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U n t er r i ch t spl a n
Co mp aring 2 -Dig it Numb e rs
Altersgruppe: 1st Gr ade
Texas - TEKS: G1.2.N O.E
Hampton City Schools Math Power Standards: 1.1aS a, 1.1aS a' ,
1.1aS a' ' , 1.1aS b, 1.1aS b' , 1.1aS c , 1.1aS c ' , 1.1aS d, 1.1aS d'
Riverside USD Scope and Sequence: 1.N B T .1 [1.11]
Oklahoma Academic Standards Mathematics: 1.N .1.4 , 1.N .1.7
Virginia - Mathematics Standards of Learning (2009): 1.1b, 2.1a
Common Core: 1.N B T .A .1
Mathematics Florida Standards (MAFS): 1.N B T .1.1
Alaska: 1.N B T .3
Minnesota: 1.1.1, 1.1.1.5
Fairfax County Public Schools Program of Studies: 1.1.b.2, 1.1.b.3 ,
1.1.b.5 , 2.1.a.5 , 2.1.a.6, 2.1.a.7
Nebraska Mathematics Standards: M A .1.1.1.a, M A .1.1.1.b,
M A .1.1.1.c
South Carolina: 1.N S B T .3 , 2.N S B T .4
Indiana: 1.N S .4
Georgia Standards of Excellence: M GS E 1.N B T .1
Virginia - Mathematics Standards of Learning (2016): 1.2.a, 1.2.b,
1.2.c , 2.1.c
Online-Ressourcen: P i l e d up
T eacher
present s
St udent s
pract ice
15
8
10
8
min
min
min
min
Opening
Class
discussion
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M at h Obj e c t i v e s
E x pe r i e nc e composition and decomposition of 1s and 10s,
respectively
L e ar n to compare two quantities (up to 100) visually
De v e l o p strategies for determining which quantity is greater
(or less) than the other
Ope ni ng | 15 min
Using an overhead projector (or online application), show base-ten
block collections of 10s and 1s.
Ensure that each quantity you show has at least ten 1s.
The total for each quantity should be no greater than 100.
The blocks can start out in clusters of 10s and 1s, but later
examples should have all of the blocks mixed.
For example, start with four 10s and seventeen 1s.
A sk the students to tell you what they know about the quantity
shown.
This question is meant to call attention to the difference
between 10s and 1s.
The students should be able to claim that there are four groups of
10 and seventeen individual 1s.
A sk the students: What can we do when we have at least ten 1s?
Based on previous use of base-ten blocks, the students should
eventually come around to the idea of c o mpo si ng (or
collecting, exchanging, etc.) ten 1s into one 10.
Now, there should be five 10s and seven 1s. Ask the students to
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identify the quantity shown.
If they are struggling, break this into pieces, such as, “Five 10s
makes how much? 50. Seven 1s makes 7. How much do we have
if we put 50 and 7 together? 57.”
Allow the time allotted to identifying quantities to depend on the
amount of work you have done with composing and decomposing 1s
and 10s, respectively.
Try to move on to the comparison portion of the opening before
too long, as this is the emphasis of the lesson.
Next, show two sets (or piles) of blocks, each with some 10s and
some 1s.
This time, it is not necessary to have at least ten 1s, but it can
and will be useful to show a few such examples.
A sk the class to try to figure out which pile has more blocks.
This question may elicit a few quick answers. Ask your students
to justify the selection, since it is very likely a quick answer was
either a guess or based off of the visual (i.e., one pile may appear
“bigger” than the other).
Encourage the class to use similar strategies to what you did in the
first part of the opening. Namely, make any possible compositions
of 1s into 10s.
Once compositions are complete, ask how the two piles can be
compared.
Pull the conversation in the direction of finding out how much is
in each pile, then comparing those values.
Your students may also find strategies that do not involve writing
the quantity with a base-ten representation, but rather using the
visuals alone.
For example, if each pile has six 10s, then only the 1s need to
be compared. The pile with more 1s is the larger pile overall.
These strategies can be entirely valid, and even clever, but be
sure that your students fully comprehend how to use them, or in
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what scenarios they cannot be applied.
Try a couple more comparisons of this type, as appropriate for the
level and pace of the class.
Use some situations where no 1s can be composed, where one
pile can form a composition, and where both can.
