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How to defeat a dragon with math - Garth Sundem

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Now we mixed up things a little bit more: on the left side of the scale, not only do we have these identical unknown masses with mass X, these three blue things, we also have some of the 1kg masses over here, actually, we have two of them. Now, we are going to figure out what X is. But before we even do that, I want you to think about a mathematical equation that can represent what is going on; that equates what we have on the left hand, with what we have on the right side of the scale. I will give you a few seconds to think about it... So let's think about what we have on the left side: we have 3 masses with mass X, so you can say we have 3x and then we have 2 masses of 1 kilogram, so in total we have 2 kg. So + 2. So one way to think about the total mass on the left-hand side is 3x + 2. Three masses with mass X, plus two kilograms. That is what we have on the left-hand side. Now, let us think about what we have on the right-hand side. We can simply count them: [counts to 14] Fourteen blocks, each has a mass of 1 kg, so the total mass will be 14 kg. And we see that the scale is balanced, not tilting down or upwards. So this mass over here must be equal to this total mass. The scale is balanced, so we can write an 'equal'-sign. (let me do that in a white coulour, I do not like that brown) Now, what I want you to think about, and you can think about it either through the symbols or through the scales, is: how would you go about -- let us think about a few things: how would you first go about at least getting rid of these little 1kg blocks? I will give you a second to think about that... Well, the simplest thing is: you can take these 1kg blocks off of the left-hand side, but remember, if you just took these blocks off of the left-hand side, and it was balanced before, now the left-hand side will be lighter and it will move up. But we want to keep it balanced so we can keep saying 'equal'. That this mass is equal to that mass. So, if we remove 2 block from the left-hand side, we need to remove 2 from the right-hand side. So, we can remove two there, and then we can remove two over there. Mathematically, what we are doing is: we are subtracting 2 kilograms from each side. We are subtracting 2 from this side, So on the left-hand side we now have 3x + 2, minus 2 we are left with just 3x, and on the right-hand side we had 14 and we took away 2 (let me write this:) we took away 2, so we are going to be left with 12 blocks. And you see that there, the ones that I have not crossed out, there are 12 left, and here you have 3 of those X-blocks. Since we removed the same amount from both sides, our scale is still balanced. And our equation: 3x is now equal to 12. Now, this turns into a problem very similar to what we saw in the last video, so now I ask you: what can we do to isolate one x, to only have one 'X' on the left-hand side of the scale, while keeping the scale balanced? The easiest way to think about it is: If I want one X on this left-hand side, that is a third of the total X's here. So what if I were to multiply the left-hand side by one-third -- -- but if I want to keep the scale balanced, I have to multiply the right-hand side by one-third. If we can do that mathematically, Over here I can multiply the left-hand side by 1/3, and if I want to keep my scale balanced I also have to multiply the right-hand side by 1/3. Multiplying it physically literally means: just keeping a third of what we had originally We would get rid of two of these. If we want to keep a third of what we had here originally, -- there are 12 blocks left over after removing those first two -- so, 1/3 of 12: we are only going to have four of these little 1kg boxes left. Let me remove all but four. (so, remove those, and those...) And I have left [counts them] 4 here. And so, what you are left with, the only thing you have left, is this 'X' - I will shade it in to show this is the one we actually have left - and then we have these 1 kilogram boxes. You see it mathematically over here: 1/3 * 3x -- or you could have said 3x divided by 3 -- either way, that gives us -- these threes cancel out, so that would give you an 'X' and on the right-hand side: 12 * 1/3 - which is the same as 12/3, is equal to 4. And, since we did the same thing to both sides, the scale is still balanced. So you see that the mass of this thing must be the same as the mass of these 4 left-over blocks. x must be equal to 4 kilograms.

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Intro to two-step equations | Algebra (video) | Khan Academy

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Now we mixed up things a little bit more: on the left side of the scale, not only do we have these identical unknown masses with mass X, these three blue things, we also have some of the 1kg masses over here, actually, we have two of them.

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Play this two-step equation game alone or with another student. This game can also be played at school by dividing the classroom in two teams. Have fun solving equations!

You can play this game alone, with a friend, or in two teams. This game is a multi-player game that can be played on computers, Promethean boards, smart boards, iPads, and other tablets. You do not need to install an app to play this game on the iPad. Have fun evaluating algebraic expressions!

The game is based on the following Common Core Math Standards:

CCSS6.EE.2
Write, read, and evaluate expressions in which letters stand for
numbers.

CCSS6.EE.3
Apply the properties of operations to generate equivalent expressions.
For example, apply the distributive property to the expression 3 (2 + x) to
produce the equivalent expression 6 + 3x; apply the distributive property
to the expression 24x + 18y to produce the equivalent expression
6 (4x + 3y); apply properties of operations to y + y + y to produce the
equivalent expression 3y.

CCSS6.EE.4
Identify when two expressions are equivalent (i.e., when the two
expressions name the same number regardless of which value is
substituted into them). For example, the expressions y + y + y and 3y
are equivalent because they name the same number regardless of which
number y stands for.

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Play this two-step equation game alone or with another student. This game can also be played at school by dividing the classroom in two teams. Have fun solving equations! You can play this game alone, with a friend, or in two teams. This game is a multi-player game that can be played on computers, Promethean boards, smart boards, iPads, and other tablets.

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Math Resources For 6th Grade | 6th Grade Math Resources Online | Math Chimp

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Math Chimp has the best 6th grade math resources online. Our resources are all free and organized by the common core state standards for math. Come visit us and play the best 6th grade math resources.

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IXL Math Practice Problems (Two-Step Equations)

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IXL Math Practice Problems (Two-Step Equations)

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IXL | Solve two-step equations | 6th grade math

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Improve your math knowledge with free questions in “Solve two-step equations” and thousands of other math skills.