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Extending Decimal Place Value Understanding Through Problem Solving

I was planning with my 5th-grade team today, and they’re getting ready to move into decimal place value. The 5th-grade standard is to extend decimal place value from the hundredths place to the thousandths place. We decided to start with a very quick Ticket In the week before the unit actually starts to get a feel for what the kiddos retained from 4th grade.

On Day 1, we’re going to focus on reading decimal numbers, starting out with decimals to the hundredths (4th-grade skill) and extending to the thousandths (5th-grade skill).

Write the following on the board/document camera:  (2 x 100) + (3 x 10) + (6 x 1) + (1 x 0.1) + (5 x 0.01). Talk with your partner about how you would write this number in standard form. Accept responses and have a class discussion about which the class feels is the correct way to write the number. Be sure that they come to the conclusion that it should be written 236.15. Who thinks they can read the number?  Accept responses. You may have students that try to read it two hundred thirty-six point fifteen because they often hear adults use that shortcut. Tell kiddos that mathematicians are more precise and would read it two hundred thirty-six and fifteen hundredths. We say the word and when we reach the decimal point, and we always include the decimal place value name.

Write the decimal place value names above the number and ask if students notice anything about the place value names. If they don’t notice the symmetry between the whole and decimal place value names, draw the arrows as shown below to illustrate the relationship.

Change the number to 1,236.158 by adding a 1 in the thousands place and an 8 in the thousandths place. Turn and talk to your partner. How should we label the place value position names of the new digits? You’re hoping that they will conclude that since the 1 is in the thousands place, then the 8 must be the thousandths place. Remember, you’re wanting them to see the relationship between the place value positions.

Continue practicing reading decimal numbers to the thousandths. Be sure to write the numbers with the place value names labeled to support the learning. Try letting the student who reads the number correctly be the one to write the next number.

Give a quick Ticket Out to determine how well students understood the concept.

Day 2 moves us into comparing decimals. Again, we’ll frame it in a problem-solving context.

Give each pair of students the two place value mats shown below, manipulative money (3 dollar bills, 10 dimes, and 10 pennies), and base-10 blocks (3 flats, 10 rods, and 10units).

Models and manipulatives build understanding of decimal place value

Huh. I wonder which is bigger, 0.9 or 0.09? Let’s read these decimals to make sure we’re clear on them. Nine-tenths and nine-hundredths. Great! I’ve given you some materials. You may use these materials to prove your answer. You also need to be able to explain in words and pictures how you decided which is the bigger decimal.

Give students some time to work in pairs on the problem, and then come back together to discuss. See if students can make any generalizations.

Give students additional numbers to build and compare. Here are some good ones to try:  0.17 and 0.4; 1.08 and 1.18; 2.2 and 2.24; 1.5 and 1.67

Be sure to bring the class back together to discuss their results and strategies for comparing. If you feel they have really grasped this lesson, you might try…

Huh. I wonder which is bigger, 0.102 or 0.14?  🙂

Click here to grab your mats! Looking for additional decimal resources? Check out my Decimals & Fractions Using Models and Manipulatives unit.  It’s a best-seller!

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  1. Donna, these are really great ideas that I’ll save for next year. I love your tickets in and out too! Is there any way you could share “blank” ones that we could use for other concepts? We’re working on %, decimals, fractions now and I’d love to use your tickets! As always, you have great ideas for teaching math concepts.


    1. Hey, Debbie! That’s actually why I uploaded them as Word documents, not PDF files. You can download them and change them however you want!

  2. I just learned about a neat way to show place value with decimals (and do a little diagnosis of understanding of fractions), tho’ it’s a candy lesson and edible lessons have their issues… I s’pose it could be done with strips of paper, though.
    Start with 100 Twizzlers and show that place… then ten… then 1…
    Then … into Decimal land! what would 1/10 of the twizzler be? Break it off (but you can’t eat it yet…) That’s going ot be the tenths place.
    Then… take that little piece~ can you find 1/10 of it?
    Nifty room for discussion…

  3. Do you have any mats that are not decimal related., I managed to find some in my closet at school but your decimal ones are way cuter.

    1. Oddly enough, Tami, I actually didn’t have a cute one for whole numbers. It was easy enough for me to modify the decimal one, though. Grab it here.

    1. Hello!

      Thank you so much for the detailed information you share on your blog. Plus the resources! I was wondering if you have a post on how you would suggest introducing decimals to students in fourth? I’ve searched your posts but didn’t quite find one on this topic. Your insights are greatly appreciated!

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