The Number Line in the Common Core

Content Objectives

Established Goals and Understandings

This unit will address several standards in the Common Core State Standards, the Mathematical Practice standards, and the course objectives.  Since the skills being addressed are prior knowledge for the high school students and the unit will serve as a review, the Common Core State Standards addressed come from the earlier grades.  The focus area of these standards being Operations and Algebraic Thinking as well as Numbers and Operations in Base Ten.  The standard goals include developing an understanding of numbers, identifying units, developing an understanding of fractions as numbers, and representing and solving problems involving addition and subtraction.²

The unit will be based around “provocative questions that will foster inquiry, understanding, and transfer of learning”. ³These essential questions will include: What is a number? How do you define addition? How do you define subtraction? How does the number line connect everything we know about the operations?

This instructional unit pushes students to acquire key knowledge and key skills in order to be prepared for the remainder of the academic year. Using number lines, Cuisenaire rods, base ten blocks, technology and active learning, students will be able to accomplish the following objectives in sequential order:

- Learn that numbers on the number line increase from left to right (addressing the direction/orientation/geometry of the number line)

- Learn the measurement principle

- Conceptualize counting by continuing the idea that each successive number refers to a quantity that is one more unit than the previous number/recognizing that the number before any given number is one less than that number

- Practice placing whole numbers on the number line (with a variety of units) and explaining why the numbers are being placed where they are (demonstrating the conceptualization of unitization)

- Partition the number line to demonstrate an understanding of fractions

- Reason with fraction placement, referencing the origin and distance

- Compare fractions using the measurement principle

- Discuss addition as putting lengths together (concrete)

- Demonstrate conceptualization of addition by discussing addition and it’s connection to measurement by addressing the numbers and the unit

- Demonstrate conceptualization of addition of fractions by discussing addition and it’s connection to measurement by addressing the fractions and the fractional unit

- Use the number line as the actual model for solving problems with addition

- Discuss the idea of orientation and how that impacts distance (particularly with signed numbers)

- Discuss subtraction as comparing lengths  (concrete)

- Demonstrate conceptualization of subtraction by discussing subtraction and it’s connection to measurement by subtracting the numbers and the unit and measuring the difference

- Demonstrate conceptualization of subtraction of fractions by discussing subtraction and it’s connection to measurement by addressing the fractions and the fractional unit

- Use the number line as the actual model for solving problems with addition and subtraction

- Discuss the idea of orientation and how that impacts distance (particularly with signed numbers) and how this idea is unified with both addition and subtraction

If students master the skills needed within these objectives, they should maintain a stronger conceptual understanding of the fractions, addition, and subtraction for their continued use in Algebra.

It will be necessary to administer diagnostic exams before the Unit to identify student areas of need and to create supplemental work for students who have already mastered both an abstract and conceptual understanding of these skills.  The students will receive a diagnostic exam to include addition and subtraction, fractions and percentages, decimals, and order of operations. To supplement learners working below or above the addition and subtraction stage, they will be working on iReady, a computer software that is adaptive that will target students directly where learning is needed.