Solving Equations involving integers Activating Prior Knowledge

Challenge. Find the missing numbers 6 3 5 1 4 9 5 8 7 11 3 6 9 3 5 8 6 10 20 Challenge. Find the missing numbers

As a balance scales, algebra tiles can be used to model and solve equations. Counter represents a + tile Counter represents a - tile Counter represents a variable Quick Review

You will need algebra (integer) tiles You will need algebra (integer) tiles. Maddy has a collection of old pennies. She sells 3 pennies to another collector. Maddy then has 10 pennies left. How many pennies did she have before she made the sale? Let p represent the number pennies Maddy started with. Write an equation that you can use to solve for p. Use tiles to represent the equation. Use the tiles to solve the equation, sketch the tiles you used. + tile - tile variable Explore Compare your equation with that of another group. Share your strategies for solving the equation using tiles. How did you use zero pairs in your solution? Discuss your strategies for finding this solution. Reflect & Share

One way to solve this equation is to use tiles. Let p represent the number of pennies Maddy had before she made the sale. The equation is: p – 3 = 10 One way to solve this equation is to use tiles. Draw a vertical line in the centre of the page. It represents the equal sign in the equation. We arrange the tiles on each side. Recall that subtracting 3 is equivalent to adding -3. So, we represent subtract 3 with 3 red tiles. + tile - tile variable On the left side, put algebra tiles to represent p – 3. On the right side, put algebra tiles to represent 10. Left side. = Right side.

Add 3 yellow unit tiles to the right side as well. To isolate the variable tile, add 3 yellow unit tiles to make zero pairs. Remove the zero pairs. Add 3 yellow unit tiles to the right side as well. + tile The tiles show the solution is p = 13. Maddy had 13 old pennies before she made the sale. - tile Left side. = Right side. variable We can verify the solution by replacing p (white tile) with 13 yellow tiles. Left side. Right side. =

x -3 = 1 Step 1: Isolate the x-tile by adding 3 yellow tiles to each side. The tiles on the left side make zero pairs. Remove the zero pairs. Step 2: The tiles now become, one x tile equals 4 yellow tiles, So, x = 4. Step 3: To verify the solution: Replace the variable tile (white tile) in the original equation with 4 yellow tiles. = MINDS ON..... To solve the equation x – 3 = 1, use tiles to represent the equation. What you do to one side of the equation, you also do to the other side.

Match each equation with an arrangement of tiles a) x + 5 = -6 b) x + 6 = -5 Match each equation with an arrangement of tiles c) x - 5 = 6 d) x - 6 = -5

a) x + 3 =9 d) x – 3 = 9 g) n + 9 = -4 b) 3 = x - 5 e) 5 + x = 7 h) 7 = n - 8 c) 3 + x = 9 f) 8 = n -6 i) 2 = p - 5 Sketch a set of algebra tiles that represents each equation. The solve the equation.

Solve each equation. Verify each solution Between 5 p.m., and midnight, the temperature dropped by 70C to 50C. Write an equation you can solve to find the temperature at 5 p.m. Brook thinks of an integer. She adds 8 to this number and the sum is 3. What is the integer? Write an equation, then solve it using algebra tiles. Complete the following word problems. Use tiles to verify each solution. Solve each equation. Verify each solution x – 25 = 34 x – 132 = -97 54 = 130 + x 176 + x = -24

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