Use some situations where the number of 10s is the same, and
some where the number of 10s differs (after any compositions).
Introduce the symbols for inequalities, as appropriate.
For example, once the class determines that one pile has 45 and
another has 48, they should be claiming that the pile with 48 has
more blocks. As a next step, show them: 45 < 48.
These symbols are an added element to the lesson. The focus
should remain on identifying larger or smaller quantities amongst
several 2-digit numbers.
T e ac he r pr e se nt s M at h game : P i l e d up - Up t o 100: L e v e l I
| 8 min
Present Matific ’s episode P i l e d up - Up t o 100: L e v e l I to the
class, using the projector. The goal of this episode is to determine
which stack of boxes contains more baseballs (i.e., which quantity
is greater).
The initial screen is devoted to familiarizing the students with the
convention of composing 1s into a 10 (or a 10 into 1s) to determine
a quantity.
The arrows between 10s and 1s can be clicked on to compose or
decompose, in similar fashion to the exchanges made with baseten blocks.
E x a m p le :
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The above quantity has more than ten 1s, meaning the left arrow can
be clicked, collecting ten 1s and forming one 10, as shown below.
Note that an arrow will be gray if an exchange is not possible in
this direction.
E x a m p le :
Each subsequent question will show two sets of boxes, with each
set containing some boxes of 10 and some boxes of 1.
The object is to determine which set of boxes contains more (or
fewer) baseballs in total.
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Again, it is implied that composition (or decomposition) will help
in determining the relationship between quantities. Connect this
to the base-ten blocks as appropriate.
In theory, getting both quantities into base-ten form will allow
for smoother conversations about comparisons.
E x a m p le :
Note that in cases such as the above scenario, your students may
not find it necessary to compose 1s into a 10 in order to answer the
question, as the stacks of 10s are identical and the stacks of 1s are
easy enough to compare directly.
Promote this type of problem solving, encouraging your students
to explain the reasoning to the class in a little more depth.
However, continue to use the arrow function as a means of
writing each quantity as a standard base-ten quantity.
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S t ude nt s pr ac t i c e M at h game : P i l e d up - Up t o 100: L e v e l
I | 10 min
Have the students play P i l e d up - Up t o 100: L e v e l I on their
personal devices.
Circulate, answering questions. Continue to connect the visuals
with the appropriate base-ten representation of the quantities
shown, and support the clever strategies your students come up
with.
Make sure the students are gaining a firm grasp of the purpose of
the arrows. Visually comparing quantities is a useful skill, but the
real aim is to compare 2-digit numbers.
As you did in the opening, consider asking the students to use
symbols to show the inequality. For example, if two stacks have
values of 37 and 34, respectively, encourage your students to be
able to write 37 > 34, in addition to understanding which stack
has more (or fewer) baseballs.
Try to encourage your students not to guess (as most screens ask
to click on the correct stack, the students have a 50% of guessing
right and gaining a false sense of understanding).
Advanced students (or students who simply appear to be
guessing) can move on to play another variant of this episode:
P i l e d up - Up t o 100: L e v e l I I . This episode contains the
same concepts as in the first episode, but offers the added
challenge of a third stack of boxes.
C l ass di sc ussi o n | 8 min
Discuss the connection between boxes of baseballs and base-ten
blocks. Ensure that your students have a firm grasp on the
connection between the two concepts.
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Most notably, verify that the groundwork of the base-ten system is
still strong, as it is the basis for comparing quantities.
To expand on what has been established, play another variant of this
episode: P i l e d up - Up t o 100: L e v e l I I .
E x a m p le :
In the above example, the number of 10s and 1s is shown. This can
be used as yet another tool in comparing the three quantities.
In the example below, those quantities are not given. This adds
another layer to the exercise, but again, composing 1s into a 10 will
help form a better comparison visually.
E x a m p le :
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If time allows, consider showing the variant of this episode that
requires students to compare four 2-digit numbers: P i l e d up - Up
t o 100: L e v e l I I I . The functionality and concepts in this episode
mirror those of the first two.
The added difficulty in comparing three or four stacks is both in
keeping track of all quantities and in forcing more sound techniques
for comparison.
As a nice side-effect, guessing becomes less fruitful as more
stacks of boxes are used.
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