Ep 22: Facile Number Sequence the Final Counting Series Episode Part 6

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We are at the end of the counting series. There are stages for decomposing numbers or structuring numbers.

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There are stages for number recognition. There's stages for early multiplication and division.

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There's stages for a lot of things and I can definitely dig deeper into those at a later date if that's something you'd be interested in.

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But the real reason that I wanted to share this information with you is that I definitely did not know it starting out my teaching career.

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And my thought is maybe you're a new teacher like I was looking to make sure that your kids really understood math.

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Maybe you're a couple years in and you feel really strongly that you're you got a good grip on teaching reading, teaching writing, and you're looking to kind of delve into math.

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I wanted this information to be readily available so that your students could benefit and so that you get a deeper understanding of how your students are doing in math and how to help them grow and succeed.

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Hello and welcome to Making Number Sense Make Sense, a podcast for elementary teachers, specifically early elementary teachers, looking to really make an impact in the number sense of their students.

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The last stage of counting is facile number sequences.

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So this is where everything really starts to come together.

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Students at this stage will be able to use a variety of not counting by one strategies to solve addition and subtraction problems.

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What are you looking out for in terms of the other areas of mathematics to know that this is where they are?

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Students at this stage will be able to count forwards and backwards to 100 and beyond.

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They'll be able to skip count by twos, threes, fours, fives, tens.

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They'll be able to recognize numbers to 100 and many three different digit numbers.

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Zero might still be a little tricky, but a lot of times they're moving beyond that.

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And at this stage, something that's important that might not be necessarily as visible in other stages is they'll really have an understanding or start to be developing a strong understanding of place value.

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So knowing that 26 is two tens and six ones, and they'll be able to use skip counting or repeated addition to solve multiplication and division problems without formal instruction on those things.

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At this stage, some of those not counting by one strategies students might be able to solve is using one like compensation, using a known result, making tens, doubles or near doubles,

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decomposing numbers, commutative property and subtraction as the inverse of addition.

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So by compensation, I'm going to tell you a little story about a mentor that I had, a teacher that I had.

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And she was talking about how one of her students says to her very confidently, I will never need to regroup.

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And she looked at him, she goes, well, what do you mean that you'll never need to regroup?

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So I think the number that he was doing was a three digit number.

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I'm just going to do a two digit for the sake of this.

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So I don't get confused, but say that the question was 40 minus four.

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What the student said was, well, I can take one away from the 40 and make it 39.

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And that way when I subtract, I don't have to regroup at all.

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I don't have to borrow at all.

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And then I'll just add the one back in.

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So instead of 40 minus four, he made it 39 minus four, which made 35.

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And he put his one back in, made 36.

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Using a known result is like if you're doing number strings, they'll use what they've learned from the previous question and apply it to their next question.

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It might be, you know, making tens or fives or friendly numbers.

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So again, if we're doing 40 minus four, well, a student might say, well, I knew that 40 minus five would be 35 because five is a friendlier number.

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And then just add another one on because he made the number one bigger and making it 36.

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Another one might be making tens or decomposing.

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So instead of working with 40 minus four, they might be more familiar with a 10 minus four because they know the tens facts or the friends of 10.

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So they'll know four. And how many more do you need to make 10?

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Six. Your answer would be 10 minus four is equal to six.

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And you still have your 30. Put them back together.

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Thirty six.

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And the community of property is realizing that when you're doing addition, the order of your add ins doesn't really matter and subtraction being the inverse of addition.

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So students in this stage will be able to look at a problem and think what.

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Strategy will be the best to solve this problem or what strategy do I think will make the most sense to me when solving this problem?

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And they'll have all of these strategies to pull from because they had been working with all of these different problems and all of these different ways to make sense of number.

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That's why it's really important to give students a ton of chances and variety in the problems that you're using so that they can get to this stage where they are ready.

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They can use what they know and then be ready to move on to the next stages of their math development.

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So through this series, we have worked with students who cannot yet count without one to one correspondence without the number sequence at all to them starting to understand the way numbers work,

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develop those three aspects of number, knowing what the symbols mean, the quantity.

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And how many that is, like how many each of these numbers is to be able to then use all of these different strategies and pull all of these different strategies to solve problems.

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So these stages build on each other as they would suggest.

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And sometimes you might have a student who's just missing this one little piece.

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And once they get it, they'll be able to fly through and move to the next strategy.

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So, again, my hope with this series was to give you an idea of what kind of to look out for in each of these strategies so that you'll be able to support your students the best you can.

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If you've enjoyed the series, make sure that you leave a review.

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You can leave a comment. You can send me a message.

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You can fill out the Google form and do not forget November 17th, 2023 sign up for the virtual Manking Math Moments Summit completely free.

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And in the next episode, I'm going to tell you about some of the sessions that I have my eye on that I am super excited to get to experience and get to learn about.