Welcome to Our Pre-Algebra Homeschool Math Course

Course Sample for Our Pre-Algebra Homeschool Math Course

Back to Basics

Let’s review the basics about place value, addition, subtraction, multiplication, and division. We want to be able to perform these functions quickly and effectively, so we can build on these and move on to more advanced topics. The rules you use for these arithmetic functions will be the same when we move on to working with things like decimals, fractions, and even variables.

Also, these functions make up most of our use of mathematics in our everyday life. If you’re purchasing items at a store and want to know if you have enough money, or what your change will be, you’ll be using arithmetic. If you want to build the largest dog house you can with the wood Grandpa gave you, you’ll be using arithmetic. If you want to know how much longer the car ride will be to Aunt Cindy’s house, you’ll be using arithmetic. When you can perform these functions quickly and accurately, it will be simple to apply them to any situation.

This unit is intended as a review; these should be facts that you know. If you can already perform all these functions, then use this review to work on your accuracy and speed.

Week 1
Day 1: Place Value

Before we can perform functions with numbers, we need to understand what numbers are. In the number system we most often use, we express numbers using ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Using only these ten digits, we can show any number by assigning values based on the position of the digit in a number. Each place in a number is ten times greater than the place to its immediate
right.

Using these place values, we can see that the number 7,023,845 actually means we have:

• 7 millions,
• 0 hundred thousands,
• 2 ten thousands,
• 3 one thousands,
• 8 hundreds,
• 4 tens,
• and 5 ones.

In other words, we have 7,000,000 + 20,000 + 3,000 + 800 + 40 + 5.

Remember that zeroes are important place holders. The zero in the hundred thousands place tells us
that there are no hundred thousands in this number, but we can’t leave it out! If the zero were not there holding that place, then all of the digits would shift to different place values:

723,845 ≠ 7,023,845.

Let’s Practice

1. In what place value, or position, is the underlined digit?

a. 42, 021
b. 5,389,000
c. 304,885,299
d. 2,654
e. 41,003

2. Write these word expansions as numbers. (Remember to use zeroes to hold places where no other digits are needed!)

a. 5 ten thousands, 3 thousands, 9 hundreds, 9 tens, and 9 ones
b. 4 millions
c. 7 hundred thousands, 4 thousands, 6 hundreds, 2 tens, and 1 ones
d. 2 hundred millions, 2 ten millions, 1 millions, 4 hundred thousands, 5 ten thousands, 8 thousands, 6 hundreds, 7 tens, and 8 ones
e. 3 ten millions, 4 thousands, 6 hundreds, 7 tens, and 7 ones

3. Write these expansions as numbers.

a. 4,000,000 + 200,000 + 30,000 + 400 + 60 + 7
b. 20,000 + 5,000 + 1
c. 3,000 + 900 + 10 + 2
d. 100,000,000 + 10 + 9
e. 800,000 + 40,000 + 5,000 + 900 + 30 + 7