## Identifying Place Values with Decimals

#### Aligned To Common Core Standard:

**Grade 4** - 4.NF.7

What are the Place Values in Common Decimal Values? Before we talk about place values in the decimal system, let's take a quick recap on what are decimal values. Decimal values are numbers or figures having one visible decimal point or as we commonly call a dot somewhere in between the numbers. Having said that, let's take a look at what is place value. All the numbers that we see and encounter on a daily basis in life follow the rules of place value. A place value tells you the place or location of a number. For example, in a number, 679, the place values of numbers go like: Starting from the right, number 9 is on the place of ones. Number 7 takes the place of tens, and number 6 takes the place of hundreds. Notice that ones are always the first digit, tens is always the second, and hundreds are always the third digit. In a decimal number, place value is a propositional system of notation in which the place/position of a number is determined by with respect to its position of the point/decimal in the number. Consider this example; 6,789.387 (6 = thousands, 7 = hundreds, 8 = tens, 9 = ones, 3 = tenths, 8 = hundredths, 7 = thousandths). These worksheets and lessons will help educate students on the names and values of places to both the right and left of the decimal place.

### Printable Worksheets And Lessons

- Pizza Slice Step-by-Step Lesson- We include a thousandths place for a point of reference.
- Guided Lesson - We point at an integer within a value. Tell us the place value of that integer.
- Guided Lesson Explanation - All 5 problems are broke down into places.
- Independent Practice Worksheet 1 - A good amount of practice for you.
- Independent Practice Worksheet 2 - More pointing and name place values.

#### Homework Sheets

So that students aren't left all alone. We include a worked through problem as reference.

- Homework 1 - What is the place value and total value of '7' in the number 5823.47?
- Homework 2 - Write the place and value of each number.

#### Practice Worksheets

A nice pack of work for this skill. A great set of drills!

- Practice 1 - What place is the selected integer in? For extra credit, tell us how you know.
- Practice 2 - What is the value of the selected integer?
- Practice 3 - We can start by looking at the place values of all of the integers in this number.

#### Math Skill Quizzes

Time to see if the skills have set in.

- Quiz 1 - The decimal point tells us where to start. To the left of the decimal point is the ones places. To the right of the decimal point is the tenths places.
- Quiz 2 - We then count up or down based on the powers of ten places.
- Quiz 3 - We start each problem by determining the place of the number that is highlighted. Then we multiply the integer at that place by the place value itself to determine the final value.

### Considerations When Teaching This Skill

This is a task that students master in grade 4, but they often begin to learn the foundation of this skill in grade 3. The spiral curriculum concept helps them move from the tenths to thousandths value over the course of this transition year. This can be taught in parts or as one entire unit. There are many differing opinions on this, and each teacher will have success with a slightly different method. I find that there are three main ingredients that lead students to master with this skill. It all starts with students understanding the concept of a base ten system. To grossly simplify this, the general concept we want them to get is that each place value differs by a power of ten. I find the most successful method for my students is to have them write numeric values and their names in words, and then have them write it place words. A general concept would be to have students convert 56 to fifty-six and then to 5 tens and 6 ones. I almost do this too much with them, but find that it really helps that base ten concept sink in. The next progression for my students is to add the concept of base ten blocks. This adds a 4th way to represent a value for them. The visual helps make it concrete for my visual learners. I also find that with this generation, most of kids are visual learners. The 5th progression I like to make with my students is to give them opportunities to count large groups of objects and have them break out the ones and tens groups. Building off of my previous example (56), I would have students count 5- ten piles, and 6 in a ones pile. From here you can go in several different directions. I have a lot of success with moving on to estimation with my students from here. I have tried teaching many different coordinating topics after this, but estimation seems to be a nice transition for students.