Tag Archives: Singapore Math

Doing Math…





IMG_2602What is a Noetic Challenge? According to Merriam-Webster’s website, the combined definition of these two words would translate to “a difficult task relating to intellect.” This may be true, but to a group of 13 fifth-grade math students, the term Noetic Challenge means logic puzzles, math games, and a collaborative effort to determine how many pencils make up a “gross!”

Meeting weekly with our math enrichment specialist, Mrs. Feldman, these top math students finished their successful elementary school years by competing in a national math competition. The Noetic Math program is designed to challenge students’ mathematical thinking by strengthening problem-solving skills. All Lower School math classes incorporate a variety of challenging word problems to Posnack’s already advanced math curriculum in order to prepare students for an accelerated rate of learning in mathematics. Since their introduction to Singapore Math last year, students in grades K-5 are focusing on the importance of relating math to real-world situations and identifying problem-solving strategies to tackle higher-order thinking word problems. Whether it’s preparing a shopping list to stay within a given budget, or calculating the square footage of classrooms in our new Fischer High School building, students are learning to recognize that math touches everything in their lives. Posnack students have become quite adept at using bar models and algebraic thinking to solve authentic problems with a variety of strategies and as a result, have learned that success in mathematics IS something to brag about.

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When presented with the idea of a math contest, Mrs. Feldman’s fifth-grade groups were excited at the idea of showcasing what they’ve learned. Over 24,000 students from more than 600 schools in 47 states participated in this contest, and Posnack students received commendations in the categories of participation, national honorable mention, and team winner. The celebration began with the awarding of certificates by Mrs. Feldman, followed by ice cream and the presentation of mini calculators to the fifth-grade math team. Certificates, ice cream, prizes? When I asked one student what the best part of the afternoon was, he replied, “We get to do even harder math now!” This student’s enthusiasm reminded me of the accomplished mathematician Paul Halmos who was quoted as saying, “The only way to learn mathematics is to do mathematics.”  I can honestly say that it’s been a thrill and an honor to watch these talented students “DO” mathematics.

Click here for more information on the Noetic Math Challenge and to see a complete list of national winners.


So….When IS Cheryl’s Birthday???


I absolutely LOVE seeing a Singapore Math problem in the news! This challenging word problem taken from a recent Singapore and Asian School Math Olympiad (SASMO) contest has stumped people worldwide, and continues to go “viral” across the Internet. In case you haven’t yet seen it, the problem looks like this:

cheryl birthday

Now that you’ve probably read the problem several times over, how is it possible that a math problem contains no numbers other than the dates? The answer to that question is actually much more simple than the solution itself. Math doesn’t have to be limited to problems involving natural numbers or integers.

  • Math is about logic and reasoning.
  • Math is about creating order and patterns.
  • Math is about making sense of something that initially appears senseless.

Tackling problems like this can help children of all ages build number sense – a skill critical to mathematical achievement and success. But even more important, problems like this help to create the thought process required for rationalizing and finding solutions for problems that span subject areas and curricula. The satisfaction gained from attempting and ultimately solving these types of puzzles creates an attitude where “I don’t get it” is replaced with “let’s try another one!

So when IS Cheryl’s birthday? If you haven’t figured it out yet, watch the video below, courtesy of the BBC. And if you’re still not sure of how they came up with the answer, ask your kids. Chances are great that their exposure to Singapore Math strategies can make solving this problem easier than blowing out the candles on Cheryl’s birthday cake.

Summer Brain Drain….


math comic

Summer Brain Drain….we’ve all heard that phrase, but is it fact or fiction? Research has shown that at the start of the new school year, students frequently assess at a level at least one month behind where they left off in the Spring. So what happens to our brains during the sweltering summer months? There is little research to suggest that our inability to continue the learning process is a result of the deterioration of neurocognitive muscle. What we do know is that certain subject areas, like math and science, require more frequent drilling and repetitive instruction. After all, it’s easy for your kids to grab a favorite book to read on a rainy day, or in the backseat on the way to the beach. Math, on the other hand, may be a tougher sell.

Posnack students this year have made tremendous strides in math. With the introduction of Singapore strategies, including bar modeling, drawing, and hands-on manipulatives, students are able to relate their classroom learning to real-life situations. So, as parents, what can you do to keep them mathematically motivated over the coming summer months? Card games, estimation activities, and flash cards can all be used to make math fun and engaging. Trips to the grocery store can turn into math challenges with children using mental math skills to estimate the total amount of money spent. Involve your child in the planning of family vacations so they can see how math is all around us – miles driven, ticket prices, elapsed time, budgeting meal allowances, and weather forecasts – these are all examples of how math is used every day.

I also highly recommend a new series of summer workbooks tied directly into the math program used this year. Each “Summer Sampler” provides an overview of skills previously learned, and offers access to a corresponding website for video demonstrations as well. I have included a link for each grade-level workbook in the side section of this blog. Clicking on the picture will take you directly to the site for easy purchasing.

