Chapter 1: Place Value, Addition, and Subtraction to One Million

Lesson One: Model Place Value Relationships

How are the place values related? Each place value increases by a factor of 10; for example, the value of 100 is ten times the value of 10.

Lesson Two: Read & Write Numbers

How do we read and write numbers? We can use three basic forms: standard form (3,215), expanded form (3,000 + 200 + 10 + 5), and word form (three thousand, two hundred fifteen) to read and write numbers. When we read numbers aloud, we read them as we would write them in word form.

Lesson Three: Compare & Order Numbers

How do we compare numbers? Is 5,127 greater or less than 927? Greater than. Why? It's greater than 927 because the 5 in 5,127 is in the thousands place (its value is 5,000), and the 9 in 927 is only in the hundreds place (its value is 900). 5,000 has a greater value than 900 does. If you have multiple numbers, then you have to compare all of the numbers similarly.

Lesson Four: Round Numbers

How do we round numbers? We can use many methods, but it is important to understand the concept of rounding. As we see here, 2,342,533 is closer to 2,343,000 than it is to 2,342,000, so we would round up to 2,343,000. There's nothing wrong with starting small with rounding and working your way up. Larger numbers are difficult to conceptualize as easily.

Lesson Five: Rename Numbers

Why do we need to learn alternate ways to write numbers? Regrouping! When I add 9 + 5, I get 14 ones. When adding with a 4-digit number, it becomes necessary to learn what to do with the extra 10 ones - I add them onto the tens column. 10 ones = 1 ten. This is also true for subtracting, which will be our next lessons!

Lesson Six: Add Whole Numbers

When adding whole, multi-digit numbers, it is important to know how to rename numbers to effectively regroup.

Lesson Seven: Subtract Whole Numbers

When subtracting whole, multi-digit numbers, it is important to know how to rename numbers to effectively regroup.

Lesson Eight: Comparison Problems with Addition & Subtraction

In this lesson, students combine their knowledge of addition and subtraction with that of charts, graphs, models, and word problems. They learn how to compare (more than, less than) and how to use those charts, models, and even key words to figure out which operation they need to use to correctly answer a real-world question.