Often times, the teacher’s guides are written following a more traditional, lecture-style of teaching. They encourage the teacher to model, or work problems, while the students watch, and then the students are asked to mimic what the teacher did with a similar problem. I challenge you to flip the script and replace the word “show” with “have the students model” and replace “tell” with “ask”. When your teacher’s guide says to show the students the difference or similarities between problems or concepts replace that with, “ask the students what they notice?” It’s these little tweaks that will go a long way toward engaging your students in meaningful discourse and ultimately deepening their understanding.

A fourth-grade teacher from Aurora, Colorado shared her strategies for engaging students in math talk in her classroom.

While this appears to be written for the students to follow, it also suggests some great questions for teachers to ask to generate more discussion.

As students are working through a task ask:

- How did you solve that?
- How do you know that’s correct?
- Can you solve it another way?
- Can you build a model?
- Can you use numbers and symbols to explain your model?
- Is that the best (most efficient) way to solve that?
- Is your answer reasonable?
- Do you agree or disagree with your partner’s answer?

So, who’s doing all the talking? Give some of these questions a try and let us know how it goes.

We’ll be presenting at the following conferences in April. Stop by and say “I’m a Math Champion” to get one of our cool buttons!

**NCSM Annual Conference 2019 | San Diego**

April 3 | 1:45 – 2:45 pm

**No More “Menacing Multiplication” and “Laborious Long Division” – Understanding Procedures through Number Sense in Grades 3-5**

As a mathematics leader, how many times have you heard teachers ask “My students are struggling, can’t I just teach them a procedure?” Teachers recognize the need for students to develop both procedural fluency and conceptual understanding but are often unsure of how to do so. Explore strategies focused on numeracy, sense-making, and fostering a conceptual understanding that will help even the most struggling student understand the abstract algorithms for multiplication and division

**NCTM Annual Meeting 2019 | San Diego**

We’ll be presenting regular and exhibitor sessions for Singapore Math, Inc. as they’re releasing their new Singapore Math Series Dimensions Math. Come meet the authors!

**#133.4 Empowering Algebraic Thinkers**

April 4 | 11:00 am – 12:00 pm

Experience how mental math strategies for grades 4–6 build confidence and understanding for future algebra students. Fill up your teaching toolbox with Singapore math strategies that prepare elementary students for advanced math.

**#255 Using Mental Math to Deepen Number Sense**

April 4 | 3:15 pm – 4:30 pm Beth made some awesome short videos!

**#360.3 Ready, Set, Play: Practicing Number Sense with Games**

April 5 | 9:30 am – 10:30 am

**NCEA 2019 Convention & Expo**

**Understanding Procedures through Number Sense: Grades 3-5**

April 23 | 1:30 PM – 2:45 PM

Join us as we work with manipulatives to understand and practice multi-digit multiplication and long division algorithms for whole numbers and decimals. Learn how to help all learners master the move from concrete to pictorial representation to the ultimate abstract algorithm with a deep understanding of regrouping and place value.

**Strategies First: Teaching Fact Fluency with Hands-on Activities and Games**

April 24 | 2:00 pm – 3:00 p.m.

If we can’t teach memorization, then what do we do? Participants will learn how to develop hands-on lessons that promote deep conceptual understanding and strengthen students’ number sense. We will explore strategies for teaching and learning addition, subtraction, multiplication, and division facts to make mathematics accessible to all students. Participants will engage in activities and games that promote automaticity with math facts, leaving with the tools needed to take what they learned and apply it immediately in their classrooms.

**MCTM Spring Conference 2019**

April 25-26, 2019

**Ready, Set, Play: Practicing Number Sense with Games**

Day/Time TBA

The headline teases: This is the maths puzzle that is baffling everyone – but could you solve it?

Yes, we can! So, don’t lose your marbles over this one.

This appears to come from a Maths No Problem! workbook, probably 2A as the article states it is a problem for 7-year-olds. The author interviews a math professor:

Math expert, Dr. James Hind, of Nottingham Trent University, said the confusing question is above the level it was set for and to reach a conclusion it is best to try a number of equations.

Dr. Hind then proceeds to use a guess and check method to solve the problem. Maybe they asked the wrong expert.

