Find Missing Numbers in a Pattern
This Grade 4 Eureka Math skill teaches students to find missing numbers in a numerical sequence by first identifying the pattern rule. Students find the difference between consecutive terms to determine if the sequence adds or subtracts a fixed amount, then apply that rule to fill in the missing term. For example, in 125,410; 135,410; ___; each term increases by 10,000, so the missing term is 145,410. This foundational skill for pattern recognition is covered in Chapter 2 of Eureka Math Grade 4.
Key Concepts
Property To find a missing number in a sequence, first determine the rule of the pattern by finding the difference between two consecutive numbers. Then, apply this rule by adding or subtracting from a known number to find the unknown term.
Examples Fill in the blank: $125,410;\ 135,410;\ \ \ \ $. To find the pattern, look at how the numbers change — each increases by $10,000$. The rule is to add $10,000$. So, $135,410 + 10,000 = 145,410$. Fill in the blank: $788,204;\ \ \ \ ;\ 768,204;\ 758,204$. Notice that the numbers are getting smaller each time, and the difference between them is $10,000$. The rule is to subtract $10,000$. So, $788,204 10,000 = 778,204$. Fill in the blank: $499,000;\ \ \ \ ;\ 501,000$. To find the pattern, compare the first and last numbers: from $499,000$ to $501,000$, the increase is $2,000$. There are two equal steps, so each step must be $1,000$. The rule is to add $1,000$. So, $499,000 + 1,000 = 500,000$.
Explanation This skill involves analyzing a sequence of numbers to find the pattern, which could be adding or subtracting 1,000, 10,000, or 100,000. Once you identify the rule, you can find a missing number that is inside the sequence. This requires applying the rule forwards from the number before the blank or backwards from the number after the blank. This strengthens your understanding of place value and number relationships.
Common Questions
How do you find the rule of a number pattern?
Subtract a term from the next consecutive term to find the constant difference. If all consecutive differences are the same, that is the rule. For 125,410 and 135,410, the difference is 10,000.
How do you find a missing number in 125,410; 135,410; ___?
The rule is add 10,000 each time. Apply it: 135,410 + 10,000 = 145,410.
Can a pattern involve subtraction?
Yes. If each term decreases by a fixed amount, the rule is to subtract. For example, 80,000; 70,000; 60,000 follows the rule subtract 10,000.
What if the missing number is between two known terms?
Use both known neighbors to verify the rule, then calculate the missing term by adding (or subtracting) the rule value from the term just before it.
Why is identifying the rule the first step?
Without knowing the rule, you cannot reliably extend or fill gaps in the pattern. The rule gives a formula: each term equals the previous term plus (or minus) the fixed amount.