Modelling Equations with Algebra Tiles Jostie & The Dangers of Algebra

Review Recall the integer tiles you have used: Recall what zero pairs are: Represent the following expressions: x + 5 x – 3 3x x + x = +1 (or 1) = -1 = +x (or x) = -x = +x² (or x²)= -x² Combining 1 positive tile and 1 negative tile, you end up with a result of 0 (also called zero model)

Explore Work with a partner. You will need one set of algebra tiles. For the equations below Use algebra tiles to represent each equation, and draw your representation in your notebook 2. Use the tiles to solve the equation, and draw your solutions. 3. Beside each drawing in your notebook, write the equation and solve it algebraically. How did you use zero pairs in your solutions? How do the 2 strategies connect to each other? x - 3 = 102x + 1 = 9

Connection To form algebraic equations using algebra tiles, we draw a vertical line to represent the equal sign. We arrange the tiles on each side of the line to represent an equation. Remember, whatever we do to one side of the equation, we do to the other side. Solution for: x – 3 = 10 On the left side, put algebra tiles to represent (x – 3), and on the right side, put algebra tiles to represent 10 To isolate the x-tile, add 3 positive tiles to make zero pairs. Add the same 3 to the other side. Remove the zero pairs. The tiles now show the solution x = 13 Algebraic Solution: x – 3 = 10 x – = x = 13

Example #2 Solution for: 2x + 1 = 9 Add 1 negative tile to the left side to form a zero model. Do the same to the right side. Remove the zero pairs. Arrange the tiles on each side into 2 equal groups. Compare the groups. One x-tile equals 4 unit tiles. Algebraic Equation: 2x + 1 = 9 2x + 1 – 1 = 9 – 1 2x = 8 2x ÷ 2 = 8 ÷ 2 x = 4

Explore – Part 2 Work with a partner. You will need one set of algebra tiles and a piece of large paper. Fold the paper into 3 sections. Build and solve the equations below using algebra tiles. Complete the following instructions on the large sheet of paper. Section 1:Solve the equation using a diagram Section 2: Solve the equation algebraically Section 3:Verify & Interpret the equation using words 3x - 8 = -x2x + 3 = 4x - 3

Example #1 Solution for: 3x – 8 = -x Algebra Tile / Diagram: In words: Three times a number minus eight is equal to the negative number Algebra: 3x – 8 = -x 3x – = -x + 8 3x = -x + 8 3x + x = -x + x + 8 4x = 8 4x ÷ 4 = 8 ÷ 4 x = 2 Represent the equation using algebra tiles Isolate the x-tiles on the left by adding 8 positive tiles to make zero pairs. Add the same 8 positive tiles to the right side. Isolate the unit tiles on the right by adding 1 positive x-tile. Add the same positive x-tile on the left side. There are 4 x-tiles. So, arrange the unit tiles into 4 equal groups. Therefore, x = 2.

Example #2 Solution for: 2x + 3 = 4x - 3 Algebra Tile / Diagram: In words: Two times a number plus three is equal to four times the number minus three. Algebra: 2x + 3 = 4x – 3 2x = 4x – x + 6 = 4x 2x – 2x + 6 = 4x – 2x 6 = 2x 6 ÷ 2 = 2x ÷ 2 3 = x Represent the equation using algebra tiles Isolate the x-tiles on the right by adding 3 positive tiles to make zero pairs. Add the same 3 positive tiles to the left side. Isolate the unit tiles on the left by adding 2 negative x-tiles. Add the same 2 negative x-tiles on the right side. Take out the zero pairs on both sides. There are 2 positive x-tiles. So, arrange the positive unit tiles into 2 equal groups.

Example #2 Solution for: 2x + 3 = 4x - 3 Algebra Tile / Diagram: Algebra: 2x + 3 = 4x – 3