Search Results for: tape diagram

Come see us at NCEA and NCTM

March 27, 2018 by Cassy Turner Leave a Comment

Spring educators’ conference season is upon us and we are thrilled by several opportunities to speak at upcoming events. The descriptions below are from conference programs.

NCEA 2018 Convention & Expo (April 3 – 5 at the Duke Energy Convention Center in Cincinnati, OH) is the largest private-education association gathering in the nation!

Strip Models, Tape Diagrams, Bar Models, Oh My!
Presenters: Cassy Turner and Beth Curran
Date: Tuesday, April 3, 2018
Time: 1:30 PM – 2:45 PM
Room: 251

Improving students’ problem-solving abilities is a major focus of mathematics education. Model drawing is a powerful tool that students can use to attack complex problems. In this hands-on, minds on session, presenters will investigate methods of teaching and assessing tape diagrams for those persnickety word problems, and explore interactive model drawing technology. Walk away with strategies for guiding student learning that you can use tomorrow!

Using Mental Math Strategies to Deepen Number Sense
Presenters: Beth Curran and Cassy Turner
Date: Thursday, April 5, 2018
Time: 11:15 AM – 12:30 PM
Room: 251

Number sense = mental math. Participants will actively explore mental math strategies used throughout the elementary grades. Engaging in mental math activities allows students to develop a relational understanding of numbers and their magnitude. Students begin to see numbers as being made up of parts and develop an understanding of how numbers can be composed and decomposed for mental calculations. Discourse around mental math allows students to expand their toolbox of strategies for solving problems and to evaluate strategies and answers for efficiency and reasonableness.

NCTM Annual Meeting and Exposition 2018 (April 25 – 28 at the Walter E. Washington Convention Center in Washington, D.C.) is the premier math education event of the year!

Do Not Invert and Multiply! Building the Bridge to Algebra Through Fractions Tasks
Date: Friday, April 27, 2018
Time: 1:30 PM – 2:30 PM
Room: 159 AB

Join Cassy Turner, Beth Curran, and Allison Coates as they work through hands-on tasks for fractions. We’ll investigate how the progression of fractions problems helps students build mastery of algebraic concepts such as naming unknown quantities, writing expressions, and laying the foundation for solving for x.

Using Anchor Tasks to Engage Learners: Deepening Understanding through Exploration and Discourse
Date: Saturday, April 28, 2018
Time: 8:00 AM – 9:00 AM
Room: 146 B

Participants will engage in active math lessons and learn how to use learning objectives to create anchor tasks that spark student interest and allow students of all levels to build on prior knowledge, explore concepts with concrete materials and engage in productive discourse to deepen conceptual understanding with a focus on problem-solving. Cassy Turner and Beth Curran will lead this interactive workshop

Beginning Bar Model Boot Camp: Getting Started with Model Drawing
Date: Saturday, April 28, 2018
Time: 9:45 AM – 11:00 AM
Room: 144 ABC

Improving students’ problem-solving abilities is a major objective of Common Core and state standards, and model drawing is a powerful tool that students can use to attack complex problems. Join Cassy Turner and Beth Curran to investigate methods of teaching and assessing tape diagrams for those persnickety word problems, and explore interactive model drawing technology.

Previewing 2017 NCTM Conference Singapore Math Sessions

March 20, 2017 by Cassy Turner Leave a Comment

The NCTM (National Council of Teachers of Mathematics) Annual Meeting & Exposition program 2017 is now online and it’s time for my annual review of Singapore Mathematics sessions.

I’ve included sessions on Tape Diagrams and Strip Models because there are no sessions this year citing Singapore Math® strategies. This is because the Common Core progression documents cite many of Singapore’s visual models. My hope is that many of the visual strategies are modeled throughout the conference – because good math is just good math!

See you in San Antonio!

Email us if you’d like a tour at NCTM through materials or to just talk all things math: Cassy (at) MathChampions.com or Beth (at) MathChampions.com

Thursday, April 6:

11:00 AM – 9:00 AM

#128 Supporting Students as They Work with Bar Models

Lead Speaker: Sue McMillen

Bar models (also called strip or tape diagrams) are a powerful visual tool for representing and solving math problems. But they can be challenging for students. Come to this hands-on session to explore a variety of strategies for scaffolding students as they learn to effectively work with bar models. Familiarity with bar models is assumed.

