Curriculum / Math / 7th Grade / Unit 3: Numerical and Algebraic Expressions / Lesson 4
Math
Unit 3
7th Grade
Lesson 4 of 11
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Expand and factor expressions with negative rational numbers.
The core standards covered in this lesson
7.EE.A.1 — Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
The foundational standards covered in this lesson
6.EE.A.3 — Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.
7.NS.A.2 — Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide 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
In Lessons 3 and 4, students expand and factor expressions with rational numbers. In Lesson 4, students see negative numbers both inside and outside a parentheses group. They will need to recall rules of multiplying signed numbers, specifically a negative times a negative is a positive number.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
For each problem, fill in the blanks around the diagram, and then write equivalent expressions in the form: ___ ( _______) = ___________
What are the values of $$q$$ and $$r$$ in each set of equivalent expressions?
a. $$q(6x+4)=3x+r$$
b. $$q\left ( \frac{1}{2}x+\frac{1}{3} \right ) = 3x+r$$
c. $$q(3x+4)=r-8$$
Expand or factor each expression.
a. $${-\frac{1}{2}(-5x+4y-16)}$$
b. $${-2\left ( 4-\frac{1}{2}h \right )}$$
c. $${-\left ( \frac{2}{3}a-\frac{3}{4}b-1 \right )}$$
d. $${-16xy+8y}$$
e. $${\frac{1}{2}x-1}$$
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
The table below includes expressions that are written in expanded form and in factored form. Complete the table. Use a diagram if needed.
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 3
Lesson 5
Topic A: Evaluating Numerical and Algebraic Expressions
Evaluate numerical expressions with rational numbers using the order of operations.
7.EE.A.1 7.NS.A.3
Write and evaluate expressions for mathematical and contextual situations.
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Topic B: Generating Equivalent Expressions
Expand and factor expressions using the distributive property and the greatest common factor.
7.EE.A.1
Add and simplify expressions by combining like terms.
Subtract and simplify expressions.
Simplify expressions by combining like terms and using the distributive property and properties of operations (Part 1).
Simplify expressions by combining like terms and using the distributive property and properties of operations (Part 2).
Write and interpret expressions in different ways to shed new meaning on a context.
7.EE.A.2
Topic C: Solving Multi-Step Problems using Expressions
Solve multi-step real-world problems with rational numbers.
7.EE.B.3 7.NS.A.3
Model real-world problems involving rational numbers using reasoned estimates.
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