Using Algebra Tiles to Solve Equations Objective: To understand the different parts of an equation, and use algebra tiles to help us solve problems. 7 Math Unit 3 May 22, 2019

Parts of an Equations! 5x + 4x + 5 = 50 Like Terms constant coefficient variable

SBAC Test ITEMS 3

SBAC Test ITEMS 4

Build this equation 5 + x = 2 On your own: x – 2 = 3 x + 3 = 7 Allow students to build the equation THEN show them the example. Allow them to solve for x as you remind them about inverse operation and isolating the x to solve for x. Remind students that a negative and positive tile is considered a zero pair because a negative and a positive of the same quantity make zero. Remind them whatever you do to one side of the equal sign, you must be do to the other side of the equal sign. Only then should you show them the example of the answer. Allow students to solve 1 step equations in collaborative groups. Provide them with the following problems: x – 2 = 3 x + 3 = 7 7 – x = 9 x – 5 = 1 2 = -x – 4 It is important for students to understand why they can’t leave a variable negative. Although you probably already know…if a variable is left negative, you truly haven’t isolated the variable. If a variable is negative, that means there is a value of -1 attached to it. It means there is a -1 times x. The inverse operation is division, therefore you divide both sides of the equal sign by -1 to truly isolate the variable.

To solve for the variable, you must do the inverse operation. Build this equation 2x = 6 -3x = 15 -12 = -4x 3x = 12 6x = 3 5 = 5x Ask students what the inverse operation of multiplication is? After they say division you can have the discussion about putting tiles into even groups with the x tiles and unit tiles. AND if the unit tiles do not fit into even groups, then they are probably dealing with a fraction or a decimal. Have student work through various problems collaboratively with the tiles. To solve for the variable, you must do the inverse operation. With tiles, in order to divide, you must create even groups of x tiles and unit tiles. x = 3

When should we NOT use tiles?   Let’s say this piece of paper represents our whole x. How many sections are there on the paper? How many positive tiles will go in each section? Using the visual, what is the value of x? Students must realize when the tiles are not a good idea to use. With division problems such as x/6 = 2, tiles can be confusing and are truly more of a nuisance than a help. Instead, student should see the pattern of using the inverse operations when solving equations and begin to apply this practice with division problems. Students should view a problem like x/6 = 2 as “x groups of 1/6 equals 2” We have to think of 𝑥/6 as 1/6 times x. We can solve for x by thinking, I need 6 groups of 2 to make one whole. This means we will need 6 parts to make one whole, and there are 2 positives in each part. How many positives are there in 1 whole x? What the students will find, is that they are multiplying 6 by 2 (6 groups OF 2) to find what x equals. Intervention

To solve for the variable, you must do the inverse operation. Build this equation This can stand for x/5     (5) (5) Provide this type of problem and discuss what portion of the equation can be solved with tiles and what cannot. Allow students who need to use tiles to add 6 to each side of the equal sign, to do so. However, when they are solving for x, allow them to see that it is easier to perform the inverse operation to solve for x. Ask students what the inverse operation of division is? After they say multiplication you can have the discussion about how the “x” cannot be split or cut. Students should discover that there will be 10 tiles in each of the 5 sections that make up x. They will quickly see that they can just multiply to solve for x. Have student work through various problems collaboratively with the tiles. Gauge your students understanding and provide extra problems to use with algebra tiles as needed. To solve for the variable, you must do the inverse operation. With tiles, you must isolate x first, then you can figure out what x equals. x = 50

Make even groups with each x Activity… Use your algebra tile mat and algebra tiles, to solve the following equations. 2x – 3 = 9 5 – 5x = -1 3x – 1 = 8 7 = 5x + 2 2x + 3 = -7 4x – 2 = -10 Zero pairs Work with the students on the following problems. Students might have an issue with using tiles with division. (Example is provided). 2x – 3 = 9 (example provided) 5 – 5x = -1 (you may need to have a conversation regarding the negative attached to the 5x.) When you feel your students are ready for independent practice allow them to do so. 2x + 3 = 3x (allow students to determine they have to combine like terms here) Gauge your students understanding and provide extra problems to use with algebra tiles as needed. Make even groups with each x x = 6