1. Models of algebraic concepts Y2Y2 XY X X2X2 Y 1 PowerPoint Presentation Developed by Harvey Almarode Modified by Carrie Newman Title Slide

2. The Equation Mat The Equation Mat consists of two Basic Mats with an equal sign in between. + _ + _ =

3. The Pieces X The rectangular yellow pieces will represent the variable, or the number you don’t know yet. 1 The small green cubes will represent one whole. If there are more than one, just count them up! The whole point of algebra is to get that yellow variable block all by itself on one side of the equal sign so you can find out its value!

4. Anything in the top (white) part of your equation math means that it is positive, or that you are ADDING. + _ What does this say?! If you said “x+2” you were right!

5. Anything in the bottom (gray) part of your equation math means that it is negative, or that you are SUBTRACTING. + _ What does this say?! If you said “x – 3” you were right!

6. If you ever have something that matches on the top (positive) and bottom (negative) of the mat, you will call it a “zero pair”. These things will cancel each other out because they are equal to ZERO! + _

7. Don’t believe me? I’ll prove it! Hold out your hand Add (+)2 green cubes to your hand. Now take away (-) 2 green cubes from your hand You’re left with ZERO green cubes, aren’t you?! That’s why we call it a zero pair! Just remember- you can only take away zero pairs on the SAME SIDE OF THE EQUAL SIGN!

8. What equation is modeled on the Equation Mat? Answer:X + 4 = 12 + __ = + X 1111111111 111111

9. What equation is modeled on the Equation Mat? Answer:X - 3 = 5 + __ = + X 111 111 11

10. What equation is modeled on the Equation Mat? Answer:X + 3 = 8 + __ = + 111 1 11 111 11

11. Show X - 3 = 7 + __ = + X 111 1111 111 Add 3 to each side of the Equation Mat 111 111 Remove the Zero Pair Answer:X = 10 Read the results

12. You can check your answers by replacing your yellow “x” block with the number of green “1” cubes that you came up with in your answer. If you come up with the same amount of green cubes on each side of the equal sign, your equation is balanced and your answer is correct! Let’s try some now!

13. + __ = + Set up X – 2 = 3 X 11 111 Add 2 to each side of the equation mat 1111 Remove the zero pair Read the resultsX = 5 Let’s check to make sure by replacing the variable in the original equation (X – 2 = 3) with our answer of 5

14. + __ = + 1 1 1 11 X Set up your original equation Replace the variable “X” with the value you found, 5 11 1 11 Now what does your equation say?5 – 2 = 3! Is that true? Then your value of x was correct! Great job!

15. + __ = + Let’s try one more together! Set up X + 4 = 9 on your mat X 1111 1 111 1 11 1 1 Subtract 4 from each side. 1111 1 111 Get rid of your zero pairs Read your results: X = 5Check your answer! Set up the original equation.

16. + __ = + X 1111 1 111 1 11 1 1 Now replace your variable with your answer. 1 1 1 1 1 Now you have 9 = 9, is that true?! Your equation is balanced and your answer is correct!

17. Extension: Can you set up and solve these problems on your mat? Sam has some baseball cards and his mom brings him 5 more. Now he has 7. How many did he begin with? + __ = + X 1 1 1 1 111 1 1 1 1 1 1 1 1 1 1 11 111

18. Let’s talk algorithms! When we talk about using the standard algorithm, we mean that we use numbers and operations to solve. It’s exactly what we’ve been doing with our blocks, but we will use inverse operations to solve. For example… Suzie had some apples and picked 3. Now she has 5 apples. What does that look like?! X + 3 = 5 What operation do you see?!Addition! What is the inverse operation of addition?!Subtraction!

19. X + 3 = 5 So let’s subtract 3 from both sides to get the variable by itself! - 3 -3 Now get rid of your zero pairs 2 +3 and -3 cancel and 5 – 3 = 2 Now to check, go back to your original equation… X + 3 = 5 … and replace the variable with your answer to check! 2

20. Let’s Practice! X – 2 = 3 Draw a Picture:Show your steps: Solution: Check:Write a word problem: Carrie had some balloons and 2 flew away. Now she has 3. X – 2 = 3 +2+2 X = 5 5 – 2 = 3 X = 5