There are positions below zero
Choose a reference zero and unit, then read negative positions.
Begin with the activity ↓How can we write a temperature below zero?
One unit below zero is −1; two units below is −2. The minus sign marks the side opposite positive positions.
A temperature does not disappear below 0°C. Three degrees below 0°C is written −3°C. Zero Celsius is a reference temperature, not an absence of temperature.
Draw a horizontal number line. Mark zero and let each equal interval represent one unit. To the right are 1, 2, 3; to the left are −1, −2, −3. Number lines may also be vertical, but our activity uses a horizontal line.
Read −3 as minus three or negative three. Here the minus is a sign attached to a number. It has a different role from the subtraction operation between the two numbers in 5−3.
Check the reference and unit before memorizing the sign. Three equal steps left of zero locate −3. This need not mean a collection of minus three objects; the number describes a position.
Zero is neither positive nor negative. +3 equals 3 and lies on the opposite side of zero from −3. As numerical values, +0 and −0 are the same zero.
Next we compare two positions. Keep the convention that values increase to the right. Before coordinates, become familiar with a reference, direction and unit on a single line.
Listen one paragraph at a time
Hold on to this distinction
−3 is three steps left of zero; 3 is three steps right. Read the sign and reference along with the digit.
Change it and check
Change the marked position. Say which direction and how many steps from zero, then check the dot.
The screen shows integer positions from −5 to 5. The number line itself does not end at these points.
Try with paper and objects
Draw equally spaced ticks, choose a central zero, and place a −2 card two steps to its left.
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-5 · number only
Five units below zero is −5.
Does your explanation include these ideas?
Explain aloud or in a drawing, then check your ideas. Different wording can express the same meaning.
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Use the same order on a number line below zero.