“I don’t get it.” the student complains.
“What don’t you get?” asks the teacher.
“Everything!” answers the student.
We’ve all heard that, especially in an algebra class. But what if I told you there is a way to avoid that conversation? It’s true. I found a way to introduce the following algebra concepts in a way that it just makes sense to students:
And the best part was that I never told them how to do algebra. It made so much sense in the format I presented that they taught themselves.
I began by showing them the fast-food menu shown here. Then I told them I was going to make some math problems based on it. They were expecting to see numbers, but I wrote:
h+f=
You should have seen their confused faces…and then the immediate change as the light came on and they shouted, “$2.90!” We did a few similar examples, and then I threw them this curve ball:
3f =
Immediately, they said, “$3.15.” I asked, “How did you get that?” They said, “We multiplied.”
“Why?” I asked, “It doesn’t say to multiply.”
“It just makes sense,” they replied. Without me telling them how, they began to see how letters could be used to replace number and how to calculate with them.
Next I gave them orders that customers had placed and asked them to write them algebraically. Notice that each one adds an incremental increase in thinking.
(x + c) + (2f + c + x) + (m + 2f + c) =
Again, I didn’t show them or tell them how to do this, yet they wrote:
2x+3c+4f+m
We worked more examples with increasing difficulty until I wrote this;
(3h + 2f + x) + (c + f + m) – (h + m + f) =
Interestingly, the students were able to distribute the negative sign across the terms – a commonly missed skill in algebra.
This led naturally into exploring the properties of mathematics:
h+6w=$8.15
Interestingly, even the 4th and 5th graders were able to do this even though they had not been taught to solve equations. They used subtraction and division in steps 1 and 2, even though the problem has an addition sign and implied multiplication (6•w). What was more amazing was that these students had been taught order of operations, yet they all subtracted before dividing.
That left me thinking, if there is this much algebraic intuition residing in their brains at age 10, how can we believe that our students can’t learn algebra?
In my 8th grade algebra class, we also used the menu to approach other concepts such as solving systems of equations.
If you’d like a free copy of the handout, click the “handout” button below. And to watch a video explaining the whole process, click the “video” button.
“What don’t you get?” asks the teacher.
“Everything!” answers the student.
We’ve all heard that, especially in an algebra class. But what if I told you there is a way to avoid that conversation? It’s true. I found a way to introduce the following algebra concepts in a way that it just makes sense to students:
- Working with variables
- Translating word problems into math
- Combining like terms
- Understanding the properties of algebra
- Solving equations
And the best part was that I never told them how to do algebra. It made so much sense in the format I presented that they taught themselves.
I began by showing them the fast-food menu shown here. Then I told them I was going to make some math problems based on it. They were expecting to see numbers, but I wrote:
h+f=
You should have seen their confused faces…and then the immediate change as the light came on and they shouted, “$2.90!” We did a few similar examples, and then I threw them this curve ball:
3f =
Immediately, they said, “$3.15.” I asked, “How did you get that?” They said, “We multiplied.”
“Why?” I asked, “It doesn’t say to multiply.”
“It just makes sense,” they replied. Without me telling them how, they began to see how letters could be used to replace number and how to calculate with them.
Next I gave them orders that customers had placed and asked them to write them algebraically. Notice that each one adds an incremental increase in thinking.
- I'd like four hamburgers, six orders of French fries, a large soda, two medium sodas, and an extra-large soda. (4h+6f+l+2m+x)
- I want three cheeseburgers, one hamburger, a small soda, two fries, a medium soda, and another hamburger. (3c+h+s+2f+m+h or 3c+2h+s+2f+m Some students combined like terms.)
- Let's see… I think I'd like three hamburgers and a cheeseburger, three fries, a large soda, two medium sodas, and an extra-large soda. Add another order of fries on that and make one of those hamburgers another cheeseburger. (3h+c+3f+l+2m+x–h+c or 2h+2c+3f+l+2m+x Changing one’s mind introduces subtraction into the expression.)
(x + c) + (2f + c + x) + (m + 2f + c) =
Again, I didn’t show them or tell them how to do this, yet they wrote:
2x+3c+4f+m
We worked more examples with increasing difficulty until I wrote this;
(3h + 2f + x) + (c + f + m) – (h + m + f) =
Interestingly, the students were able to distribute the negative sign across the terms – a commonly missed skill in algebra.
This led naturally into exploring the properties of mathematics:
- Commutative property: h+f=f+h
- Associative property: (2h+f)+(c+m)=(2h+m)+(c+f)
- Distributive property: 2(h+m)=2h+2m
h+6w=$8.15
Interestingly, even the 4th and 5th graders were able to do this even though they had not been taught to solve equations. They used subtraction and division in steps 1 and 2, even though the problem has an addition sign and implied multiplication (6•w). What was more amazing was that these students had been taught order of operations, yet they all subtracted before dividing.
That left me thinking, if there is this much algebraic intuition residing in their brains at age 10, how can we believe that our students can’t learn algebra?
In my 8th grade algebra class, we also used the menu to approach other concepts such as solving systems of equations.
If you’d like a free copy of the handout, click the “handout” button below. And to watch a video explaining the whole process, click the “video” button.
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