Table Tiling Activity Level 1 Consider the following task. Table Tiling Maria makes square tables then sticks tiles to the top. She uses three types of tiles: whole tiles, half tiles and quarter tiles. The sizes of the square tabletops are all multiples of 10 cm. Maria only uses quarter tiles in the corners and half tiles along the edges of the table. How many of each type of tile will Maria need to make a 50 cm by 50 cm square? Here is one tabletop. You can also access a sketch here: ​
Table Tiling Sketch 1. Complete the following table: Table Dimensions Number of (cm) Quarter Tiles 10 x 10 Number of Half Tiles Number of Whole Tiles 30 x 30 40 x 40 50 x 50 20 x 20 3. What do you noticed about the number of quarter tiles? 4. What patterns do you notice regarding the number of half tiles? What about whole tiles? 4. Can you predict the number of each type of tile needed to construct a 100 cm by 100 cm? Table Tiling Activity Level 2 Consider the following task. Table Tiling Maria makes square tables then sticks tiles to the top. She uses three types of tiles: whole tiles, half tiles and quarter tiles. The sizes of the square tabletops are all multiples of 10 cm. Maria only uses quarter tiles in the corners and half tiles along the edges of the table. How many of each type of tile will Maria need to make a 50 cm by 50 cm square? Here is one tabletop: Access a sketch of the 20 cm by 20 cm at the following link: ​
Table Tiling Sketch​
, then perform the following steps, answering the questions that follow. 1. Construct the 30 cm by 30 cm square. 2. How many quarter tiles are needed to make a 50 cm by 50 cm square? What conclusions can you draw about the number of quarter tiles needed to make any sized tabletop? 3. How many whole tiles are needed to make a 50 cm by 50 cm square? Write a rule for the total number of whole tiles used to make any sized square tabletop. Explain your reasoning. 4. How many half tiles are needed to make a 50 cm by 50 cm square? Write a rule for the total number of half tiles used to make any sized square tabletop. Explain your reasoning. 5. Can you predict the number of each type of tile needed to construct a 100 cm by 100 cm? Table Tiling Activity Level 3 Consider the following task. Table Tiling Maria makes square tables then sticks tiles to the top. She uses three types of tiles: whole tiles, half tiles and quarter tiles. The sizes of the square tabletops are all multiples of 10 cm. Maria only uses quarter tiles in the corners and half tiles along the edges of the table. How many of each type of tile will Maria need to make a 50 cm by 50 cm square? Here is one tabletop: Access a sketch of the 20 cm by 20 cm at the following link: ​
Table Tiling Sketch​
, then perform the following steps, answering the questions that follow. 1. How many whole tiles are needed to make a 50 cm by 50 cm square? Write a rule for the total number of whole tiles used to make any sized square tabletop. Explain your reasoning. 2. How many half tiles are needed to make a 50 cm by 50 cm square? Write a rule for the total number of half tiles used to make any sized square tabletop. Explain your reasoning. 3. How many quarter tiles are needed to make a 50 cm by 50 cm square? What conclusions can you draw about the number of quarter tiles needed to make any sized tabletop? 4. If Maria was only able to buy whole tiles and had to cut her own half and quarter tiles, how many whole tiles would Maria need to purchase to make a 50 cm by 50 cm square? 5. Write a rule or generalization for the total number of whole tiles that Maria would need to purchase to construct any sized square tabletop. Show your work or explain how you came up with your generalization.