4th Grade Number and Shape Patterns Worksheets with Answers (Free PDF)

4th grade patterns worksheet – Maths PDF

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This 4th grade patterns worksheet covers number and shape patterns (Common Core 4.OA.C.5), with a free PDF to print.

Key takeaway: This worksheet helps fourth grade students practice generating patterns from rules, finding rules from lists and tables, and describing features such as odd and even terms.

Topic: Number and Shape Patterns (4th grade)
Content: 20 worksheet problems, from easy to challenging
Standards: 4.OA.C.5
Answers: On a separate page, so you can try every worksheet problem first
Format: Free printable PDF, US Letter, black and white

This worksheet helps fourth grade students practice generating patterns from rules, finding rules from lists and tables, and describing features such as odd and even terms. Also, toothpicks, coins, and tanks of water show how patterns appear in real situations.

There are 20 problems. The first five build patterns from a start and a rule, and the next three use input and output tables. Then, four problems explore odd and even features and last digits. Also, the last eight are word problems about toothpick squares, which numbers appear, a coin jar, packs of fish, triangles of sticks, a draining tank, and checking claims. Then, allow about 30 minutes.

This worksheet has 20 problems on number and shape patterns. Problems ask for terms made from a rule, the rule behind a pattern, input-output tables, and features such as odd and even numbers (Common Core 4.OA.C.5).

Grade 4 · Common Core State Standards: 4.OA.C.5

4th grade patterns worksheet: worksheet problems 1 to 10

1 – Add 4 pattern

First, start at 5. The rule is add 4. Write the first six numbers.

2 – Subtract 6 pattern

Next, start at 40. The rule is subtract 6. Write the first six numbers.

3 – Multiply by 3 pattern

Then, start at 2. The rule is multiply by 3. Write the first five numbers.

4 – Find the rule

Now, look at the pattern.

A number pattern with two missing terms.

Write the rule. Then find the two missing numbers.

5 – Subtract 15 pattern

Also, start at 100. The rule is subtract 15. Write the first five numbers.

6 – Complete the table

First, the rule is add 9. Find the missing outputs.

Outputs are missing.

7 – Multiply by 4 table

Next, the rule is multiply by 4. Copy and complete the table.

Input	2	3	5	6	9
Output	?	?	?	?	?

8 – Rule from a table

Then, find the rule for this table.

Input	2	4	6	8
Output	7	9	11	13

9 – All odd numbers

Now, start at 1 and add 2 each time. Write the first six numbers and describe what you notice about odd and even.

10 – Odd and even take turns

Also, start at 3 and add 5 each time. Write the first six numbers. Describe the pattern of odd and even numbers.

Worksheet problems 11 and up

11 – All even numbers

First, start at 4 and add 6 each time. Write the first six numbers. Are the terms odd or even? Explain why the rule makes this happen.

12 – Doubling pattern

Next, start at 6 and multiply by 2 each time. Write the first five numbers. What do you notice about the last digits?

13 – Toothpick squares

Ethan makes squares in a row with toothpicks.

Squares in a row.

Write the rule for the number of toothpicks. How many toothpicks does he need for 4 squares? For 5 squares?

14 – Which numbers appear?

Now, a pattern starts at 1 and adds 3 each time. Which of these numbers will appear in the pattern: 25, 29, 34?

15 – Jar of coins

Jamal puts $12 in a jar on Monday. Each day after that he adds $4. Write how much is in the jar on each day from Monday to Friday.

16 – Packs of fish

First, a pet store sells fish in packs of 6. Make a table for 1, 2, 3, 4, 5 and 8 packs. How many fish are in each?

17 – Triangle sticks

Priya builds a row of triangles with sticks.

Triangles made of sticks.

Continue the pattern. How many sticks does she need for 10 triangles?

Worksheet problem 18 and after

18 – Draining tank

Then, a tank holds 200 gallons. It loses 25 gallons each hour. The table shows the first hours.

Hours and gallons in the tank.

How many gallons are left after 5 hours? After how many hours is the tank empty?

19 – Mei's rule

Mei starts at 7 and adds 8 each time. Will 63 be in her pattern? Will 100? Explain without writing every term for 100.

20 – Sofia's tenth term

Also, a pattern starts at 4 and adds 5 each time: 4, 9, 14, 19, and so on. Sofia says the 10th number is 49. Is she right? Show how you know.

Key facts behind this 4th grade patterns worksheet

Key facts

A pattern rule gives a starting number and an operation to repeat.
Next, each number in a pattern is called a term.
Adding an odd number makes terms alternate odd and even; adding an even number keeps them all odd or all even.
Then, in an input-output table, the same rule turns every input into its output.
Shape patterns grow by adding the same number of pieces at each step.

Common mistakes with this 4th grade patterns worksheet

Students say all terms are odd because the rule adds an odd number. Adding an odd number flips between odd and even, so the terms take turns.
Students say terms are even only because they look even. Instead, starting with an even number and adding an even number always gives an even number.
Students add each hour in a draining story instead of subtracting. When the amount decreases, the rule subtracts.
Students list terms one by one to check a large number. Subtract the start and divide by the step to see whether the result is a whole number.

Tips before you start the worksheet problems

Write the rule above your list before you start. Reading it again between terms helps prevent adding when you should subtract.
For each table, find the rule from the first pair and then check it on the others. One pair is not enough to be sure.
Teachers can ask students to share the features they notice in a doubling pattern and explain each one using the rule.

Download the 4th grade patterns worksheet as a PDF with the button below and keep it with your notes.

4th grade patterns worksheet: frequently asked questions

How do you find a rule from an input and output table?

Compare each input with its output and look for the same operation each time. If inputs 1, 2, 3 give outputs 5, 6, 7, the outputs are 4 more than the inputs. Test the rule on every pair.

How do you know if a number is in a pattern that starts at 5 and adds 6?

Subtract the start and divide the result by the step. For 29, 29 minus 5 is 24, and 24 divided by 6 is 4, a whole number, so 29 appears. For 30, 25 divided by 6 is not whole, so it does not.

Why do the last digits of a doubling pattern repeat?

The last digit of each double depends only on the last digit before it, so the same digits come back in a loop. Starting at 3, the terms 3, 6, 12, 24, 48 have last digits 3, 6, 2, 4, 8, and the cycle continues.

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