Relevant Decimals Lesson

This is a lesson that I tried with a 5th grade class to give a context to decimal addition and subtraction. Most of the math problems I’ve found involving decimal computation seem “artificial.” They have a “real world” connection, but the connections are irrelevant to most 5th graders. In order to make the connections more relevant (as Dan Meyer posted in a recent blog: students want to solve it) I came up with a context for a problem that had the math content embedded, but also involved the students in the problem itself. Credit for this lesson needs to go to a 3-5 EBD class at my school. The students in this class about 3 yrs ago, loved to make tops out of connecting cubes. They did this because they were told that they couldn’t bring in any toys to class (Bey Blade was the hot toy at the time). Since they couldn’t bring in these spinning, battle tops, they created their own with connecting cubes.

The first time I witnessed these students spinning their tops, the big question they wanted to know, was whose top spun the longest. I filed the idea away until about a week ago when some 5th grade teachers at my school asked for some help with decimals. The following is the lesson I used – thanks to this class of students. It’s written as it was done. I know what I’d change when I do it again. Please take a look. Use it if you like. I’d love to hear about your results and how you change it to make it better!

Standards:

5.NBT.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

5.NBT.3 Read, write, and compare decimals to thousandths.

a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).

b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Materials:

Connecting cubes

Decimats, or Base-ten manipulatives for modeling

Stopwatches (we used an online stopwatch that measured to thousandths of a second)

Opening:

Give students a copy of the decimat and ask what decimals might be represented. Follow up with these possible questions: What might hundredths or thousandths look like? How could you use this to model 0.013? 0.13? Share your thoughts with your partner/team?

Work Session:

The task is to design a spinning top, using connecting cubes, that will spin for as long as possible. Your group may want to design 2 or 3 tops, then choose the best from those designs. Once a design is chosen, students will spin their top and time how long it spins using a stopwatch. Each group will do this 4 times. Students should cross out the lowest time. Students will then use models and equations to show the total time for the top three spins. Students will show, on an empty number line, where the total time for their three spins lies. Students must justify their placement of this number on a number line.

Here is a sample top (thanks for asking for this Ivy!)

Closing:

Students present their tops and their data, then compare their results.

Possible discussion questions:

Whose top spun the longest?

How do you know?

How much longer did the longest spinning top spin than the second longest spinning top?

Show your thinking using a model.

How many of you would change your design to make it spin longer?

How would you change it?

Students used models to explain their thinking to each other and construct viable arguments.

1. Ivy Meek says:

Will you explain more about how the kids make tops using connecting cubes? I’d like to try this activity out with my class, but am having a hard time imagining what the students built. Thank you!

2. Ivy,
Sorry so long for the reply. I’m updating this post to include a picture of a student design. including that would’ve been a great idea to begin with.

Mike

3. Dawn Ingram says:

You said you knew how you would change it. How is that? (btw, this is on my lesson plan for the first week of school.)

1. Dawn, Thanks for the question. I would change my introduction to the task. I told the students they were going to design a spinning top using connecting cubes and I thought that would be engaging enough and would provide an opportunity for some writing (to the company who makes the cubes). My presentation wasn’t as engaging as I thought it would be. One other thing I’d do is spend some time practicing using a stop watch. Making sense of the times they got were confusing and some students needed time to make sense of the idea that the longest time was better than the shortest time. Finally, I would allow for the competitive nature to drive the lesson further. Once students created their tops and timed their spins, a redesign might have been appropriate. I would have kept the task growing and the students would have gotten some more purposeful practice with decimals.