Comparing integers
Comparing integers in Grade 8 Saxon Math Course 3 involves ordering positive and negative whole numbers on a number line or by using inequality symbols. Students learn that on a number line, larger numbers are always to the right, which means all positive integers are greater than all negative integers, and negative numbers closer to zero are greater than those farther from zero. This skill is fundamental to number sense and algebraic reasoning.
Key Concepts
Property To compare integers, find their positions on a number line. Numbers increase in value as you move from left to right. The symbol's small end ($<$ or $ $) always points to the smaller number.
Examples Since $ 1$ is to the right of $ 3$, we write $ 1 3$. Since $ 5$ is to the left of $2$, we write $ 5 < 2$. $| 5| |3|$ because this comparison simplifies to $5 3$.
Explanation The number line doesn't lie! Any number to the right is greater than any number to its left. Think of it like a race: the runner at position $ 2$ is ahead of the runner at position $ 5$.
Common Questions
How do you compare two integers?
Use a number line. The integer farther to the right is greater. Use inequality symbols: > means greater than, < means less than.
Which is greater: -3 or -7?
-3 is greater than -7 because -3 is closer to zero and farther to the right on the number line. -7 < -3.
How do you order a set of integers from least to greatest?
Place the integers on a number line from left to right, or sort negative integers by decreasing absolute value, then positive integers by increasing value.
Is 0 greater than any negative integer?
Yes. Zero is greater than every negative integer because 0 is to the right of all negative numbers on the number line.
How does Saxon Math Course 3 teach integer comparison?
Saxon Math Course 3 uses number lines and real-world contexts like temperature and elevation to help students correctly order and compare integers, building intuition for the number system.