Shunya Chart and Math Way : Addition and its Properties
The previous article introduced Shunya Chart and demonstrated how it can help elementary students experience mathematics. In this article, I show how a mentor can help students explore elementary operation of addition and its properties (commutative property and associative property) in one go.
In Saxon Math, the properties are not introduced until Saxon Math 6/5. In Shunya chart method, the properties are introduced as natural extensions of the elementary operators. Even if students do not remember the names of the properties, they will intuitively learn to recognize the flexibility of the property and will be able to apply in many ways.
Shunya chart may be on a whiteboard with magnetic beads or on ground (similar to Hopscotch).
Elementary Operator : Addition
Consider addition of 2 and 3.
Have the child move marker 2 steps forward and then 3 steps further. That is 5 steps in total.
2 + 3 = 5
This is a great time to introduce commutative property instead of doing it in later grades.
Have the kids change the order in which they add the numbers. Have the child first move the magnet 3 steps forward and follow it up with 2 steps.
3 + 2 = 5
Students can explore if it matters which number they start with.
3 + 2 = 2 + 3 = 5
Commutative Property: Order in which you combine the numbers does not change the outcome
You may extend the exercise to 3 numbers.
2 + 3 + 4 = 9
Students can explore all the combinations in which they can add the numbers and make observations.
2 + 3 + 4 = 9
3 + 2 + 4 = 9
4 + 2 + 3 = 9
Note1: I refrain from calling it “Commutative property of addition”. The goal is to introduce the flexibility inherent in operators and leave the limitations to later. In context of division, students will investigate if commutative property applies to division as well.
Note2: The section below shows how commutative property can be further extended to introduce combinations (permutations and combinations). This is best revisited later on, but is being depicted here to show how the extensions.
In how many combinations can the numbers be arranged?
(First number can be picked three ways) x (second number can be picked two ways) x (last number can only be picked on way)
3 x 2 x 1 = 6 combinations
Is the sum of numbers the same in all 6 cases?
Have two children work on addition of three numbers.
Have one child first move the magnet 2 steps from (0,0) and then follow it up with 3 steps. Have a second child use a different magnet and take it further by 4 steps.
(2 + 3) + 4 = 9
Now have first child add 3 & 4. Ask the second child to add 2 with the outcome of (3 + 4) = 7.
2 + ( 3 + 4 ) = 9
The associative property: Changing the grouping of the addends does not change the outcome
Below is snapshot of the Shunya chart on whiteboard with magnetic beads.
The next blog will introduce subtraction and negative numbers. It will also revisit the properties we dealt in this article.