Lesson: Lesson 9 Working with Algebra Tiles

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Lesson Objective

SWBAT use physical models to perform operations with polynomials

Lesson Plan

Opening

Remind students about what each tile represents (they have not seen this since Lesson 1). Yellows represent x2, x, and 1 and reds represent –x2, -x, and -1 respectively. Yellow plus Red of the same shape = 0.

Example 1: Use Algebra Tiles to Find the Sum

  1. 1.     Have students refer to Unit 4 Lesson 1 to model the addition of polynomials.
  2. 2.     Have them draw the first polynomial in the first box
  3. 3.     Then draw the second polynomial in the second box
  4. 4.     Remove any zero pairs by canceling out
  5. 5.     Combine the remaining tiles in the 3rd box to show the sum.
  6. 6.     Have students complete the You Try, drawing the tiles for each polynomial and each step
  7. 7.     Go over the you try

 

Example 2: Use Algebra Tiles to Find the Difference

  1. 1.     Have them draw the first polynomial in the first box
  2. 2.     Then draw the second polynomial in the second box
  3. 3.     Distribute the negative by visually showing the change in color (positive Yellow becomes negative Red and negative Red becomes positive Yellow) in the second box.
  4. 4.     Remove any zero pairs by canceling out.
  5. 5.     Combine the remaining tiles in the 3rd box to show the sum (note to students that you are “subtracting” by using the additive inverse)
    1. a.     Note, the dialogue box to the right highlights this: Subtraction means to add the inverse. We find the opposite by flipping/changing the color of our tiles.
    2. 6.     Have students complete the You Try, drawing the tiles for each polynomial and each step
    3. 7.     Go over the you try

Example 3A: Using Algebra Tiles to Multiply Binomials (Area Model)

  1. 1.     Explain to students that this is a visual way to show the multiplication of binomials
  2. 2.     Ask students how they would represent x and +3 using tiles, then draw the tiles in horizontally
  3. 3.     Ask students how they would represent 2x and + 1 using tiles. Then draw the tiles vertically
  4. 4.     Multiply and show that x • 2x would give you 2x2 (and that’s why you’d get 2 big squares!)
  5. 5.     Multiply and show that 3 • 2x would give you 6x (and that’s why there’s 6 sticks)
  6. 6.     Multiply and show that 1 • x would give you 1x (and that’s why you have the other stick)
  7. 7.     Show that 3 • 1 gives you 3 (and that’s why you have 3 little boxes)
  8. 8.     Ask how many total sticks there are (that’s combining like terms!)
  9. 9.     Summarize by explaining that this is a visual way of representing the foil method
  10. 10.  Have students complete the You Try
  11. 11.  Go Over the You Try

Example 3B: Using Algebra Tiles to Multiply Binomials (Area Model)

  1. 1.     Students now need to work backwards.
  2. 2.     One helpful tip is discussing the idea of area and length and width. I drew dotted lines to show that the original terms can’t be longer or wider than the area
  3. 3.     First have students figure out what terms should go where (x and 5 on the horizontal and x and 2 on the vertical). Then, taking what they know about signs and factoring to fill in the signs of the constants.
  4. 4.     Summarize by explaining that this is a visual way of representing factoring a trinomial
    1. a.     Note: it might help to have students identify and write the trinomial first, then factor it to connect the tiles to previous knowledge.
    2. 5.     Have students complete the You Try
    3. 6.     Go Over the You Try

Independent Practice

Have students work through independent practice.

Closing

Have students share out and summarize what they learned today.

Assessment

Collect the Independent Practice as a Lesson Assessment.


Reflection:

What works:  Having manipulatives in front of students to help work through problems is a huge plus. Also, when using the tiles, having students do the problems using the algorithm on a sheet of loose leaf helps builds connections

 

What didn't work: Some students demonstrated a misunderstanding of what a term like 2x actually means. They had a tough time seeing 2x as 2 of an unknown quantity, and thus did not make the connection of the coefficient being the number of tiles until it was explicitly discussed and demonstrated. Lastly, students had trouble with the area model and the different signs – it was a key step to have students first write the trinomial as represented by the tiles, then work backwards.

 

Lesson Resources

Unit 4 Lesson 9 Working with Algebra Tiles.docx  
268

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