Materials
- Paper
- Pencil
Direct Aim
To discover the basis for algebraic laws
Age of Interest
???
First Presentation
1. Write out the following pattern of equations.
1 + 0 = 1
2 + 0 = 2
3 + 0 = 3
2. Then tell them, I am going to make the next one.
4 + 0 = 4
3. Ask them if they would like to make the next one. If they can do so. Then add the following one. Let the child do this as many times as they would like.
Second Presentation
4. Show them this pattern.
6 + 0 = 6
18 + 0 = 18
9 + 0 = 9
5. Then say, lets see, I would like to make the next one and apparently, it does not matter which number I choose first. That is called a random set. So I will choose what I like, and I like 6 (use the child’s age). so
6 + 0 = 6
6. You can now see if they would like to choose their own number. Let the child make as many of these equations as they would like.
Third Presentation (the child should have learned the commutative law of addition using beads earlier)
1. Have the child watch you put down the following equations.
3+8=8+3
6+12=12+6
4+11=11+4
2. Then say “I am going to make another one just like these. Then highlight how here is the “3”, and there, on the other side is the same number, “3.” Likewise for the “8”, but notice, that the “8” is first on the other side, but it was second on the first side. “3” was first on the first side, but now it is second on the other side. Then say, “I like the number 7 and the number 15, so I am going to use those numbers.
7+15 = 15+7
Ask the child to make their own equation. Let them take their time finding it. They need to have moved into this written, symbolic form of abstract thinking for this to work. As a note, for some children, they may find this pattern immediately, and so you can let them make the pattern immediately following step one if you notice excitement or interest.
3. If you can see that the child continues the pattern. Then do a second, and a third, and as many as they can. If the child is not able to see the pattern. Then add another set. If they still cannot see the pattern, then suggest that we try this on another day, and if they want to try it again, they can ask. (They might figure this out on their own and then they will come running to you excitedly).
4. If the child’s linguistic abilities are good, then have the child describe what they are “seeing.” At this point, you do not need to introduce abstract definitions of what they “see”, namely A + B = B + A. Let them discover that symbolic notation on their own.
Exercise
Suggest to the child that they make their own sets of numbers that are similar and use as big as numbers as they are able to do.
You can expand this set of presentations to include all the associative and commutative properties in arithemtic, as well other similar patterns such as multiplication by 1.