My second grader has a “Think about it” section on his homework that asks the following question: How do you think knowing that 125 + 150 = 275 can help you solve 275 - 150 = ?
My wife and I tried to explain it in terms of addends and sums, but he says his teacher doesn’t use those words in class. I’m not sure how else to explain it to him simply enough that he can understand, especially since I don’t know the terminology his teacher is using. The entire worksheet is about 3-digit subtraction.
Addition and subtraction are opposite operations (that’s good enough for a second grader, I think). Also, you can teach a rudimentary form of algebra and take the first equation and subtract 150 from both. Also, subtracting 150 is the same as adding negative 150. Does he know about negative numbers?
if you know 2 and 3 makes up to 5, then 5 minus either 2 or 3 equals the other. use objects if needed. emphasize that big numbers are just the same as the little ones but fatter.
A number line is a good tool here. Explain that addition is equivalent to moving to the right on the line, and subtraction moves to the left.
So if you start at 125 and move 150 spots to the right, you’d end up at 275. If you then start at 275 and move 150 spots to the left, you’re back at 125.
So if you already knew that starting at 125 and moving 150 spots to the right puts you at 275, then you know that moving 150 spots back to the left will put you back where you started.
I assume he understands subtraction and addition (if not why is he dealing with three digit numbers).
Have him see
1 + 5 = 6
6 - 1 = 5
6 - 5 = 1
Do this for a bunch of other numbers til it makes sense. Assuming the problem really is as you stated - it really is just a matter of understanding that subtraction is the “opposite” of addition.
I work with data all day long and took advanced math classes all through middle and high school - and don’t remember once seeing the term “addend” - to the best of my knowledge this is the first I have seen it (granted I became an English major in College).
Also - IIRC - we didn’t learn about negative numbers until 5th grade when I was in school.
Do you have any paperclips? Or other small objects?
Clear off a tabletop.
Put down 2 paperclips in one pile. Put 3 paperclips in another pile.
Take an index card (or post-it note or whatever) and put the number “2” on it next to the 2 clips and put another card with “3” on it next to the 3 clips. Ask your child how many clips you have. Child should say “5.” Put “5” on a piece of paper to the right of the two piles.
Now pick up the 3 clips and say “How many clips do I have if I take away 3 clips?” Hopefully your child will say “2.” You say “that’s right!” Now point to the three pieces of paper and say “See, if I start with 5 clips (point at the 5) and I take away 3 clips, I have 2 clips (point to the two).” Do this over and over with piles of differing sizes until your child gets the pattern that if you take away the second pile of clips, you are left with the number next to the first pile of clips without having to count the clips.
Once your child gets the pattern, pour out half the box of clips into one pile and half into the next pile. Prepare the index cards and put down the first one and say “there are 125 clips in this pile.” Similarly, put a card with 150 next to the second pile. Then put the third “total” card with 275 on it down. Ask your child how many clips are left if you take away the second pile. Hopefully, your child should point to the 125 on the first card.
Now have a talk about how if you have two numbers added together and you take away the second number, you are left with the first number.
And reinforce this with some more clips and cards exercises.
We have basically used the advice most you have already given: show him how numbers such as 2 + 3 = 5 and that reversing that (5 - 3 = 2 or 5 - 2 = 3) can provide the answer to the subtraction question.
He does understand that, so maybe that’s sufficient enough for this particular question.
We haven’t used visual aides, but that was the next step. I also really liked friedo’s suggestion to use a number line. I remember number lines being helpful to me in early math classes.
Feel free to keep responding. I’m certainly not a teacher and I welcome advice!
It’s hard to answer without knowing what sort of thing flies with that particular teacher. A perfectly correct answer can be graded down because it isn’t the expected answer, that is, it’s not like the examples or instruction given in class.
I’d say that the two equations are just two different ways of writing the same thing. Same relationship, different emphasis in the description.
Then I’d be visual, but rather than having individual items, I’d draw two rectangles next to each other. One would be labeled 125 and the other would be labeled 150. Then I’d draw a bracket or dimension lines showing the length of both and label it 275. Which would work unless the teacher had spent a lot of class time explaining that addition and subtraction are opposites.
I wouldn’t touch a number line with a ten foot pole unless I knew that my second grader already knew what one was and how to use it. Unless I really disliked the poor kid. Especially not to illustrate an answer involving three digit numbers. Maybe if I didn’t like the teacher and had a really long sheet of paper.
Clearly, your son has learnt about subtraction. Well, what does he think subtraction means? Tell him "275 - 150 means the number that you add to 150 to get 275. That’s the definition of subtraction (or ‘minus’ or whatever word your son uses); that’s what subtraction is all about. So to figure out the answer to 275 - 150, you have to figure out what number you add to 150 to get 275.
If you happen to know that 125 + 150 = 275, then you know that 125 is the number you add to 150 to get 275. And another way of saying the exact same thing is ‘275 - 150 = 125’. It means the exact same thing as ‘125 + 150 = 275’; it’s just stated using different words/symbols.".
Wow - and they actually use these words in ELEMENTARY school. I had the highest standardized math score of anyone in my class in elementary school (only like 60 people).
I specifically remember two incidents in math in elementary school:
In third grade - a kid named Eddie couldn’t get 7 x 3 = 21 and 3 x 7 = 21. We spent the WHOLE class just going over this - over, and over, and over. To this day - I SWEAR my brain slightly processes 7 x 3 faster than any other single digit multiplication problem (we only memorized up to 9 or 10 (not 12 like I think some did).
That was third grade - I am pretty sure I wouldn’t have gotten or appreciated words like subtrahend. I know Eddie wouldn’t have. I had enough problems understanding why “colonel” was pronounced “kernal” that was either 2nd or 3rd grade.
The other was when I was in fifth grade I remember the teacher teaching addition of fractions and they were only going up to stuff like 1/2 + 1/6. I remember sitting there and visualizing breaking my locker (in my mind a frontal view) into six pieces - realizing that 1/2 would take up three of these and adding in the extra sixth.
Visualizing always helps me - and you cant visualize 125 of anything. Even when I deal with complex problems today - I still break it down into something I can visualize.
Yeah, this is where we started with the 2 + 3 = 5, and then the numbers from his problem: 125 + 150 = 275. He seemed to understand that for the most part, so hopefully it will stick.
I’m not sure any math problem should be explained to a second grader. Explanation may aid in their understanding of concepts, but it won’t help at all with what the teacher expects, which is to answer a problem in an accepted, expected way.
At that stage, learning is invariably focused on 2 things: the teacher and the text. Go outside that and you’re setting your child up for a rough time in school - especially if they’re bright.
Does his math curriculum use the concept of fact families? That’s what schools around here use starting in 1st grade, I think. I’d start any discussion about this problem by talking about the fact family those three numbers make.
What worked with my daughter was the word backwards. Not inverse, not opposite, backwards.
“Subtraction is addition backwards. 1+2=3 going forwards and 3-2=1 going backwards. 1-2-3, 3-2-1.” I said that to her and she glazed-over for a second and then it was like the proverbial lightbulb. I don’t know why it worked, but it did.
Anyway, my kid was taught all those words no one can remember back in early elementary school too. We just don’t use those terms as adults, I think. I bet most of the people reading this can recite the quadratic formula off the top of their head though.
You’re kinda making pretty big assumptions about a teacher and a class. The op states that the question was: “How do you think knowing that 125 + 150 = 275 can help you solve 275 - 150 = ?” So the whole point is to have the kid understand the concept.
