide an overview of an implementation at the Keys School in Palo Alto. Dr. Yeap will be using questions, concrete materials and visuals to explore problems across content and grade level.

-> Interested in one school’s experience? Head to the adoption session.
-> The second session has Ban Har Yeap. Enough said.

Friday, April 19 9:30am – 10:30am – Some conflict

#372 – Singapore’s Visual Models to Reason and Make Sense of Problems
Lead Speaker: Andy Clark

We will focus on the visual models and visualization used in the highly successful Singapore curriculum. These aspects offer students entry points to complex problems and develop deep understanding of topics such as operations with fractions, ratio, and algebraic manipulation. We will also discuss examples of their rich problems. Suitable for educators teaching Grades 6-8.

Friday, April 19 9:45 AM – 11:45 AM  – Some conflict

#396 – Bar Modeling, Percent Decrease, and the Common Cold
Lead Speaker: Kathleen Hill
Co-Speaker: Jennifer Luebeck

Lesson using the investigative approach with an interactive computer simulation and the mathematical tool of a bar model to help students make sense of the variables that affect the spread of disease. Suitable for educators teaching Grades 6-8.

Friday, April 19 11:00 AM – 12:00 PM – Some conflict

#425 – Linking Bar Diagrams and the Standards for Mathematical Practice
Lead Speaker: Robin Silbey

This highly interactive presentation teaches bar diagramming, a powerful, visual–logical problem-solving strategy focused on reasoning. You’ll draw bar diagrams to represent and solve several word problems. Through the lens of the Standards for Mathematical Practice, you’ll see how bar diagramming develops mathematical proficiencies. Hands-on session designed for teachers working with grades 3 – 8.

-> Looking for a specific lesson with a little bit of bar modeling? Head to the second session
-> Andy and Robin are always insightful. I’d aim to hit both the first and third sessions!

Friday, April 19 2:30pm – 3:30PM – No conflict

#542.3 – Lessons from Singapore: Developing Number Sense/Problem Solving with Visual Models
Exhibitor Workshop: Houghton Mifflin Harcourt

See an American version of Singapore’s highly successful curriculum and its use in the U.S. The session will focus on how Singapore’s visual models and effective pedagogy enable all students to develop number sense and solve complex problems so they are ready for the Common Core State Standards–based assessments.

Satuday, April 20 10:00 AM – 11:00AM – No conflict

#681.3 – Implementing Singapore Math: A Collaborative Effort
Exhibitor Workshop:

Explore how the Primary Mathematics series was used as a tool to build a higher-performing mathematics program in a low-performing school. The presenter will share data, pictures, teacher reflections, successes, and challenges of implementing this focused and coherent curriculum.


Thoughts from NCTM session on Singapore Math + Technology

Last week I presented with Lauri Susi at the National Council of Teachers of Mathematics (NCTM) 2012 Annual Conference in Philadelphia.  Here was our session description:

470 – Technology + Singapore Strategies = Number Sense
Lead Speaker: Cassandra Turner
Co-Speaker: Lauri Susi

Visual reasoning is a powerful tool for making sense of mathematics. Learn successful visual strategies and instructional methods from Singapore that allow students to develop a deeper understanding of number concepts using hands-on manipulatives and software. Walk away with strategies for guiding students’ learning that you can use tomorrow.

We displayed the above image of lions on the screen while discussing the Concrete-Pictorial-Abstract progression of understanding. A teacher raised her hand and said something along the lines of:

I don’t like that picture. There are male lions and female lions, they aren’t the same. I can’t add them together and students get confused in upper grades when they think that these can be added.

Which is such a great comment. Why? Because this illustrates one of those interesting points that isn’t always in a student textbook and as the teacher you have to be aware of it : labels matter. Yet it isn’t so obvious at a kindergarten level.

2 male lions and 3 female lions make 5 lions altogether.

Well, they’re all lions and we’re looking at a part-whole understanding of addition. Here’s another image from the kindergarten book:

2 boys and 3 girls make 5 children.

2 daisies and 2 tulips make 4 flowers.

So how does this apply to later, more advanced concepts? Consider:

  • 2 ones and 3 ones make 5 ones.
  • 2 tens and 3 tens make 5 tens.
  • 2 tens and 3 ones make 23 ones.
  • 2 dimes and 3 pennies make 5 coins and they also make 23 cents.
  • 2/5 and 3/5 make 5/5
  • 2/5 and 3/4 make…hmmm, we need some common terminology here.

Thanks kindergarten and first grade teachers for laying this foundation!