Grade 7 Mathematics Unit 6 Equations Estimated Time: 20 Hours
[C] Communication [CN] Connections [ME] Mental Mathematics and Estimation
Grade 7 Mathematics Curriculum Outcomes Outcomes with Achievement Indicators Unit 6
[PS] [R] [T] [V]
Problem Solving Reasoning Technology Visualization
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Grade 7 Mathematics Curriculum Outcomes Outcomes with Achievement Indicators Unit 6
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Unit 6: Equations
Unit 6 Overview Introduction Students will focus on developing skills and knowledge necessary for understanding how to solve equations using a variety of methods. The big ideas in this unit are: • • • •
An equation states a relationship between two expressions; specifically, that the two expressions are equal. Preservation of equality is at the core of solving equations. An equation can be solved by systematic trial, using a two-pan balance model, using algebra tiles, or solved symbolically by using algebraic techniques. Equations can be used to model and solve problems.
Context The students will begin to solve equations using systematic trial and inspection. The students will often know the solution to an equation instantly. However, they will be asked to explain their reasoning before they move on to solving equations with two-pan balance models and algebra tiles. Students will solve equations that involve positive and negative integers and they will solve equations that are limited to no more than two steps. Ultimately students will apply algebraic techniques, requiring the use of preservation of equality, in order to solve equations.
Why are these concepts important? Developing a good understanding of solving equations will permit students to: • Become good problem solvers. Students will be able to decide on an appropriate method for problem solving and determine if their answer makes sense. • Be able to manipulate formulas using algebra and know how to verify answers when studying subjects like chemistry, physics, and calculus to name a few.
“It is hard to convince a high-school student that he will encounter a lot of problems more difficult than those of algebra and geometry.” Edgar Watson Howe (1853-1937)
Grade 7 Math Curriculum Guide
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Strand: Patterns and Relations (Variables and Equations)
General Outcome: Represent algebraic expressions in multiple ways. Specific Outcome
Elaborations: Suggested Learning and Teaching Strategies
It is expected that students will:
It is assumed that students can: 7PR4. Explain the difference • recognize patterns in a table of values between an expression and • write a pattern rule for a number pattern an equation. • use a pattern rule to find the value of a given term [C, CN] (Cont’d) This outcome was introduced in Unit 1 (see achievement indicators 7PR4.2, 7PR4.3, and 7PR4.4). Identifying the difference between an algebraic expression and an equation can now be further developed. Achievement Indicators 7PR4.6 Provide an example of an expression and an equation, and explain how they are similar and different.
Recall that an algebraic equation is a mathematical statement that two expressions are equal. In an equation such as 2a + 5 = 11, we are searching for one input value, or value that can be substituted for a, that would produce the desired output value of 11. Students should now be exposed to expressions where the constant term is negative, e.g. 4x – 7 is equivalent to 4x + -7, thus the constant term is -7.
Grade 7 Mathematics Curriculum Outcomes Outcomes with Achievement Indicators Unit 6
184
Strand: Patterns and Relations (Variables and Equations)
General Outcome: Represent algebraic expressions in multiple ways. Suggested Assessment Strategies
Resources/Notes
Paper & Pencil 1. Which are expressions? Which are equations? How are they similar? How are they different? A. 2 – x B. 5v = 20 h C. =4 3 D. w + 7 2. Does the algebra tile diagram below model an expression or an equation? Explain.
3. Below are three algebraic expressions and/or equations. 4p + 5 = 55 4p – 5 = 55 4p – 5 A. Which are equations and which are expressions? Explain why. B. List ways in which they are similar and ways in which they differ.
Math Makes Sense 7 Lesson 6.1 Unit 6: Equations TR: ProGuide, pp. 4–9 Master 6.9, 6.18 CD-ROM Unit 6 Masters ST: pp. 220–225 Practice and HW Book pp. 132–134
4. Have students complete concept maps for expressions and equations such as: Sample Responses Essential Characteristics
Non-Essential Characteristics
Essential Characteristics
Non-Essential Characteristics
= sig n
Examples
Equation
al s equ ssion xpre e o Tw
Non-Examples
3x
+
4
Two cons
Equation
Examples 6 2x =
ble Varia More than one operation
=
7
y= 2 4 + 3 = 7
Grade 7 Mathematics Curriculum Outcomes Outcomes with Achievement Indicators Unit 6
