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U n t er r i ch t spl a n
De t e rmining Eve n o r Od d Ad vanc e d
Altersgruppe: 1st Gr ade , 2nd Gr ade
Virginia - Mathematics Standards of Learning (2009): 2.20, 2.4 c
Virginia - Mathematics Standards of Learning (2016): 2.2.c
Fairfax County Public Schools Program of Studies: 2.20.a.6,
2.4 .c .1
Online-Ressourcen: E ar l y B i r d
Opening
T eacher
present s
St udent s
pract ice
Class
discussion
Mat h
Pract ice
15
12
8
6
6
8
min
min
min
min
min
min
Closing
M at h Obj e c t i v e s
E x pe r i e nc e parity as an addition problem
L e ar n to determine whether there is an odd or an even number
of objects in a configuration
De v e l o p a connection between sums and parity
Ope ni ng | 15 min
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For the following set of examples, poker chips (disks) are used to
represent various collections and sums.
A sk: If I have 4 red disks and 5 green disks, do I have an even
number of disks or an odd number of disks in total?
Early responses will likely rely on combining the disks and
counting off pairs until either no disks or one chip remains. It may
be worthwhile to visualize this strategy, but encourage your class
to come up with multiple solutions.
In particular, try to remind your students that a number is even
when it can be written as the sum of two equal addends. While
this could require putting all of the disks together, you can also
point out that if one group has 4 and the other has 5, then the sum
is 4 + 5. There is no way to move the disks to get two groups of
exactly the same size (let them try this), so the sum must be o dd .
Note that this method does not require finding the actual sum.
A sk: What if I added 3 more green disks? Is the total even or odd?
One option is to start over, meaning there are now 4 reds and 8
greens.
Your students may point out that all of the red disks can be put
into pairs, as can the green disks. Since no disks is without a pair,
the sum must be e v e n .
It is less obvious whether 4 and 8 can be written as a sum with
equal addends, so encourage a student to show whether or not
two groups of the same size can be made.
Since 4 + 8 = 6 + 6, the total is e v e n .
Such a strategy is demonstrated below.
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Instead of starting from scratch in the above example, you can point
out that 4 red and 5 greens together were odd. We are adding
another odd number (3) to that.
A sk: How do we know if a number is odd?
Responses should refer to having pairs with one left over object
(tangible) or not being able to write the number as a sum with
equal addends (conceptual).
The first description may be more useful when trying to
generalize the sum of two odd numbers, since the left over
object from each addend can be put together to form a pair,
making the number e v e n .
In the Discussion portion of the lesson, your class will attempt to
generalize the connection between the parity of a sum and the
parity of the addends.
Consider discussing one or two more examples. Vary the parity of
the addends and perhaps even the number of addends, in order to
provide more of a challenge.
T e ac he r pr e se nt s M at h game : E ar l y B i r d - P ar i t y P uz z l e s |
12 min
Present Matific ’s episode E a r ly B ir d - Pa r it y Pu z z le s to the class, using
the projector. The goal of this episode is to determine whether each
configuration contains an even or an odd number of birds. The screens
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shown are from Preset Mode.
In the above configuration, the determination of even versus odd can be
made based on the right-most bird. The other birds are aligned in such a way
that pairs can be made vertically (shown below). Since the right-most bird
has no partner, the number of birds is odd.
Of course, the birds can also be moved to create these pairs more clearly, or
to split the birds into two or more groups. As you progress, field responses
from your students, trying at least two different methods before submitting
an answer. This will help your students understand the flexibility and
multiplicity of solutions. In particular, attempt to find at least one solution for
each screen that involves addition.
E x a m p le :
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In the above example, your students may have a sense that each of the two
collections contains an odd number of birds (per the example from the first
screen). As such, this becomes a question about the parity of the sum of
two odd numbers.
While your students may be comfortable concluding that the sum of two
odds is even--based on the opening of this lesson--it would be worthwhile to
ask for some justification about why . Using pairing, as in the first screen,
each grouping will leave one bird without a partner. However, these birds can
be paired together. Since all birds are paired, there must be an even number of
birds overall. Link this discussion to the actual numbers of birds (i.e., 7 + 5 is
even). Point out that knowing the sum is n o t a necessary step for finding out
whether the sum is even or odd.
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S t ude nt s pr ac t i c e M at h game : E ar l y B i r d - P ar i t y P uz z l e s
| 8 min
Have the students play E a r ly B ir d - Pa r it y Pu z z le s on their personal
devices. Circulate, answering questions. Continue to develop useful,
repeatable strategies, especially those involving equal addends or parity of
sums. Encourage your students not to guess but rather to explain their
answers to each other before selecting an answer on-screen.
Remember that the birds can be moved to different places on the screen.
Therefore, you can encourage your students to practice finding the parity of
sums by moving the birds on screen (if the birds are not already in two or
more groupings).
C l ass di sc ussi o n | 6 min
A sk: Will it always be true that the sum of two even numbers is
even?
Follow this question up with a discuss about why or why not .
A sk: What can we say about the sum of two odd numbers?
Whether you field correct or incorrect responses, encourage your
students to explain their thinking. Addressing incorrect answers
may help pave the path for a better conceptual understanding.
A sk: Can we say anything about the sum of an even number and an
odd number?
Again, dive into why a general conclusion can be made.
Make sure your students are working to understand the concepts
behind each conclusion instead of seeing each as a fact to
memorize.
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M at h P r ac t i c e : P ar i t y o f S ums W o r kshe e t | 6 min
To expand on the determination of the parity of sums, you can use
the worksheet P ar i t y - Odd Or E v e n .
This worksheet shows sums of two or three addends and asks
whether the sum is even or odd.
Note that the addends have values significantly larger than those
in the episodes from this lesson.
The idea here is ascending away from the necessity of drawing
out the number of objects and instead evaluating each addend
based on its ones place.
E x a m p le :
In the above examples, there are a number of ways to determine
parity, but try to move the class away from needing to find the
overall sum.
Instead, note that 16 and 18 are even, so the sum of 16 and 18 is
even. Thus, adding 2 (even) to an even sum yields an even number.
This type of conclusion will be more successful provided the
connection between parity and addition has been thoroughly
uncovered during the class discussion.
C l o si ng | 8 min
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Present Matific’s episode E a r ly B ir d - A d v a n c e d Pa r it y Pu z z le s to the
class, using the projector. The screens shown are from Preset Mode.
A sk: How can we determine if there are an odd number or even
number of birds?
Field responses from your students, displaying their strategies by
moving the birds as needed. In the example above, the
configuration has many birds that can be paired vertically, but the
birds on the end appear to be without an obvious partner.
However, they can be partnered together.
Continue to seek out solutions that connect parity with addition
as well.
E x a m p le :
A sk: How can we use addition to help us determine if the number
of birds is even or odd?
Here, a natural divider is by color. There are five brown birds
(odd) and six grey birds (even), yielding an odd sum.
Of course, the birds can be split in many different ways, so show
several splits (per your students’ suggestions).
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Use this example to solidify the principles connecting addition with
parity, as discussed throughout this lesson. By visualizing the pairs
or groups, your students will move away from memorizing which
types of sums are even or odd, while moving toward a conceptual
understanding.
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