October 23, 2023 • 9 mins
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In this week's episode, we’ll look into the next counting stage Intermediate Number Sequence. In this stage, of counting, we will really start to see all of our hard work come together as students become more confident and successful problem solvers, specifically with subtraction!
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Episode Transcript
Available transcripts are automatically generated. Complete accuracy is not guaranteed.
(00:00):
We are about halfway through the counting series and I'd like to talk to you really quick about something very exciting that is happening November 17th through the 19th, 2023.
(00:12):
There is going to be a Making Math Minds virtual summit that is completely free over those days and George truly will be presenting all about the counting stages so you can really see it come to life.
Now I am not the only one presenting. There are over 20 other really, really awesome and interesting looking presentations that I can't wait to dive into.
(00:34):
The link to register will be right in the show notes. Mike is at absolutely free for the weekend.
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.
(01:00):
The next stage of counting is the initial number sequence.
Now in this stage of counting, your students have developed advanced counting strategies that are more than just counting by ones and are able to solve problems through 100 using numbers through 100.
Take for example, 67 plus 5. A student at this stage might be able to use the count up from strategy.
(01:26):
So they count up from the first number 67 to the number that they need to solve the problem. So in 67 plus 5, they would say 67, 68, 69, 70, 71, 72.
They'd be able to know when to stop because they can track how many counts they have made.
And the most common way that kids track the counts that they've made in a problem like this would be using their fingers.
(01:50):
So it's really important for students to have their finger patterns ready so they know exactly when to stop counting and what the answer is.
They might also use a count up to strategy, which is different from the count up from strategy because in the count up to strategy, they're missing the add end and they'll have to figure that out.
So the problem would be something like 18 plus what number is equal to 22 versus the other one you had the two add in 67 plus 5.
(02:18):
This one, the example is 18 plus blank equals 22. They'd have to count up to 22, which is the answer that they're looking for.
So starting at 18, 19, 20, 21, 22. And again, tracking on their fingers, they would be able to tell, OK, I've made my how many counts I've made would be 4.
And then the answer would be 4. 18 plus 4 is equal to 22.
(02:42):
At this point, they may be able to solve count down to problems, which are subtraction problems where they know the number that they're starting with and the number they're subtracting, not necessarily if a number is missing.
So they may be able to solve 15 minus 3, but they might not be able to solve 15 minus what number is equal to 12. So again, they count on their fingers.
(03:04):
15 minus 3, 15, 14, 13, 12.
Now, you'll notice in these problems, the number that they're counting up to or counting down to is usually not more than five.
And the reason for that is you're wanting the students to develop different strategies for counting.
And if they're counting very, very long strings of numbers, it kind of takes away from the flexibility of being able to create strategies.
(03:28):
So for these kinds of problems, when you're working on this counting stage and supporting them and making it to the next one, the focus really is the strategy versus how high or how low they can count.
Now, what are you looking out for that might let you know that your students are at this stage?
Like I said, mentioned the types of problems that they'll be able to solve is a huge indicator.
(03:49):
But beyond that, they'll need to be able to track their accounts, which is a huge marker of this stage.
Most students in this stage can already count to 100 and beyond.
They may be able to count backwards from 30, maybe not yet to 100.
They'll be able to recognize numbers to 100, but might make some reversal errors like calling 37, 73.
(04:13):
And they may also be able to name some three digit numbers like 527, but 502 might still cause a mistake.
That zero there can be a little bit tricky.
They also might be able to skip count by tens on the decade, like 10, 20, 30, but maybe not off of the decade, like 14, 24, 34.
So how can you help students at this stage of counting?
(04:37):
Now, of course, most important is that you're giving them opportunities to solve different kinds of problems.
So whether that be through number talks, through problem solving sessions, really giving them a chance to work through it with on their own or with partners
and talking about things will help them in this strategy really be able to solidify and start to be able to choose the strategy that works best for the problem that they have.
(05:03):
In terms of the other skills that would support students at this counting stage, a big one is working with the hundreds chart and hundreds chart activities.
The reason for this is, like I said, they might still be confusing the order of their numbers, like 37 instead of 73.
So you're going to want to give them a chance to really get familiar with number patterns and the way that they look and the way that they act, so to speak,
(05:29):
so that they'll be able to use that information for problems with higher numbers.
This is my favorite hundreds chart activities.
This one is so easy to do. It's a hundreds chart puzzle.
So for this one, you would print off a hundreds chart or 120 chart, laminate it usually and then cut it up and then have students put it back together.
The bigger or smaller the pieces are changes the level of difficulty.
(05:52):
If you're just starting, you might just cut on the decade.
So it's just like lines vertically or horizontally so they can start to put numbers together that way and then maybe change to things that are more difficult with smaller pieces.
That one is really easy to do and the kids really enjoy my students, at least always really loved puzzles and doing any kind of puzzle.
So that's a great one.
Something that might help you if you're wanting students to write numbers and really dive deep into patterns is fill in the missing numbers, spin and fill.
