![]() You might be beginning to notice that I repeat the same lines over and over again. What we do to one side, we do to the other. By dividing by 2, this will show us what 1x equals. If we are unsure here, what do we need to do? This is telling us that 2 xs makes 6, but we need to figure out what 1 x makes. What we do to one side, we do to this other. What number represents nothing? Zero! So how do we make plus 8 into zero? What do we need to do? Again, this line of questioning is ESSENTIAL from moving students from following a list of directions into ACTUALLY understanding why inverse operations work. (And you can later explain why mathematically we have to move the +8 first, but that isn’t something I do here.) To move the +8, we need to make it into NOTHING. It’s easiest to move because it isn’t attached to the variable. ![]() We need to get out our detective skills and isolate the variable. Using the equations 2x+8=14 again, what if we are unsure of what plus 8 equals 14. So let’s chat about inverse operations with 2-operation equations. By starting with nice numbers, I am better ensuring the success of my students understanding the concept of solving equations before making it more complicated. When students have trouble with number sense, decimals tend to make things even more challenging. And the reason I do this is to help students truly grasp what the equation is saying and what value x has. Meaning I want to make sure that the answer comes out to be a whole number. One thing to note, and I maybe should have mentioned this earlier, is I try to use only “nice” numbers when we are starting out. Then the next day, we talk about multiplication and division. I’m testing this theory fully this school year, so stick around to see the results!įrom here, I give students a practice of just one-step equations involving addition and subtraction. I’ll probably introduce it for 2 step equations. ![]() Too many times I’ve seen students get hung up on the algorithm rather than the logic of the problem. I typically talk about what you do to one side, but I am doing it differently this year. Then we remember that the number minus 7 equaling 19 is the same as 19 + 7! X equals 26. When we walk through the x-7=19, I still use the phrasing, “We know that something minus 7 equals 19.” Our goal is for students to think about it that way because that helps bring meaning to it.īut this time we aren’t so sure. Let’s dive deeper into inverse operations. Sometimes I will ask for a certain method when we first learn about it, but most of the time, my students get the freedom to choose the method that works best for them. I am going to teach you multiple ways to go about solving for the value of x. So I have that conversation with students. Yes, these is typically one answer to a problem, the but the journey there is up to personal interpretation. We even try them each out as they are shared to show they work! Math is such a creative subject in the sense that there isn’t just one way to do things. While that last one helps lead into the conversation of inverse operations, it is important to validate all of the responses. Another student shared that we could “guess & check with a calculator.” And then typically a student brings up the idea of inverse operations by saying we could add 7 to 19 to find the value of x. ![]() ![]() I love to see the creativity that some of the students come up with! One year, I had a student suggest using a number line to count 7 spaces from 19. I find that asking them to come with 2 or 3 ideas helps them navigate the question better. I have students turn and discuss with a partner. If we don’t know what minus 7 creates 19, how can we mathematically figure it out? This is where the idea of inverse operations begins. ![]()
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