My first-grade daughter is struggling with learning how to count small change (half-dollars, quarters, dimes, nickels, and pennies). She can identify all the coins just fine. What she can’t do is look at an assorted pile of four to eight coins and work out how many cents it is. Unfortunately, that’s part of her school work, and she’ll be tested on it soon.
The problem is, as I see it, is that the kids have not been taught long addition yet. Long addition looks like this:
1
**25
10
10
5
1
1
--
2
50
--
52 cents**
So anyway … my daughter cannot yet do the adding in her head yet, even as she can identify the coins and their amounts. So without counting in the head, and without long addition, how else can a first-grader learn to add up change? What are good techniques I can use to help her learn?
Also: are there any good websites out there that can drill this specific skill?
A round-about way would be for her to take two coins, add them up, then take that number plus one more coin, add them up, and so on. It’s halfway to long addition, but using pairs of numbers that she (should be) comfortable with.
5, 5, 1, 25, 10
5+5=10
10+1 = 11
11+25 = 36
36+10 = 46
The thing is, she should know long addition, assuming she can add numbers greater than 10 together! She’s probably just intimidated when there’s a whole lot of numbers, because that looks scary, but reminding her how she does math like 16+17…“carry the one”…, you can then start adding a third to the set…16+17+18 = …“carry the two”…, and so on. Reinforcing this separately from coins is a good idea too, so that she’ll be more comfortable when faced with other situations where she’ll have to add large numbers or large amounts of small numbers together.
When they were teaching us how to count coins back in first grade we had a sort of candy store. Each piece of candy was a certain number of cents, and we’d get the candy only if we made the correct change. Would something like that help?
How about working on sorting them into even amounts? Two quarters = 50cents, two dimes and a nickel = a quarter, etc. It’s a different way of seeing it that’s not necessarily so math-like.
No. First graders are not going to understand the concept of “carry the two”. I’m also going to guess that the amount of change in this quote isn’t going to be similar to what a first grader will be expected to work with.
**bordelond **- can you give us some handfuls of change that’s been sent home with your daughter? At first grade, I’d expect them to be pretty simple “quarter and a nickel” or “dime and a penny” combinations.
There are a large number of flash games available on the web to teach this skill and many kids pick it up very fast this way. Just Google first grade counting change game or something similar.
Can she skip count? That is, count by 5s and 10s? If not, she has to do that first.
Second she has to get the idea of substituting. Start backwards as it is easier: you write a number on a piece of paper and she has to stack the right number of pennies there. Then give her a dime and have her give you the right number of pennies. Then a nickel. Then a quarter. And so on. Each time she has to give you the right number of pennies.
Then you either show her or she comes up herself along the way with the idea of giving you nickels and dimes instead of pennies for larger denominations. Counting all those pennies is annoying which is after all why we have dimes and quarters.
As you move up, dimes and pennies are usually easiest, then nickels and half dollars, then quarters.
Probably once she can do it backwards she will be able to do it forwards. If not then show her how – but only after she can do it backwards. It is usually not the addition skills but the idea that is the problem. It’s funny how some ideas just catch and others do not – Eldest got money and making change right away but had enormous difficulty with the notion that additin and subtraction are just reverse processes – when I showed him how to check his work this way he was entirely unconvinced that this would always be so, thought it was some kind of trick.
Actually … what mnemosyne posted was exactly the type of work she is being assigned. Any combination of eight or fewer coins, up to about $1.50 (judging by her homework problems).
I wish they did go with a unit where the kids added up two-coin combinations … that would seem like a logical intermediate step.
It actually sounds like the class is learning coin counting before they are mastering the equivalent math, which seems kind of wrong to me! If she is getting combos like 5, 5, 25, 10, 25, 1 then she needs to be able to add 5+5+25+10+25+1 in one go, which requires understanding how to “carry the two (or more, depending on the combo!)”, or pair them up (5+5)+(25+10)+ etc which at the minimum requires an understanding of “carrying the one”.
While I’d try the things suggested in this thread to help with the coins, this is a great opportunity to reinforce how numbers work, and why. I’ve seen math presented this way at the K-2 level:
Does she really understand that 7 is “seven ones” and 17 is “seven ones and one tens”? I’ve helped my mom enough in her classroom to know that this is a HUGE step in understanding how addition and subtraction work. If she can take 17+15 and understand that 7+5 makes 12 = “two ones and one ten, so place the ten in the tens column”, then you have 1+1+1 ten = 30, with the two makes 32. I know that this sounds rather complicated, but for a lot of kids, it makes a lot of sense.
This is the first random link I’ve found that presents numbers this way. Once she grasps this, then the coins will make a lot more sense!
I think so … they did a unit about a month ago where they were shown visual representations of 10s (bars 10 cubes high) and 1s (cubes). They’d show 3 bars and 4 cubes, and she’d have to write down “34” as the answer. She did fine with that EXCEPT when they showed high numbers of items – like if it was 8 bars and 7 cubes. I taught her just to count out the bars, write that number down as the 10s, and then count out the cubes and write that number down as the 1s. She got through it and made an A on that test.
Go back and see if she can still do it, then use bars and blocks to compare to money. Show her 2 bars and 5 blocks, ensure that she still understands what number that represents, and then make the connection to a quarter. Do the same with the other coins, and then start adding them up… 5 blocks (nickel) and one bar (dime) is ___? Gradually increase the number of coins, and reduce the need for blocks and bars unless she gets stuck, and then she can draw it out again. Constantly reinforce what she’s learning, and revisit it whenever you get the chance, using every opportunity to connect it to the new things she’s facing. Go to the store and buy something, and have her count out the change to pay for it (preferably at a quiet hour, when you won’t piss off everyone in line behind you!) She’ll get it eventually…everyone does!
People keep telling me that kindergarten is the new first grade and first grade is the new second grade… I dunno, this just sounds so advanced for first graders when you look at it. Maybe I’m just too far away from it.
Then again, I learned all this coin stuff by being given change by my parents to buy candy.
The first thing she needs to do is to master counting by 5’s, 10’s, and 25’s. This is actually easier than you might think. I taught kids who could not add 3 plus 4 count by 5’s up to 100 with no problem. Just have her chant the sequence several times a day. It becomes sort of like a song and is easily memorized.
Next teach her to sort the coins with the largest coin at the bottom. So if she has 2 quarters, 3 dimes, and a nickel, she counts using the sequence with the quarters first.
“25, 50,” counting and touching the quarters.
“60, 70, 80,” touching the dimes.
“85,” touching the nickel.
Perhaps the reason they are teaching this so early is that it really doesn’t require any knowledge of complex two-digit addition. It’s just counting along a number sequence.
This is explicitly true at my daughter’s school – they trotted out an advanced curriculum last year which aims to teach every class one grade level ahead. Since last year was the first year they did that, her kindergarten year was basically a mash-up of kindergarten and first-grade work.
I’m not sure that benefitted my daughter, in hindsight.
I teach my second-graders these skills–this sounds pretty advanced for first grade. It’s easiest for them to count the coins from largest to smallest values, and to count up. If she has a handful with two dimes, three nickels, three pennies, and a quarter, she’d rearrange them so her counting sounded like, “One quarter is 25, plus two dimes is 35, 45, plus three nickels is 50, 55, 60, plus three pennies is 61, 62, 63.”
But even this requires skip-counting by tens starting on 5, and that’s kind of a difficult concept.
I definitely would stay away from long addition. Kids at this age are very concrete and literal, and it’s nearly impossible for kids to get why long addition works. If they treat it like a magic spell that spits out the right answer, they’re likely to get it wrong.
I think it just depends on the district these days.