5 Types of Addition Strategies
Summary
TLDRIn this educational video, Krystina introduces five strategies for solving addition problems, emphasizing their importance for building math skills. She warns against directly teaching these strategies to students, as they should emerge naturally from their understanding of numbers. The strategies include compensating, give and take, decomposing, breaking apart by place value, and the traditional algorithm. Krystina stresses the importance of number sense and place value in mastering these strategies, suggesting that teachers should encourage students to choose the best strategy for each problem rather than imposing a one-size-fits-all approach.
Takeaways
- 📚 The video discusses five strategies for solving addition problems, emphasizing that these should not be directly taught but should emerge naturally from students' understanding of numbers.
- ⚠️ Warning: The strategies discussed are not meant to be taught to all students universally, but rather to be aware of the different ways students might approach problems.
- 🔍 The strategies might be named differently by various educators, and the video encourages using names that reflect the mathematical concepts involved.
- 🧠 The strategies are based on students' number sense and understanding of place value, which are foundational for effectively using these strategies.
- 🔄 The strategies include compensating, give and take, decomposing, breaking apart by place value, and the traditional algorithm.
- 📈 The compensating strategy involves rounding numbers and then compensating for the difference, which helps in understanding the relationship between numbers.
- 🔄 The give and take strategy is similar to compensating but involves adjusting both numbers to make the addition easier.
- 📉 Decomposition involves breaking numbers into smaller, more manageable parts to facilitate addition.
- 🔢 The place value strategy involves breaking numbers into their place value components and adding them separately.
- 📘 The traditional algorithm is a systematic, step-by-step method taught in many educational systems for addition.
- 💡 The video stresses the importance of allowing students to choose the strategy that makes the most sense for the problem at hand, rather than prescribing a single method.
Q & A
What is the main focus of the video series introduced by Krystina?
-The video series focuses on different strategies for solving addition problems, including time, measurement, and money addition, with the goal of building math minds in students.
Why does Krystina advise against directly teaching all five strategies to students?
-Krystina advises against directly teaching all five strategies because students naturally use these strategies based on their understanding of numbers. Forcing them to learn all the strategies could cause confusion and doesn't allow for the organic development of number sense.
What is the 'compensating' strategy in solving addition problems?
-The compensating strategy involves altering a number in a problem (e.g., rounding 399 to 400), solving the modified problem, and then adjusting the result to compensate for the change made initially.
How does the 'give and take' strategy differ from the 'compensating' strategy?
-The 'give and take' strategy differs because instead of rounding a number, students shift part of one number to the other to make the numbers easier to work with. For example, a student might take 1 from 456 and add it to 399 to make 400 and 455.
What does Krystina mean by 'decomposing' in math addition?
-Decomposing refers to breaking one of the numbers in the addition problem into smaller, more manageable parts, which are then added sequentially to simplify the process.
Why does Krystina prefer not to use number lines for the decomposing strategy?
-Krystina prefers not to use number lines for the decomposing strategy because it is difficult to make the hops proportional, which can lead to confusion. Instead, she uses arrows or simpler methods.
What is the role of number sense in using these addition strategies?
-Number sense is crucial because students must understand the relationships between numbers and how they interact. Without strong number sense and place value understanding, students will struggle to use these strategies effectively.
How is the 'place value' strategy used in addition?
-In the place value strategy, students break down the numbers into their place values (hundreds, tens, and ones) and then add each place value separately before combining the sums.
What does Krystina mean by the traditional algorithm, and why does she not prioritize it?
-The traditional algorithm refers to the step-by-step process of adding numbers by columns, carrying over when necessary. Krystina doesn’t prioritize it because it doesn't build number sense or place value understanding, as it can be done mechanically without deeper understanding.
What is Krystina's ultimate goal in teaching students these strategies?
-Krystina's goal is to help students develop enough number sense and understanding of place value to choose the most appropriate strategy for each problem, rather than forcing them to use all strategies or rely solely on the traditional algorithm.
Outlines
📚 Introduction to Addition Strategies
The speaker introduces a series of videos aimed at explaining various addition strategies that students use. These strategies are not meant to be taught directly but are ways students might naturally approach solving addition problems, including those involving time measurement and money. The speaker, Krystina, warns that these strategies should not be directly taught to all students, as they may not be applicable in all situations. Additionally, the names for these strategies might vary, and the speaker emphasizes the importance of understanding the mathematical concepts behind the strategies rather than the specific names or methods of notation.
🔢 The Compensating and Give and Take Strategies
Krystina discusses two addition strategies: 'compensating' and 'give and take.' The compensating strategy involves rounding numbers to the nearest convenient number and then compensating for the difference. For example, adding 399 to 456 by rounding 399 to 400 and then subtracting one to adjust for the overestimation. The give and take strategy is similar but involves adjusting both numbers involved in the addition. The speaker uses the example of adding 9 and 7, where a student might adjust one number to make a more convenient sum, like rounding 9 up to 10 and adjusting the other number accordingly.
