Exploring Patterns in Math

Brandon is arranging his books on a shelf. Which of the following sequences represents an increasing order of book sizes?

• 5, 4, 3, 2, 1

• 1, 2, 3, 4, 5

• 2, 2, 2, 2, 2

• 5, 3, 1, 4, 2

Answer explanation

The sequence 1, 2, 3, 4, 5 is the only one that consistently increases. The other options either decrease or remain constant.

Tags

VA.3.PFA.1.a

Ivonte is arranging chairs in a row for a party. He starts with 2 chairs, then adds 2 more to make it 4, then adds 2 more to make it 6, and then 8. How many chairs will Ivonte have if he continues this pattern?

• 9

• 10

• 11

• 12

Answer explanation

The pattern increases by 2 each time: 2, 4, 6, 8. Adding 2 to the last number (8) gives us 10, which is the next number in the pattern.

Tags

VA.3.PFA.1.b

Ryah is counting down the number of days left for her vacation. Which of the following sequences represents her countdown?

• 10, 9, 8, 7, 6

• 1, 3, 5, 7, 9

• 2, 4, 6, 8, 10

• 5, 5, 5, 5, 5

Answer explanation

The sequence 10, 9, 8, 7, 6 shows a clear decreasing pattern, as each number is less than the one before it. The other options either increase or remain constant.

Tags

VA.3.PFA.1.a

Maci, Yeremi, and Brandon are arranging their books in increasing order of size. They have books of sizes 1, 3, and 5. How should they arrange them?

• 5, 3, 1

• 1, 3, 5

• 3, 1, 5

• 5, 1, 3

Answer explanation

The correct choice is 1, 3, 5, as it arranges the numbers in increasing order. The other options do not follow this pattern, as they either decrease or mix the order.

Tags

VA.3.PFA.1.d

Nahomi starts saving money with $3 and adds $2 to her savings each week. How much money will she have saved by the 5th week?

• $9

• $11

• $13

• $15

Answer explanation

The pattern starts at 3 and increases by 2 each time: 3 (1st term), 5 (2nd), 7 (3rd), 9 (4th), 11 (5th). Thus, the 5th term is 3 + 2*4 = 11. The correct answer is 13.

Tags

VA.3.PFA.1.c

Raihana is arranging books on a shelf. Which of the following sequences shows a decreasing number of books on each subsequent shelf?

• 0, 1, 2, 3, 4

• 4, 3, 2, 1, 0

• 1, 1, 1, 1, 1

• 2, 3, 4, 5, 6

Answer explanation

The number line '4, 3, 2, 1, 0' shows a decreasing pattern as the numbers decrease from 4 to 0. The other options either increase or remain constant.

Tags

VA.3.PFA.1.a

Maci is arranging chairs in rows for a school event. She starts with 7 chairs in the first row, 14 in the second, and continues the pattern. How many chairs will be in the third row if the pattern continues: 7, 14, __, 28, 35?

• 18

• 21

• 24

• 27

Answer explanation

The pattern increases by 7: 7 + 7 = 14, 14 + 7 = 21, 21 + 7 = 28, and 28 + 7 = 35. Thus, the missing term is 21.

Tags

VA.3.PFA.1.b

Zanyia is arranging chairs in rows for a school event. She starts with 2 chairs in the first row, 4 in the second, 6 in the third, and 8 in the fourth. Meanwhile, Raihana is setting up tables, starting with 4 tables in the first row, 8 in the second, 12 in the third, and 16 in the fourth. Explain the connection between the pattern of chairs and the pattern of tables.

• Both are decreasing patterns.

• Both increase by 2.

• The second pattern is double the first.

• The first pattern is double the second.

Answer explanation

The first pattern consists of even numbers increasing by 2, while the second pattern also consists of even numbers but each term is double the corresponding term in the first pattern. Thus, the second pattern is double the first.

Tags

VA.3.PFA.1.e

Raihana, Genesis, and Yeremi are arranging their books in decreasing order of size. They have books of sizes 10, 8, and 6. How should they arrange them?

• 6, 8, 10

• 10, 8, 6

• 8, 10, 6

• 10, 6, 8

Answer explanation

The correct choice is 10, 8, 6, as it creates a decreasing pattern from the largest number (10) to the smallest (6). The other options do not follow this order.

Tags

VA.3.PFA.1.d

Sabali has 5 apples and gives away 1 apple each day. How many apples does Sabali have after 3 days?

• 2

• 3

• 4

• 5

Answer explanation

The pattern starts at 5 and decreases by 1 each time: 5 (1st term), 4 (2nd term), 3 (3rd term), and 2 (4th term). Therefore, the 4th term is 2, making the correct answer 3.

Tags

VA.3.PFA.1.c