2:00 PM – 3:00 PM

#261 Visual Models to Solve Routine Word and Non-Routine Algebraic Problems: Lessons from Singapore

Lead Speaker: Andy Clark

Many students struggle with word problems, whether in elementary grades with a variety of whole number and fraction operations or the middle grades with ratio, proportion, and algebraic problems. This session will demonstrate how visual models help students see mathematical relationships and solve even the most complex problems and applications.

Friday, April 7

11:00 AM – 12:00 PM

#420 Using Tape Diagrams to Solve Ratio/Proportion Problems

Lead Speaker: Connie Laughlin

See how tape diagrams can be used to foster algebraic thinking. We will examine and illustrate how tape diagrams can be used to develop and support proportional and algebraic reasoning. Tape diagram solutions will be compared to traditional solutions to illuminate the usefulness of this tool.

12:30 AM – 1:30 PM

#476.1 Motivating Students through High-Level Problem Solving Using Models in a Collaborative Setting

Lead Speaker: Kelly Barten, Singapore Math, Inc.

Sarah Schaefer will explain how to use models and other strategies to solve challenging word problems from the original Singapore Math® program: Primary Mathematics. Workshop participants will learn how to increase student achievement while persevering and making connections between mathematical content and NCTM’s Mathematics Teaching Practices.

2:00 PM – 3:00 PM

#529.2 Hands-On Operations: Using Manipulatives for Understanding of ALL Four Operations

Lead Speaker: Kelly Barten, Singapore Math, Inc.

I’m delighted to joining Kelly to present this hands-on session at the invitation. I hope you can make it to this one.

Join Cassy Turner and use place-value manipulatives to understand and practice addition, subtraction, multi-digit multiplication, & long division algorithms for whole numbers. Learn how to help all learners master the move from concrete to the representation to the ultimate abstract algorithm with a deep understanding of regrouping and place value.

3:30PM – 4:30 PM

#565 MMMMM (Making Math More Meaningful with Models) in Pre-K–2

Lead Speaker: Duane Habecker

Too often we push our students directly to abstract algorithms without first giving students the prerequisite experience with models such as empty number lines, number bonds, arrow method, area model, etc. Teachers will learn how to use these models to make math meaningful for their students.

Filed Under: Math Events Tagged With: NCTM Conference

Visit us at Upcoming Math Conferences

February 27, 2017 by Cassy Turner Leave a Comment

Beth and Cassy are attending and presenting at the following educational conferences this spring. Please email if you’d like to schedule a time to chat!

Cassy will be attending:

2017 ASCD Annual Conference & Exhibit Show
March 25–26, 2017 | Anaheim, California

Beth and Cassy will be presenting:

2017 NCSM (National Council of Supervisors of Mathematics) Annual Conference
April 2-5, 2017 | San Antonio, Texas
Using Anchor Tasks to Ignite Learners: Coaching Teachers to Facilitate an Inquiry-Based Learning Model
Wednesday, April 5
Session Time: 5 2:15 – 3:15

Cassy will be presenting:

2017 NCTM Annual Conference and Exposition
April 5-8, 2017 | San Antonio, Texas
Hands-On Operations: Using Manipulatives for Understanding
Friday, April 7
Session Time: 2:00pm – 3:00 pm

Beth and Cassy will be presenting:

2017 NCEA Convention & Expo
St. Louis, MO
April 18-20, 2017 | St. Louis, Missouri
Using Anchor Tasks to Ignite Learners: Facilitating Inquiry-Based Math Lessons
Thursday, April 20, 2017
Session Time: 9:30 AM – 10:45 AM

Cassy will be presenting:

SDE’s National Conference on Teaching Math
July 10-14, 2017 | Las Vegas, Nevada
Wednesday, July 12, 2017
9:15 – 10:30 Understanding ALL Operations: A Hands-On Manipulative Tool Kit
11:00 – 12:15 The Best iPad® Apps for Singapore Math!
1:45 – 3:00 Filling in Knowledge Gaps
3:30 – 4:45 Strip Models, Tape Diagrams, Bar Models…Oh My!

Filed Under: Math Events Tagged With: ASCD Conference, NCEA Conference, NCSM Conference, NCTM Conference, SDE Conference

Assessing Bar Model Solutions

April 12, 2016 by Cassy Turner 6 Comments

It’s important in a Singapore style program for students to understand bar model drawing as a tool to help visualize relationships between the known and unknown in a word problem. It helps students see the algebraic structure in problems in a more concrete manner. Developed by a Primary Mathematics Project team of the Curriculum Development Institute of Singapore in the 1980’s, the Model Method for problem solving (as it’s known in Singapore) was designed as a pictorial stage to help students learn abstract mathematics.

