4th Grade · 4.OA.C.5

Number patterns in 4th grade

Number patterns are lists of numbers made by following a rule, such as "start at 4 and add 6", which gives 4, 10, 16, 22 and so on. In 4th grade, your child builds number and shape patterns from a rule. Your child then looks for things that are true about the pattern even though the rule never said them.

What the standard says

The official Common Core wording, quoted exactly. The plain version follows.

4.OA.C.5 Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself.

What it means, in plain words

A pattern rule says where to start and what to do each time. "Start at 1, multiply by 2" gives 1, 2, 4, 8, 16. Each number in the list is called a term. Shape patterns work the same way, with a rule such as "triangle, square, square, then repeat". Pattern rules can add, subtract, multiply or repeat a group of shapes.

Number patterns in 4th grade go one step past following the rule. After building the pattern, your child looks for features the rule did not mention and explains them. With "start at 4, add 6", every term is even, because an even number plus an even number is always even. The ones digits also repeat: 4, 0, 6, 2, 8, then 4 again.

The rule is always given. This topic is not about guessing a hidden rule from a few numbers, because a list like 1, 2, 4 could go on as 8 (doubling) or as 7 (adding 1, then 2, then 3). With a repeating shape pattern, your child can also use the length of the repeat to find a shape far down the line without drawing every shape.

Your child should be able to:

Build a number pattern from a rule, such as "start at 6, add 4"
Continue a shape pattern from its rule
Point out a feature the rule does not mention, such as terms that switch between even and odd
Explain why that feature keeps going

Example

Start at 2 and add 5. What are the first six terms, and what do you notice?

Start at 2 and keep adding 5: 2, 7, 12, 17, 22, 27.
The terms go even, odd, even, odd.
Adding 5, an odd number, turns an even number into an odd one and an odd number into an even one, so the switching never stops. The ones digits also repeat: 2, 7, 2, 7.

Example

The rule is "square, circle, circle, then repeat". What is the 23rd shape?

The pattern repeats every 3 shapes, so shapes 3, 6, 9 and so on end a repeat.
$7 \times 3 = 21$ , so shape 21 is the last circle of the 7th repeat.
Shape 22 starts a new repeat, so it is a square. The 23rd shape is a circle.

Where children usually get stuck

Given "start at 4, multiply by 2", your child writes 4, 6, 8, 10.
Most patterns from earlier grades were adding patterns, so the child adds 2 out of habit instead of reading the rule.
What helps. Read the rule out loud before each step and say the step as a sentence: "4 times 2 is 8." The pattern is 4, 8, 16, 32.
Asked what else is true about a pattern, your child only repeats the rule: "it adds 5".
The child thinks the rule is the only thing there is to say. Noticing a feature the rule does not mention is a new kind of question in 4th grade.
What helps. Write the terms in a column and ask one small question at a time: Are they even or odd? What do the ones digits do?
To find the 40th shape in a pattern that repeats every 3 shapes, your child draws all 40 shapes and loses count along the way.
The child has not yet seen that the length of the repeat lets you jump ahead.
What helps. Color the last shape of each repeat and count by 3s: 3, 6, 9 and so on. Shape 39 ends a repeat, so the 40th shape is the first shape of the pattern.

Try four practice questions

Real 4th grade questions from our question bank, easiest first. Answer them right here, check each one, and see a worked solution for any question.

