Lesson 4: Referents - Area Referents Examples

   Multimedia

A video describing FILL IN is provided.



EXAMPLE 1

After retiling a kitchen with 1 ft² tiles, Jakob has 25 tiles left. He decides he will use these tiles in a boot room at the rear of his home. He lays some of the tiles along two sides of the walls as shown in the diagram below. How many more tiles will Jakob need to purchase to tile the boot room.


Solution


Step 1: Calculate the number of tiles needed for the whole project.

Jakob has placed 7 tiles along the length of the room, and he would need a partial tile as well to fill the extra space. He can round up to 8 tiles.

He has placed 5 tiles along the width of the room, but again, he would need partial tiles to fill the extra space. He can round up to 6 tiles for the width.

Step 2: Calculate the number of tiles needed by multiplying the length by the width.

tiles needed for whole project = length × width
= 8 × 6
= 48 tiles

Step 3: Calculate how many more tiles are needed

remaining tiles needed = 48 tiles - 25 tiles
= 23 tiles

Jakob will need 23 more tiles.

EXAMPLE 2

Seed beads are used to decorate moccasins. A 24 g package of beads will cover approximately 20 in2. Explain how a referent could be used to determine how many packages of beads would be needed to completely decorate these moccasins?

Solution


A referent for a square inch is a large stamp. However, such a small referent would require too much counting. Using a larger item, such as a cell phone, might work better.

Step 1: Determine the surface area of a cell phone screen.

It would take 2 rows of about 4 stamps to cover the screen of a phone. This means a cellphone's screen would have the area of about 8 in2.

Step 2: Determine the number of cellphones screens needed to cover the moccasins

An estimate would be:

  • 1 cellphone screen to cover the toes
  • 2 cellphone screens along the outside of the foot
  • 2 cellphones screens along the inside of the foot
  • 1 cellphone screen behind the heel
  • 2 cellphone screens on the inside of the ankle
  • 2 cellphone screens on the outside of the ankle
  • 1 cellphone screen on the front
  • 1 cellphone screen on the back

So about 12 cellphone screens would cover one moccasin, meaning about 24 cellphone screens would cover both moccasins.

Step 3: Estimate the area of the leather

Area of leather = 24 × 8 in2
= 192 in2

Step 4: Calculate the required number of packages of beads.

Because this is an estimate, we can round 192 in² to 200 in² because 200 in² is easier to work with.

\(\begin{align} \text{number of packages}&=\frac{200\,\text{in}^{2}}{20\,\text{in}^{2}/\text{bag}} \\ \\ &=10\,\text{bags} \end{align}\)

About 10 packages of seed beads will be needed to decorate the moccasins.


Now, it is your turn! Complete the questions in your Chapter 7, Lesson 4 Practice Makes Perfect that refer to Area Referents.



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