Curriculum / Math / 6th Grade / Unit 5: Numerical and Algebraic Expressions / Lesson 3
Math
Unit 5
6th Grade
Lesson 3 of 12
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Lesson Notes
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Use variables to write algebraic expressions.
The core standards covered in this lesson
6.EE.A.2 — Write, read, and evaluate expressions in which letters stand for numbers.
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.
6.EE.B.6 — Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
The foundational standards covered in this lesson
4.OA.A.2 — Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
4.OA.A.3 — Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
Using variables in expressions is a concept and skill that students will return to and build on in 7th and 8th grades. In using variables to represent unknown or changing values, students are decontextualizing the situation to represent the values as symbols which they can manipulate (MP.2).
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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
Sarita has a fish tank in the shape of a rectangular prism. The bottom of the fish tank measures $${10}$$ inches by $$8$$ inches. Sarita wants to add some sand to cover the bottom of the tank, and she uses the formula $${ V=l × w × h}$$ to determine the volume of sand she needs.
a. If the height of the sand measures $$2$$ inches, what is the volume of sand needed?
b. If the height of the sand measures $${3.5}$$ inches, what is the volume of sand needed?
c. Sarita cannot decide how high she wants the sand to be in the tank. What expression can she use to represent the volume of sand needed for any height of sand?
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In each example, write an expression to represent the quantity.
a. Thomas is $$x$$ years old.
b. Reina has $$5$$ more quarters than dimes.
a. A numeric expression like $${5+(8+2)^2}$$ has one and only one value. What is it?
b. Consider the expression $${ {5+(x+2)^2}}$$. What are some values it can have? Make sure you organize your work so anyone can tell which value for the expression goes with which $$x$$ value.
c. How many different values can an algebraic expression like $${5+(x+2)^2}$$ have?
Introducing Equivalent Expressions 2, accessed on Dec. 18, 2017, 3:07 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.
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
A frame shop creates custom frames for different sized pictures. A customer has several rectangular-shaped photographs that he wants framed. All of the photographs measure $${10 {1\over2}}$$ inches for the width but vary in the length.
The manager at the frame shop knows she can use the formula for perimeter to determine the amount of wood that she’ll need for each photograph: $${P=2l+2w}$$.
a. One of the photos is $${15}$$ inches long. How much wood is needed for the frame?
b. Another photo is $${20 {3\over4}}$$ inches long. How much wood is needed for the frame?
c. What expression can the manager use to determine the amount of wood needed for any photograph the customer has?
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.
Next
Evaluate algebraic expressions.
Topic A: Numerical Expressions with Exponents
Understand the meaning of exponents.
Standards
6.EE.A.1
Evaluate numerical expressions involving whole-number exponents.
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Topic B: Introduction to Algebraic Expressions
6.EE.A.26.EE.A.2.C6.EE.B.6
6.EE.A.26.EE.A.2.C
Write expressions for verbal statements and vice versa (Part 1).
6.EE.A.2.A6.EE.A.2.B
Write expressions for verbal statements and vice versa (Part 2).
Topic C: Equivalent Expressions & Applications
Identify equivalent expressions (Part 1).
6.EE.A.36.EE.A.4
Identify equivalent expressions (Part 2).
Write equivalent expressions using the distributive property (Part 1).
Write equivalent expressions using the distributive property (Part 2).
Write algebraic expressions for application situations (Part 1).
6.EE.B.6
Write algebraic expressions for application situations (Part 2).
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