I have been teaching a group of students struggling with place value this week. I started off with my usual trading game lesson, thinking it might be too boring because I thought they might have done this before. Imagine my shock when the group had obviously NEVER played this game before. I picked up some base ten blocks I had on the maths shelf and asked if they had worked with these before and they all chorused with “yeeeeessssss.”
So, this blog post is all about the power of the humble trading game and why it is important to use when teaching students early place value concepts. I also want to pose the scenario that place value can be taught effectively without the use of base ten blocks and the only reason we use them is that we always have and they often appear in the standard tests all students experience from time to time.
What is the Trading Game?
You will need:
A pair of students.
A trading board. Depending on the stage of the students it can be 2, 3 or 4 columns. The columns can be labelled with the names of the places. I like to use a double page in their exercise book so it can be used to a variety of place value activities.
Matchsticks. Other materials that will work include pop sticks, interlocking cubes and paperclips.
A ten sided dice.
Cards with the numbers from 0 to 9 on them.
How to play:
Have one student roll the dice and the other student work with matchsticks.
Student A rolls the dice and calls out the number.
Student B collects and places the correct amount of matchsticks and places them in the ones column.
Keep rolling and placing matchsticks until the students can see a group of 10.
Take the group of 10, place and elastic band around the bundle and place in the tens column.
Keep rolling and placing matchsticks until there are 10 bundles of 10. Take the 10 bundles and place an elastic band around them and put in the hundreds column.
At any time you can stop the students and ask them to place the number cards underneath each set of matchsticks to show the total number of matchsticks that are on the trading board.
Mix it Up
The basic trading game can be modified to suit whatever skill you are focussing on. Stick to the numbers you are focusing on whether it be numbers to 100 or 1000.
Use a timer and get students to take turns rolling and bundling.
Time how long it takes for the first group to get to 100.
Have a target number and see who gets the closest.
Make a really big number by adding all student’s matchsticks together on one trading board.
Get 2 pairs of students to place their trading boards together, place number cards on each board and show how to add the two amounts together using physical trading of the matchsticks.
Play the game with a variety of materials so the students see that the action of trading is always the same.
Use real world contexts such as filling orders of paperclips and lollies.
Find out who can get the most/least/middle number of matchsticks on the board in a given time.
Use plastic dollar coins and trade for $10 and $100 dollar notes. (This can work as a class reward system by displaying on a whole class chart)
Use a 20 sided dice.
Why is it an essential experience for mastering place value?
Students physically trade objects as a mirror for the trading that happens in the abstract concept of number place value. This helps to build a deep and intrinsic awareness of the how the power of 10 works in making numbers move from one place to the next.
Students are able to get a real sense of the size of the collection.
They are able to connect the amount of items (and later numbers) in each place with a digit in a number.
If you use the trading game as a basis for introducing addition and subtraction it shows students how we can be flexible with numbers. Being able to undo a bundle is essential for teaching students that numbers are flexible and can be moved around to help add and subtract.
Why should the Trading Game be used BEFORE base ten blocks are introduced?
Base ten blocks are permanently stuck together and so it is difficult to imagine they are singular blocks joined together. Many students see the piece of the set as 1 of something rather than the amount of singles they are made up of. This can make interpreting how big each place is difficult.
Base ten blocks are not able to be broken apart for flexible addition and subtraction of numbers. Students who have experience with groups of objects can easily see that you can move parts of a number around.
Students need to have a firm grasp of the place value system being made up of single items bundled together in powers of ten before they are introduced to the symbolic base ten blocks. This gives students a sense of how big numbers really are.
When students are ready for base ten blocks, they will have a well developed sense of how much bigger one place is to the other. They will also be able to tell how many more matchsticks they need to trade to the next place. Students will start to get annoyed at how tedious the bundling process is when they understand how many rolls of the dice it will take to get to a particular number. When you see students showing these things, bring out the the base ten blocks and show them how someone has invented a model to represent the bundling they have been doing. The transition to using the base ten model will be much easier when students demonstrate they are mathematically ready to use it.
The best way I have found to transition students to base ten blocks is the play the trading game with the base ten blocks. After spending a few lessons bundling they will love the ease of base ten blocks, plus the tactile connection to their bundling experiences will still be there.
Have fun trading your way to place value success!