(06:20):
So for this activity, they kind of have two spinners.
They have one decade spinner, so like a 10 spinner and then a one spinner all in a mat.
And so they'd spin the first number to get their decades.
So say it was 60 and then the next one would be the one.
So if they got 60 and five, their number would be 65 and they can put that number anywhere in the little puzzle piece or small piece of the hundred start that they have.
(06:44):
And then from there, they'd have to figure out, OK, I have 65 and what are the other numbers I need to fill in that are close to 65.
So spin and fill is a really easy game to play.
They can have a hundred start available if they need it.
And that way they can get a little hands on practice with it.
Also side a little side practice of writing their numbers and being careful about the order of their numbers.
(07:08):
So it's less easy to get confused.
And of course, there's tons of missing number like print and go worksheets that are great for morning work or early finishers, things like that.
And similar to in figurative counting, the stations or types of centers that I mentioned previously, you're going to want to keep having students practice counting on or developing other strategies.
(07:30):
One that I did not mention last time is called how many candies and similar to the previous station, it involves spinners.
I love spinners because I can put exactly which numbers I want the kids to work on or the number range.
And then from there, they really be able to develop some strategies and practice in a larger name range than a dice might provide.
(07:52):
So for that one, they would spin the first spinner, which is like a hidden hand and it just has a number next to it.
So the idea is hiding in that hand is however many.
So say that they spun a nine, there'd be nine candies hiding in the hand and then they would spend the next spinner and it tells them how many more to add to the hand.
(08:14):
So that one would be like nine, ten, eleven, twelve if they got three.
So again, the numbers that they would add to it are small within five, but it also lets them get a lot of practice in a lower number range.
So they can focus on the strategy, not necessarily the counting larger numbers that comes more in hundreds chart activities,
(08:35):
coral counting, counting collections, that kind of thing when you start to work with bigger numbers.
Since they're still working on the counting down from strategy, so fifteen minus blank equals twelve.
You might want to do some missing number type activities so they can figure out and practice that skill to get them ready for the next stage of counting.
(08:57):
If you have any questions or anything you would like me to follow up with you on, you can always send me a message on Instagram.
I also have a Google form down in the show notes that you can fill out if you have any requests, any other comments.
I read every single one.
Don't forget to register for the free Making Math Minds Virtual Summit if you're listening before November 17th, 2023.
(09:21):
Though probably they'll have one next year. I don't know when though, but that is a great opportunity to get lots and lots of free professional development.
They also offer certificates so you can get that.
So you'd have to check with your district, but you might also be able to get those credits towards your teaching license or renewing your teaching license.
So until then, you'll hear me next time.
We are about halfway through the counting series and I'd like to talk to you really quick about something very exciting that is happening November 17th through the 19th, 2023.
(00:12):
There is going to be a Making Math Minds virtual summit that is completely free over those days and George truly will be presenting all about the counting stages so you can really see it come to life.
Now I am not the only one presenting. There are over 20 other really, really awesome and interesting looking presentations that I can't wait to dive into.
(00:34):
The link to register will be right in the show notes. Mike is at absolutely free for the weekend.
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.
(01:00):
The next stage of counting is the initial number sequence.
Now in this stage of counting, your students have developed advanced counting strategies that are more than just counting by ones and are able to solve problems through 100 using numbers through 100.
Take for example, 67 plus 5. A student at this stage might be able to use the count up from strategy.
(01:26):
So they count up from the first number 67 to the number that they need to solve the problem. So in 67 plus 5, they would say 67, 68, 69, 70, 71, 72.
They'd be able to know when to stop because they can track how many counts they have made.
And the most common way that kids track the counts that they've made in a problem like this would be using their fingers.
(01:50):
So it's really important for students to have their finger patterns ready so they know exactly when to stop counting and what the answer is.
They might also use a count up to strategy, which is different from the count up from strategy because in the count up to strategy, they're missing the add end and they'll have to figure that out.
So the problem would be something like 18 plus what number is equal to 22 versus the other one you had the two add in 67 plus 5.
(02:18):
This one, the example is 18 plus blank equals 22. They'd have to count up to 22, which is the answer that they're looking for.
So starting at 18, 19, 20, 21, 22. And again, tracking on their fingers, they would be able to tell, OK, I've made my how many counts I've made would be 4.
And then the answer would be 4. 18 plus 4 is equal to 22.
(02:42):
At this point, they may be able to solve count down to problems, which are subtraction problems where they know the number that they're starting with and the number they're subtracting, not necessarily if a number is missing.
So they may be able to solve 15 minus 3, but they might not be able to solve 15 minus what number is equal to 12. So again, they count on their fingers.
(03:04):
15 minus 3, 15, 14, 13, 12.
Now, you'll notice in these problems, the number that they're counting up to or counting down to is usually not more than five.
And the reason for that is you're wanting the students to develop different strategies for counting.
And if they're counting very, very long strings of numbers, it kind of takes away from the flexibility of being able to create strategies.