Programs based on a Singapore Math approach start bar model drawing in either 2nd or 3rd grade, making this a challenging problem for many 2nd graders, but not a guess and check problem. Visualization of problem-solving actually starts in kindergarten!

See if you can solve this one like a 7-year- old. Submit your solutions by the end of the month!

Our last Word Problem Wednesday problem was from the chapter on the “Model Method and Algebra” from The Singapore Model Method for Learning Mathematics.

We had several correct answers submitted. Here’s a worked example from Shirley Davis:

How did you do?

We are pleased to announce the return of Jumpstart, an intensive, two-day workshop for current and potential users of Primary Math and Math in Focus, as well as any teacher interested in incorporating these techniques into their own classroom, regardless of current curriculum. If you are:

- new to the Singapore approach to math instruction…
- needing a refresher to boost your math teaching skills…
- wanting to incorporate the best practices from Singapore into your current curriculum…or
- curious about the reasons for Singapore’s remarkable success…

…then this workshop is for you!

*Click here to get all of the details on this exciting program!*

https://singaporemathsource.com/jumpstart-your-singapore-math-summer-2019/

**Roanoke, VA | July 8-9, 2019:**

Register Now!

**Phoenix, AZ | July 18-19, 2019*:**

Register Now!

**Minneapolis-St. Paul, MN | July 25-26, 2019:**

Register Now!

**Golden, CO | July 29-30, 2019:**

Register Now!

**Irvine, CA | August 1-2, 2019:**

Register Now!

*Jumpstart AZ does not have a Day 2 Choose your own adventure option. You will cover similar content over 2 days with Cassy!

Do you want to be notified when a **Jumpstart Your Singapore Math Instruction** is scheduled near you? Fill out the form below:

The book models the Unitary Method as well as 3 variations on an algebraic solution. The author’s end this problem with the following commentary

The Model Method is a means, not and end in itself. It helps students formulate an algebraic equation to solve the problem. While more able students can proceed quickly to the absract algebraic method to solve problems without drawing a model, others may still need to rely on drawing the model as a problem-solving heuristic.

Wise words, indeed! On to the problem:

**$120 is shared among 3 friends, Ava, Ben, and Carlos. If Ava receives $20 less than Ben, and Ben receives 3 times as much money as Carlos, how much does Carlos receive?**

Submit your solutions by the end of the month!

Last month’s Word Problem Wednesday problem was from the chapter on Real-World Problems Math in Focus 2A:

We had several correct answers submitted. Here’s a worked example from Minnesota math teacher and coach Kris Simonsen:

How did you do?*Scridb filter*

**Tom has 275 comic books in his collection. Chris sells 82 comic books to Tom. Then Chris has 148 comic books left. How many more comic books does Tom have than Chris now?**

Submit your solutions by the end of the month!

Last month’s Word Problem Wednesday problem was from Dimensions Math 4A (available spring of 2019).

We had several correct answers submitted. Here’s a worked example from intrepid reader Shirley Davis:

How did you do?*Scridb filter*

At that time, I was already a huge fan of the Singapore Math program. I had taught it in several grade levels and collaborated with two teaching partners to write a 40-hour training program that was submitted to the State of California. I even traveled to Singapore on a week-long learning adventure to see the curriculum at its source. That trip was a life-changing experience.

Despite being nervous (OK, terrified), the school was pleased with my work. Over that summer, I visited another dozen schools and came to the delightful realization: I had discovered my life’s work.

Ten years on, my passion for mathematics education is as strong as ever; I’m so grateful for the opportunity to work with teachers in their classrooms on a regular basis.

By any measure, 2018 was a super successful year for me and Beth Curran, Math Champions’ trainer extraordinaire. Over the past year, we worked with teachers at dozens of schools and presented at several educator conferences. We won international contracts and hosted highly-praised workshops.

This year will always be special for another exciting reason. (Drum roll, please!)

It was an honor to be invited to join the core team writing Dimensions Math in 2016, and difficult to keep quiet about my role as reviewer and lead author of the Teacher’s Guides for K-5. Beth joined the Dimensions team in 2017 and is the co-author of the Kindergarten Teacher’s Guides.

All our hard work with Dimensions Math came to fruition in 2018. Dimensions Math was launched in April at the NCTM Annual National Conference to plenty of fanfare. I was thrilled to see the fruits of our labor; teachers’ positive reactions to DM was icing on the cake. To learn more about Dimensions Math, visit this page.