The model method has been incorporated into the Progressions documents for the Common Core State Standards for Math (CCSSM) as a “tape diagram”. The CCSSM glossary defines a tape diagram as:

“A drawing that looks like a segment of tape, used to illustrate number relationships. Also known as a strip diagram, bar model, fraction strip, or length model.”

As such, bar models are becoming ubiquitous in elementary schools. Books have been written about Singapore’s model method, my favorite being The Singapore Model Method for Learning Mathematics:

There’s plenty to be covered with bar models, and I thought I’d share answers to the most commonly asked questions I get from teachers on model drawing:

How do you get kids to draw models when they already know the math?
How do you assess them?

When models are introduced in Singapore textbooks, the problems are very simple and students will typically know what operation to use. The first part whole models in Primary Mathematics, Common Core Edition are in the 3A textbook:

And the first part-whole model lessons in Math in Focus are in 2A:

Those are pretty easy word problems and most kids are waving their hands, with that “I KNOW the answer” look on their faces. It’s important to reiterate to students, “I’m sure you know the answer and even the equation to get there. What we’re learning today is a new way of drawing a model for our word problem so that we can work with more challenging problems in third grade. Problems like”:

A father shares $60 among his three sons and one daughter. If the daughter gets twice the amount that each son gets, how much money does his daughter receive?

or from 4A

We’ll come back to that one.

When assessing word problems, the solution method is a significant part of the answer. Students should expect to show their work to get full credit for a problem. As a teacher, it’s important to keep in mind that there is no one-way to draw a bar model.

A word problem might consist of points for the method of solving as well as points for correct computation and answers. To encourage students to draw and become proficient with bar models, I have used a rubric for assessment:

1 point for a representative diagram – Does the model make mathematical sense?
1 point for correct labeling, including the “?” to represent what is unknown.
1 point for computation on the first step and, if more than one step…
1 point for computation on the second or more steps
1 point for a correct answer in a complete sentence

Let’s look at an example. This is a student-written two-step word problem from third grade:

Does the bar model make sense? +1 point

Are the bars labeled? Are question marks in the correct places? +1 point

Is the computation to figure out the value of one unit correct? 384 ÷ 6 = 64 +1 point

How about the computation on the second step? 64 x 5 = 320 +1 point

Is the answer in a complete sentence? +1 point

So, what’s the deal with the 64 ÷ 6 equation? A byproduct of requiring students to show their work is that oftentimes, they will leave work on the paper, just in case. As a teacher, I love that this provides me with some insight into this student’s thought process:

I’m pretty sure I know what I’m doing, but I still am a little confused.

Which is exactly what the student said when I asked her about the extra equation. She realized her answer couldn’t be right because:

I ended up with 14 remainder 4 meatballs, and how could that happen?

Without a system to evaluate, you end up with:

I’m drawing boxes because I’m supposed to… I don’t get it.

This model doesn’t make sense. The student’s computation is slightly off, but she knows she needs to add. A teacher can also see from this model that more re-teaching and practice is necessary for this student and probably others in the class.

As students progress, the rubric may change. At the end of a unit/school year, the same problem might be worth three points; one apiece for diagram, computation, solution. I often tell students, “You don’t need to draw the model if you feel you understand the problem, however, you will be graded either all correct or all incorrect. Without the models I can’t give you partial credit for your thinking.”

Most students draw them anyway as a way to check their work. Some just start to see them in their heads. Here are a couple of examples from the end of a fractions unit in 5A

How would drawing a model have helped this student?

Filed Under: Math Resources, Tales from the classroom, Training Tagged With: Model Method, Singapore Math word problems, tales from the classroom

Who to see at NCSM 2016?

March 20, 2016 by Cassy Turner Leave a Comment

Each year I attend the NCSM Annual Conference for my own personal professional development. The sessions on teacher development and coaching are invaluable! I don’t have my full schedule planned yet, but thought I’d share a few of the speakers that I make a point to see each year.

The National Council of Supervisors of Mathematics is designed for math Lead, Coaches, anyone with a commitment to improving mathematics education. Their vision is built upon the pillars of:

First off, don’t miss my session where Lauri Susi and I will be sharing the latest in Bar Model/Tape Diagram technology! It’s the last session on Monday, so plan to hang around afterward with questions.

