1
U n t er r i ch t spl a n
M aking Te n - M is s ing Ad d e nd s
Altersgruppe: K i nde r gar t e n, 1st Gr ade
Virginia - Mathematics Standards of Learning (2009): K .4 c , K .6
Virginia - Mathematics Standards of Learning (2016): 1.7 .b, K .6
Fairfax County Public Schools Program of Studies: K .4 .c .1, K .6.a.1,
K .6.a.2, K .6.a.3 , K .6.a.4 , K .6.b.1
Online-Ressourcen: A Qui c k T e n
Opening
T eacher
present s
St udent s
pract ice
Class
discussion
Mat h
Worksheet
12
12
10
5
5
5
min
min
min
min
min
min
M at h Obj e c t i v e s
E x pe r i e nc e visuals for completing to 10
P r ac t i c e finding the missing addend in a sum
L e ar n the pairs that together make 10
De v e l o p flexibility with summing two 1-digit numbers
Ope ni ng | 12 min
Copyright 2015 www.matific.com
Closing
2
Using a tens frame (physical, drawn on the board, projected, etc.), fill in some
squares with an object of one color or type (e.g., red marbles). Provide an
orientation for the marbles that is not necessarily easy to count at first
glance. Such an example is shown below.
A sk: How many more marbles are needed to make a complete 10?
By this point, your students should be well aware of the strategy
of simply counting the unfilled squares. However, the larger goal
is to tie in the pairs that together make a complete 10, while
using the lens of addition with a missing addend.
Field answers, but focus primarily on the why portion.
On the board, w r i t e : 5 + _ _ = 10.
Discuss briefly how the explanations your students provided can
result in this equation with a missing addend. As with the visual,
one addend and the sum are known.
Keep track of all pairs that sum to 10 using a table or a series of
equations. Grow the list through your examples.
You can also use your visual to emphasize that orientation will not alter the
resulting pair of addends. For example, both the number of red marbles and
the number of marbles needed to complete the 10 are easier to count if the
red marbles are moved to the configuration below.
Copyright 2015 www.matific.com
3
Filling in the remaining slots with blue marbles yields the configuration below.
This configuration leads to many possible strategies. One such strategy is
finding a new pair based on the starting pair of 5 and 5 (or the equation 5 + 5
= 10).
A sk: How can we change this just a little bit to find a new pair that
makes 10?
One of the simplest ways is to replace a red marble with a blue marble
(shown below). This yields a visual that connects with the pairing of 4 with 6,
the equation 4 + 6 = 10, or even the missing-addend equation 4 + _ _ = 10.
This not only provides a new pair, but clearly opens the door to find more.
Note that replacing a blue with a red from the 5 and 5 configuration will give
the same pairs, but this will also drive at the commutative property.
Move on from using a tens frame to using small collections of
objects. Project or draw a grouping of objects.
Below, 7 stars are used.
A sk: How many more stars are needed to make a complete 10?
For the first couple of examples, show the objects in
configurations that are easy to count or manipulate.
Below, the 7 stars are initially shown in a line. They can then be
manipulated to leverage the aforementioned strategies.
Copyright 2015 www.matific.com
4
Of course, promote unique strategies your students come up with for
counting the original collection of objects, while trying to help them
determine which strategies are most useful and repeatable. Counting and
basic addition should not be new, but the idea of finding a missing addend
may be.
Ultimately, the goal is to provide tools for connecting which pairs of numbers
together make 10, so encourage flexibility in thinking and solutions. Continue
to write down any new pairs that arise, or point out that the pair is already on
the board.
Proceed to more complicated configurations, expanding strategies as
needed. Other strategies will also be covered when presenting the episode
for this lesson.
T e ac he r pr e se nt s M at h game : A Qui c k T e n - M ake T e n
w i t h Obj e c t s | 12 min
Present Matific’s episode A Qu ic k T e n - M a k e T e n w it h Ob je c t s to
the class, using the projector.
The ultimate goal of this episode is to build an association between the pairs
of numbers that sum to 10. Each screen provides a collection of objects, and
asks what other number will complete the number of objects to 10. As was
covered in the opening, some basic counting strategies will be useful here.
Each screen will give a visual similar to the one below. Note that after a
couple of seconds, a curtain closes on the image. The curtain can be reopened, but it will close shortly thereafter once again.
