Pre-Alg Lesson 12

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Pre-Algebra

Lesson 12

Objectives

1. Mapping out whats been done to a variable using order of operations2. Using flow charts to solve equations1. Observing that we have to use reverse order of operations to find the value of a variableMaterials and Handouts Homework

1. Copy the arrows and boxes onto thicker paper and cut them out. Itwould be great if I could put packing tape or laminate over the boxes

so we could write on them with white board markers.

5-10

minutes

Go over homework

5

minutes

Warm-up/Review

1. Have them write in all the values in the flow chart by evaluating each expression2. Then have them write whats being done to the expression each time by puttingthe operation over the arrow.

Instruction

1. Have them work through each of the three flow chart examples.a. I do the first one with them,b. We do the second togetherc. They should be able to do the third on their own.

2. Explain that in the last problem, a new word popped up: equation. What do theythink it means?

a. Equation means: An expression squirted out a specific number whensomething was plugged in originally, so we write it as expression=the

number squirted out

b. Solving an equation means: Taking the number that was squirted out andundoing everything the expression did to find the original number that was

plugged in.

3. Play a game using the manipulatives on the next page.a. They make an expression using the arrows and boxes on the next page.b. I roll a die (dont let them see it) an plug it into the expression and tell them

the result

c.

They have to figure out what I rolled. If they figure it out, they get a point. Ifthey cant figure it out, I get a point.

d. Repeat with a new expression.4. Then go through the real-world Natalia example with them. Make sure theyre

writing the expression, then drawing the flow chart, then writing the equation,

then going backwards to solve for the variable.


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Pre-Algebra Name:_______________

Lesson 12 Date:_________

Intro to Solving Equations Class Work

Exercise 1:Lets review what we did in the last lesson by evaluating some expressions.

a. Fill out the flow chart if

a2a 2a+1

2a+1

3

3(2a+1)a+23(a+2)3(a+2)-1

a2 2a2a2-3

2(a2-3)

a2-3

2


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b. Next to each arrow, show whats being done from one box to get to the next box. Forexample, to go from the middle box, to the right, is being multiplied by so put a

above the arrow.

Exercise 2: These flow chart things are pretty cool right? They show what has been done to a

number or variable andthey show the order of operations as well.

a. Draw the flow chart that created the expression below.

b. If you plug in for what does the expression produce? Fill in the chart:

c. Suppose that, for some reason we know that the expression produced the number 33 andwe want to go backwards to find the value of that produced this result. So we know that

. Put 33 in the box on the far right and try to go backwards to find .

Exercise 3:Lets try it again

a. Draw the flow chart that created the expression

b. If you plug in for what does the expression produce? Fill in the chart:


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c. Suppose that, for some reason we know that the expression produced the number 5 and wewant to go backwards to find the value of that produced this result. So we know that


Exercise 4: And again


b. If you plug in what does the expression produce? Fill in the chart:

c. Suppose that, for some reason we know that the expression produced the number 162 andwe want to go backwards to find the value of that produced this result. So we know that


Exercise 5: Try drawing the whole flow chart for yourself.


b. If you plug in what does the expression produce? Fill in the chart:


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c. Solve the equation

Definition of Equation

_____________________________________________________________

_____________________________________________________________

What it means to solve an equation

___________________________________________________________________

___________________________________________________________________

Exercise 6:Lets see if we can use this new knowledge to help us analyze some real life situations.

a. Natalia brings in a bunch of cupcakes for the students in homework caf. Each student hadtwo cupcakes except for Jess who only had one. There were no cupcakes left over. If there

were students, write an expression for how many cupcakes were consumed.

b.

Make a flow chart of the expression

c. If there had been 6 students in homework caf, how many cupcakes were eaten?

d. If 23 cupcakes were eaten, write an equation that represents this situation

e. Use your flow chart to find how many students there were if 23 cupcakes were eaten.


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Pre-Algebra Name:_______________

Lesson 12 Date:_________

Intro to Solving Equations Homework

1. In the flow chart, one value has been written in with red. Fill in the rest of the flow chart.

2. Consider each flow chart:a. What equation is the person trying to solve? Use the variable

b. Whats the solution to their equation?

c. What equation is the person trying to solve? Use the variable

d. Whats the solution to their equation?

a2a 2a+1

2a+1

3

3(2a+1)a+23(a+2)3(a+2)-1

a2 2a2a2 -3

61

2(a2-3)

a2-3

2


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e. What equation is the person trying to solve? Use the variable

f. Whats the solution to their equation?

3. Draw a flow chart for each equation, then go backwards to solve the equation.a.

b.

c.

d.

4. In a game, someone asked Ari to: Think of a number Subtract 1 from your number Multiply the result by 2 Add 6

a. Draw a flow chart to represent this game.

b. If Ari 10, what equation could you solve to figure out what number Ari originally thoughtof? Find the number.


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5. Lizzy decides to keep a pet T-rex. The T-rex, so that he doesnt hurt anyone, eats steaksevery day. Each steak costs . Lizzy goes out shopping and spends on non steak items

in addition to the money she spends on steaks.

a. Write an expression to represent how much money Lizzy spent when she went shopping.b. Draw a flow chart to represent this expression.

c. If Lizzy spent total, use your flow chart to determine how many steaks a day the T-rex eats.

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Pre-Alg Lesson 12