Thanks to all of our school clients who have put their trust in us. Partnering with teachers and schools is our core service and favorite role. Here’s what 2018 looked like in numbers (and we’re all about numbers, you know):

38 – Schools/districts/nations chose us to help improve their math instruction

24 – Repeat clients

15 – States visited

3 – Countries visited

2 – International Contracts Won through competitive RFP processes; we’re training teachers for Guam’s Department of Education and the Ministry of Education in the Republic of Palau!

When teachers tell us things like this about their time with us, we know we’ve found our calling:

*-Kami Orbin, 2 ^{nd} Grade, Mid-Valley Elementary School, Throop, PA*

*Cassy made training a joy! She had endless energy, sprinkles in lots of humor, and has so much knowledge of the material. She had endless resources and suggestions, offered help when needed. So approachable and patient. I like math now!*

*-Julie Bas, Director of the Lower Grades, Carden Hall, Newport Beach, CA*

Math Champions hosted Jumpstart your Singapore Math Workshops in four cities: Charlottesville, VA; Tulsa, OK; Fort Collins, CO; Saint Paul, MN. Teachers from 18 states attended these two-day workshops on how to best get started using the Singapore Math approach.

We are thrilled by the praise teachers have given this program:

*-Keith Griffin, 1 ^{st} and 2^{nd} grade Math Specialist, City Academy School, St. Louis, MO*

*This is the best training I’ve been to. Every minute was enjoyable and educational. I feel better going into the school year and am excited to teach the Singapore way. It was life-changing and mind-blowing!*

*-Jen Irish, 3 ^{rd} Grade Teacher, Terra Academy, Vernal UT*

We love to share what we’ve learned with our colleagues. We were honored that speaker proposals were selected and we gave presentions at the following conferences:

We want to hear from you! Share your success stories or challenges and let us know how we can help you.

We’re busy planning for 2019. Much more in store next year…

- Jumpstart in July: 5 venues planned for this popular summer introduction program.
- Coaches Academy! Save the date: December 2-6, 2019.

Happy New Year!*Scridb filter*

**There are twice as many nails as screws in a bin. If 510 of the nails and 75 of the screws are used, there will be the same number of nails as screws. How many nails were in the bin to start with?**

Submit your solutions by the end of the month!

Last month’s Word Problem Wednesday problem was from Math in Focus Grade 3.

How did you do?*Scridb filter*

The author, Sara Kronstain, has almost a decade of experience guiding elementary and middle school mathematicians to become critical thinkers and problem solvers. She teaches fifth-grade math and is the Kindergarten-6th Grade Math Department Chair at St. Anne’s-Belfield School in Charlottesville, Virginia.

When I was in school, my math classes were typical of what one would expect a “traditional” math class to look like. I remember sitting in my elementary and middle school classes, watching as my teachers modeled problem after problem. The class would listen and then practice many of the same types of problems in our notebooks. While this type of teaching may achieve the immediate goal of learning a mathematical procedure, it does not guide students to reach an integral part of learning mathematics: problem-solving (Cai & Lester, 2010).

Singapore Math is comprised of a framework with problem-solving being the center of learning mathematics. This framework is built around five key components – metacognition, process, attitudes, skills, and concepts – all being of equal importance in developing mathematical problem solving in students. Whereas traditional math classes may place primary importance on developing skills and concepts in students, the additional three components of metacognition (self-regulation of learning), process (reasoning, making connections, and applying knowledge), and attitudes (perseverance, confidence, interest) are all key to developing critical thinking and problem solving skills in students (Ministry of Education Singapore, 2006).

A typical Singapore Math lesson is taught with a concrete-pictorial-abstract approach. Where many of my lessons as a math student began in the abstract stage (solving equations), the concrete and pictorial stages allow students to create and solidify their own understanding of a topic. The concrete stage refers to using hands-on materials to model a mathematical situation. The pictorial stage consists of diagrams and other visuals, thus building students’ learning in a tangible way (Maths No Problem!, 2018). The concrete and pictorial stages allow students to understand why math works the way it does before learning the procedure of how to solve using an algorithm.