📈 Decomposition and Place Value Strategies
The speaker explains the 'decomposition' strategy, where students break down numbers into smaller, more manageable parts before adding them. This can be done using manipulatives like base ten blocks or by simply writing out the equation. The 'place value' strategy involves breaking numbers down by their place value (hundreds, tens, ones) and adding each place value separately before combining the results. Krystina emphasizes that these strategies require a strong understanding of number sense and place value, which are foundational to successfully applying these methods.
✅ The Traditional Algorithm and Encouraging Strategy Selection
Krystina describes the traditional algorithm for addition, which is a systematic approach taught in schools and involves carrying over values as necessary. She notes that while this method is reliable, it may not always be the most efficient or intuitive for students. The speaker advocates for building students' number sense and place value understanding so they can choose the most appropriate strategy for a given problem. The goal is not to have students solve every problem using all strategies but to recognize which strategy makes the most sense for a particular problem and to encourage their natural development of these strategies.
Mindmap
Keywords
💡Compensating
💡Give and Take
💡Decompose
💡Number Sense
💡Place Value
💡Traditional Algorithm
💡Manipulatives
💡Number Line
💡Chunking
💡Expanded Form
Highlights
Introduction to a series of videos on addition strategies for students.
The five types of addition strategies will be explored to enhance math problem-solving.
Warning that these strategies should not be directly taught to all students.
Different names for strategies may exist, emphasizing the importance of understanding the math behind them.
Explanation that strategies manifest differently but remain fundamentally the same.
The 'compensating' strategy explained with an example.
The 'give and take' strategy, similar to compensating but with a different approach.
The 'decomposing' strategy involves breaking numbers into manageable chunks.
The importance of number sense in executing addition strategies effectively.
The 'breaking apart by place value' strategy, also known as the 'hundreds, tens, and ones' method.
The traditional algorithm for addition, its pros and cons.
The necessity of building number sense and place value before introducing the traditional algorithm.
Encouragement for students to choose the best strategy based on the problem at hand.
Advice for teachers to observe and discuss strategies rather than prescribing them.
The goal of the video series is to help teachers recognize and understand various addition strategies.
Final thoughts on the importance of allowing students to naturally develop their own strategies.
Transcripts
well with textbooks having students use
different strategies to solve addition
problems I wanted to do a short series
of videos to share with you what those
strategies are and how they help kids
not only do normal addition problems but
also time measurement and money addition
problems I'm Krystina ton of old they're
recovering traditionalist and today we
are going to do the first video in this
series that will take a look at the five
types of addition strategies in our
quest to build our math minds so we can
build the math minds of our students now
a couple of warnings I guess before we
get started number one I'm going to talk
about these strategies but they are not
strategies that you should directly
teach to all of your students
I want you to be aware of these
strategies because these are possible
ways that students think about solving
addition problems but we should not be
directly teaching them to our students
there are certain times when they will
use them in certain times that they
won't it's not like kids need to use all
five of these to solve any addition
problem they ever encounter now the
second warning is that you might call
them by different names you might have
different names for these strategies
when I first started doing this in my
classroom when a student would use this
strategy we would name it after the
student this is Sierra strategy is in
this awesome the way that Sierra solved
this one of the Articles that I read in
the teaching children's mathematics
which is published by NCTM I can't
remember the title of it it can't member
the who authored it but I remember the
gist of the article was that we should
stop naming them these cute names and
really name them after the mathematics
that is happening so I'm gonna be using
names that I use to talk about the math
that we are doing in the strategy you
might call them something different but
these are the names that I personally
use for them now the other thing I want
you to be aware of
is that to me there are five distinct
strategies you might end up seeing kids
who will combine or have variations on
these strategies but these are the main
basis of the five strategies and as my
dog wants to make an appearance so just
a moment I'll be right back
and so one of the things that actually
ends up happening is that we will see
these strategies but in different
formats like a kid might use the same
strategy but they were doing it using
base ten blocks whereas another kid just
wrote out the equation so just because
they're using manipulatives or an
equation or a number line to show their
strategy does not make it a different
strategy they're using a different model
to show that strategy so how they notate
it does not determine the strategy we
need to be paying attention to what is
the mathematics that they are doing for
this problem it doesn't matter how
they're showing that mathematics the
strategy is based upon how what they are
doing with the numbers and what's the
root of the mathematics all right so
let's dig in to those five types of
addition strategies okay we're going to
start with the strategy I like to call
compensating and for all of these we're
gonna use the same problem 399 + 456 and
I like to call this one compensating
because to me compensating is when you
do something you're not supposed to do
and you need to compensate for it