1Warm-up
Mia is generating a pattern. She starts at 4 and follows the rule: multiply by 3. The table below shows Mia's first four terms.
Start Next 1 Next 2 Next 3
4 7 10 13
Select the statement that best describes Mia's pattern.
A
Mia used a different multiplier than the rule gives.
B
Mia made a multiplication error after earlier terms were correct.
C
Mia added the rule number instead of multiplying by it.
D
Mia's terms are correct.
Show the answer and how to solve it
The answer is "Mia added the rule number instead of multiplying by it." Mia's terms (4, 7, 10, 13) come from adding 3 each time, but the rule says to multiply by 3. The correct sequence would be 4, 12, 36, 108.
1. 1Look at Mia's table. Mia starts at 4 and follows the rule: multiply by 3.
2. 2Find the correct sequence by multiplying by 3 at each step.
3. 3Compare Mia's terms (4, 7, 10, 13) to the correct sequence (4, 12, 36, 108). The very first generated term is wrong: Mia wrote 7, but it should be 12.
4. 4Notice Mia added 3 each time: $4 + 3 = 7$ , $7 + 3 = 10$ , $10 + 3 = 13$ . Mia added the rule number instead of multiplying by it.
5. 5The answer is "Mia added the rule number instead of multiplying by it."
Common mistake. A common mistake is assuming any wrong pattern means the student used the wrong multiplier. Mia's terms grow by a constant amount (adding 3), not by multiplication. Checking whether the gap between terms is constant (addition) or whether each term is a multiple of the last (multiplication) reveals the true error.
The idea underneath. To evaluate a multiplied pattern, divide each term by the previous to find the actual factor. Here, $7 \div 4 = 1.75$ — not a whole number — which signals addition rather than multiplication. When consecutive terms share a constant difference instead of a constant ratio, the student added instead of multiplied.
2On level
A number pattern starts at 23 and follows the rule "add 9." Which option shows the starting number followed by the next three numbers in the pattern?
A
23,23,32,41
B
23,32,41,50
C
23,33,43,53
D
23,32,41,51
Show the answer and how to solve it
The correct sequence is 23, 32, 41, 50. Adding 9 to 23 gives 32, adding 9 to 32 gives 41, and adding 9 to 41 gives 50.
1. 1Apply the rule "add 9" to the starting number 23.
2. 2Apply the rule again to the new term, 32.
3. 3Apply the rule one more time to 41.
4. 4The pattern is 23, 32, 41, 50. Choose the option that shows this sequence.
Common mistake. A common mistake is using the wrong operation (subtract instead of add) or being off by 1 (adding 10 instead of 9). Always re-read the rule and apply it exactly to the previous term, step by step.
The idea underneath. Each new term in an add or subtract pattern comes from the PREVIOUS term — not from the starting number. Apply the rule one step at a time.
3On level
A number pattern starts with $3$ and uses the rule 'multiply by $4$ .' Which option shows the next three numbers in the pattern?
A
7,11,15
B
12,48,142
C
12,48,192
D
12,16,20
Show the answer and how to solve it
The pattern starts at $3$ and uses the rule 'multiply by $4$ .' Multiplying step by step gives $3 \times 4 = 12$ , then $12 \times 4 = 48$ , then $48 \times 4 = 192$ . The next three numbers are $12$ , $48$ , and $192$ .
1. 1The starting number is $3$ and the rule is 'multiply by $4$ .' To find each new term, multiply the previous term by $4$ .
2. 2Find the first new term: $3 \times 4$ .
3. 3Find the second new term: $12 \times 4$ .
4. 4Find the third new term: $48 \times 4$ .
5. 5The next three numbers in the pattern are $12$ , $48$ , and $192$ .
Common mistake. A common mistake is adding $4$ each time instead of multiplying by $4$ . With this rule, the first term is $3 \times 4 = 12$ , not $3 + 4 = 7$ — the rule means multiplication, not addition.
The idea underneath. When a rule tells you to multiply by $4$ , apply that rule at every step. Each new term equals the previous term times $4$ — not the previous term plus a fixed amount.
4Stretch
The rule is: purple star, orange circle, teal triangle, then repeat. Drag shapes from the element bank into the empty spaces to complete the pattern.
Tap or click a shape at the top, then tap an empty box to place it.
Drag elements:
Show the answer and how to solve it
The first empty space is filled with an orange circle, the second with a purple star, and the third with a teal triangle.
1. 1The rule is: purple star, orange circle, teal triangle, then repeat. The repeating unit has 3 shapes that always cycle in this order.
2. 2The first empty space is the 2nd shape in the pattern. The shape just before it is a purple star, which is the first shape in the rule. The next shape in the rule is orange circle. The first empty space is an orange circle.
3. 3The second empty space is the 4th shape. The shape just before it is a teal triangle, which is the last shape in the rule. The rule restarts, so the next shape is purple star. The second empty space is a purple star.
4. 4The third empty space is the 6th shape. The shape just before it is an orange circle, which is the second shape in the rule. The next shape in the rule is teal triangle. The third empty space is a teal triangle.
5. 5The completed pattern repeats the rule three full times: purple star, orange circle, teal triangle, purple star, orange circle, teal triangle, purple star, orange circle, teal triangle.
Common mistake. A common mistake is copying the shape just before a blank. The shape before the second empty space is a teal triangle, but teal triangle is the last shape in the rule, so the cycle restarts as purple star — not another teal triangle.
The idea underneath. A repeating pattern works like a cycle: every shape stays at the same position inside the repeating unit each time it comes around. To fill a blank, find where it falls inside the cycle and use the matching shape from the rule.