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. [7-NS1a]
Example: A hydrogen atom has 0 charge because its two constituents are oppositely charged.
b. Understand p + q as the number located at 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. [7-NS1b]
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. [7-NS1c]
d. Apply properties of operations as strategies to add and subtract rational numbers. [7-NS1d]
ACOS 2009 Correlation
Sixth Grade
1.3 - Formulating algorithms using basic operations on fractions and decimals.
2 - Solve problems involving decimals, percents, fractions, and proportions.
Seventh Grade
1 - Demonstrate computational fluency with addition, subtraction, multiplication, and division of integers.
1.1 - Formulating algorithms for performing operations on integers.
1.2 - Determining with algorithms to use when performing operations on integers.
2.1 - Determining absolute values of integers by finding their distance from zero.
3 - Solve problems requiring the use of addition, subtraction, multiplication, and division on rational numbers.
3.1 - Describing the method used to solve problems involving rational numbers.
3.5 - Using inverse properties of rational numbers with respect to addition and multiplication.
Eighth Grade
1.3 - Utilizing alternative representations to solve problems involving rational numbers.
7.NS.1 - Adding and Subtracting Positive and Negative Numbers - http://nrich.maths.org/5947 - an introduction to adding and subtracting positive and negative numbers -- this is a little different than ones I've seen before and incorporates ideas of two color counters and fact families.
7.NS.1 - Worthless Words Contest - Worthless Words.pdf - The attached pdf has a worthless words chart (3 per page) and a list of worthless words that my classes found one year (not an exhaustive list). A word is a "worthless word" if the values associated with he letters in each word add up to zero.
7.NS.1 - Hot Summer...Cold Winter -http://www.yummymath.com/2012/hot-summer-cold-winter-2/ -Problem asking students to choose hottest and coldest temperatures from a list. They then explore the differences in the hottest and coldest temperatures. A number line representation is used.
7.NS - Hot Air Balloon Integers on Math Village -http://www.mathvillage.info/node/62 - site includes problems, videos, and applets using hot air balloons to introduce integers.
7-NS1
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. [7-NS1a]
b. Understand p + q as the number located at 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. [7-NS1b]
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. [7-NS1c]
d. Apply properties of operations as strategies to add and subtract rational numbers. [7-NS1d]
ACOS 2009 Correlation
Sixth Grade
- 1.3 - Formulating algorithms using basic operations on fractions and decimals.
- 2 - Solve problems involving decimals, percents, fractions, and proportions.
Seventh Grade- 1 - Demonstrate computational fluency with addition, subtraction, multiplication, and division of integers.
- 1.1 - Formulating algorithms for performing operations on integers.
- 1.2 - Determining with algorithms to use when performing operations on integers.
- 2.1 - Determining absolute values of integers by finding their distance from zero.
- 3 - Solve problems requiring the use of addition, subtraction, multiplication, and division on rational numbers.
- 3.1 - Describing the method used to solve problems involving rational numbers.
- 3.5 - Using inverse properties of rational numbers with respect to addition and multiplication.
Eighth GradeCMP2 Correlation
7-NS1a
7-NS1b
7-NS1d
7-NS1a
7-NS1b
7-NS1c
7-NS1d
7-NS1d
Resources
North Carolina's Lessons for Learning
James Bond - 7NS1
"Sign" Your Name - 7NS1
From Harding Math Specialist
My Humble Opinion
Skills
- Add rational numbers
- Subtract rational numbers
- Represent addition on a number line diagram
- Represent subtraction on a number line diagram
- Describe situations in which opposite quantities combine to make 0.
- Ready for part b
Vocabulary- Additive inverse
Seems to be a more detailed description of the content to be taught regard Integers (to include rational numbers). No new content.