You might be thinking, "Come on, Kate. I may be bad-at-math,* but I know how to add."
THE most common problem I see in math-fearful people is that they never attached real, physical meaning to algorithms. They may have learned how to execute a series of steps, and they can repeat that, but if there's no deeper meaning behind the algorithm, any increasing complexity feels like starting all over from scratch. Whereas, once you have the meaning, building complexity feels fun, like mastering one level of a game and then increasing the level of your play. So let's build a stronger foundation, shall we? And if we've got the foundation already, let's remember what it's like to be learning so that we know how to talk to our kids productively about math.
Addition is just counting.
Counting one by one is fine for small numbers, but it gets to be slow and annoying for big numbers, so we use ADDITION to help us count in groups.
When I introduce addition to my own children, I do so with physical games and physical tools. You can use any small, countable thing for your tool. Dry beans. Pennies. Pebbles. Whatever.
I use glass beads, in two different colors: blue for positive, orange for negative -- for now, all you need is one color. Because positives are easier to think about, I'll use my blue.
I have the child pick a handful of beads, and then I pick a handful of beads. We put them both on the table, and then count them altogether.
Great! We have two groups. 5 and 8.
In math, "AND" is just another word for +. When we say 5 AND 8, we mean 5 + 8. And when we count them altogether in one big group, we get 13.
SWEET! We are adding!
Now... your child might be doing something in math called RE-GROUPING. Which means, to make it easier to figure out this problem, let's MAKE TEN.
Our number system is called a BASE-TEN system, which just means that there are ten symbols we use to write numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
And when we run out of counting symbols (at 9) we must use DOUBLE DIGITS to count the next set of numbers.
The first set of nine numbers can be counted simply. Written down, all these numbers exist in the ONES PLACE, which just means that in the number 4, we are counting 4 ones. So 4 just means 4.
(Duh, Kate.)
But once you're into double digits, you have a TENS PLACE. And any symbol in the TENS PLACE stands for a set of ten. Which means that,
in the number 40,
4 does not mean 4
in the number 40
4 is FOUR TENS
and 0 is ZERO ONES
In a two-digit number, each symbol has a different meaning!!!
So all of a sudden counting, something you've known how to do for decades, is feeling way more complicated than you thought! Remember that your children are learning to navigate these patterns from scratch, without years and years of rote practice.
And that if you never learned to navigate it with meaning behind the symbols, OF COURSE it feels scary and disorienting!
So nowadays, instead of jumping straight to symbols and algorithms, we teach kids with pictures and manipulatives (physical objects like my glass beads). And we teach them to MAKE TEN.
With a preschooler, I would probably just straight count these beads. But with my kindergartener, who is into it (not all kindergarteners are ready -- and do not feel like this is a good vs. bad thing, because we're ALL working on something! Lucia doesn't have all her letters yet, despite being 6)
With Lucia, I will encourage her to MAKE TEN
It's easiest for me to see ten if I arrange my beads two by two:
I always try to make the FEWEST moves possible to make a group of ten. In this case, it means taking a pair of 2 beads from the pile of 5, and transferring them to my pile of 8:
Order, unfortunately, matters, because the left hand digit in our two-digit number represents sets of tens. So swap piles to put your sets of ten on the left, and the leftover set of 3 on the right.
As a savvy, life-long user of numbers, you might recognize that we have, laid out in front of us, the number 13. Because my child is at an age where she is learning to connect digits to meaning, I then put it into written form beneath my piles. The first post-it stands for groups of ten -- I have 1 group of ten. The second post-it stands for leftovers that get counted by 1. I have 3 leftover.
My number is:
1 ten + 3 ones. = 13
If this seems easy and obvious to you, great! You have a strong foundation of understanding physical meaning behind mathematical symbols for addition! Remember that your kids may still need some reinforcement and practice and TIME to integrate this, and have all the patience in the world as they practice this discovery themselves. Time is SUCH a gift, and you should give it generously.
If it seems like a revelation, great! You are building real life meaning to go with a lifetime of symbols you've been using habitually. You have just deepened your understanding!
And if this still seems scary and confusing, shout out to me in the comments! You may need more time or a different way of thinking about it -- and that is WONDERFUL. Tell you what, we have lots and lots and LOTS of time right now! So let's take all we need.
If you'd like a resource that supports this lesson, I HIGHLY recommend BIG NUMBERS by dragon box. It's addictive, so just be aware of that, but it is also intuitive and a wonderful way to practice these skills. Both my 6yo and 10yo play it and love it. Though the 10yo probably doesn't need it as much anymore, she's just in it for the fun -- know that some 10 year olds would totally still need this game, and don't be afraid to meet yours where she's at.
* Recall that your humble teacher doesn't BELIEVE in "good at math" or "bad at math." There is only LEARNING math vs. feeling stuck and you should feel absolutely free to dabble in both states of being because they are transient states with all the world of freedom to travel back and forth!
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