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U n t er r i ch t spl a n
Ad d ing 3-Dig it Numb e rs
Altersgruppe: 2nd Gr ade , 3 r d Gr ade
Virginia - Mathematics Standards of Learning (2009): 2.21, 2.6a,
2.6b, 2.8
Virginia - Mathematics Standards of Learning (2016): 2.6.a, 2.6.b,
3 .3 .a, 3 .3 .b
Fairfax County Public Schools Program of Studies: 2.21.a.1,
2.21.a.2, 2.21.a.3 , 2.6.a.2, 2.6.b.1, 2.6.b.2, 2.6.b.3 , 2.6.b.4 ,
2.6.b.5 , 2.6.b.6, 2.6.b.7 , 2.6.b.8, 2.8.a.3 , 2.8.a.4
Online-Ressourcen: M ake C hange
Opening
T eacher
present s
St udent s
pract ice
Class
discussion
Mat h
Worksheet
Pract ice
15
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10
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M at h Obj e c t i v e s
E x pe r i e nc e visuals for addition up to 1000
P r ac t i c e regrouping in order to find sums more easily and
quickly
De v e l o p strategies for adding 3-digit numbers with more
fluidity
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Ope ni ng | 15 min
Show base-ten blocks on the board using an overhead projector (or
online application).
If your class does not have familiarity with base-ten blocks, walk
through a couple of quick examples involving collections of 100s,
10s, and 1s.
For these examples, simply show a random collection and ask
what number is represented by the blocks.
The goal is to acquaint your students with the visuals for 100s,
10s, and 1s, but it is also worthwhile to mention how regroupings
work (or compositions and decompositions).
For example, show or mention that ten 10s can be regrouped
into one 100 (and vice versa).
For the remaining portion of the opening, focus on sums of two
addends.
The first example or two should not require any regrouping.
For example, show 136 and 442 with base-ten blocks.
A sk the class: What two numbers are represented here?
Then ask : How can we find the sum?
If your students struggle to come up with an answer, ask them: If
the first number has one 100 and the second has four 100s, how
many do they have in total?
Eventually, you should move the base blocks together and
rearrange them such that the 100s are grouped together, the 10s
are grouped together, and the 1s are grouped together.
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This example only requires counting the total for each place
value in order to find the sum, but it is a valuable stepping stone
to the examples with regrouping.
The next couple of examples should require exactly o ne
regrouping.
i.e., ensure that each quantity you show has e i t he r at least ten 1s
or at least ten 10s in total .
The sum should be no greater than 1000.
For example, show 136 and 482 with base-ten blocks.
A sk the class: What two numbers are represented here?
Then ask : How can we find the sum?
As a first step, your students may suggest getting the 100s, 10s,
and 1s into groups, respectively. This thinking should be
encouraged.
A sk the class: We have eleven 10s. What should we do when
there are at least ten 10s?
If your students struggle to come up with an answer, remind them
that ten 10s can be regrouped into (or exchanged for) a 100.
From here, you can ask how many blocks you have in each place
value (e.g., six 100s), then put them together to arrive at the
correct sum of 618.
After your class seems to have a decent grasp on regrouping, move
on to a couple of examples requiring t w o regroupings.
For example, show 136 and 486 with base-ten blocks.
A sk the class: What two numbers are represented here?
Then ask : How can we find the sum?
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By this point, your students should quickly suggest getting the
100s, 10s, and 1s into groups, respectively.
A sk the class: What do we do next?
Again, by this point, your students should recognize that there are
more than ten 1s (here, 12) and more than ten 10s (here, 11), so
regrouping will be needed.
As before, ten 1s can be regrouped into (or exchanged for) a 10,
and ten 10s can be regrouped into a 100. [Doing this leaves six
100s, two 10s, and two 1s.]
A sk the class: What is the sum?
As all possible regroupings have been formed, no place value has
at least ten corresponding blocks, so the sum (622) can be seen
readily.
Ideally, the class will have a strong sense of when to regroup and
how regrouping affects the sum before moving on to the episode
for this lesson.
However, this episode gives an opportunity for more practice
with finding sums via regrouping.
T e ac he r pr e se nt s M at h game : M ake C hange - A dd 3 - Di gi t
N umbe r s | 8 min
Present Matific ’s episode M ake C hange - A dd 3 - Di gi t
N umbe r s to the class, using the projector. The goal of this
episode is to sum 3-digit numbers, where only one regrouping is
necessary.
Each screen begins with two sets of chips, each representing an
addend in the sum.
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There is also a machine used for making exchanges.
Ten 1s can be regrouped into one 10, or ten 10s can be regrouped
into one 100.
E x a m p le :
In the example above, the two groupings of chips have a total of
more than ten 10s.
