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PBS Math Club
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Khan Academy
© 2016 Khan Academy

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Integers | Class 6 (India) - old | Math | Khan Academy

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The set of integers from 1 to infinity is called Natural numbers. When we add 0 to this, we get whole numbers. A set of 0, natural numbers and their opposites, make up 'integers'.

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CC BY-NC-ND 3.0

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Math.7.NS.A.1b

Common core State Standards

Math: Math

7: Grade 7

NS: The Number System

A: Apply and extend previous understandings of operations with fractions

1b:
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

a. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.

b. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

c. Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

d. Apply properties of operations as strategies to add and subtract rational numbers.

Download Common Core State Standards (PDF 1.2 MB)

|

Math.7.NS.A.1d

Common core State Standards

Math: Math

7: Grade 7

NS: The Number System

A: Apply and extend previous understandings of operations with fractions

1d:
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

a. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.

b. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

c. Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

d. Apply properties of operations as strategies to add and subtract rational numbers.

Download Common Core State Standards (PDF 1.2 MB)

Thought starters

1. How does the use of number lines help students visualize integer operations?

2. How does this approach support long-term conceptual understanding as compared to rote memorization of rules?

3. Why is it important to use both horizontal and vertical number lines?

School Details

Willard Middle School
2425 Stuart Street
Berkeley CA 94705

Data Provided By:

Teachers

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This 7th grade math teacher aims to ensure long-term conceptual understanding of integer operations knowing that students often stumble when only taught to follow the rules. She realizes that the use of number lines is essential for mastery and consistent with what students will do in Algebra I.Her students visualize the number values and operations on a number line helping them easily add integers of any size.

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CC-Attribution Kelsey Knapp

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CC BY-SA 4.0
© 2016 OpenEd Inc.

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Assessments, Homework, Lesson Plans, Videos, Games. Over a million resources aligned to Common Core, PARCC, SBAC

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Teach, Assess, and Analyze with the largest K-12 Resource Library

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Chris Robinson
CC-BY 3.0

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Wha? Explain in the comments. And thanks again to Chris Robinson for the submission.

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Donald Garner
CC-SA

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The 'Integer'y is Still Out: Introduction

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below sea level? These topics and more will be addressed in this webquest. There is something here for everyone, so let's get started.

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Stanley Park
CC-BY-SA 3.0

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Many students prefer to simply use mental "algorithms" or rules to add integers. NO PROBLEM, this is great. It is very important to understand how negative and positive integers work, and this will help students quickly apply a few rules to correctly add integers with only their BRAINS.

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Glover
CC-BY-SA 3.0

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Khan Academy
© 2016 Khan Academy

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Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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Khan Academy
© 2016 Khan Academy

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Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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Tom DeRosa
CC-A-NC 3.0

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Last year my students had their usual struggles with adding and subtracting integers at the beginning of the year (this is not just a middle school problem). So I used a game I found online called Twenty Five, where students would draw from a regular deck of cards and add them to a pile, trying to reach a target sum of 25. Red cards were negative and black cards were positive, and each new card would be added to all the ones put on the pile before it. Presumably students were writing down each addition problem they did. It was a waste of time: it was hard to monitor whether students were adding correctly during the game, and difficult for students to keep track of and add up 10, 15 or 20 numbers quickly.

Since then I have been laboring over an idea for my own game, since I believe this would help my students internalize an essential skill. I came up with a complete game, but it was too complicated for classroom use (based on my experience with Like Terms ); too many rules and steps to get caught up in would leave the core activity lost in the fray. It could be suited for an advanced class, block schedule or playing at home. In a regular 45-55 minute class, things need to be simpler.

I actually eschewed any game this year and focused on the number line as a simpler tool for students to use to add and subtract integers correctly. What dawned on me last weekend was that the number line was the missing piece to the puzzle. Here now, for the first time ever, is Plus/Minus.

Materials

1. Standard 52-card deck of playing cards

2. Paper and pencils.

3. 2 objects to mark a goal and starting location

Setup

1. Students draw a number line on a piece of paper, at least from -10 to 10 with room for more.

2. Have 2 objects (maybe candy the winner can eat afterwards?) to mark the location of the goal and the current location of the players

3. No cards are dealt. There is a face down draw pile and face up pile for each card drawn.

Game Play

1. Flip the top card from the draw pile. This is the goal. Black card are positive whole numbers and red cards are negative (aces are 1 and all other face cards are 10). The starting point is zero.

2. Each student takes a turn flipping the next card from the draw pile. They add that number to 0 and move to the resulting location. If they reach the goal number, they win. If not, their turn is over and each player takes a turn moving back and forth on the number line until someone reaches the goal.

3. After one or several games (depending on time) , switch to subtracting all numbers.

While They Play
Students must write down each simple addition or subtraction problem they are doing throughout each game. This is what you can check and grade immediately as you are monitoring the game. Follow up with homework for practice.

Extension/Assessment

At the end of this lesson, use a mini-poster where students have to show an example, write out how to do it (what the rule is) and most importantly include the correct answer. Hang the best ones up on the wall (as you should always do with good examples of student work).

When To Play

This would be a good game to play after a day where you had introduced the concepts or when you were reteaching. I think that the number line makes this concept easy to understand with little upfront work, but that is an assumption on my part. Use it whenever you feel it is appropriate.

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Adding and Subtracting Integers Card Game

# data[].attributes.attachment_link.description
Last year my students had their usual struggles with adding and subtracting integers at the beginning of the year (this is not just a middle school problem). So I used a game I found online called Twenty Five, where students would draw from a regular deck of cards and add them to a pile, trying to reach a target sum of 25.

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CC-BY-ND-NC 4.0

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Multiplying and dividing with integers (Pre-Algebra, Explore and understand integers) - Mathplanet

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This is similar to the rule for adding and subtracting: two minus signs become a plus, while a plus and a minus become a minus. In multiplication and division, however, you calculate the result as if there were no minus signs and then look at the signs to determine whether your result is positive or negative.

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PBS Math Club
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Adding Negative Numbers | Mean Girls and Darth Vader | PBSMathClub