• 2-5 Distributing, Combining Like Terms, and Special Case Equations

    Posted by Kevin Cassidy on 11/1/2018

    For two days, we tackled several learning targets. Each one has it's own notes. For one video lesson that reviews all concepts, see this (it's the same as my previous blog post as it covers all the material). Distributing, collecting like terms, and special cases.

    1) I can distribute a number to remove parentheses in an equation. 

    Explanation: This is like ordering a 2 burger value meal that comes with a drink and fries. If five people order it, then they get 10 total burgers, 5 fries, and 5 drinks. Algebraically, we do with when we see 3(x+2) and we multiply the number outside by each thing inside to get 3x + 6. It's like multiplying the number of orders by each of the items in the meal. 

    distribution

     

    2) I can collect like terms in an equation. 

    Explanation: This is like having bannas and apples in a row. Three bananas, then two apples, then two more bananas. We can combine the "like terms;" in other words, put all the banans together, so we have five bananas and two apples. Algebraically, this might look like 3b + 2 +2b = something. We can combine the b's to get 5b + 2. We should always circle the operation with the number to keep track of positive and negative terms.

    collectingliketerms

     

    3) I can solve a "special case equation" and can recognize when a) x has no solution (1=0) or b) x is all real numbers (x = x, or 1 = 1, or same = same).

    specialcases

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  • Lesson 2-4: Variables on Both Sides of the Equation

    Posted by Kevin Cassidy on 10/30/2018

    Learning Target: Students will be able to move variables to one side of the equation, using addition or subtraction. 

    In this lesson, we looked at several manipulatives to model the problem, including algebra tiles and the balance scales with chess pieces in class. Essentially, we can subtract x's from both sides of the equation so that one side of the equation collects the x's and one side collects the whole numbers. Here's our notes:

    variblesonbothsides1

     

    variablesonbothsides2

     

    variablesonbothsides3

     

    To review, here's a video lesson that covers material from lesson 2-4 and 2-5.

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  • 2-3 Writing two step equations

    Posted by Kevin Cassidy on 10/25/2018

    Learning target: I can write an equation based on a word problem or a number sentence. 

    In this lesson, we translated words into equations, like the ones we've been looking at (3x + 2 = 8). 

    Here's some vocab we added to our notebook to help with the problems. The key idea is to brainstorm above the words for each part of the word problem. 

    1

    Students should be able to solve the following two problems:

    Write as an equation:

    Three less than eight times a number is 61.

    Answer:  -3 + 8x = 61

    or:          8x - 3 = 61

    Also, based on a word problem, students should be able to set up and solve:

    c

    To review, watch this video: 2-3 Writing equations

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  • 2-2 - Two step equations

    Posted by Kevin Cassidy on 10/23/2018

    Learning Target: Students will solve two step equations using opposite operations.

    Example:

     twostep1

    twostep2

     

     

    Stuck? Try the balance scales here:

    Balance Scales - EquaTwo step Equations (Khan Academy)tions

    Also, use the khan acedemy review videos:

     

    Hw: page 125 all, page 127-128 all. Assigned Monday 10/22 and Tuesday 10/23. 

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  • 2-1 One step equations with rational numbers

    Posted by Kevin Cassidy on 10/19/2018

    For the past three days, we've worked on the following learning target:

    I can solve a one-step equation that has rational number coefficients. 

    coefficient is the number in front of a variable. For example, 2x, the 2 is the coefficient. 

    Here's examples and notes:

    a

    b

    Video lesson to review:

    One step equations with rational coefficients

     

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  • Chapter 2 - Review of One step equations

    Posted by Kevin Cassidy on 10/17/2018

    For about 2-3 days in class, we worked on the following learning target:

    I can solve a one-step equation by using opposite operations.

    Example and notes:

     

    onestep1

    onestep2

    KEY IDEA: Balance... whatever we do to one side of the equation, we have to also do to another.

    KEY IDEA 2: In order to solve for the variable, we have to "undo" whatever is happening to it.

    To review this idea with basic addition and subtraction problems with variables, see the following video lesson: 

    Balancing Equations

     

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