Understanding Place Value, Decimal Numbers and Integers


I’m Dr. Tim Hudson, the curriculum director at Dreambox. I appreciate a couple of minutes of your time to show you one of our amazing mathematics Virtual Manipulatives that helps students learn and understand place value, and decimal numbers, and integers. We casually refer to this tool, internally, as the “zooming number line.” It’s highly interactive, engaging, and builds conceptual understanding. You can try this lesson for yourself at our website. It’s one of our fifth grade sample lessons at dreambox.com.

In this lesson, a student needs to place a pin at 5158 on the number line. As you can see, she grabs the pin but realizes that the number line doesn’t show enough detail. It’d be like finding one specific mile marker on a map of United States. She could take a guess, but instead, she chooses to use the magnifying glass that zooms in on the number line by a factor of ten. She clicks “zoom in” and sees that she’s on her way to the correct answer. She also sees that surrounding comic book style image start to pixelate as well.

To ensure she understands the scaling involved as she’s solving this problem, she can see a trail of number line bread crumbs below showing where she’s been. Note how the red line of the pin is visible in both of the blue ranges on the other number lines below. This connection is critical to her understanding of scale, magnitude, and the relationships between the numbers.

Dreambox lessons use consistent learning progressions and ensure students make coherent connections between mathematical ideas. So we also use this same zooming number line Manipulative with decimal numbers. In this example, the student scrolls the number line in search of -71.1. She uses the 100 times magnifying glass, but is off by just a bit. So she zooms back out and uses the 10 times magnifying glass instead to locate this negative number.

In order to deeply understand place value, students not only need to be able to locate a specific point on a number line, but they must also understand the relative magnitude of two numbers. For example, even though 3000 and 2001 are both greater than 2000, they have very different locations on the number line relative to 2000. Imagine on a map of the United States how easy it would be to see the difference between the distance of 2000 miles and a distance of 3000 miles. On that same map, it would be virtually impossible to distinguish a 2000 mile distance from a 2001 mile distance. At times like these, rounding and approximating are useful and natural strategies.

To support student understanding of scale and rounding, we also have approximation lessons that use our zooming number line. This student needs to locate 9798 on the number line but was given a starting range on the number line that only marked increments of 500. So she zooms out and chooses a different magnification range. Our Dreambox lesson leaves her old selection visible as a reference point. She uses her number sense to zoom in again and places the pin. Even though the red line is slightly off the exact value with the pin, we give this pin a wider range because this lesson is developing scale with approximation. Her pin placement is precise enough given the problem.

At Dreambox, we have a thousand K5 lessons built for our adaptive learning platform that differentiate for each student, whether they’re in pre-K or about to enter middle school. Our experienced classroom teachers, talented programmers, and brilliant creative team are passionate about partnering with schools and teachers to help all students learn, think critically, and succeed in mathematics.

On behalf of our amazing team, I want to thank you for your time.

Dr. Tim Hudson
Curriculum Director
Dreambox Learning