Negative Numbers

Teacher Guide | Grade 6 Mathematics | FAST Success Kit
Florida B.E.S.T. Standards: MA.6.NSO.1.1, MA.6.NSO.1.2, MA.6.NSO.1.3
@ Learning Objective 5-10 min lesson
Students will: Understand positive and negative integers, plot them on a number line, find absolute values, and compare/order integers in mathematical and real-world contexts.

Why this matters for FAST: Understanding negative numbers and their relationship to positive numbers is foundational for Grade 6. Students must visualize integers on number lines, understand absolute value as distance, and apply these concepts to real-world situations like temperature, elevation, and money.

% Materials Needed
! Common Misconceptions to Address

Misconception #1: Thinking -8 is Greater Than -3

Students see 8 is bigger than 3, so they think -8 > -3. They forget that negative numbers work in reverse!

How to Address:

"Use the number line! Numbers get SMALLER as you move left. -8 is to the LEFT of -3, so -8 is LESS than -3. Think about temperature: -8 degrees is colder (smaller) than -3 degrees!"

Misconception #2: Thinking Absolute Value Can Be Negative

Students write |-5| = -5, not understanding that absolute value is always positive or zero.

How to Address:

"Absolute value measures DISTANCE from zero. Distance is always positive! |-5| asks 'How far is -5 from zero?' Answer: 5 units. The answer is always positive!"

Misconception #3: Confusing Opposites with Absolute Value

Students think the opposite of -4 is |-4| = 4, mixing up two different concepts.

How to Address:

"Opposite changes the sign (positive becomes negative, negative becomes positive). Absolute value removes the sign (makes everything positive). The opposite of -4 is +4. The absolute value of -4 is also 4. Same answer, different concepts!"

Number Line Reference

-5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5

Left = Smaller | Zero = Middle | Right = Larger

$ Lesson Steps
1

Activate Prior Knowledge (1 min)

Ask: "What's the temperature outside today? What if it's cold - can temperature go below zero? What number shows 5 degrees below zero?" (Negative 5 or -5)

2

Introduce the Number Line (2 min)

SAY THIS:

"Zero is our starting point. Numbers to the RIGHT of zero are positive. Numbers to the LEFT of zero are negative. The farther right, the bigger. The farther left, the smaller. So -10 is smaller than -2!"

3

Teach Opposites (1 min)

SAY THIS:

"Every number has an opposite. The opposite of 3 is -3. The opposite of -7 is 7. Opposites are the same distance from zero but on opposite sides. When you add a number and its opposite, you get zero!"

4

Introduce Absolute Value (2 min)

SAY THIS:

"Absolute value is the DISTANCE from zero. We use these symbols: | |. The absolute value of 5 is 5 (written |5| = 5). The absolute value of -5 is also 5 (written |-5| = 5). Both are 5 units away from zero!"

Key point: Absolute value is ALWAYS positive or zero (never negative)!

5

Compare and Order Integers (2 min)

Practice: "Which is greater, -4 or -9?" (-4, because it's to the right on the number line)

Order from least to greatest: -7, 2, -3, 0, 5, -1

Answer: -7, -3, -1, 0, 2, 5

6

Real-World Contexts (1 min)

  • Temperature: -10 degrees is colder than -5 degrees
  • Elevation: -100 feet (below sea level) is lower than -50 feet
  • Money: -$20 (debt) is worse than -$5 (less debt)
? Check for Understanding

Quick Exit Ticket (Ask the whole class):

"Which statement is TRUE?"

A) -6 > -2   B) |-7| = -7   C) -5 < -3   D) |4| = |-4|

Correct answers: C and D

C: -5 is to the left of -3, so -5 < -3. D: Both have absolute value of 4.

& IXL Skills to Assign After This Lesson

Recommended IXL Practice:

Integers on number lines Compare integers Order integers Absolute value Opposites Integer word problems
^ Differentiation & Extension

For struggling students: Use a thermometer visual - students can physically see that -10 is "below" -5. Start with smaller numbers (-5 to 5) before expanding the range.

For advanced students: Introduce comparing absolute values (Is |-8| > |5|? Yes!). Have them create real-world scenarios using negative numbers.

For home: Send Parent Activity sheet. Families can discuss temperatures, check elevation maps, or talk about bank accounts.

FAST Success Kit | Grade 6 | Negative Numbers Standards: MA.6.NSO.1.1, MA.6.NSO.1.2, MA.6.NSO.1.3