Curriculum / Math / 7th Grade / Unit 2: Operations with Rational Numbers / Lesson 6
Math
Unit 2
7th Grade
Lesson 6 of 18
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Lesson Notes
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Efficiently add and reason about sums of rational numbers.
The core standards covered in this lesson
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.D — Apply properties of operations as strategies to add and subtract rational numbers.
The foundational standards covered in this lesson
5.NF.A.1 — Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)
6.NS.B.3 — Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
In each problem, point A is shown on the number line and point B is a given distance from point A.
For each problem, write two addition equations that could be used to determine the location of point B.
a. Point B is 4 units away from point A.
b. Point B is $${6 {1\over4}}$$ units away from point A.
c. Point B is $${5 {1\over3}}$$ units away from point A. (A = $${3 {2\over3}}$$)
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Two numbers, $$p$$ and $$q$$, are shown on the number line below, and $${|p|<|q|}$$.
Determine if the sums below are positive or negative. Explain your reasoning.
a. $${p+q}$$
b. $$-{p+q}$$
c. $${p+(-q)}$$
d. $$-{p+(-q)}$$
The temperature of water in a lake at 9:00 a.m. is $$-2.6$$ËšC. By noon, the temperature of the water had risen by $$5.1$$ËšC. By 9:00 p.m., the temperature of the water had fallen by $$12.8$$ËšC from what it had been at noon.
Write an addition problem to represent the changing temperature of the water, and find the temperature of the water at 9:00 p.m.
A set of suggested resources or problem types that teachers can turn into a problem set
15-20 minutes
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
5-10 minutes
Point A is located at $$-4.5$$, and point B is $$3.25$$ units from point A. Write two addition equations that could be used to determine the location of point B. Model this on the number line below.
Find the sums.
a. $${-3+ \left (-2 {1\over4} \right )}$$
b. $${5.7 + (-12.2)}$$
c. $${-9 + 3 {2\over5}}$$
d. $${-{10\over3} + 18}$$
e. $${-2+3+(-1)+5}$$
Next
Understand subtraction as addition of the opposite value (or additive inverse).
Topic A: Adding and Subtracting Rational Numbers
Represent rational numbers on the number line. Define opposites, absolute value, and rational numbers.
Standards
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.B7.NS.A.1.D
Determine efficient ways to add rational numbers with and without the number line.
7.NS.A.1.C7.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
Add and subtract rational numbers using a variety of strategies.
7.NS.A.17.NS.A.1.A7.NS.A.1.B7.NS.A.1.C7.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.A7.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.B7.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.27.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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