You can move all of the 100s, 10s, and 1s together and arrange by
place value first, as was done with the base-ten blocks, if you
prefer.
Otherwise, your students may simply be able to recognize that
there are enough 10s to require regrouping.
In this case, you are still able to move the chips together after
regrouping.
E x a m p le :
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Placing ten 10s chips into the machine (shown above) yields one
100 chip (shown below).
At this point, the regrouping is complete, so the chips can be
(arranged and) counted by place value.
E x a m p le :
From here, the 100 can be removed from the machine and placed
anywhere on the screen.
To be consistent with the opening portion of this lesson, encourage
the class to bring the 100s together, then the 10s and 1s.
If all possible regroupings have been made, then the number of
chips of each place value can simply be counted to find the sum.
Some students may wish to make other regroupings without using
the machine.
In general, there is nothing wrong with attempting other methods.
In fact, some may be equally beneficial and just as logical,
visually.
In these cases, ask your students to justify the steps they are
taking as you walk through their unique methods. Encourage
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outside-the-box thinking, as long as it is supported in correct
mathematical principles.
Each screen in this episode will present a sum that requires a
maximum of one regrouping (i.e., one use of the machine).
Note that this regrouping may be of 1s or 10s.
Even though it is known that only one regrouping is needed,
continue to look for places to regroup until the class feels
confident that nothing more needs to be done. This will stop your
students from having merely a process-based understanding.
S t ude nt s pr ac t i c e M at h game : M ake C hange - A dd 3 - Di gi t
N umbe r s | 8 min
Have the students play M ake C hange - A dd 3 - Di gi t N umbe r s
their personal devices.
Circulate, answering questions. Continue to develop useful,
repeatable strategies.
Encourage the use of the regrouping machine, as it serves as a
reminder of the types of compositions that can make addition
more successful.
Advanced students can move on to play another variant of this
episode: M ake C hange - A dd: M ul t i pl e R e gr o upi ng .
This episode contains the same concepts as in the first episode,
but offers the added challenge of requiring more regroupings.
i.e., the regrouping machine can be used for both the ones and
tens.
This lays the groundwork for both mental math and any
algorithms for addition that involve composition.
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C l ass di sc ussi o n | 10 min
Check in with your class to make sure they are gaining comfort with
the general idea of composing 1s into a 10 (or 10s into a 100).
Use this time to try some examples involving two regroupings, three
addends, or regrouping involving both 1s and 10s simultaneously.
An example requiring two regroupings is the sum of 246 and 175.
This can be approached in the same fashion as the examples with
only one composition, by first grouping ten 1s into a 10.
Then, there will be a total of twelve 10s, so another composition
can be made.
At this point, the steps should be primarily driven by your
students’ suggestions.
An example with three addends is the sum of 151, 433, and 264.
The process for this example will mirror what has been done for
the examples with one or two regroupings.
This example requires only one regrouping, which is a good way
to start, since the focus should be on how (if at all) adding a third
addend changes the methodology or process.
If time allows, move on to an example requiring multiple
regroupings.
Perhaps most importantly, show examples of a slightly less
process-based nature.
For example, start with the sum of 297 and 518.
The previous methods would suggest regrouping the 1s and 10s,
as there are at least ten of each.
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However, consider the proximity of 297 to 300.
Consider reminding your students that adding hundreds is a fairly
straight-forward process, and certainly a nice option for mental
math.
Move three 1s from 518 to 297, leaving groups of 515 and 300.
Even though the 1s and 10s in the pile of 300 have not been
regrouped into a 100, the sum can still be found quite easily.
Of course, to complete the visual, you can explain why the 1s and
10s can be exchange together for a 100 (or separately, if that is
easier for your students to follow).
This type of example still uses regrouping, but in a way that requires
some in-the-moment thinking.
Encourage your students to avoid memorization and process, and
instead embrace the fact that every mathematical question is
unique. While some methods are repeatable, it is important to
have more than one method when approaching problems.
M at h W o r kshe e t P r ac t i c e : A ddi t i o n S t r at e gi e s - Up T o
1000 - L e v e l 1 | 5 min
To expand on the determination of the parity of sums, you can use
the worksheet A ddi t i o n S t r at e gi e s - Up T o 1000 - L e v e l 1 .
This worksheet shows sums of two addends, where sums are up to
1000.
E x a m p le :
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In the above example, there are two types of setups.
The first question is not looking for the sum, but rather a way to
regroup the numbers such that the sum has one addend that is a
power of 10.
The second and third sums can be found by similar reasoning,
which is implied but not required.
It may be worth noting that while the second overall sum
appears to be simpler after regrouping, the third sum may not
benefit from regrouping.
While a variety of strategies can be discussed in finding the missing
values and sums, the key point of the lesson is regrouping, so be
sure to return to that with some regularity.
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