Let’s connect! Find me via the NCSM Conference app or email: cassy (at) singaporemathsource (dot) com

April 11, 2016, 4:00 PM – 5:00 PM

#1706 A Picture + Technology = Understanding x 10

Lead Speaker: Cassandra Turner
Co-Presenter: Lauri Susi
Room: OCC 202

Tape Diagrams, Bar Models, and other pictorial representations sit at the intersection of CCSSM, problem solving and technology! Come solve problems from the simple to the complex, and investigate a web-based program and iPad app that will help anyone incorporate this practical and visual problem-solving strategy into their classrooms.

April 11, 2016, 9:30 AM – 10:30 AM

#1101 Who Are You and What Do You Want To Create?
Lead Speaker: Lucy West

What is the most important skill you can cultivate to influence the system in which you work in positive and productive ways? Are you caught in old thinking patterns and outdated notions associated with hierarchical structures and defined roles? Do you have the skill set and the courage to speak up in ways others will listen and even act upon? When the pressures of new standards, high-stakes testing linked to student and teacher evaluations seem relentless and you are faced with tough decisions about where to focus your energy, how do you maintain your integrity yet stay in the game? Join me to reflect on what the research says is the most important condition needed for any organization to thrive.

#1102 A Curriculum Developer Looks at the Common Core and Its Testing
Lead Speaker: Zal Usiskin

The CCSSM constitute an ideal curriculum, while PARCC, SBAC, and the other tests constitute a tested curriculum. To what extent are these curricula in sync with each other and to the NCTM Standards (another ideal), and to what extent do these curricula agree with curricula in other countries?

April 11, 2016, 10:45 AM – 11:45 AM

#1203 Digital Tools and Three-Act Tasks: Marriages Made in the Cloud
Lead Speaker: Arjan Khalsa

Bring your iPad and your inquisitive mind. What do you notice? What do you wonder? How can you lead your district to use free, online tools effectively? This session features mathematical tasks with video anchors and online, virtual manipulatives. Themes will include: inquiry, rich discourse, perseverance, and authentic connections for grades 3–5.

#1207 Working in Harmony: Orchestrating Effective Parent Education
Lead Speaker: Barbara Blanke

It is critical to work in harmony with parents to support ALL students’ mathematical learning. Our coaching teams implemented informational meetings, parent coffees, Problems of the Month, and family mathematics nights to nurture parents’ understanding of the CCSSM. Receive ready-to-use resources to educate and build constructive partnerships.

April 11, 2016, 2:45 PM – 3:45 PM

#1607 Leading Change: Professional Development (PD) Moves That Promote New Ways of Thinking, Learning, and Teaching
Lead Speaker: Kim Rimbey

Meaningful PD opportunities provide time for participants to develop pedagogical content knowledge while reflecting on practice. But teachers want to walk out the door with “activities they can use tomorrow.” Join us as we examine strategic PD moves that customize and enhance presentations while layering classroom tasks with deep adult learning.

April 13: 8:45 AM – 9:45 AM

#3102 Critical Connections
Lead Speaker: Greg Tang

Teaching students to make sense of problems may be the single most important thing we can do. But what exactly does that look like? Join us as we make surprising connections between part-whole models, comparison word problems and simultaneous equations. Mathematics is amazing when it actually makes sense!

#3103 Demonstrating Understanding of Algebraic Concepts
Lead Speaker: Robyn Silbey

Other than following a series of prescribed steps, how can students show they have deep conceptual understanding? First, you’ll explore one algebraic concept that connects ideas and demonstrates true understanding. Then, leader actions and thought processes applying to daily instruction will be shared. Every student can fully understand algebra!

April 13: 11:45 AM – 12:45 AM

#3302 How to Create a Mathematics Teacher Specialist Network
Lead Speaker: Robert Kaplinsky

We have developed a thriving network of over 140 mathematics teacher specialists from five counties that regularly meets to collaborate and save time by pulling the best ideas from the group. Members state that it is the best ongoing professional development they receive. Learn how to grow one in your area and avoid potential implementation issues.

April 13: 3:30 PM – 4:30 PM

#3604 Practical Suggestions for Recasting our Homework Policies and Practices
Lead Speaker: Steve Leinwand

Little in life is a greater waste of time than doing and going over mathematics homework. This session will review typical practices, available research, and propose a set of changes that result in far more impactful homework policies and practices.

Filed Under: Math Events Tagged With: NCSM Conference