Number sense refers to an intuitive feeling for numbers and their various uses and interpretations, an appreciation for various levels of accuracy when calculating, the ability to quickly detect arithmetical errors, and a common-sense approach to using numbers.

Number sense is characterized by a desire to make sense of numerical situations. Number sense is a way of thinking that must permeate all aspects of mathematics teaching and learning if mathematics is to make sense. When highlighting number sense, students focus on their solution strategies rather than on a “right answer”, on thinking rather than on the mechanical application of rules, and on student-generated solutions rather than on teacher-supplied answers. Learners will acquire a good sense of number if they are engaged in purposeful activities requiring them to think about numbers and number relationships and to make connections to quantitative information seen in everyday life. Learners should be encouraged to develop their own techniques for finding the answer, to consider many ways to work out each problem, to consider the form their answers might take, and to share their reasoning. Where number sense is a priority, learners are active participants who share their hypotheses, reasoning and conclusions and who are given opportunities to create their own procedures.

Consider the Following Examples:

When asked to find the product of 48 and 0.5 mentally, one person converted 0.5 to 1/2 , and then took 1/2 of 48 to get an answer of 24. In contrast, another person mentally “wrote” 48 above 0.5 in his mind and multiplied 5 and 8, remembering the 0 and “carrying” the 4. Then he calculated 5 times 4, getting 20, and added the 4 he carried, getting 24. Counting the number of decimal places in his problem, he knew to insert the decimal point in his answer between the 4 and 0, thus arriving at the answer, 24.0 or 24. Which person displayed number sense?

In computing the product of 4.5 and 1.2, one learner carefully lined up the decimals and then multiplied, bringing the decimal point straight down and reporting a product of 54.0. Reflection on the answer should have caused her to realize the product was too big. Multiplying 4.5 by a number slightly more than 1 produces an answer a little more than 4.5. Instead, the learner applied an incorrect procedure (line up the decimals in the factors and bring the decimal point straight down) and did not reflect on whether the resulting answer was reasonable.