2. ALGEBRA TILES TUTORIAL The four basic operations demonstrated using signed numbers created by J. Wright Hit the Back Arrow at any time to end the presentation

3. ALGEBRA TILES TUTORIAL Click “Explanation” for the entire show or click on an operation. Explanation Add Subtract Multiply Divide

4. Our Tiles: I’m equal to +1!! I’m equal to -1!! + -

5. The Rules: Rule #1: a + (- a) = 0 Rule #2: a + 0 = a = 0 + + = +++ - - + Add Subtract Multiply Divide Home

6. Addition (Both +): Solve the following problem using tiles: 2 + 3 Model 2… Model 3… Addition means to combine, so….. = 5 ! ++++++++++

7. Addition (Both -): Solve the following problem using tiles: -2 + (-3) Model -2… Model -3… Addition means to combine, so….. = -5 ! - ----- ----

8. Addition (+ and -): Solve the following problem using tiles: 2 + (-3) Model 2... Model -3… Addition means to combine, so….. = -1 ! Zero ++++ --- --- Subtract Multiply Divide Home

9. Subtraction: TAKE AWAY ….OR…. ADD THE OPPOSITE ! 7 - ( + 2 ) ….OR…. 7 + ( - 2 ) MEANS: So… 7 - 2 is equal to...

10. Subtract (+ and -): Solve the following problem using tiles: 2 - (-3) Model 2… Model -3… Subtraction means ADD the OPPOSITE, so….. = 5 ! ++++ --- --- +++ Review Addition?

11. Subtraction (- and +): Solve the following problem using tiles: -2 - (+3) Model -2… Model 3… Subtraction means ADD the OPPOSITE, so….. = -5 ! - -- - ++++++ --- Review Addition?

12. Subtraction (Both + or -): Solve the following problem using tiles: 2 - (+3) Model 2... Model 3… Subtraction means ADD the OPPOSITE, so….. = -1 ! Zero ++++ Add Multiply Divide Home ++++++ --- Zero

13. Multiplication: What does multiplication mean? 2 X 3 The 2 means two piles…..we’ll use rectangles! The 3 represents how many objects are in each pile

14. Multiplication (Both +): Solve the following problem using tiles: 2 X 3 Create 2 piles Fill each rectangle with 3 tiles ++++++ Add contents of all rectangles! = 6 !

15. Multiplication (+ and -): Solve the following problem using tiles: 2 X (-3) Create 2 piles Fill each rectangle with 3 negative tiles Add contents of all rectangles! = -6 ! --- ---

16. Multiplication (Both -): Solve the following problem using tiles: -[2 X (-3)] = -2 X (-3) Add Subtract Divide Home Let’s look inside the brackets... 2 X (-3)…..We already solved that example! Let’s model the answer! But don’t forget the sign outside the brackets!…We want the OPPOSITE so... Let’s rewrite this problem using brackets! --- --- +++ +++ = 6 !

17. Division: What does division mean? 6  2 The 2 means separate into two piles…..we’ll use rectangles! The 6 represents the total number of objects

18. Division (Both +): Solve the following problem using tiles: 6  2 Separate into 2 equal piles ++++++ Add contents of one rectangle! Model 6 +++ = 3 !

19. Division (+ and -): Solve the following problem using tiles: -6  2 Separate into 2 equal piles Add contents of one rectangle! Model -6 = -3 ! --- --- ---

20. Division (Both -): Solve the following problem using tiles: -[(-6)  2] = -6  (-2) Add Subtract Multiply Home Let’s look inside the brackets... -6  2…..We already solved that example! Let’s model the answer! Let’s rewrite this problem using brackets! --- --- But don’t forget the sign outside the brackets!…We want the OPPOSITE so... +++ +++ = 3 !