Sequences
Sequences in Grade 4 Saxon Math Intermediate 4 teaches students to identify and extend counting patterns that follow a specific rule. A sequence is a list of numbers that counts up or down by a fixed amount. For example, 10, 20, 30 counts up by tens and the next term is 40, while 21, 18, 15 counts down by threes and the next term is 12. Students learn to find the rule by calculating the difference between consecutive terms, verify the rule against multiple pairs, and apply it to predict future terms — skills that underpin algebra and data analysis.
Key Concepts
Property A counting pattern is a sequence . A counting sequence may count up or count down, following a specific rule.
Examples The sequence $10, 20, 30, ...$ counts up by tens. The next number is $40$. The sequence $21, 18, 15, ...$ counts down by threes. The next number is $12$.
Explanation Think of a sequence as a number puzzle! It is simply a list of numbers that follows a secret rule. Your job as a math detective is to find that rule so you can figure out what numbers come next in the pattern.
Common Questions
What is a sequence in Grade 4 math?
A sequence is a list of numbers that follows a specific rule, counting up or down by the same amount each time. For example, 10, 20, 30, 40 has a rule of add 10.
How do you find the rule of a sequence?
Subtract consecutive terms: for 45, 38, 31, 24, compute 45 - 38 = 7. Check the next pair: 38 - 31 = 7. The rule is subtract 7.
What are the next two numbers in 45, 38, 31, 24?
Apply the subtract-7 rule: 24 - 7 = 17, then 17 - 7 = 10. The next two numbers are 17 and 10.
Why should you check the rule on more than one pair?
Checking only the first two numbers can lead to a wrong rule. Always verify against at least two consecutive pairs to confirm the pattern is consistent.
Can sequences count down as well as up?
Yes. Sequences can count up by adding a fixed number or count down by subtracting. Determine the direction by checking whether the terms increase or decrease.