so the 399 this is when you will see
kids say well like that's almost 400 so
if I just add 400 to 456 that would be
856 but you weren't supposed to add 400
so we need to compensate for what we did
so this strategy only works if kids
understand the relationship between the
numbers that are in this problem and how
they've changed the problem so they need
to look at that and understand that they
added one more than they were supposed
to so they need to come at the end and
subtract one of those a way to get to
their answer of 855 now all of these
strategies the reason I love these
strategies is that they work no matter
what kind of addition problem you are
working with
so even when kids are learning just
their basic facts you will see kids who
will do these strategies you'll hear
kids say well nine plus seven that's
like having ten plus seven which is 17
and then I just need to take away one to
get to the sixteen and then it can
extend even further into work with
decimals and so on so the reason that I
love helping kids develop these
strategies is that they last kids beyond
just what they're doing with that one
problem when they really understand how
numbers work they will use these
strategies no matter what size of
numbers they are working with okay one
that is really similar to compensating
is one that I call give and take so it's
the kids who want to use 400 because
they see that that would be nice but
instead of just rounding it to the 400
they decided I'm gonna take one from the
456 and give it to the 399 so that I
have 400 but then I'm only left with 455
in that space now so it goes directly
they can get directly to their answer
after they have kind of done this
adjustment so they're still moving
things around but they do all of the
adjustments before they go to actually
solve the problem so with our young kids
that might look like this with the nine
plus seven you might see a kid who says
well I'm gonna take one from the seven
and give it to the nine so I've got ten
and then I've got six left over so 10
plus 6 gives me the 16 so again these
are really related but it's like what
are they seeing as the relationships how
are they going about the problem so
that's what really makes a difference
between the two strategies another
strategy that kids will devise is that
they will see that 456 and they'll say I
don't want to
all at once they will want to break it
apart into chunks that make sense for
them and this is what I call decomposing
because it's just like decomposing in
science it's a breaking it down into
smaller pieces so you might see a kid
who this might show up like on a number
line they might show it on a number line
I don't really like to show this one on
a number line because it's hard to be
proportional so I'm doing this on an
iPad so don't judge me if my hops are
not totally proportional I know they
should be but you might see a kid who
says I want to do add one here because
it's going to get me to the 400 sounds
similar to what we've been doing already
in these other strategies right but it
looks a little bit different from this
point on is that once they get there
then you might see a kid who goes okay
now I'm gonna add 400 I'm gonna do a big
chunk of it and then I'm gonna add a 50
right but the hard part here is that
they need to know how much they've added
they have to keep in mind that they need
to add the entire 456 but they can do it
in chunks but they have to keep track of
what those chunks have added up to so
along the way they need to be holding in
their head that they've done 450 and 1
and then think about how much more do
they need right they need to know once
they've done 451 how much more is that -
456 so they need to know that there's
five more see there's no my hop four
five looks the same as hot 450 and then
they would get to 855 okay so there's a
lot of number sense that goes into play
here they need a lot of knowledge about
how these numbers work the general idea
is that they are keeping one of the
numbers the same the 399 and then
they're breaking apart the other number
into smaller chunks and that doesn't
matter if they do it on a number line or
one of my favorite ways to show this is
just using arrows to show what I am
doing so that I don't have to worry
about being proportional so I'm gonna do
399 I'm just doing a little arrow I'm
not using the equal sign because you can
get this big mathematical run-on
sentences what I like to call it so I
just use arrows instead of equal signs
here so I've got 399 + 1 gets me to the
400
and then I'm going to add another 400
gets me to 800 and then maybe this time
I might add the 55 all at once it
doesn't matter what their chunks look
like as long as the general idea is that
they're breaking one of the numbers down
into chunks to make it friendlier to add
again it doesn't matter if they do that
on a number line or they show it with
these arrows or they make different
equations for every single step that
they do the idea is that they're just
breaking it down into smaller chunks to
make it friendlier to add kids will do
this same thing with like 9 plus 7 right
they might do 9 add 1 gets me to 10 adds
that add the 6 gets me to 16 now this
looks a lot like give-and-take
but it's because there's not a whole lot
of ways to break up the 7 right you may
even see a kid who maybe can't add the 6
all at once so they add one more and
they get to 11 they add one more they
get to 12 and so on it goes they just
add one by one by one alright that's the
extreme form of decomposing is doing it
one by one by one but even with these
upper amounts you might see a kid here
at that 400 stage they might not be able
to add the 400 all at once they may add
100 then another hundred then another
hundred then another hundred right the
ideas they're breaking it down into
friendly chunks that are friendly for
them alright another strategy that where
kids are breaking apart numbers is where
they break apart by place value some
textbooks will call this the hundreds
tens in one strategy I don't really like
that strategy because it limits kids to
thinking they can only do it with
hundreds tens and ones when they get
into decimals I want them to still be
able to use this strategy the general
