Higher-Order-Thinking for All Students

Set the bar high and watch as your students rise to the challenge

Let’s face it: real-world problems don’t come in neat rows…

However, the mind-growing challenges of math enrichment (or non-routine problem solving) are often only rationed out to students identified as “gifted.” Is that really good teaching practice?

Research has shown that an important condition for learning is the expectation that students will do so. Allowing students to press through challenges, and believing that they can and will succeed, leads to excitement and ownership of learning.

According to Jo Boaler of Stanford, teachers must establish the correct mindset for students to succeed in math. This “growth mindset” starts with the belief that I am a math person. And it’s not just for gifted students (check out Jo’s recent TEDxStanford talk here).

Education advisor Ken Robinson has tackled the question, “Do schools kill creativity?” And over 43 million people have watched his explanation of why looking at things in new ways is so important (see Ken’s funny and informative presentation here).

The word is out: problem-solving, number flexibility, and higher-order-thinking are skills that benefit all students. (Not to mention, they make math fun!)

Of course, over-burdened teachers might be reluctant to embrace another “opportunity” (a.k.a, item on their to-do list). This is especially true in situations in which programs have been cut and teachers are short on resources.

We hear you, teachers, and we’ve got your back!


Meet Plus!

Think of Plus as an outside-the-box math supplement to your curriculum.

It’s free to use.


Each month, we add a new “Challenge of the Month” to stretch students’ thinking and problem-solving skills. The challenge consists of a set of grade-appropriate problems. As students progress through each problem successfully, the difficulty increases.

Whenever your students have access to an Internet-enabled device, they can pick up right where they left off with the current challenge. Students work at their own pace, earning medals with each new problem solved (and also having fun, of course!).

At the end of each month, students receive a certificate as a reward for their hard work (see the example at the end of this post).


The first challenge is already here!

Our first monthly challenge taps students’ spatial thinking by posing a pattern-based problem.

Below is a peek at what this challenge looks like, but if you’d rather try it for yourself, we’ve posted a couple of examples on the Plus main page — if you like what you see, sign up for more (again, Plus Happy Numbers is 100% free).

The challenge begins fairly simply by showing students a model and prompting them to copy the pattern. This first task, with one object and a background identical to the model, is easily accessible to all students and helps them understand the task.


The complexity increases when the background (in this case, a scarf) is manipulated and the number of objects in the pattern is increased. How will students tackle this challenge? Will they rely on their mental map? Or will they come up with a more concrete, coordinate-based system for placing the objects, such as “top row, third box”?





For those students who’ve mastered the scarf challenge on a simple grid background, we further increase the complexity by introducing a colored rug background. Notice that the colored pattern is random. Also, there’s less differentiation between the objects to be placed.

Plus.HappyNumbers.com ensures that English Language Learners can enjoy the challenges of higher-order-thinking, too! A Spanish version is available, and both languages have audio support for non-readers to remove the obstacle of language from math learning.



How to get started with Plus?

If you already have a Happy Numbers account:

– From your Happy Numbers account, switch to Plus Happy Numbers and follow the instructions. Plus challenges will be added directly to your students’ accounts.

If you don’t have a Happy Numbers account:

– That’s no problem, just sign up at Plus.HappyNumbers.com and follow the directions to set up your class. It takes less than 5 minutes to set up and is super easy for students to get started.


Enjoy and share your thoughts with me at em@happynumbers.com!

Educationally yours,


P.S.: Check out the award certificate students receive for working on the March challenge: