The Math Number Name Collection Box
We spend a lot of time asking students to calculate with numbers, compare them, round them, and put them into equations. What happens when we give students one number and simply ask them to explore it?
That is the idea behind the Math Number Collection Box.
Each student begins with a 2, 3, or 4 digit number. Instead of completing a page of problems, students are challenged to investigate that number and represent it in as many different ways as possible.
Think about your own name, or someone you know.
A person named Jennifer might also be called Jen or Jenny. That same person might also be called Mom, daughter, sister, auntie, teacher, neighbor, or friend. Each name describes or represents her in a slightly different way, but underneath all of those names, she is still the same person.
Numbers are similar.
The number 100 might be:
- 100
- one hundred
- 10 × 10
- 50 + 50
- 200 ÷ 2
- 1,000 ÷ 10
- 10 tens
- 100 ones
One student might draw 100 dots, write 50 + 50, or show 100 with base ten blocks. Another student might represent 100 as a fraction, decimal, multiplication equation, measurement conversion, or connection to another currency. All of these “names” look different, but they represent the same number.
That is part of the thinking behind the Number Name Collection Box. How many names, representations, relationships, and stories can we discover for one number? A number becomes something to think about when we ask questions like:
- When is this number too big?
- When is this number too small?
- When is this number a lot?
- When is this number a little?
- What is almost this number?
- What is this number between?
- What do you notice about this number?
Numbers may be universal, but their meaning can change dramatically depending on where we are in the world and what we are measuring. That is another beautiful aspect to Number Name Collection Boxes. It is accessible for all. Every student can begin somewhere. Students can work at their own level and bring their own knowledge, experiences, interests, and creativity to the task. As students learn more mathematics, the activity grows with them. New operations, fractions, decimals, factors, multiples, measurement conversions, equations, and real world connections give students entirely new ways to represent a number.
If we think again about the number 100.
What does it mean to have 100 dollars?
What about 100 euros?
100 pounds?
100 yen?
100 pesos?
The numeral stays the same, but its value as money changes depending on the currency.
Where in the world would 100 units of currency buy the most?
Where would it buy the least?
Is 100 a lot of money everywhere?
What could you buy with 100 in another country?
Currency is only one possibility. One hundred kilometers feels different from 100 miles. A temperature of 30 means something very different when it is measured in Celsius rather than Fahrenheit. One hundred people might be enormous for a classroom, small for a school, and almost invisible in a major sports stadium.
This makes the Number Name Collection Box a perfect activity for the beginning of the school year.
Early in the year, I can learn a tremendous amount by watching What representations students choose.
At the end of the year, students can return to their number collection boxes and see evidence of their own growth right in front of them.
Beyond showing growth, the Number Name Collection Box is also a wonderful substitute lesson.
Students already understand the structure, there is no complicated new content for a substitute to introduce, and children can work independently at their own mathematical level.
It is meaningful mathematics without requiring every student to be on exactly the same problem at exactly the same moment.
Since the activity expands with students’ knowledge, you can use it more than once and leave it for a substitute to use more than once during the year without it really being the same lesson. The students themselves have changed, so the mathematics they produce changes too.
Since I have been using Number Name Collection Boxes for so long that I do not know where I originally found this.
Try It in Your Classroom
