Mathematics Grade 7 File Name: Unit 1.8 Lesson

Unit 1.8 Patterns and Relations Handout.doc 1

Unit 1.8: Patterns and Relations Lesson: Reading and Writing Equations Objectives: Students will use learn to create expressions and equations using algebra tiles which contain only positive whole numbers. Students then will learn to solve simple algebraic equations using positive numbers by the use of algebra tiles. Procedure: Algebra is not much use if we do not use it to solve questions and problems. So in order to do this we will start with a manipulative called algebra tiles. Algebra tiles are small rectangles and squares we use to solve equations. Do several examples on the overhead, Creating Expressions using algebra tiles: An algebra tile is a small square or rectangle. The rectangle is used to represent a variable, we now will start to call this variable x all the time. The small squares (we will use big ones later) are used to represent whole numbers. So:

= x, the rectangle is used to represent a variable.

= 1, this is used to represent a whole number in this case a 1. Example: So to create an expression x+4, we would show:

This totals to give us x+4

Mathematics Grade 7 File Name: Unit 1.8 Lesson

Unit 1.8 Patterns and Relations Handout.doc 2

Example: Create an expression using algebra tiles for the expression 2x+3

Example: Create an expression using algebra tiles for the expression 4x+1

Example: Create an expression using algebra tiles for the expression 3x+6

Example: What expression do the following algebra tiles represent?

Since there is only one rectangle, this represents a x, and the 5 small squares represent 5 ones, so the expression is ____________.

Mathematics Grade 7 File Name: Unit 1.8 Lesson

Unit 1.8 Patterns and Relations Handout.doc 3

Example: What expression do the following algebra tiles represent?

This set of tiles represents ___________________. Now that you know how to create an expression, the next step is to create an equation. Remember that an equation has two sides, a left and a right, which are balanced (equal). They are separated by an equal sign. Algebra tiles do not have an equal sign so we use a vertical line to show the equal sign. Example: 2x+3=7 would be shown the following way:

The expressions on each side are created like we did before.

Mathematics Grade 7 File Name: Unit 1.8 Lesson

Unit 1.8 Patterns and Relations Handout.doc 4

Lets do a few more: Example: Create an equation using algebra tiles for the equation 3x+2=8

Example: Create an equation using algebra tiles for the equation 2x+4=8

Mathematics Grade 7 File Name: Unit 1.8 Lesson

Unit 1.8 Patterns and Relations Handout.doc 5

Identifying Equations from Tiles: Now lets move the other way, I will give you the tiles and you tell me what the equation is: Example: What is the equation for the following tiles?

_______________________________

Example:

What is the equation for the following tiles?

_______________________________

Mathematics Grade 7 File Name: Unit 1.8 Lesson

Unit 1.8 Patterns and Relations Handout.doc 6

Example:

What is the equation for the following tiles?

_______________________________

Solving Equations: Now that we can create expressions and equations using algebra tiles, it is time to work with solving equations. To solve an equation means that you want to know what the x variable represents. This is some times called isolating the variable. There is one Major rule in solving equations: DO THE SAME THING TO BOTH SIDES. Lets start: First we need an equation to solve: X+1=6

If you think of an equation like a teeter-totter, where the sides must stay balanced, it is

easy to solve equations. We want the , to be by it self. So to do that

we can take a from each side. Because we do it from both sides, the equation stays balanced (both sides equal).

Mathematics Grade 7 File Name: Unit 1.8 Lesson

Unit 1.8 Patterns and Relations Handout.doc 7

So it looks like this:

This leaves the following after the tiles have been removed from each side:

So _________________________________________

Mathematics Grade 7 File Name: Unit 1.8 Lesson

Unit 1.8 Patterns and Relations Handout.doc 8

Lets try another one: Example: Equation: x+4=7 First draw the equation using algebra tiles.

Now to solve this you need to get the x tile alone, how do you do that? ________ __________________

This leaves:

So the solution is : ___________________________________

Mathematics Grade 7 File Name: Unit 1.8 Lesson

Unit 1.8 Patterns and Relations Handout.doc 9

Another type of equation that we found was when a variable is multiplied by a number. For example, a number multiplied by 2 is 6. The equation is 2x=6 As tiles this looks like:

To solve this equation, we have to use grouping. So line up the one tiles in two rows so that each is across from an x tile. Make sure that the ones are equal in amount.

Now each x tile represents 3 ones. A little separation makes this easy to see.

Each x tile is equal ____________________________________

Mathematics Grade 7 File Name: Unit 1.8 Lesson

Unit 1.8 Patterns and Relations Handout.doc 10

Lets try another: Draw the tiles for the equation 3x=12, and solve for x. Now group them so that each x tile has an equal amount of one tiles across from them.

By looking at one x tile and what is across from it, we can solve x for 4. So ________________________________

Mathematics Grade 7 File Name: Unit 1.8 Lesson

Unit 1.8 Patterns and Relations Handout.doc 11

Now lets combine the two together. Example: 2x+1=7

To solve this we need to first remove the 1-tiles like we did before. So now we have the following after the 1 tile was removed from each side.

Mathematics Grade 7 File Name: Unit 1.8 Lesson

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Since we have two x tiles on the left, arrange the one-tiles into two equal groups. So ___________________________________. Ok, lets do another example. Example: Equation this time is 3x+5= 11 First we have to remove the one-tiles from each side equally.

Mathematics Grade 7 File Name: Unit 1.8 Lesson

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This leaves: Now group them up into groups: So, _____________________________________

Mathematics Grade 7 File Name: Unit 1.8 Lesson

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Applications: Example: Bob is working for his uncle picking strawberries after school. He gets paid 5 dollars a day, plus he gets 3 dollars for every pail of strawberries he can pick. On Monday he was paid 14 dollars. Create an equation using “P” for the number of pails of strawberries he picked. Show this equation using tiles and demonstrate with the tiles how to solve for how many pails of strawberries he picked. Solution: Equation is ___________________________ Tiles are: Tile Solution is: He picked ____________ of strawberries.

Mathematics Grade 7 File Name: Unit 1.8 Lesson

Unit 1.8 Patterns and Relations Handout.doc 15

Example: A class of 18 students were divided up into groups of 3 to play monopoly. How many groups were there? Equation is _________________ Create the equation using tiles. Group the tiles. Each group contained ___________________.

Mathematics Grade 7 File Name: Unit 1.8 Lesson

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Example: A class has 5 more boys then girls. If the class has 17 students, how many are girls are there? The equation is: ______________________ Tiles:

The soloution is: ________________________ There are ____ girls in the class.

Mathematics Grade 7 File Name: Unit 1.8 Lesson

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Example: Candy bars come in packages of 4 at the fair. If Franklin purchases a total of 20 bars, how many packages did he buy? Equation is :_____________________ Tiles: Grouping gives: Solution: _______________________ Franklin purchased _____ packages of bars.

Mathematics Grade 7 File Name: Unit 1.8 Lesson

Unit 1.8 Patterns and Relations Handout.doc 18

Last one: A class was divided into groups of 4 with 2 left over to do a project on the Amazon River Basin. If the class had 18 students, how many students were in each group? Equation is: __________________________ Tiles: Now solve the tiles: Solution: _____________________ Each group has _____ members in it.

Mathematics Grade 7 File Name: Unit 1.8 Lesson

Unit 1.8 Patterns and Relations Handout.doc 19

Students are to complete the following assignment: Page 41&42 #1- 10