Number sense, specifically middle school number sense, is an intriguing topic in the world of education. As a math teacher, I was amazed at how some students would compute numbers in their head while others liked to work out problems by hand. Let’s break down what number sense is, how you can teach it, and discuss 4 strategies to use with your students to develop this life-long skill.
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What is number sense?
Is number sense a skill that is taught or a skill that is innate to strong math students? Let’s think abstractly – are you a born leader? Or can you learn to be a leader?
Number sense is the ability to be flexible and fluid with numbers.
- As a young elementary math student, understanding that since 5 is half of 10, 50 must be half of 100.
- Being able to add 58 + 14 by breaking the 14 into 12 and 2, so that you are adding 60 + 12 quickly in your head.
- It is understanding that if you have half of an object, and you take half of that, you naturally have a fourth of the original object.
Number sense is not rote memorization or the ability to navigate an algorithm quickly.
Should I teach number sense?
Simply put – YES!
Number sense is another tool to add to our students’ problem-solving toolkit. At the end of the day, we are teaching students to think. We can build this number sense slowly over time by being intentional in our questioning and the way we model our thinking and strategies.
4 strategies for building MIDDLE SCHOOL number sense
Model different methods
It is easy to model the method that you are most familiar with. I was hesitant to teach decimal multiplication using partial products or an area model; I was more familiar with the standard algorithm. Instead, I took the opportunity to teach multiple methods, and allowed students to work with the method that felt the most comfortable for them. It was interesting to see how the same student would use different methods depending on different factors. By teaching different methods, you are allowing middle school students to determine which method works best for the problem at hand thus strengthening their math reasoning.
When I taught Algebra 1, one of my favorite units was on polynomials. As a student, I learned the acronym FOIL stood for…first, outside, inside, last…but I had no clue as a student what I was doing. Then as a teacher, I learned to double distribute and how to use the box method (which is just an area model).
Marilyn Burns says in her book, “When children think that there is one right way to compute, they focus on learning and applying it, rather than thinking about what makes sense for the numbers at hand.”
Discuss computing strategies
This method can fit inside any lesson. If you are covering division of fractions, you can ask students how many halves are in six wholes and to explain their thinking. After a student responds with their process for solving, an additional questioning strategy would be to not acknowledge whether the student is correct or not, and ask for ANOTHER student who solved it differently to explain their thinking. Middle school number sense can be strengthened by not acknowledging what is correct right away, but by giving students ample time to share many different ways to solve. When students know that you are more interested in HOW you arrived at the answer than whether the answer is right, they will think more creatively about ways to solve.
Utilize friendly numbers and estimation
Teaching students to utilize friendly numbers to estimate solutions is another number sense strategy. In the real world, people often estimate when they are working with numbers. (Maybe not engineers or accountants). Sixth and 7th grade students are asked to apply percents to problem situations and frequently those examples include calculations involving money. Teaching and showing students how to utilize friendly numbers (½, 1, 2, 5, 10, 25, 50, 100) to get you close to the actual solution is one way to incorporate number sense.
Parts and Wholes
There are so many part and whole relationships in middle school math. Think: fractions and decimals, ratio and proportional reasoning, and percentages. When we build that understanding of a part to whole relationship between numbers or representations, they are able to apply it to other mathematical concepts. Consider questions like “if half a cake feeds 4 people, how many people will a whole cake feed?”
When can I incorporate number sense?
Low lift opportunities in your normal instruction, incorporate:
- wait time (for your feedback response)
- asking for multiple strategies
- shifting your line of questioning to incorporate estimation
For higher lift opportunities, try:
- Daily warm up – pose questions that would solicit different strategies for solving
- A formal number talk – this structure focuses on using mental math to develop an understanding of numbers and operations. Present a problem to students, give them time to solve mentally, and collect responses focusing on HOW they arrived at their answer. In middle school, you might ask for the sum of 15.6 and 8.6. See how many different methods students used mentally to arrive at their answer.