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ber is an estimate, it appears this student was able to correctly locate the proximity of each number in the relationship to the benchmark fractions. It is interesting to note that the student has no calcula tions associated with each rational number, but was able to place the numbers in relation to the other fractions. This next student, see figure 6, identified integers between negative one and positive two, then subdi vided between each integer into tenths. The student converted each number into its decimal form. This shows the student is comfortable with numbers written as a decimal, which is common among middle school students. By subdividing the number line into tenths, this student was able to most accu rately show the placement for each of the rational numbers.

centages without a calculator. The eighth graders had to order the rational numbers that included fractions, decimal, percentages, scientific notation, and negative numbers, also without a calculator.

Figure 6: Using Tenths as a Guide to Placing Ra tional Numbers

This article covers the use of number lines to de velop students number sense for rational and nega tive numbers. We focused on ordering rational numbers and how the topic progresses across sev eral grades. Mathematics specialists can use the number line to help teachers assess students ’ ra tional number development. The number line sets the stage for positive and negative integers, and rational numbers.

Figure 5: Using Benchmark Fractions to Place Ra tional Numbers

The last student, see figure 7, used decimals to order the set of rational numbers. The previous student used tenths, while the next used twentieths. The students used their decimal number knowledge to order the numbers from least to greatest. The second student was unsuccessful in placing the numbers correctly. The samples were taken from a variety of students in fifth, sixth, seventh and eighth grade. Students were asked to order a set of rational numbers from least to greatest using a number line and any other strategy they knew appropriate for their grade lev el. Fifth grade students were given no calculator and had to order the number sets that included fractions and decimals. Sixth and seventh grade students had to order fractions, decimals and per Conclusion

Figure 7: Using Twentieths as a Guide to Placing Rational Numbers

Utilizing number lines throughout multiple grade levels, help students build confidence in their abil ity to understand all numbers. Number lines help for whole number development that translates easi ly to other types of numbers. From benchmarking numbers in the primary grades to comparing and order rational numbers in upper elementary and percentages in middle school grades, the number line is a representation that help develop students ’ number sense.

References

Diezmann, C. & Lowrie, T. (2006). Primary Stu

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