Showing patterns in T-tables

Showing patterns in T-tables

Lessons

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.
  • Introduction
    Introduction to Showing Patterns in T-tables:
    a)
    What is a T-table?

    b)
    How do you show a growing pattern in a T-table?

    c)
    How do you show a shrinking pattern in a T-table?

    d)
    Summary of patterns in T-tables


  • 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?
    a)
    Fill in the circles
    Showing Patterns in T-tables

    b)
    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?
    a)

    Showing Patterns in T-tables

    b)

    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.
    a)

    Showing Patterns in T-tables

    b)

    Showing Patterns in T-tables


  • 4.
    T-table patterns: word problems
    Complete the T-table for the scenario and answer:
    a)
    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

    b)
    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

    c)
    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

    d)
    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