The Number Line in the Common Core

Objectives

By the end of this unit, students will be able to understand and acknowledge that the number line is a measurement tool rather than a counting tool.  As the number line shows the relationship of number placements in different base-ten scales, students will describe and demonstrate decimal expansions on the number line.  The metric system (for linear measurement) will be presented as an example of base-ten scales and students will be able to use the number line with millimeter, centimeter, decimeter, and meter markings to measure line segments to the nearest tenth of a centimeter, a tenth of a decimeter, or a tenth of a meter.  Presenting the metric system in scientific notation and relating it to the number line in a set of consecutive powers of ten; 1000, 100, 10, and 1 or 1, 0.1, 0.01, and 0.001 will be used as a form of formative assessment of the unit study. 

I expect this unit to take around two to three weeks or ten to fifteen class periods.  Although most of the class activities are designed to take only one class period, I would like to take enough time to make sure each lesson is fully understood.  This unit study will be the first math lesson of the year before opening the textbook!  Since the concept of decimal expansion includes Common Core Standards from 4^th through 7^th grades, students are already familiar with a lot of prior knowledge, and hopefully will be ready to be active participants in this unit study. 

This curriculum unit consists of the following topics:

1. Placing whole numbers in base-ten on the number line

This lesson is to introduce the curriculum unit to students by presenting number line segments that are in different base-ten scales. Students will be able to make connections among different numbers and how they are related in different base-ten scaled number line segments.

2. Decimal expansions

After students are introduced to different scales of the base-ten system, they will explore the decimal system.  Decimals are in a base-ten number system that provides a more precise collection of numerical expressions than whole numbers.  Students will compare the magnitude of different decimal numbers by expanding each digit and place value of a given decimal number on a number line segment.

3. The metric system

Students will apply their knowledge of decimal expansions to the metric system, a decimal system of base-ten applied to measurements, by using a centimeter to represent 1, 10 for a decimeter, and 100 for a meter.

4. Scientific notation

In this section, students will make connections and express length measurement in the metric system in terms of scientific notation, which also is fundamentally based on the decimal system with a base-ten scale.

5. Repeating decimals

This exercise is for students to develop a convincing argument establishing that every real number with a repeating decimal eventually finds its own address on the number line and therefore it is a rational number.  Students in small groups will find decimals with a periodically repeating expansion and investigate systematic rules associated with different patterns when converting fractions to decimals. 

The decimal expansion method will repeatedly be used throughout the entire academic year, and especially when we study the irrational numbers towards the end of the 8^th grade.  Students will be able to use the Pythagorean theorem to locate some irrational numbers, such as Ö2, Ö3, and Ö5 geometrically on the number line and investigate the precision of the placements by showing decimal expansions.