# Place Value and Decimals

## Supporting Understanding in Middle Grades and Middle School

Understanding place value is critical for success in any math curriculum.  Understanding base 10 is critical for many functional skills, as well.  Using money requires that students are able to count by 5’s and 10’s as well as understanding how cents are denominated as hundredths.  With the growing emphasis in STEM (Science, Technology, Engineering and Math) to help students prepare for twenty-first century jobs, our students need to be fluent in decimals as well as having the ability to understand numbers through billions.

### Place Value and Common Cores State Standards

Any math curriculum is going to follow a “spiral design,” which means that each grade will address each math concept at an increasingly complex level.  Students begin to build familiarity with numbers to 100 in kindergarten, though they are only expected to master numbers to 20.   Still, “Hundred Day” celebrated on the hundredth day of school, is common in Kindergarten and first grade, and sometimes on through second grade, if the teacher(s) decides that the students would benefit from the extra experience with manipulatives and other visual and tactile means of understanding the magnitude of one hundred.   A hundred chart that your students can use for any number of activities is a great tool for understanding numbers to 100.

Another tool for introducing and building place value understanding is a set of one centimeter cubes, rods, squares and cubes, representing ones, tens, hundreds and thousands.

I have combined the place value blocks with a hundred chart to help first and second grade students understand how to build two digit numbers.

### Place Value Common Core State Standard for 4th Grade

4.NBT.A.2  Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

### Strategies for Middle Grades (4-6) and Middle School Students

Get It In their Mouths

I had a very wise principal, Felicia Barge, who became a math teacher after being an acoustic engineer.   She advised me to “Get it in their mouths.”  Have students read the numbers you want them to understand.  I found she was right—that additional expectation that students would read numbers aloud helped them write dictated numbers more accurately, as well as helping them add and subtract numbers with decimals.

With the two templates I provide you here, write the number model on the board, have students write them in the spaces on their templates, and have them read the number.  Example:

2,304,209.27  would be read “Two million, three hundred four thousand, two hundred nine and twenty seven hundredths.”

Your students will have graphic display that you can use to demonstrate different characteristics.  You can demonstrate how adding zeros to the right of your whole numbers and to the left of your number does not change the VALUE of the number.

You can demonstrate how 1,000,000 is ten times as large as 100,000.

Once you start dictating the numbers, have them repeat them before they start to write.  Once again, keep the numbers in their mouths.

Give them Lots of Practice

Dictate numbers, and have your students write them on the templates. Start them with a digit in every place, and start with thousands.  Leave the empty (zero) places for the end, when students have gained a strong grasp of all the places – ones through millions, tenths through thousandths.

Give Them Some Power

Once your students are consistently writing and naming large, multiple digit numbers, turn the table and have single students write a number on their templates and have them dictate their numbers to their peers.  Have peers check peers work, as well.  Remember, there are such things as good mistakes.

Help your students see where they are consistently working well, or if they continue to make the same kinds of mistakes.

I provide you with two sets of place value templates.   You can use the second one to make some REALLY big numbers.  By asking your students to apply what they learned to a million, they will expand their understanding of the decimal system, and be ready for more challenges at later grades or higher levels.

Assess for Independence

You will need to start fading the templates at some point, so your students can write, read and dictate multiple digit numbers without the template.  Part of fading could be to make boxes for the numbers, i.e. 7 boxes for digits in a million, 7 boxes with a decimal for ten thousands with hundreds, etc.

True independence is the ability to write numbers without a template, or boxes.   You want to give your students both formal (summative) and informal (formative) assessment.

The template to a million with decimals to hundredths.

The template to a billion with decimals to a hundred thousandths for expanded practice.

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