Maths challenges: Embracing ‘Higher Order Thinking’ for all students

Happy Numbers

While you teach small groups, Happy Numbers serves as an independent math center, providing individualized instruction for the rest ...

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Mathematics maestros Happy Numbers have launched Plus, an exciting outside-the-box supplement for the Maths curriculum. Every month, a free challenge is launched - each consisting of a set of age-appropriate problems. As students progress through each problem successfully, the difficulty increases. The challenges are designed to stretch students’ thinking and problem-solving skills.

At its core, the Palo Alto-based Happy Numbers is based on the best pedagogical practices for approaching each skill and concept: visual modeling, using concrete manipulatives and other time-tested approaches to Maths instruction. These new challenges are a great way to get learners enthused about Maths - as co-creator Evgeny Milyutin puts it

“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.

“Of course, over-burdened teachers might be reluctant to embrace another “opportunity” (ie item on their to-do list). This is especially true in situations in which programmes have been cut and teachers are short on resources. We hear you, teachers, and we’ve got your back!”

Whenever students have access to an Internet-enabled device, they can pick up right where they left off with the current challenge. They 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.

The first challenge is already here!

Happy Numbers’ first monthly challenge taps students’ spatial thinking by posing a pattern-based problem. The team have posted a couple of examples on the Plus main page — if you like what you see, you’re encouraged to sign up for more (again, Plus Happy Numbers is 100% free).

Here, Happy Numbers introduce one such challenge:

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 coloured rug background. Notice that the coloured pattern is random. Also, there’s less differentiation between the objects to be placed.

Visit or email Evgeny Milyutin on for more information.

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