Please feel free to comment or email with any questions you may have. I know you share in the pride I have for the enthusiasm and success your children have shown this year with the new math curriculum. The phrase “I Love Math” has become, for many, the new mantra when I pass by in the hallways. Let’s keep up the excitement and replace “Summer Brain Drain” with “Summer Brain GAIN!”




A look through the window….


They say that the eyes are the windows to the soul. The same idea holds true in school where bulletin boards are the figurative windows into the classroom. Walk down the hallway of an elementary school building and it’s easy to see not just what’s taking place in the classrooms, but the culture of the school as well. Is the content rich with student created materials at all levels? Is there evidence of higher order thinking? Is technology being used in an innovative way? Do you see cross-curricular integration?narrative essays

If you walked down the hallways of the Posnack Lower School, you would be able to answer a resounding YES to all of the above questions. The content of these bulletin boards is aligned with the framework for what is referred to as 21st Century Skills. Partnership for 21st Century Skills (P21), a consortium of educators, businesses, and community leaders, believes that education must be transformed in such a way as to prepare students for the challenges they will face in the workplace ahead. This transformation is accomplished through the promotion and development of skills essential for success in the 21st century. trees 2nd grade

What are these skills and what are schools doing to move this idea from theory to reality? These crucial skills include the ability to reason and make decisions through the use of critical thinking and problem solving strategies, the management and evaluation of information using media and technology, the effective communication of ideas and concepts, and the application of learned knowledge and skills to real-world situations.flat fanny

So, how do our bulletin boards reflect that Posnack students are on their way to developing these skills? Look closely and you’ll see something other than just pretty pictures. The Kindergarten penguin has a QR code which, when scanned, directs you to a site containing facts about penguins. First Grade is incorporating more than geography into their study of states – they are including math by counting and graphing state quarters, and encouraging the use of technology by videotaping class presentations. The Second Grade board features narrative writing about the type of trees students would like to create; a timely assignment coinciding with the upcoming celebration of Tu B’Shevat. Third and Fourth Grade classes are building communication and writing skills as they master the writing process through the development of persuasive and expository essays. Fifth Grade boards showcase Singapore Math bar models to explain the problem solving strategies of complex word problems.

All Posnack teachers are building a pathway to the 21st century. Every day they encourage students to discover new methods and strategies designed to take them on this journey towards excellence. This is an exciting time to be a part of the Posnack experience. The opportunities are endless and the rewards ahead will be plentiful. But the bulletin boards only capture a fraction of the tremendous learning taking place. Peek into the windows of Posnack and see for yourself.


My half is bigger than your half!!


How many times have you divided a sandwich, cookie, or cupcake perfect-cookie-in-halfbetween two children only to hear them utter those dreaded words? If one cookie is divided into “halves,” can one half really be bigger than the other?

Welcome to what I like to call Misconceptions About Fractions 101. Even before your child enters school, they have already been exposed to many scenarios involving fractions, however, their understanding of fractions is usually incomplete. To complicate matters even further, students have already learned that multiplying whole numbers results in a larger whole number, but now we teach them that multiplying two fractions results in a smaller fraction! Is it any wonder that around the time when computations involving fractions occur in third grade, many children begin experiencing difficulty in math?

So aside from measuring ingredients for recipes, slicing pizza, and cutting sandwiches into equal parts, why do we really need to learn about fractions?

Recent research suggests that understanding the concept of fractions is the basis for all higher-level mathematics; from algebra to physics to chemistry. Understanding fractions is not about memorizing complex rules or teaching students to “multiply by the reciprocal” when dividing. Understanding fractions is about learning how numbers relate to one another and being able to identify fractional parts on a number line.

Since a basic tenet of classroom instruction is to build upon a child’s prior knowledge, often times a teacher may first have to clarify misconceptions and ideas a student has about fractions before proceeding with formal instruction. Students need to have a conceptual understanding of what numerators and denominators mean beyond the traditional definition of the numerator being the number on the “top” and the denominator the number on the “bottom.” Teachers at Posnack use fraction bars that correspond to Singapore Math bar models to help students understand equal parts of a whole number, and to identify the relationship between the numerator and denominator. By using fraction bars or bar models as opposed to the traditional “pizza” model, students are better able to visualize the problem and make the connection between the concrete and the abstract.

Singapore Bar Models are used for more than just solving fraction problems. Beginning in second grade, students are learning how to solve a variety of word problems using the model drawing strategy. Parent workshops will be held during the month of October to share with you the ways in which you can help your child use model drawing strategies to solve problems by developing algebraic thinking skills.

In the meantime, can you solve the following fraction problems? Send me your answer as a “comment” along with how YOU solved this problem. I look forward to seeing many of you at the upcoming workshops – the dates and times will be announced later this week.

EX #1 (Grades 3-5): Terra’s monthly allowance is $48. She puts ½ of her allowance into savings and gives ¾ of the remaining money to a local charity. How much money does Terra have left for herself each month?

EX #2 (Grades 6-8): When Erin and Amy went shopping, they started with a total of $91. Amy spent $25 and Erin spent 3/5 of her money. At that point, Amy realized her remaining money was 3 times Erin’s remaining money. How much money did Amy have when she started shopping?