2.6: Peculiar Patterns
Can you describe the pattern with the letters below? Can you write the next two rows of the pattern? In this concept, we will practice identifying patterns and extending them.
T M T
T N N T
T O O O T
Guidance
When identifying a letter pattern like the one above, the first thing we should do is describe anything we notice. For example, each line in the pattern has one more letter. Also, each line has a T at the beginning and at the end. Then, try to figure out what is changing from one line to the next.
Example A
Complete the next two rows.
Write the letters.
K
K L
K L M
K ________________
K ________________
Solution:
Each row in the pattern has one more letter. The letters are in the sequence of the alphabet. The fourth row should be KLMN. The fifth row should be KLMNO.
Example B
Complete the next two rows.
Write the letters.
C D
C D E
C D E F
________________
________________
Solution:
Each row in the pattern has one more letter. The rows always start with C, and then the letters are in the order of the alphabet. The fourth row should be CDEFG. The fifth row should be CDEFGH.
Example C
Complete the next two rows.
Write the letters.
F G H
F G H I
F G H I J
________________
________________
Solution:
Each row in the pattern has one more letter. The rows always start with F, and then the letters are in the order of the alphabet. The fourth row should be FGHIJK. The fifth row should be FGHIJKL.
Concept Problem Revisited
We saw the following pattern in the Concept section.
T M T
T N N T
T O O O T
In this pattern, each row has one more letter. Also, each row begins and ends with a T. In the middle of the T's, the number of letters goes up by 1 for each row. The letters in the middle of the T's are the next letter in the alphabet, starting with M.
The fourth row should be TPPPPT. The fifth row should be TQQQQQT.
Vocabulary
One type of pattern is when a characteristic (like letters) appear in a certain order. In the letter pattern below, each row has the next letter of the alphabet at the end.
C D
C D E
C D E F
Guided Practice
1. Complete the next two rows. Write the letters.
- A B
- B C C
- C D D D
- D ___________________
- E ___________________
2. Complete the next two rows. Write the letters.
- E E F
- G G H
- I I J
- ___________________
- ___________________
3. Complete the next two rows.Write the letters.
- S O D
- S O O D
- S O O O D
- ___________________
- ___________________
Answers:
1. DEEEE; EFFFFF
2. KKL; MMN
3. SOOOOD; SOOOOOD
Practice
1. Complete the next two rows. Write the letters.
- X Y Z Z
- X Y Z Z Z
- X Y Z Z Z Z
- X ___________________
- X ___________________
2. Complete the next two rows. Write the letters.
- M O O N
- M M O O N
- M M M O O N
- M___________________
- M___________________
3. Complete the next two rows. Write the letters.
- R A R
- R B B R
- R C C C R
- R ________________
- R ________________
4. Complete the next two rows. Write the letters.
- A B B
- B C C
- C D D
- ___________________
- ___________________
5. Complete the next two rows. Write the letters.
- C A T
- C A A T
- C A A A T
- ___________________
- ___________________
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Image Attributions
Students identify and extend patterns.