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pattern talk 21

Picture
Pattern #124
Student 1
  • I see the diagonal, then 3 groups of n on the outside, then the bottom group. My equation is D = (n+2) + 3n + (n+1).

Student 2
  • Left and right, each is n. Top and bottom, each is (n+2). The leftover dot is 1 less than n. My equation: D = 2n + 2(n+2) + (n-1).

Student 3
  • I saw these 4 in the right corner in every step. My equation is D = 4 + 2n + 2(n-1) + (n+1).

pattern talk 22

Picture
Pattern #126
Student 1
  • I see top and bottom as 2 groups of (n-1). The middle has (n+1) by (n). My equation is R = 2(n-1) + n(n+1).

Student 2
  • I move one rod from the bottom row to the top to make it a complete “rectangle” of (n+2) by (n). The leftover rods on the bottom row is (n-2). My equation is R = n(n+2) + (n-2).

pattern talk 23

Picture
Pattern #130
Student 1
  • I always see 2 groups of (n+1). The leftover dots are (n-1). My equation is D = 2(n+1) + (n-1).

Student 2
  • I see the bottom dot separately. The rest are n groups of 3. So, it’s D = 3n + 1.

Student 3
  • I saw step 1 in every step, so a constant of 4. Then I see (n-1) groups of 3. My equation is D = 4 + 3(n-1).

Student 4
  • I saw (n+1) groups of 3 dots. But there are always 2 [red] dots missing. So, D = 3(n+1) – 2.

Student 5
  • I see 4 groups of n. But there’ll be overlaps to subtract. That overlap is (n-1). My equation is D = 4n – (n-1).

Student 6
  • I always see two groups of 2 on the outside. The middle dots are (n-1) groups of 3. My equation is D = 2(2) + 3(n-1).

pattern talk 24

Picture
Pattern #106
Didn't realize we repeated a pattern. We did this already in Pattern Talk 15.

Student 1
  • I see a square of side n. The leftover is 2 groups of n with overlap of 1. My equation is A = n^2 + 2n – 1.

Student 2
  • I see 2 overlapping squares. The overlapped region is also a square. My equation is A = 2n^2 – (n-1)^2.

Student 3
  • I see a large square that’s always missing 2 pieces: A = (n+1)^2 – 2.

Student 4
  • I see 2 groups of n on top and bottom. The middle is a rectangle of dimensions (n-1) and (n+1). My equation is A = 2n + (n-1)(n+1).
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  • NT 1-4
    • PT 1-4
  • NT 5-8
    • PT 5-8
  • NT 9-12
    • PT 9-12
  • NT 13-16
    • PT 13-16
  • NT 17-20
    • PT 17-20
  • NT 21-24
    • PT 21-24
  • NT 25-28
    • PT 25-28
  • TEACHERS