Unit 4
Addition and Subtraction on the Number Line
Unit Goals
- Students learn about the structure of a number line and use it to represent numbers within 100. They also relate addition and subtraction to length and represent the operations on the number line.
Unit Narrative
In this unit, students are introduced to the number line, an essential representation that will be used throughout students’ K–12 mathematical experience. They learn to use number lines to represent whole numbers, sums, and differences.
In a previous unit, students learned to measure length with rulers. Here, they see that the tick marks and numbers on the number line are like those on a ruler: both show equally spaced numbers that represent lengths from 0.
Students use this understanding of structure to locate and compare numbers on number lines and to estimate numbers represented by points on number lines.
Locate and label 17 on the number line.
Number line. 31 evenly spaced tick marks. First tick mark labeled 10, sixth mark labeled blank, eleventh mark labeled blank, sixteenth mark labeled 25, twenty-first mark labeled 30, twenty-sixth mark labeled blank, thirty-first mark labeled blank.
What number could this be? _____
Students then learn conventions for representing addition and subtraction on a number line: using arrows pointing to the right for adding and arrows pointing to the left for subtracting. Students also use number lines to represent addition and subtraction methods discussed in Number Talks, such as counting on, counting back by place, and decomposing a number to get to a ten. The reasoning here deepens students’ understanding of the relationship between addition and subtraction.
The number lines in this unit show a tick mark for every whole number in the given range, though not all may be labeled with the numeral. As students become more comfortable with this representation, they may draw number lines that show only the numbers needed to solve the problems, which is acceptable.