(03:28):
So for these kinds of problems, when you're working on this counting stage and supporting them and making it to the next one, the focus really is the strategy versus how high or how low they can count.
Now, what are you looking out for that might let you know that your students are at this stage?
Like I said, mentioned the types of problems that they'll be able to solve is a huge indicator.
(03:49):
But beyond that, they'll need to be able to track their accounts, which is a huge marker of this stage.
Most students in this stage can already count to 100 and beyond.
They may be able to count backwards from 30, maybe not yet to 100.
They'll be able to recognize numbers to 100, but might make some reversal errors like calling 37, 73.
(04:13):
And they may also be able to name some three digit numbers like 527, but 502 might still cause a mistake.
That zero there can be a little bit tricky.
They also might be able to skip count by tens on the decade, like 10, 20, 30, but maybe not off of the decade, like 14, 24, 34.
So how can you help students at this stage of counting?
(04:37):
Now, of course, most important is that you're giving them opportunities to solve different kinds of problems.
So whether that be through number talks, through problem solving sessions, really giving them a chance to work through it with on their own or with partners
and talking about things will help them in this strategy really be able to solidify and start to be able to choose the strategy that works best for the problem that they have.
(05:03):
In terms of the other skills that would support students at this counting stage, a big one is working with the hundreds chart and hundreds chart activities.
The reason for this is, like I said, they might still be confusing the order of their numbers, like 37 instead of 73.
So you're going to want to give them a chance to really get familiar with number patterns and the way that they look and the way that they act, so to speak,
(05:29):
so that they'll be able to use that information for problems with higher numbers.
This is my favorite hundreds chart activities.
This one is so easy to do. It's a hundreds chart puzzle.
So for this one, you would print off a hundreds chart or 120 chart, laminate it usually and then cut it up and then have students put it back together.
The bigger or smaller the pieces are changes the level of difficulty.
(05:52):
If you're just starting, you might just cut on the decade.
So it's just like lines vertically or horizontally so they can start to put numbers together that way and then maybe change to things that are more difficult with smaller pieces.
That one is really easy to do and the kids really enjoy my students, at least always really loved puzzles and doing any kind of puzzle.
So that's a great one.
Something that might help you if you're wanting students to write numbers and really dive deep into patterns is fill in the missing numbers, spin and fill.
(06:20):
So for this activity, they kind of have two spinners.
They have one decade spinner, so like a 10 spinner and then a one spinner all in a mat.
And so they'd spin the first number to get their decades.
So say it was 60 and then the next one would be the one.
So if they got 60 and five, their number would be 65 and they can put that number anywhere in the little puzzle piece or small piece of the hundred start that they have.
(06:44):
And then from there, they'd have to figure out, OK, I have 65 and what are the other numbers I need to fill in that are close to 65.
So spin and fill is a really easy game to play.
They can have a hundred start available if they need it.
And that way they can get a little hands on practice with it.
Also side a little side practice of writing their numbers and being careful about the order of their numbers.
(07:08):
So it's less easy to get confused.
And of course, there's tons of missing number like print and go worksheets that are great for morning work or early finishers, things like that.
And similar to in figurative counting, the stations or types of centers that I mentioned previously, you're going to want to keep having students practice counting on or developing other strategies.
(07:30):
One that I did not mention last time is called how many candies and similar to the previous station, it involves spinners.
I love spinners because I can put exactly which numbers I want the kids to work on or the number range.
And then from there, they really be able to develop some strategies and practice in a larger name range than a dice might provide.
(07:52):
So for that one, they would spin the first spinner, which is like a hidden hand and it just has a number next to it.
So the idea is hiding in that hand is however many.
So say that they spun a nine, there'd be nine candies hiding in the hand and then they would spend the next spinner and it tells them how many more to add to the hand.
(08:14):
So that one would be like nine, ten, eleven, twelve if they got three.
So again, the numbers that they would add to it are small within five, but it also lets them get a lot of practice in a lower number range.
So they can focus on the strategy, not necessarily the counting larger numbers that comes more in hundreds chart activities,
(08:35):
coral counting, counting collections, that kind of thing when you start to work with bigger numbers.
Since they're still working on the counting down from strategy, so fifteen minus blank equals twelve.
You might want to do some missing number type activities so they can figure out and practice that skill to get them ready for the next stage of counting.
(08:57):
If you have any questions or anything you would like me to follow up with you on, you can always send me a message on Instagram.
I also have a Google form down in the show notes that you can fill out if you have any requests, any other comments.
I read every single one.
Don't forget to register for the free Making Math Minds Virtual Summit if you're listening before November 17th, 2023.
(09:21):
Though probably they'll have one next year. I don't know when though, but that is a great opportunity to get lots and lots of free professional development.
They also offer certificates so you can get that.
So you'd have to check with your district, but you might also be able to get those credits towards your teaching license or renewing your teaching license.
So until then, you'll hear me next time.
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