Writing two step word problems
In the second story ('bought games for $6 each and had $34 left, how many games?'), 87 - 6m = 34 gives m = 53/6, about 8.83, which is not a whole number of games. Interventions avoid asking students to solve it and raise it as a discussion point instead.
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Starting from the equation 87 - 6m = 34, the video writes real-world story problems it could solve: spending money on games, or people leaving a room in groups. It shows that 6 and m can swap meanings, and then changes the equation to the inequality 87 - 6m ≥ 34 to ask for the most Sal can spend per game.
You'll be able to
- write a story problem that matches a two-step equation.
- explain what each number and the variable mean in a story.
- turn a phrase like 'at least' into an inequality.
Key words
- equation
- A statement that two expressions are equal, like 87 - 6m = 34.
- inequality
- A statement that compares two expressions using signs like ≥ or <.
- variable
- A letter, like m, that stands for an unknown amount.
- at least
- That amount or more, written with ≥.
Transcript
- So here I've already written down an equation, 87 minus 6m is equal to 34. And what I wanna do in this video is think about the types of problems that this might solve in the real world. And you might wanna pause this video and think about that yourself. So let me just come up with a few together.
So one might be, let's say that Sal, I'll write a word problem or a story problem here, Sal saved $87. He bought, I don't know, let's say six toys, or let's say six games and had $34 left, $34 left. How much was each game? How much was each game? Now, how did I come up with this?
Well, I see here that I'm starting with 87 of something and I'm subtracting something from it and I have something left over. So that made my brain say, okay, maybe I started off with a certain amount of money, or the person in the problem starts off with a certain amount of money, and then they're spending it somehow.
And the six could describe how many things this person bought. And so that's why I wrote Sal bought six games and had $34 left. And in that case then, this m would tell you how much each game was. So then you could solve this equation for m and then that would be the price of the game.
Now, you could do something similar where instead of six representing the number of games, maybe six is actually the cost of each game and m is the number. So you could say instead of he bought six games, you could say he bought games, bought games for $6 each and had $34 left.
How many games did he buy? How many games did he buy? And so once again, you can interpret the six as the number of games and then your m as the cost of each game, or you could view six as the cost and m as the number that Sal in this case actually bought. Now, we could do similar things if instead of it, and it doesn't have to be we started with money, it could be people leaving the room, 87 people are in the room and people are leaving the room of groups of six, or you might say that there's six groups that left the room and how many people were in each group if you had 34 leftover?
And a related interesting question is, what if instead of this equality, what if this was a inequality? So what if it said 87 minus 6m is greater than or equal to 34? Well, then you could have a similar context. Like I said before, Sal started with $87. He bought six, or he wants to buy, let's write it this way, he wants to buy, he wants to buy six games.
And then we could say, what's the most that he could spend per game? What is the most he can spend per game on average, spend per game on average, to have at least $34 left over, to have at least, and this at least is where we're talking about what he has left over or what I'm going to have left over has to be greater than or equal to 34.
So at least $34 left over. And so now when you're going to get something where m is going to have to be less than or equal to something, so that tells you that m can't be more than whatever we solve for in this inequality. So I'll leave you there. Hopefully this makes you appreciate that an equation like this can be used to solve many different types of problems.
And it's actually pretty fun to think about to actually construct to make a problem that can be solved with any given equation.
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