Copyright 2015 www.matific.com
5
Depending on how comfortably your students can work with the pairs that
together make 10, some of these screens may be fairly straight-forward. If
not, it can be a challenge to find what number will complete to 10. However,
the work done in the opening should help.
The above example is the easiest possible case to count, so it becomes a
matter of discussing with your students how to find the missing value. As
before, focus on the why while also connecting simple number sentences,
such as 1 + _ _ = 10.
Some--but not all--configurations will have a construction that makes them
easier to count. In the example below, the rectangular array allows for skipcounting by 2s or 3s. While this helps in finding the number of objects
present, your students still need to find useful strategies for finding how
many more are needed to complete a 10.
Copyright 2015 www.matific.com
6
Once again, tie in a number sentence: 6 + _ _ = 10. While your students should
become more and more comfortable recognizing pairs that sum to 10, you
can also recall visuals from the opening (or previous lessons). Below, the
tens frame uses different colors to distinguish a starting amount (red) and
the amount needed to complete the 10 (blue).
As you progress through the screens, the curtain will close slightly sooner,
adding a layer to the challenge. This should serve as incentive to solidify the
relationships between the pairs of numbers that sum to 10. Additionally, your
students will need to have effective strategies for counting the number of
objects in the collections, due to the limited time.
Copyright 2015 www.matific.com
7
S t ude nt s pr ac t i c e M at h game : A Qui c k T e n - M ake T e n
w i t h Obj e c t s | 10 min
Have students play A Qu ic k T e n - M a k e T e n w it h Ob je c t s on their
personal devices. Circulate, answering questions. Continue to develop useful,
repeatable strategies. Encourage the use of the pairs that sum to 10 in order
to find how many more are needed to make 10 from the starting value.
Encourage your students to write out the corresponding number sentence.
Advanced students can move on to play A Qu ic k T e n - M a k e T e n w it h
F in g e r s a n d Ob je c t s . This episode displays e it h e r a collection of
objects or two hands with some fingers up, then asks what number will
complete the number shown to 10. Once again, the curtain will close on the
image fairly quickly. Students must leverage their knowledge of pairs that
together make 10, as well as counting strategies.
C l ass di sc ussi o n | 5 min
Ask your students what they found challenging about finding the number that
completes the 10. Through student responses, determine which was more
challenging: counting the number of objects or finding the missing number.
Discuss what strategies worked best, as well as whether your students
developed a decent connection between the pairs that together make 10.
Consider also asking a couple of quick questions to test their pair knowledge,
such as “What number goes with 4 to make 10?”
Copyright 2015 www.matific.com
8
M at h W o r kshe e t P r ac t i c e : A ddi ng W i t h Unkno w ns C o mpl e t i ng T o 10 | 5 min
For practice, have students work through A d d in g W it h Un k n o w n s C o m p le t in g T o 1 0 on their personal devices. This worksheet shows
examples of equations with missing addends, as shown below.
Much of the work in this lesson has shown missing-addend exercises in
visual form. Here, this is explicit. Circulate, answering questions, particularly
clarifying any uncertainty surrounding pairs that make 10, commutativity, and
0. Note that 0 will be handled more extensively in the closing section, so
consider providing hints and encouraging exploration at this stage, instead of
having complete discussions.
Copyright 2015 www.matific.com
9
C l o si ng | 5 min
A sk: What number together with 1 makes 10?
Follow this with 2, then 3, and so on, up to 9. Write each sum on
the board.
The first sum will be 1 + 9 = 10, and the last will be 9 + 1 = 10.
Take a minute to discuss how the order of the numbers does not
matter, inviting your students to explain why that is the case.
Depending on time, you can also discuss how increases the first
addend by 1 coincides with a decrease in the second addend by 1
(and vice versa). While this was done in the opening, the idea
often requires revisiting.
A sk: What is the missing number in the equation (shown on the
board) 10 + _ _ = 10?
Have a brief discussion about why the missing value is 0, and
what this could mean practically or visually.
Follow this by writing 0 + _ _ = 10 on the board. Combine the
previous discussions about 0 and commutativity to reach a
conclusion here.
Promote the unique solutions your students come up with as
well. The involvement of 0 can be challenging or unclear at first,
meaning your students may need to revisit this topic again later.
Copyright 2015 www.matific.com