Using Algebra Tiles to Combine Like Terms Objective: To understand the different parts of an equation, and use algebra tiles to help us solve problems.

Important Vocabulary! Equation – An equation is a mathematical statement that uses an equal sign to show that two expressions have the same value. To solve an equation that contains a variable, find the value of the variable that makes the equation true. This value of the variable is called the solution of the equation. Term – the parts of an expression that are added or subtracted. Like Term – Two or more terms that have the same variable raised to the same power. Coefficient – The number that is multiplied by a variable in an algebraic expression. Constant – A value that does not change. Equivalent Expression – Equivalent expressions have the same value for all values of the variables.

Parts of an Expression! 5x + 4x + 5 Like Terms constant coefficient variable

Your Turn… 6y + 5x + 2y = 42 Coefficients? Variables? Like Terms? Constant? Coefficients = 6, 5, 2 Variables = y and x Like Terms = 6y and 2y Constant = 42

Discovery What do you think the different tiles stand for? Why? Even though students may have had experience with the algebra tiles, most probably have not. Allow students 5 minutes to “play” with the tiles so they can get it out of their system. Have them make a separate pile of each shape on their desks. Have them place their Tile Mat in front of them. Ask students what they think the tiles stand for and why. (Some students may already know…) Most students will try to stack the unit tiles end to end on top of the x tile to equate say the x tile equals 5. It is important you clarify this misconception. When the student stack them end to end there is a small section which the unit tiles do not cover. This is the “unknown” portion of the x tile and the reason it is represents x. The students may discover that the “short” side of the x tile is the same height as the unit tile. So, x times 1 equals x. This discovery of how the sides of the tiles relate to each other will be important as they finish middle school math and move into high school math. Allow the student to discover why the blue square is x2. Allow them to take 2 x tiles and put them against the length and width of the blue square to see it stands for x • x or x2 The single unit tile stands for 1.

What do these stand for? Why? Algebra Tiles Have student flip the tiles over and see that the opposite sides are red. Ask them why they think they are red and what they stand for? If students do not discover the red tiles are negative representations of that particular tile, tell them. What do these stand for? Why?

Let’s Try It Represent the following equations on your tile mat. Compare your answer with a neighbor. Assist each other as needed. 5 + x = 2 5 – 5x = -1 2x – 5 = 9 Ask student to use the tiles to represent (NOT SOLVE) the following equations on the tile mat: Now ask students to return to the first equation, build it again and model how to solve the equation. Note: Ask students “what does it mean to isolate?” Give real life examples of what “isolate” means and relate it back to what it means to isolate x. Since we need to isolate the x to solve the equation, we will need to turn the 5 positives into zero. How can we get those 5 positives to make zero? We will use inverse operations by placing 5 negatives with the 5 positives. An equation is like a balance. If we place 5 negatives on one side of the equation, we MUST do it to the other side of the equation as well. We will be left with x on one side of the equal sign, and 2 positives and 5 negatives on the other side of the equal sign. Remove the zero pairs, and students will have 3 negatives left. This means the answer will be x = -3.

Combining Like Terms x2 What does this tile represent? What do these tiles represent? -x2 x -x Students should be familiar with the algebra tiles from the activity in week 1 and know what each tile represents. This is just an overview. When combining like terms, students need to discover that “plus negative” is the same as “minus” or subtraction (Most students will come to the conclusion on their own, but some will be confused with how we know we are subtracting if there is no minus sign. Teachers must clarify the negative sign IS the minus sign). Have a brief discussion about zero pairs. Clarify any misconceptions. Briefly talk about combining tiles. Provide students with examples, “Do you think I can combine the x2 tile with the unit tile? Why or why not?” Allow students to discover (with your lead) that only like-tiles can be combined. Gauge your students understanding and provide extra problems to use with algebra tiles as needed. 1 -1

These are NOT the same shape Combining Like Terms 4x + 5 Can these be combined? Explain your reasoning. 4x + 5x Can these be added together? Explain your reasoning. These are NOT the same shape In the first example, the tiles are different shapes and different sizes (different colors too since they are positive). In the second example, the tiles are all the same size and same shape. Therefore, they can be combined together. Have a discussion about whether tiles are be combined if they are all red (or negative). Clarify that in order for tiles to be combined, the shape of the tile is important. Gauge your students understanding and provide extra problems to use with algebra tiles as needed.

Let’s Try It! 3x + 4 – 2x 3x + 5 2x2 – 6x +2 x2 – 2x – 3 3x2 + 3x – 5x Represent the following expressions on your tile mat. Compare your answer with a neighbor. Assist each other as needed. 3x + 4 – 2x 3x + 5 2x2 – 6x +2 x2 – 2x – 3 3x2 + 3x – 5x Ask student to use the tiles to represent (NOT SIMPLIFY) the following expressions on the tile mat: 3x + 5 3x + 4 – 2x 2x2 – 6x +2 X2 – 2x – 3 3x2 + 3x – 5x Some misconceptions include: Some students will be very literal thinkers with the tiles. When asked to display 2x some students will put down 2 unit tiles and an x tile instead of 2 x tiles. Now ask students to return to the last expression, build it again and model how to re-group the tiles by combining “like” tiles together. If there are any zero-pairs, remove them from the mat. Gauge your students understanding and provide extra problems to use with algebra tiles as needed.

Combining Like Terms: Build It! x2 x2 x x x 1 1 1 2x2 + 3x + 5 +x2 – 5x – 1 Try these: 2x2+4x+2x2 – x 3x2 – 2x – 1 – 3x2 – 2x – 2 x2+2x+1 – 3x2 – x 3x2 – 3x + x2 – 1 + 2x – 3 1 1 x2 -x -x -x -x -x -1 The teacher will display on the PPT the first polynomial. Students can display the tiles as you display the tiles on the PPT. Allow students to see the zero pairs and the resulting answer. You may need to complete additional problems with students. Have students put the like tiles together. This will help them see the zero pairs and be able to rewrite the expression easier. Gauge your students understanding and provide extra problems to use with algebra tiles as needed.

Combining Like Terms: Build It! x2 x2 x x x 1 1 1 2x2 + 3x + 5 +x2 – 5x – 1 Try these: 2x2+4x+2x2 – x 3x2 – 2x – 1 – 3x2 – 2x – 2 x2+2x+1 – 3x2 – x 3x2 – 3x + x2 – 1 + 2x – 3 1 1 x2 -x -x -x -x -x -1 The teacher will display on the PPT the first polynomial. Students can display the tiles as you display the tiles on the PPT. Allow students to see the zero pairs and the resulting answer. You may need to complete additional problems with students. Have students put the like tiles together. This will help them see the zero pairs and be able to rewrite the expression easier. Gauge your students understanding and provide extra problems to use with algebra tiles as needed. What’s left?? 12

Summary Write 2 – 3 sentences explaining how you use algebra tiles to combine like terms. Pretend you are teaching this concept to a 4th grader.