I am thinking of a two digit number between 30 and 40 that is both an even number and a multiple of 8. Can you guess the number? As elementary teachers, we have all played these fun games with students and are pleased when they work out the correct answer. In this case, 32.
Now, what is your favorite or lucky number?
Many people have a favorite or lucky number for a variety of personal reasons. I know I do. It is 43. When I was 43, I was diagnosed with skin cancer. The physician noticed the spot during a routine medical appointment to treat an allergy infection. Luckily, the melanoma was caught early before it could metastasize - a key to successfully treating and survival of this type of skin cancer. Consequently, on that important day in my life, forty-three became both my lucky and favorite number.
But, in regard to numeracy thinking, why is the number 43 important besides the fact that I have a personal connection to that specific number?
Let’s examine the number 43 with regard to its importance in a general numeracy sense. 43 is a number that may represent a specific quantity of objects or the number 43 appears in a cardinal mathematical counting sense. But, those two reasons are far too easy and common place. Let’s dig a bit more to see if we can come up with a deeper understanding.
From a numeracy standpoint, the number 43, like all whole numbers, is permanently fixed at a specific point on a number line. It is one less than 44 and one more than 42, and we can say something relative about the number 43 in comparison to not just adjacent numbers, but all whole numbers. It is both a prime and odd number, and it is not divisible by 2. We also know the number 43 is between 40 and 50, and 43 is closer to 40 than it is to 50. Suddenly, we know much more about my favorite number, 43, but in a much more mathematical sense. All of these numeracy observations are relatively easy for middle school students and beyond, but why do a significant number of elementary students struggle when confronted with my favorite and lucky number 43 as well as other two and three digit numbers?
In Title 1 elementary schools specifically, the number 43 as well as whole numbers of any magnitude may be a problem for many kids. Why? Simply put, they did not master a number line mental ‘fixity’ of whole numbers during their primary grades, and whole number misunderstanding has pointed consequences. For example, when students lack mental fixity of whole numbers, they are not adept to ‘round’ numbers like 43 to the nearest ten quickly - compounding estimation issues of several numbers in any of the four algorithmic operations. Furthermore, positive integers seemingly 'float' to them and are not fixed in space - as developmentally prepared students should be by the third and fourth grades.
When students struggle with general number sense, teachers often provide 100, 120 and 200 number charts to assist kids in visualizing the relative location of numbers. This pedagogical tool is a great start; however, there is an alternative that readies intermediate elementary students to mentally fix whole numbers in space without the need for a chart. This intervention is easy to implement, and it is a simple series of number lines activities discretely segmented by skip counting 1’s, 2’s, 10’s, 5’s, 3’s and 4’s, in that sequencing order. The intervention number line work should include two digit and three digit numbers above 110 - another specific number point where a significant number of Title 1 students commonly struggle. Fortunately, in about ten class days of quick mini lessons with associated homework, intermediate grade level students master this numeracy skill, and then they are mathematically ready to examine the multiple physical meanings of whole numbers. Fundamental numeracy issues described above usually do not vanish on their own. It requires specific intervention work that directly addresses the problem, or students will not connect and secure dependent mathematical conceptual understanding during core daily lessons.
Visit the Formative Loop ‘Resources Library’ to download the resource number line series at formativeloop.com.