Building core math skills in elementary and middle school
By the end of middle school, students have been exposed to basically every type of useful math skill there is. Many higher level math skills are not useful in the average person’s everyday life. That’s not a typo…I said it…and I’m not sorry…😆. Trigonometry, calculus and the quadratic formula have their place in the world, but most of us can get by as adults without remembering how to find a derivative, or do a trig proof!
There is an incredible amount of value however, in studying theses higher level math skills. It challenges our way of thinking and seeing the world, it fosters perseverance in problem solving and just generally grows our brain power by building new neural pathways – thumbs up for neuroplasticity!
No matter where you’re from or what curriculum you are following, the math skills students are taught before entering high school are the real meat and potatoes of math that will help you feel prepared for the adult world of taxes, mortgages and bills. They are also the skills that will be built upon and applied in more complex ways in high school. Here is a list of what I believe to be the 7 most important math skills that students should master before entering high school:
- Whole number operations
- Decimal number operations
- Fraction operations
- Integer operations
- Order of Operations
- Percent of a Number
- Interchanging decimals, percents and fractions
Math is a progression
You must grow good roots before you can bloom.
First, we learn about numbers: what they are, how to represent and build them, etc. Concepts like subitizing, counting, hierarchical inclusion and number conservation are at the very foundation of number sense. Graham Fletcher is a wealth of information on this topic with his progression videos.
Gradually, as the numbers we work with get bigger, the concept of place value comes into play. We learn the relationship between the place value positions of our base-ten number system. We skip count, compare and order numbers and work with number lines.
As we become more comfortable with our number system, we start to “do stuff” with the numbers: hello operations! Developing these math skills takes years. We need tons of practice, hands-on experiences and the space to play and think flexibly about manipulating numbers. Developing strong mental math skills with whole numbers is a must before moving on to decimals and fractions.
Eventually, the concept of “partial numbers” in the form of decimals and fractions comes into play. We learn to represent them and spot them in the “real world”. Adding, subtracting, multiplying and dividing decimals and fractions should not be rushed. In my work as a tutor with high school students, it is these skills that seem to be lacking the most.
Mixed in there, are the very important topics of integers and percent. Finding real world examples of integers and percent is pretty easy. Temperature, altitude and money are my go-tos for integer examples, and percents are easily seen in discounts, interest and taxes.
All of these very important skills are the foundation of what’s to come in high school. If any one of these areas are lacking, it becomes very difficult to progress as there will be gaps in the learning that serve as road blocks along the path.
What is the best way to teach these math skills?
This may be an impossible question to answer, but I’ll try my best!
My teaching experience, as well as my time studying many inspirational math teachers has lead me to believe very strongly that the key lies in facilitating student-centered learning and developing conceptual understanding first. Read more on these topics here.
In a nutshell, I have found that the following framework for new topics works best for my students:
- Exploration activity – 3 Act Tasks are my favourite for this! Check out Dan Myer, Graham Fletcher and Kyle Pearce & Jon Orr for these. You can also get your hands on my Student-Centered Mental Math Starter Kit for free by filling out the form in the side bar to the right of this post âž¼
- Sharing and consolidating strategies – This is where teaching math becomes an art. As teachers, we must take our students’ ideas and organize them into efficient strategies and procedures that can be used for future math problems. I also firmly believe that we should never push one particular strategy on our students. There are almost always multiple ways to arrive at at correct answer and allowing students to chose their path is important.
- Practice – Here is where I believe self-pacing is key. Not all students will grasp new topics at the same speed. Some will need much more exposure and varying levels of support. I’ve been following The Modern Classrooms Project for a while now and I love their framework for self-paced, mastery-based learning. If you’ve ever struggled with the desire to tailor your lessons to the individual needs of your students but found yourself completely overwhelmed with how to make that happen – visit their site and listen to their podcast!
- Also in the “Practice” stage, I need to emphasize how important I think games are for all grade levels. Keep it simple and choose games that can be played individually, and in groups. Here is a set of 36 versatile math games that cover the majority of the essential math skills mentioned in this post (bonus: they’re in both printable and digital formats).
Assessing math skills
Daily formative assessments through verbal questioning, exit tickets or self-checking activities will provide you useful information on when and how to proceed.
There is an increasing amount of creative self-checking activities available out there. Boom learning is a phenomenal platform for this. You can also find some incredible self-checking resources in the form of pixel art, mazes, digital games and so much more on Teachers pay Teachers. Here are some of my favourite teacher sellers for this:
I hope you’ve found this blog post helpful! If you’d like to connect with me, I’d love to hear from you! Feel free to comment below, or find me on Instagram: @mathcoachcanada.
