Curriculum / Math / 7th Grade / Unit 3: Numerical and Algebraic Expressions / Lesson 1
Math
Unit 3
7th Grade
Lesson 1 of 11
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Evaluate numerical expressions with rational numbers using the order of operations.
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.
7.NS.A.3 — Solve real-world and mathematical problems involving the four operations with rational numbers. Computations with rational numbers extend the rules for manipulating fractions to complex fractions.
The foundational standards covered in this lesson
6.EE.A.2.C — Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s³ and A = 6 s² to find the volume and surface area of a cube with sides of length s = 1/2.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Evaluate the following numerical expressions.
a. $${-2(5+(3)(-2)+4)}$$
b. $${-2((5+3)(-2+4))}$$
c. $${-2(5+3(-2+4))}$$
d. Can the parentheses in any of these expressions be removed without changing the value of the expression?
Watch Out for Parentheses, accessed on Oct. 6, 2017, 2:16 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
An expression is shown below with three expressions that are not equivalent to it. Explain the error(s) that were made in writing each expression.
$$\frac{6-3(4-8)}{2(1+2)^2}$$
a. $$\frac{6-3(4-8)}{2(1+2)^2}$$$$\neq \frac{3(-4)}{2(3)^2}$$
b. $$\frac{6-3(4-8)}{2(1+2)^2}$$$$\neq \frac{6-3(-4)}{(6)^2}$$
c. $$\frac{6-3(4-8)}{2(1+2)^2}$$$$\neq \frac{6-12}{(2+4)^2}$$
d. Evaluate the expression.
Evaluate: $${\frac{1}{2}(-3-1)^2-\left ( 10 \div \frac{5}{6} \right )}$$
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A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Evaluate the expression below. For each successive expression you write, explain what you did to create an expression equivalent to the expression before.
$${\frac{2-3(4-6)^2}{\frac{1}{2}}}$$
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Lesson 2
Topic A: Evaluating Numerical and Algebraic Expressions
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
Expand and factor expressions with negative rational numbers.
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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