Measurement--Discovering the Need for Standard Units
In my previous two blog posts, I shared how comparison is the foundation for early childhood measurement experiences followed by the exploration and use of nonstandard units to connect counting with measurement concepts.
Eventually, the need for standard units should be developed. But how can you help children see how having a consistent unit that’s recognizable to all helps us build a shared understanding in mathematics and in life? Here’s an activity that’s been a hit with my students.
Racing to Standard Units activity
What You Need:
· Ramp-building materials (cardboard, blocks, tubing, masking tape)
· Matchbox cars
· Nonstandard units (drinking straws, craft sticks, cotton balls)
What Kids Do:
Students work in groups to design and build a ramp. They send their car down the ramp and use ONE OF THE NONSTANDARD UNITS to measure how far their car travels from the end of the ramp across the floor. (Each group uses a different unit.) Have groups record their results for four trials.
Bring the groups back together and have each group share their results. Write all the groups’ results on the board without any units.
The results might look something like this:
· What do you notice about the data?
· Why is there such a range of distances?
· Was this a fair experiment?
· What could we do to make it fair?
· Why does the size of the unit you measure with matter?
· What unit do you think goes with each of the data points on our graph?
Fill in the units together. The table might now look something like this:
This inquiry activity helps children discover a big idea in measurement:
The size of the unit of measure is inversely related to the number of units you’ll need to do the measuring. A small unit? You’ll need a bunch. A large unit? Fewer with do. The unit matters!
A great book for reinforcing this idea is:
How Big is a Foot (Myller, 1991)
In this story, a king instructs the royal carpenter to build a bed for his wife. But since no one has ever seen a bed before, the carpenter isn’t sure the correct size. The king, using his footsteps as units, tells the carpenter to make the bed 6 feet long and 3 feet wide. Of course, the little carpenter’s feet are smaller and well, you can see where this is going. We need standard units so our beds fit!
The Racing to Standard Units activity and the How Big is a Foot? book both relate to linear measurement. But have you considered that temperature (degrees), time (minutes, hours, days), and money (coins and currency) are also standard units of measurement? We need standard units to measure each of these so that we have a common understanding of their value.
Here is a game guaranteed to be a winner with kids and coins!
Coin Trading Game
The Coin Trading game helps kids practice coin values and explicit trading (trading up) 5 pennies for a nickel and 2 nickels for a dime. If you want to add quarters to the game, you can!
Watch the game being played by two of my sons here.
Materials: one die, coin board for each player, pennies, nickels, dimes
How to play:
1. Each player draws a three-column grid on their paper and labels the columns Penny, Nickel, and Dime. This is their game board.
2. Put the pile of coins in the center of the table. Take turns rolling the die and adding the corresponding number of pennies to your board.
3. For instance, if Player A rolls a 4, the player takes four pennies and puts them on their board in the penny column.
4. The idea of the game is to show, in any column, the smallest number of coins possible. So as soon as you have enough pennies to “trade up,” you may do so. For example, if you have five pennies, trade them for a nickel and place the nickel in the nickel column. As soon as you have two nickels, “trade up” for a dime and place the dime in the dime column, and so on. 5. The first player to have five dimes in the dime column is the winner.
*Note: This game was originally published in Marilyn Burns' book About Teaching Mathematics. You can also find it in Math-Positive Mindsets: Growing a Child's Mind without Losing Yours.
As I shared in my previous post about nonstandard units, Three Act Tasks provide kids with real-world contexts for measuring. You can find over 100 Three Act Tasks created by my students at the University of Houston. on this YouTube channel! Check 'em out!
Here are two of my favorite tasks for standard units of measurement.
Savage Rice Three Act Task
Main Question: How many cups of rice does the bag contain?
Spilled Milk (great for conversions in measurement)
Main Question: How much milk was spilled on the floor?
Final Thoughts About Teaching Measurement Well
I’ve often thought teaching all content in mathematics through a measurement lens would allow for authentic, real-world applications of almost all elementary school mathematics concepts.
Measurement truly is among the strongest real-world connections in mathematics.
To teach measurement well, I recommend keeping the following in mind:
• Real-World Scenarios: Be certain all activities are positioned in “real-world” scenarios that speak to children’s interests and experiences. Three Act Tasks are great for this!
• Benchmarks: When we help children develop benchmarks for standard units, like the width of their finger being about one centimeter or the length from fingertip to elbow being about one foot, they have handy references for abstract mathematical ideas. For more on benchmarks in measurement, check out Chapter 7 of my book Math-Positive Mindsets: Growing a Child’s Mind without Losing Yours.
• Open-Ended Problems: Measurement must always be taught using hands-on, math-positive problem situations that allow for productive struggle and multiple avenues for finding an answer. Students must be actively doing, experimenting, and performing—not passively observing or filling in worksheets.
• Estimation: Wherever possible, encourage children to estimate prior to measuring and revisit their estimate when they are halfway through to revise it if necessary. This builds number sense and helps children develop reasoning skills along with a math-positive mindset.
I hope these ideas are helpful in your work building math-positive mindsets with your children and students. Thanks for checking in!