Foundational Mathematics for Corequisite Courses: Succeeding at College Mathematics

1.

Draw a number line from -10 to 10 using increments of 1.

2.

Write all 6 mathematical sentences that compare the numbers -4, -7, and 5.

3.

Draw a number line and give the approximate locations of the numbers -45, 22, and 65.

4.

Write all mathematical sentences that compare the numbers -45, 22, and 65.

5.

Give a representation of the relative locations of the numbers 23 and 32 and write two mathematical sentences comparing them.

6.

Give a representation of the relative locations of the numbers -23 and -32 and write two mathematical sentences comparing them.

1.

Draw a number line from -100 to 100 using increments of 10.

2.

Write all mathematical sentences that compare the numbers -60, 0, and 80.

3.

Draw a number line from -800 to -600 using increments of 25.

4.

Write all mathematical sentences that compare the numbers -750, -625, and -675.

5.

Represent the number 34 using base-10 blocks.

1.

Give a representation of the relative locations of the numbers -47 and -83 and write two mathematical sentences comparing them.

2.

Represent the number 238 using base-10 blocks.

3.

What number is represented by the following blocks?

4.

Explain why the above arrangement of base-10 blocks is not ideal. Then give a better arrangement and explain why it's better.

1.

Although we are most familiar with base-10 numbers, this is not the only system of numbers that is used. Computers have three other number systems that it uses: binary (base-2), octal (base-8), and hexadecimal (base-16). We are going to explore those bases to understand how they work.

The primary difference is that the size of rods and trays are different. When working in base-10 it takes 10 pieces to go up to the next shape. In base-8 it only takes 8. Here is the visual representation of the number \(127_8\text{.}\)

Determine what this number is in base-10 and explain your logic.

2.

Converting numbers from base-10 to base-8 is a bit more complicated. Try to imagine that you have a bunch of loose blocks that you're filling into different trays that are built around the number 8 instead of the number 10. Work from the largest trays and work your way down.

Convert 89 to base-8 and explain your process in words.

3.

Using the logic that you developed, convert 14 to base-2 and explain your process in words.

1.

Base-16 requires us to introduce more symbols into our system of digits. The following diagram represents all of the single-digit numbers in that system.

Based on this diagram, what do you think the base-10 representation \(10_{16}\) of is? Explain your logic.

2.

Convert \(AC_{16}\) to base-10. Explain your reasoning.