idea is that they're breaking it down
and they are adding the the values
together in each place value and then
they're putting those together so some
of you may see this as expanded form so
sometimes it doesn't again it doesn't
matter how you model it it is the idea
of what's the mathematics that we are
doing I'm going to do a really shortened
version of this here and you could have
it out in expanded form but we're doing
the same thing the idea is that I'm
adding my hundreds together I have three
and 400 that gives me 700 I add my tens
together 90 plus 50 is a hundred and
forty and oftentimes what you'll hear
kids do right here is they'll be
thinking off to the side here that
that's already 840 then when they add
their ones they get the 15 whoops and
then they can add that to the 840 and
they get their 855 right all they're
doing is adding the chunks by place
value and this kids will naturally do if
they have a lot of work with place value
all of these strategies are dependent
upon number sense and place value you
cannot directly teach it if kids don't
already have a foundation of number
sense and place value now these are
things that we go really deep into in my
number sense courses but I'll also link
to some free videos that I have about
the basics of number sense so that you
can get a foundation of where to start
with your kids because if they don't
have these ideas they'll never be able
to really latch on to these strategies
now with 9 plus 7 you don't really have
a place value strategy because there
aren't any other place values you just
add your ones and your ones when we get
into things like 19 + 17 then you've got
some place values to work with and then
they'll add their tens with their tens
and their ones with their ones but
before that there's no real place values
to have to work with here alright our
last one is the traditional algorithm or
what in the United States we call the
traditional algorithm this is the way
that we traditionally learned how to
solve addition problems set it up and we
add our ones and then we carry it over
add our tens carry that over and then
we've got our answer now it's called an
algorithm because you can program a
computer a calculator to do it it is the
same steps every single time there's no
real decision-making to have to do here
you don't need number sense you don't
even have to have place value here all
you have to do is single-digit addition
and then be able to carry the one over
and carry the one over there's no
real judgment that has to go into this
which is one of the reasons why we use
it you do the same steps over and over
again and it works every single time but
it is devoid of place value and it's a
devoid of number sense unless we bring
that in as teachers that's why in most
states the standards bring in the
traditional algorithm at 4th grade
before that time we need to be building
their number sense and their place value
to help them be able to see and build
those other strategies that we've talked
about we want kids to be able to look at
a problem and decide the best way to
solve it because sometimes the
traditional algorithm yes it works but
sometimes it takes longer to solve the
problem using the traditional algorithm
than one of those other strategies so
the main idea from these videos what I
want you to really take away from it is
yes there are five different ways to
solve an addition problem but we do not
need to be making kids solve this one
problem five different ways we need them
to be able to look at the problem and
then decide for themselves what's the
best way to solve this problem what
makes sense because what makes sense for
this problem the 399 + 456 is different
then what should make sense for the
problem 323 + 456 how we solve these two
problems should be different
we should not approach them the same way
this one with the 399 is just begging me
to round that to a 400 or make that a
400 nothing in the 323 + 456 says round
this do compensating or give-and-take
but yet we could make kids do it we
could make them solve it that way but it
doesn't make sense - we want them to
have these strategies at their disposal
if it makes sense on that problem and
the only way that we help kids be able
to do that is by building their number
sense in place value so that they can
look at the problem first and say what
makes sense with this problem so
remember that these five strategies are
not things that you should directly
teaching to your students kids naturally
do these strategies based upon their
understanding of the numbers that are in
the problem we cannot directly teach
these strategies to students it comes
when they see relationships within the
numbers and they say oh I see how I
could use this and do this with it we
can't directly teach it even though our
textbooks try to that's why you will
spend weeks and weeks trying to get them
to use these strategies and by the end
of it all you really get our students
who are thoroughly confused ok I want
you to be aware of these strategies and
be watching for kids who are naturally
doing these and then have them talk
about and discuss what they're doing
instead of you directly telling them how
to solve using these strategies so this
video was to help you see the possible
ways that kids could solve addition
problems not that they have to solve
every problem five different ways I just
want you to be aware of these different
ways because if you were at all like me
back when I first started teaching the
only way I knew how to do it was the
traditional algorithm and when kids
solved it a different way I really had
no clue what they were doing I could not
tell what they were doing and I would
just say and don't do it that way do it
this way and I would tell them this way
to do the traditional algorithm the ways
that kids are solving these are
important pieces but they needed to be
coming naturally from them not us
directly teaching them so I want you to
be aware of them so that you can be
watching for them and pull them out when
you see kids using them all right I hope
that this video helped you build your
math mind so you can go build the math
minds of your students have a great day
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