Curriculum / Math / 7th Grade / Unit 2: Operations with Rational Numbers / Lesson 11
Math
Unit 2
7th Grade
Lesson 11 of 18
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Add and subtract rational numbers using a variety of strategies.
The core standards covered in this lesson
7.NS.A.1 — 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.
7.NS.A.1.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.
7.NS.A.1.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.
7.NS.A.1.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.NS.A.1.D — Apply properties of operations as strategies to add and subtract rational numbers.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
This is a flex lesson that can be used in a variety of ways, depending on the individual class. There are no anchor problems, as teachers can determine what specific concepts are best to look at with the whole class. The Problem Set Guidance is a collection of problems and activities that may be used for this day.Â
A set of suggested resources or problem types that teachers can turn into a problem set
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Four points are shown on the number line below.
a. The value of the expression $${-2{1\over3}+p}$$ is positive. What point could represent the value of $$p$$?
b. The value of the expression $$-2{1\over3}-p$$ is positive. What point could represent the value of $$p$$?
The expression $${{3\over4} - {7\over8} }$$ represents the location of point B. Point A is located in a different place on the number line and is the same distance from 0 as point B. Mark the approximate location of point A on the number line below.
Brad’s checking account starts off with a balance of $126.50. Throughout the week, Brad pays a bill for $87.21, and pays $5.64 for breakfast. He deposits $15.00 but then pays another bill for $55.25. At the end of the week, he gets a notice from the bank that he has a negative balance. How much does Brad need to deposit into his account to get to a $0 balance?
An example response to the Target Task at the level of detail expected of the students.
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
Lesson 10
Lesson 12
Topic A: Adding and Subtracting Rational Numbers
Represent rational numbers on the number line. Define opposites, absolute value, and rational numbers
7.NS.A.1
Compare and order rational numbers. Write and interpret inequalities to describe the order of rational numbers.
Describe situations in which opposite quantities combine to make zero.
7.NS.A.1.A
Model the addition of integers using a number line.
7.NS.A.1.B 7.NS.A.1.D
Determine efficient ways to add rational numbers with and without the number line.
Efficiently add and reason about sums of rational numbers.
Understand subtraction as addition of the opposite value (or additive inverse).
7.NS.A.1.C 7.NS.A.1.D
Find and represent the distance between two rational numbers as the absolute value of their difference.
7.NS.A.1.C
Subtract rational numbers with and without the number line.
Add and subtract rational numbers efficiently using properties of operations.
7.NS.A.1.D
7.NS.A.1 7.NS.A.1.A 7.NS.A.1.B 7.NS.A.1.C 7.NS.A.1.D
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Topic B: Multiplying and Dividing Rational Numbers
Determine the rules for multiplying signed numbers.
7.NS.A.2.A 7.NS.A.2.C
Multiply signed rational numbers and interpret products in real-world contexts.
Determine the rules for dividing signed numbers.
7.NS.A.2.B 7.NS.A.2.C
Divide signed rational numbers and interpret quotients in real-world contexts.
Convert rational numbers to decimals using long division and equivalent fractions.
7.NS.A.2.D
Multiply and divide with rational numbers using properties of operations.
7.NS.A.2 7.NS.A.2.C
Topic C: Using all Four Operations with Rational Numbers
Solve problems with rational numbers and all four operations.
7.NS.A.3
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