Most Singapore Math lessons begin with an anchor task, allowing students to explore these three stages. The anchor task is a question that allows students the chance to deeply explore a topic and develop multiple methods for solving a problem (Ban Har, 2013). Let us say, for example, a group of fifth graders were posed the problem, “The distance of a race is 3km. Lily ran two-fifths of the distance. How many kilometers did Lily run?” Students would be given the opportunity to freely explore this question by using manipulatives such as fraction bars, fractions circles, or paper (for folding) along with writing materials. Here are a few examples of possible student responses to this question:

Add ⅖ + ⅖ + ⅖**. **Students may use fraction bars, fraction circles, or pictures. Students become familiar with the phrase “3 groups of ⅖”.

Three boxes are each split into fifths. Two of each of the fifths in all three boxes are shaded in. The shaded parts are added together.

A bar with the length of 3 wholes can be split into five parts. Each part has a value of ⅗. Then add ⅗ + ⅗ .

Three boxes are split into 5 equal groups, first by placing one half in each group. Then, split the leftover half into five parts (tenths). Each group will have one half of a whole and one tenth of a whole. Combine two groups by adding two halves to two tenths.

In this example, the repeated addition method reinforces addition with fractions, while the last method has students thinking about and manipulating fractions in a much more complex way. Thinking back to the five key components of Singapore Math, students in this example are refining their process of learning operations with fractions by making connects across operations. It is powerful that these responses are coming from students, as they are building their understanding of math through collaboration with their peers. In sharing methods, listening to other’s methods, and processing others methods, students are also developing their metacognition. This question could also be modified and challenge students to problem solve in an even deeper way. “What if the total distance was ½ km? What if the total distance was 3 ½ km?” Students can then go back to the concrete, pictorial, and abstract stages and continue to build on their problem-solving abilities.

At the end of the day the primary purpose of this math lesson, or any math lesson for that matter, is not simply to learn how to multiply fractions by a whole number. The most important takeaways are the critical thinking, questioning, collaboration, and problem-solving that happens among students. Teachers are not preparing students to go out into a world where they will simply be asked to recite an algorithm. While a goal is for each child to develop a deep love of math, the biggest hope is that students learn to ask questions, logically think through problems, and make sense of the world around them.

Ban Har, Yeap. (2013, June 13). Singapore Math at the Blake School, Hopkins, MN. Retrieved from __http://banhar.blogspot.com/search?q=anchor+task__

Cai, Jinfa, & Lester, Frank. (2010, April 8). Problem Solving. *National Council of Teachers of Mathematics.* Retrieved from __https://www.nctm.org/Research-and-Advocacy/Research-Brief-and-Clips/Problem-Solving/#brief__

Kaur, Berinderjeet. (2018, March 29). Building the Maths house: Singapore’s curriculum framework. *Oxford Education Blog*. Retrieved from __https://educationblog.oup.com/secondary/maths/building-the-maths-house-singapores-curriculum-framework__

Ministry of Education Singapore. (2006). *Mathematics Syllabus Primary*. Retrieved from __https://www.moe.gov.sg/docs/default-source/document/education/syllabuses/sciences/files/2007-mathematics-%28primary%29-syllabus.pdf__

Maths No Problem! (2018). *Concrete Pictorial Abstract.* Retrieved from __https://mathsnoproblem.com/en/the-maths/teaching-methods/concrete-pictorial-abstract/__*Scridb filter*

Imagine starting your day in first grade with a question about favorite holiday treats. Students can answer the question and instantly you have meaningful data that can be organized into a tally chart, picture graph, or bar graph for students to analyze. Or, students can build a bar graph with post-it notes as they make their choices. Then, spend some time analyzing the results.

Ask 5th graders if they traveled over Thanksgiving break. If so, how far? Now use this data to find mean, median, and mode, or to create a histogram for students to analyze. Or, chart the temperatures over the course of a couple of weeks and use this data to create a line graph.

Third and fourth graders could tally the number of candles in their homes for the holidays and use this data to create a line plot. Fourth graders can use their line plots to explore finding the median.

Planning a holiday party? Survey the students on what should be served and what activities should be included. Students can present the findings in a graph and use the results to determine how much and what needs to be donated or purchased to make the party a success.

The holidays are a great time to share family traditions. Why not use that information to meet some graphing and data analysis standards?

For other ideas to keep students engaged in learning read Mental Math Breaks from December 2017.*Scridb filter*