Hmong Border Patterns

Lab: Hmong Border PatternsName:______

Directions: Often wall hangings have borders around the edge. In this lab you will create different patterns of tiles and then use these tile patterns to go around the border. You may use colorful triangle pieces, squares, or other shapes to make your patterns. You will need a lot of tiles in 2 different colors.

A Hmong flower cloth square design is placed in the center of a border mat. For a first example, we will use 2 different colored triangle shapes to be in our basic pattern.

The first pattern we will use is:

Tile Design 1: Hmong Design in Border Mat B

Start in the upper left corner and repeat the pattern around the square border. It gives this design.

Notice the basic pattern had 2 values used repeatedly, green and pink. (or gp) The first value of the basic pattern is green (g) and the second value of the basic pattern is pink (p). When we continued with the gp pattern around the Hmong design, we were able to end by placing the last two tiles of green and pink. When this happens, the border is complete, since it was made with complete copies of the basic pattern. (We did not end up placing a green tile on the last square.)

This pattern is considered complete, since it starts with the first element in the pattern in the upper left corner and ends with the last value in the pattern just below it (wrapping the border around the center clockwise).

Using your tiles, try making the following patterns as shown in the table below and find out if each pattern makes a complete pattern.

Using these patterns, which will be complete patterns for this Border problem (Border Mat B):

Basic PatternIs it complete (Y or N)

g pY

gpp______

ggpp______

ggppg______

ppppgg______

Prediction: Create a new basic pattern that you predict will be complete:

Test it out. Did your prediction work? Explain:

In order to make a completed pattern border, what must be true about the basic tile pattern?

Tile Design 2: Now try this for Border Mat A:

Basic PatternIs it complete (Y or N)

g p______

gpp______

ggpp______

ggppg______

ppppgg______

Prediction: Create a new basic pattern that you predict will be complete:

Test it out. Did your prediction work? Explain:

In order to make a completed pattern border, what must be true about the basic tile pattern?

Tile Design 3: Now fold and tuck your Border Mat B to create this sized border:

Using the following patterns, which will be complete patterns for this Tile Design 3:

Basic PatternIs it complete (Y or N)

g p______

gpp______

ggpp______

ggppg______

ppppgg______

Prediction: Create a new basic pattern that you predict will be complete:

Test it out. Did your prediction work? Explain:

Compare/contrast: How are border problems 2 and 3 similar and how are they different?

Generalization: Overall, how do you know if a specific pattern will repeat as a border pattern so that the pattern will complete. (Relate the number of values in the basic pattern to the number of squares in the border.)

Hmong Border Patterns Comparing Basic Patterns

The first basic pattern used in Border Mat I was:

Tile Design 1: Hmong Design in Border Mat B

Starting in the upper left corner and wrapping around the border, we created this border.

Tiling with GP Pattern Open Border Mat for Tiling

1. Which of the following Basic Patterns will look identical to this gp tiling about the border? Assume you always start in the upper left corner and wrap around “clockwise”.

Basic PatternTiling will look the same as gp? (yes or no)

gpp______

gpgp______

pgpg______

gppgpp______

2. Based on your data, when will a new Basic Pattern give the same tiling as gp?

3. In general, when will two Basic Patterns be equivalent in their tilings around a border?

4. Which of the following basic patterns are equivalent ( to each other in their tilings)?

a) rbrrbb) rbbc) bbrrbbd) rbre) rbbrbb

Some Generalization Statements about the Hmong Border Patterns

Which of the following are true?

A) The pattern will complete if the total number of values in the pattern used can be divided into the total number of squares in the border without a remainder.

B) You can complete the border pattern with a whole patterning sequence if you can take the amount of squares in the border divided by the number of elements in the pattern and get a whole number.

C) You will have a completed border pattern when the number of tiles in the pattern is a factor of the number of squares in the border.

D) If the number of tiles divides equally into the number of squares in the border, it will result in a completed pattern border.

E) The number of tiles in the pattern must be a multiple of the number of squares in the border for this to result in a completed pattern border.

F) Overall, the number of spaces in the border mat pattern must be divisible (without any remainder) by the number of units in the basic pattern (for the basic pattern to be complete).