Math Wheels for Note-taking?

Extensions for Gifted Students in Middle School Math


What do extensions for gifted students in middle school math look like in your school and in your classes? Do you have a gifted specialist that helps out with extensions; or is it up to you to provide extensions for your gifted students?

We discussed these ideas (and more!) during our Extensions for Gifted Students session in July (if you’d like to listen or see the presentation instead of read this post, head to the Free Resource Center and get started with that session…the session is about 30 minutes.

That session recording has actually been cut into two blog posts…this one, which is more research-related and the second one, which is about specific things you can do to structure your classroom for ‘built-in’ extensions.

Let’s get to it!

First off, let’s look at what we mean by extensions….so we have a kind of ‘mutual’ definition that we’re working with as we go through this post

To me, extensions for gifted students are ways to ‘stretch’ the learning…go deeper
or wider with the concepts…to extend the learning.

  • Extensions work within the current curriculum rather than moving into a new curriculum. 
  • Extensions can also include non-curricular tasks that are ‘thinking’ tasks that aren’t tied to a particular concept in the curriculum.

Benefits of Extension Activities

WHY should we use extension activities? What are some of the benefits?

We want to meet our students’ needs, and they can certainly be wide and varied needs!

Because they are so varied, it can really be a challenge to meet ALL the needs. And it can be challenging to plan extension activities.

However, providing extension activities provides several benefits for our gifted students. According to the blog post Enrichment vs Extension in the Regular Classroom, extension activities:

  • Allow students to apply new knowledge to the next level…with more challenging problems

  • Allow gifted students to avoid work that is repetitive. …we don’t want to just assign MORE of the same type of problem just because students work more quickly

  • Allow students to have their own educational experiences to some extent

Creating an 'Extensions-Friendly' Classroom Environment

Since it can be difficult to plan extension activities for all the units, let’s think about how we can make it a little easier to provide extension activities for gifted students, by looking at what an ideal classroom environment can look like (and ultimately benefit ALL students). 

The article, Extension, Enrichment and/or Acceleration, describes the idea of having a ‘productive environment,’ which in my opinion can:

  • have some types of ‘built-in’ extension opportunities
  • and also help us reach students who have difficulties

According to the article, a few characteristics of a productive classroom environment are that the environment:

  • Is learner-centered rather than teacher- or content-centered
  • Emphasizes learner independence
  • Opens opportunities for innovation and exploration…like the surface area exploration we discussed in one of our other math sessions
  • Focuses on acceptance rather than judgement
    • like acknowledging answers that may be incorrect and then asking WHY students think it’s correct, how did they get to that answer, etc
  • Allows for varied groupings
  • Encourages flexibility rather than too rigid a structure
  • Focuses on concepts rather than procedures
  • Uses rich tasks that enable higher order thinking skills (HOTS) rather than more of the same (MOTS). In the live session, we talked about a great example from the book Mathematical Mindsets as well as a great decimal activity that used to be on the site, youcubed.
  • A productive environment also develops and values productive communication

Discussions in a Productive Classroom

Thinking about discussion and communication, in the book, Building Thinking Classrooms, the author talks about using shifts in the ‘mode of engagement.’

  • He explains that when students are doing a task, their mode is ‘doing’.
  • From that mode, they can be shifted to ‘justifying,’ which he says involves students convincing themselves that
    they’re correct….so they’re communicating more with themselves and the group they’ve been working with
  • Then the mode can be shifted to ‘explaining, ’ which is harder than justifying because it requires students to articulate thought for an audience outside of the group 
  • From explaining, he talks about shifting to ‘teaching’ another group, which is different than just explaining and therefore an increase in challenge
  • And finally, the shift can be made to create a new task for someone else to complete, which is the most difficult mode of engagement

Now, he doesn’t talk about about these modes in the context of gifted students, but I think using activities that allow for this kind of communication and shifts to the different modes are ways we can provide extensions for students as part of our regular classroom instruction and environment.

Wrapping up Extensions for Gifted Learners, Part 1

In the next post, we’ll look at several types of activities that fit into the idea of a productive classroom and into the modes shared above.

To wrap up this post, I have a few DOs and Don’ts for extensions for gifted students, from the article Six Strategies for Challenging Gifted Learners:

A few Dos

  • Pre-assess your students. Find out their strength as well as those areas you may need to address before students move on
  • Plan for differentiation. Consider pre-assessments and extension activities.
  • Encourage high-ability students to take on challenges. Because they’re often used to getting good grades, some gifted students may be hesitant to take risks and be incorrect

A few of the Don’ts the article suggests are, Don’t…

  • Confuse high achievers with high-ability students. High achievers put in the time and effort to succeed in school, but high-ability students might not. Their ability might not translate into academic achievement
  • Assume that all gifted students are the same and that one strategy works for all
  • Assume that by making gifted students tutors, you’re providing a learning extension
    • we did mention the idea of teaching as a mode of engagement in this post and that is a bit different than tutoring or helping another student
  • Confuse extension activities with additional work. Gifted students need deeper and more complex assignments.

Join me in the next Extensions for Gifted Students post for specific activity ideas for the classroom, or, if you don’t want to wait, head to the session in the Free Math Resource Center and listen in:-)


Welcome to Cognitive Cardio Math! I’m Ellie, a wife, mom, grandma, and dog ‘mom,’ and I’ve spent just about my whole life in school! With nearly 30 years in education, I’ve taught:

  • All subject areas in 4th and 5th grades
  • Math, ELA, and science in 6th grade (middle school)

I’ve been creating resources for teachers since 2012 and have worked in the elearning industry for about five years as well!

If you’re looking for ideas and resources to help you teach math (and a little ELA), I can help you out!



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