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.
Learning Targets (I can)
Explain what integers are.
Use integers to describe quantities and/or real-world contexts.
Describe the relationship of integers to 0.
Represent integers on number lines with varied endpoints.
About the Math
Explain what integers are.
An integer is a number that can be written without a fractional component. They can be positive or negative. Zero is an integer.
Use integers to describe quantities and/or real-world contexts.
Integers explain real-world situations. They can explain altitude, temperature, sea-level, profits, and much more. Students should be comfortable thinking about integers in these contexts.
Describe the relationship of integers to 0.
Integers are related. Their distance from one another is one way to think about the relationship. "3" is one away from "2" and "4." But it is related to other integers as well. "3" is 7 way from "10" and "-4."
Represent integers on number lines with varied endpoints
Integers can be represented on number lines. When working with integers on number lines, it is important that the endpoints (and location of 0 - if present at all) change. Students should be able to place -10 on a number line with the endpoints of -20 and 20, -20 and 0, -50 and 0, or something different. Each time, studetns should be able to justify the location of integers.
Essential vocabulary for this standard includes rational numbers, opposites, positive, negative, and integers.
The article linked below from NRICH provides a variety of contexts to help students understand how positive and negative numbers can be used to describe actions in real-life situations.
These tasks can be used with small group or whole group instruction.
When I woke up the temperature was 5 degrees below 0. By noon the temperature rose and then declined again by evening. The evening temperature ended up being 7 degrees. What could have been the temperature at noon? What was the difference between the noon temperature and the evening temperature? Explain your thinking.
What is an example of negative numbers in real life? (loss of yards in football, temperature, sea level, withdrawals from accounts)
A dolphin can swim up to 150 feet below sea level. Write a negative integer to represent the depth that a dolphin could possibly dive.
Aoki says that any negative integer can be greater than a positive integer. Justin disagrees. Who is correct? Explain your reasoning. (absolute value can be part of the discussion)
Katrina is playing a game. On her first turn she earns 5 points and on the second turn she loses 7 points. How many points does she have? Illustrate your answer using a number line.
SLIDE-BASED TASKS
These links are HCPSS created instructional tasks. These tasks are provided in Google slides.These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first(often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.
These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them.
Print Resources
Book Thumbnail
Book Title
Grade
Pages
Teaching Student-Centered Mathematics
6-8
What is Her Net Worth?, Activity 10.9, Page 181 (American) Football Statistics, Activity 10.10, Page 183 Find the Zero, Activity 10.11, Page 185
These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.