| Solving Multi-Step Problems |
| GOAL: I can solve multi-step equations with one variable. |
| Learning Standards |
Common Core Standard: 7.EE.1 |
| Resources |
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RED BOOK Reference:
Pages: 149 ─ 153
Practice on page 152,
#17-29 odds. |
BLACK BOOK Reference:
Pages: 94 ─ 98
Practice on page 98,
#11-17 odds, #21-29 odds,
#31-37 odds, and #45-53 odds. |
| Lesson Vocabulary |
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| Equivalent Equations |
Equations that have the same solutions. |
| Addition Property of Equality |
Adding the same number to both sides of the equation doesn't change the equation. |
| Subtraction Property of Equality |
Subtracting the same number from both sides of the equation doesn't change the equation. |
| Isolate |
Means to get a variable all alone by itself. You do this using the other properties mentioned in this section.
Once you have the variable all alone by itself, you have the answer to the algebra problem. |
| Inverse Operations |
Inverse operations "undo" other operations. For example, subtraction undoes addition; multiplication undoes division; and so on. Every mathematical operation has an inverse operation. |
| Multiplication Property of Equality |
Multiplying both sides of the equation by the same number doesn't change the equation. |
| Division Property of Equality |
Dividing both sides of the equation by the same number doesn't change the equation. |
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Strategies and Content Practice |
Notes |
Begin
(prepare) |
Check for prior knowledge.
Tell me how much you remember about solving the two-step problems?
Tell me how much you remember about the distributive property? |
Remember, Algebra Uses
"Aunt Sally" Upside-Down
Aunt Sally (add or subtract first)
My Dear (multiply or divide second)
Excuse (exponents come third)
Please (parenthesis come last) |
| Engage |
Have students read pages 94 ─ 98.
Read aloud same with students, emphasize definitions and example problems. Show demonstration videos for Lesson 2-3 (above).
Solving multi-step problems in similar to solving two-step problems.
The main difference between the two versions is that multi-step problems can first be simplified before the two-steps are used to find the answer.
Some of the more common simplifying steps we see in the multi-step problems include:
* Combining Like Terms
Combining Like Terms example problems...
(a) 8A + 10 ─ 5A = -14 Answer: A = ─8
(b) 7 ─ 4B ─ 2 = 29 Answer: B = ─6
* Distributive Property
Distributive Property example problems...
(a) 3(2X ─ 4) = 12 Answer: X = 4
(b) 4(3X + 1) = 15 Answer: X = 11/12
(c) 3 ─ (2X ─ 1) = 8 Answer: X = ─2
* Eliminating Fractions by Multiplying by a Common Multiple of the Denominators
Eliminating Fractions example problems...
(a) ½X + 2/3 = 4 Answer: X = 20/3
(b) 2/3X ─ ½ = 5/12 Answer: X = 11/8
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Assess
(formative) |
After example problems and videos, have students try to solve the Sample Problems below. After students have had time to complete them, click on the Solutions link and go through the step-by-step process for solving each problem. Repeat if necessary with additional example problems in the book and re-assess. |
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| Apply |
For practice, students can either try the Practice Assignment below or from the textbook: Page 98, #11 ─ 53, evens, odds, or all.
Click HERE to download the Practice Assignment.
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Depending on class conditions, you may allow students to work with each other.
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Assess
(formative) |
Click HERE to download the Answers to the Practice Assignment. |
Depending on level of understanding, you may accept this pre-assessment grade and allow students who have mastered these concepts to skip the formal assessment exercise. |
| Apply |
Click HERE to download the Graded Assignment. |
Click HERE to download answers to the Graded Assignment.
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| Sample Problems |
Sample Solutions |
| 2(3x + 5) = 40 |
Click Here for step-by-step solution. |
| 2(x + 2) = 4(x ─ 5) |
Click Here for step-by-step solution. |
| 4(3x + 2) = 9x ─ 10 |
Click Here for step-by-step solution. |
| 7x ─ 3 = 3(3x + 5) |
Click Here for step-by-step solution. |
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