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Pattern Building

Composite Rules

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What comes next?

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What comes next?

Whiteboard Questions

  • When moving to the next figure, what is growing and what colour is the same?
  • How many blocks do you need for:
    • Figure 4?
    • Figure 10?
    • Figure 15?
    • Figure 100?
  • What does Figure 100 look like?
  • What does Figure Zero look like?

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Patterns

  • For figure 5:
    • ___ yellow blocks
    • ___ groups of 5 red blocks

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Patterns

  • For figure 5:
    • 3 yellow blocks
    • 5 groups of 5 red blocks
  • For figure 20:
    • __ yellow blocks
    • __ groups of 5 red blocks

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Patterns

  • For figure 5:
    • 3 yellow blocks
    • 5 groups of 5 red blocks
  • For figure 20:
    • __ yellow blocks
    • __ groups of 5 red blocks
  • Want a rule for total number of blocks:

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Patterns

  • For figure 5:
    • 3 yellow blocks
    • 5 groups of 5 red blocks
  • For figure 20:
    • 3 yellow blocks
    • 20 groups of 5 red blocks
  • Want a rule for total number of blocks:
  • For figure N:
    • 3 yellow blocks
    • N groups of 5 red blocks

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Patterns

  • For figure 5:
    • 3 yellow blocks
    • 5 groups of 5 red blocks
  • For figure 20:
    • 3 yellow blocks
    • 20 groups of 5 red blocks
  • Want a rule for total number of blocks:
  • For figure N:
    • 3 yellow blocks
    • N groups of 5 red blocks
  • Total number of blocks:
    • B=5N + 3

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What Changes? What Stays the Same?

B=5N+3

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Whiteboard Questions

  1. What changes at each position?
  2. How does it change?
  3. What does not change?
  4. Which part of the rule is represented by the red blocks?
  5. Which part of the rule is represented by the yellow blocks?

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In Groups

  • Use snap cubes
  • Build first three figures for the rule:

Number of blocks = figure number x 5 + 2

(This can also be written as y=5x+2 if x is the figure number and y is the number of blocks)

  • Use different colours for the constant and changing blocks
  • When done, do a gallery walk

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In Groups

  • Come up with a pattern:

Number of blocks = figure number x ______ + _______

(B=_N+_ or y=_x+_)

  • Build the first three figures with your pattern

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  • Use different colours for the constant and changing blocks
  • When done, do a gallery walk
  • (What does figure zero look like?)

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In Groups

  • Using your same pattern:

Number of blocks = figure number x ______ + _______

(B=__N+___ or y=__x+__)

  • Build another block set that uses the same pattern but looks completely different
  • Then a third completely different set with the same pattern

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Whiteboard Questions

  1. How many blocks in 5th figure?
  2. How many blocks in 10th figure?
  3. How many blocks in the 21st figure?
  4. How many blocks in 100th figure?

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  • If you had 100 blocks, could you build the 13th figure?
  • If you had 100 blocks, could you build the 20th figure?
  • If you had 100 blocks, could you build the 35th figure?
  • If you had 100 blocks, could you build the 50th figure?

Explain how you know.

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