Using Negative Numbers to Make Sense of Contexts

10 min

Teacher Prep
Setup
Groups of 2. Give students 1 minute of quiet think time, followed by partner and whole-class discussions.

Narrative

The purpose of this Warm-up is to introduce positive and negative numbers in the new context of money and inventory. The table shown here will also be used in a following activity. While students may notice and wonder many things about this table, interpreting the meaning of positive and negative numbers in this context is the important discussion point.

When students articulate what they notice and wonder, they have an opportunity to attend to precision in the language they use to describe what they see (MP6). They might first propose less formal or imprecise language and then restate their observation with more precise language in order to communicate more clearly.

Launch

Arrange students in groups of 2. Display the table for all to see. Ask students to think of at least one thing they notice and at least one thing they wonder. Give students 1 minute of quiet think time and then 1 minute to discuss with their partner the things they notice and wonder.

Student Task

What do you notice? What do you wonder?
item quantity value in dollars
hammer -12 85.14
washer 300 -15.00
bolt -25 10.54
nail 500 -22.50
wrench -4 51.88
flashlight -18 123.23

Sample Response

Students may notice:

  • Some quantities and values are negative.
  • If a quantity is negative, then the value in dollars is positive.
  • If a quantity is positive, then the value in dollars is negative.

Students may wonder:

  • How much money did they make?
  • How much money did they spend?
  • Why are the quantity and the value in dollars opposite signs?
  • Did they buy 12 hammers or sell 12 hammers?
  • How much did one flashlight cost?
Activity Synthesis (Teacher Notes)

Ask students to share the things they noticed and wondered. Record and display their responses without editing or commentary. If possible, record the relevant reasoning on or near the table. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and respectfully ask for clarification, point out contradicting information, or voice any disagreement.

If the idea that a negative quantity means that an item was sold and resulted in a positive amount of money does not come up during the conversation, ask students to discuss this idea.

Standards
Addressing
  • 6.NS.5·Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.
  • 6.NS.C.5·Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

10 min