Showing patterns in T-tables

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Intros
Lessons
  1. Introduction to Showing Patterns in T-tables:
  2. What is a T-table?
  3. How do you show a growing pattern in a T-table?
  4. How do you show a shrinking pattern in a T-table?
  5. Summary of patterns in T-tables
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Examples
Lessons
  1. T-table block patterns: addition
    The T-table shows a growing pattern of blocks. How many blocks are added to make a new figure each time?
    1. Fill in the circles
      Showing Patterns in T-tables
    2. Fill in the circles
      Showing Patterns in T-tables
  2. T-table block patterns: extending a growing pattern
    Extend the number pattern in the T-table. How many blocks are in the 5th figure?

    1. Showing Patterns in T-tables

    2. Showing Patterns in T-tables
  3. T-table line segment patterns
    Complete the growing pattern by drawing line segments. Complete the next figures and fill in the rest of the T-table.

    1. Showing Patterns in T-tables

    2. Showing Patterns in T-tables
  4. T-table patterns: word problems
    Complete the T-table for the scenario and answer:
    1. If Jamie makes $11 every hour that he works at a hot dog stand, how much will he earn for 5 hours of work?

      Showing Patterns in T-tables
    2. Anna is buying trading card packs. She really wants to find a rare card! After buying her first pack, she has $37 left in her wallet. If every card pack is $5, how much money will she have left over after buying the 5th pack?

      Showing Patterns in T-tables
    3. Garrett makes a bracelet design using trapezoids and triangles. At each stage, two triangles and a trapezoid are added. If there are 12 triangles, how many trapezoids were used?

      Showing Patterns in T-tables
    4. Kiera makes an increasing pattern with blocks. The figures in sequence use: 4 blocks, 7 blocks, 10 blocks, and then 13 blocks. After making the fourth figure, she has 15 blocks left. Does Kiera have enough blocks to make the 5th figure?

      Showing Patterns in T-tables
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Practice
Topic Notes
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In this lesson, we will learn:

  • T-table are tools for keeping track of patterns and can help you predict the next terms in the pattern
  • There are growing patterns and shrinking patterns involving figures and blocks/line segments/shapes or more realistic problems involving time and money

Notes:

  • A T-table is a table with 2 columns (or more) that keeps track of patterns.
Showing Patterns in T-tables
    • A T-table is a table with 2 columns (or more) that keeps track of patterns.
    • The second column (right) keeps track of the number of things being counted (ex. blocks, line segments, dollars, etc.)

  • The two types of patterns you will see in T-tables are:
    • growing patterns where the numbers in the pattern are getting bigger (increasing) in each successive line of the T-table
    • shrinking patterns where the numbers in the pattern are getting smaller (decreasing) in each successive line of the T-table

Example: a growing pattern with blocks starts with a 4-block figure and adds 2 each time to make the next figure has a T-table filled out like this:
Showing Patterns in T-tables
  • T-tables allow you to predict and calculate the next terms in the pattern
    • Using the previous block example, you can continue the pattern even if you don’t have pictures of the next figures (4th and 5th figures):
Showing Patterns in T-tables

    • The same idea will apply for a shrinking pattern, but the relationship between each row will be subtracting an amount instead of adding.