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U n t er r i ch t spl a n
Pat t e rns in Tab l e s
Altersgruppe: 5 t h Gr ade
Virginia - Mathematics Standards of Learning (2009): 1.17 , 4 .14 ,
4 .15 , 5 .15 , 5 .17 , 6.17 , K .14
Virginia - Mathematics Standards of Learning (2016): 5 .18
Fairfax County Public Schools Program of Studies: 1.17 .a.6,
4 .14 .a.2, 4 .15 .a.1, 4 .15 .a.2, 4 .15 .a.3 , 4 .15 .a.4 , 5 .15 .a.8,
5 .17 .a.1, 5 .17 .a.2, 6.17 .a.1, K .14 .a.3
Online-Ressourcen: B r i c ks and T abl e s
Opening
T eacher
present s
St udent s
pract ice
Mat h
Pract ice
6
10
14
14
3
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 sequences of numbers
P r ac t i c e observing patterns
L e ar n to record data in a table
De v e l o p methods to investigate relationship between
variables
Ope ni ng | 6 min
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Display the following sequences:
1. 4, 8, 12, 16, _ _ _ , 24
2. 1, 4, 7, 10, _ _ _ , 16
3. 6, 11, 16, 21, _ _ _ , 31
4. 19, 22, 25, 28, _ _ _ , 34
5. 8, 16, 32, 64, _ _ _ , 256
6. 3, 9, 27, 81, _ _ _ , 729
7. 1, 1, 2, 3, 5, 8, _ _ _ , 21
8. 1, 4, 9, 16, 25, _ _ _ , 49
A sk the students to copy the sequences into their notebooks and
fill in the missing number.
When the students are done working, review solutions. Discuss any
questions the students may have.
A sk: How are the first four sequences different from the fifth and
sixth sequences?
The first four sequences are ar i t hme t i c se q ue nc e s . To get
from one term to the next, we add the same number each time.
The fifth and sixth sequences are ge o me t r i c se q ue nc e s . To
get from one term to the next, we multiply by the same number
each time.
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S ay: The seventh and eighth sequences do not fit either of these
patterns. What is happening in the seventh and eighth sequences?
The seventh sequence is a list of the F i bo nac c i numbe r s . The
Fibonacci numbers are a list where the next term is found by
adding the two terms before it. The eighth sequence is a list of
the pe r f e c t sq uar e s .
T e ac he r pr e se nt s M at h game : B r i c ks and T abl e s - N umbe r
S e q ue nc e s | 10 min
Using Presentation Mode, present Matific ’s episode B r i c ks and
T abl e s - N umbe r S e q ue nc e s to the class, using the projector.
The goal of the episode is to observe a pattern of block structures and
create a table indicating the number of different colored blocks.
E x a m p le :
S ay: Please read the instructions.
The instructions say, “Complete the missing 4 cells in the table.”
S ay: Let’s look at the table. What does it show?
The table shows the number of rows and the number of blocks in
each structure.
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A sk the students to count the blocks in the structures and state
the missing values in the table.
Click on each to enter the values that the students state. When
the table is complete, ask: What patterns do you see within the
table?
Possible responses may include:
1. One row is counting by ones, and the other row is counting by fours.
2. In each column, one number is 4 times the other.
3. Each structure consists of rows of 4 blocks, so every time we add a row,
we add 4 blocks.
Click on
.
If the answers are correct, the episode will proceed to the next problem.
If the answers are incorrect, the problem will wiggle, and the incorrect entries
will be shaded brown.
The episode will present a total of three problems.
S t ude nt s pr ac t i c e M at h game : B r i c ks and T abl e s - N umbe r
S e q ue nc e s | 14 min
Have the students play B r i c ks and T abl e s - N umbe r
S e q ue nc e s and B r i c ks and T abl e s - C o mpl e t i ng
S e q ue nc e s on their personal devices. Circulate, answering
questions as necessary.
M at h P r ac t i c e : P at t e r ns i n T abl e s W o r kshe e t | 14 min
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Distribute the following problems to the students. Have them work
in groups of three or four on the problems.
Look at the patterns below. What does the 5 th figure look like? The 10th? The
20th?
After the students have had sufficient time to at least attempt each
problem, share. A sk: In the first pattern, what will the fifth figure
look like? How do you know?
T
​ he fifth figure will be a 5 by 5 square that is made up of 25 small
squares. This continues the pattern. First there is a 1 by 1 square,
then a 2 by 2 square, then a 3 by 3 square, and finally a 4 by 4
square. The next figure will therefore be a 5 by 5 square.
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A sk: What will the tenth figure look like? What will the twentieth
figure look like?
The tenth figure will be a 10 by 10 square. The twentieth figure
will be a 20 by 20 square.
S ay: Now let’s consider the second pattern. What is the pattern
here? What will the fifth, tenth, and twentieth figures look like?
Each figure here is a rectangle. The first figure is 1 square wide
and 2 squares tall. The second figure is 2 squares wide and 3
squares tall. The third figure is 3 squares wide and 4 squares tall.
The fourth figure is 4 squares wide and 5 squares tall. So the
width of each figure is equal to the figure number. The height is
one more than the width. So the fifth figure will be 5 squares
wide and 6 squares tall. The tenth figure will be 10 squares wide
and 11 squares tall. The twentieth figure will be 20 squares wide
and 21 squares tall.
S ay: Now let’s consider the third pattern. What is the pattern here?
What will the fifth, tenth, and twentieth figures look like?
Each figure here makes an “L” shape. The first figure is just a
single square. In the second figure, we see the “L” shape appear. It
is made up of 3 small squares. The third figure is made up of 5
small squares. The fourth figure is made up of 7 small squares. In
each figure, we keep the “L” shape but we make it larger by adding
2 small squares. So the fifth figure will make a larger “L” shape
and will be made up of 9 small squares. The tenth figure will be
made up of 19 small squares. The twentieth figure will be made
up of 39 small squares.
S ay: What is the pattern in the fourth problem? What will the fifth,
tenth, and twentieth figures look like?
Here, to get from one figure to the next, we add a row on the
bottom of the figure. Each row contains an odd number of
squares. The top row has 1 square, the second row has 3 squares,
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the third row has 5 squares, and the fourth row has 7 squares.
Each time we add a row, we add the next odd number. So for the
fifth figure, we need to add a row of 9 to the bottom of the fourth
figure. So the fifth figure will be 5 rows tall and will consist of a
row of 1, a row of 3, a row of 5, a row of 7, and a row of 9, for a
total of 25 squares. The tenth figure will be 10 rows tall and
contain 100 squares. The twentieth figure will be 20 rows tall and
contain 400 squares.
S ay: What is the pattern in the fifth problem? What will the fifth,
tenth, and twentieth figures look like?
The fifth pattern looks like a staircase. The first figure is just a
single square. The second figure contains 3 squares. The third
figure contains 6 squares. The fourth figure contains 10 squares.
So the fifth figure will have 5 columns and will consist of a
column of 1, a column of 2, a column of 3, a column of 4, and a
column of 5, for a total of 15 squares. The tenth figure will
contain 55 squares. The twentieth figure will contain 210
squares.
C l o si ng | 3 min
A sk each student to write a sequence of numbers on a piece of
paper. They should leave a blank somewhere in the middle of the
sequence.
A sk the students to swap papers with a partner.
The partner should fill in the blank based on the pattern.
They should swap papers again and check their partner’s work.
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