High Impact Tutoring Built By Math Experts
Personalized standards-aligned one-on-one math tutoring for schools and districts
In order to access this I need to be confident with:
2D shapesHere you will learn about shape patterns, including how to create and justify a rule and extend a pattern for repeating and growing shape patterns.
Students will first learn about shape patterns as part of the operations and algebraic thinking in 4th grade.
Shape patterns are groupings of different shapes that follow given rules. The shapes can be polygons, 3D shapes, letters or any other type of image.
There are two types of shape patterns – repeating and growing.
For example,
This is a simple repeating pattern.
In a repeating pattern, a part of the pattern is repeated over and over again. This part is called the core.
The core of this pattern is:
For example,
This is a more complex growing pattern.
There are parts that stay the same and other parts that change.
Here, the yellow hexagon stays the same, and 2 green triangles and 1 blue rhombus are added each time.
How does this relate to 4th grade math?
Use this worksheet to check your 4th grade students’ understanding of shape patterns. 15 questions with answers to identify areas of strength and support!
DOWNLOAD FREEUse this worksheet to check your 4th grade students’ understanding of shape patterns. 15 questions with answers to identify areas of strength and support!
DOWNLOAD FREEIn order to identify and extend repeating shape patterns:
In order to identify and extend growing shape patterns:
Create a rule for the pattern and find the next shape.
This pattern goes blue triangle, red heart, yellow circle and then repeats.
2Use the core to find and justify the next part in the pattern.
The next shape is:
because the last shape shown is:
Create a rule for the pattern and find the next shape.
Identify the core – the part of the pattern that repeats.
This is a repeating pattern with letters that goes A, B, B, H, A, T.
Notice that A is used twice in the core. Sometimes parts of the pattern are repeated within the core. Always look at all the shapes given to confirm the pattern.
Use the core to find and justify the next part in the pattern.
The next letter is A because the next part starts at the beginning of the core.
Create a rule for the pattern and find the next shape.
Identify the core – the part of the pattern that repeats.
This is a repeating pattern with cubes that goes purple, purple, orange, purple, red, purple.
Notice that purple is repeated multiple times within the core. Always look at all the shapes given to confirm the pattern.
Use the core to find and justify the next part in the pattern.
The next shape is because the last part of the core shown is
.
Create a rule for the pattern and find the next shape.
Identify what is changing and what is staying the same.
Create a rule based on Step 1.
Start with 1 purple triangle, then 1 red heart. Repeat, adding 1 more purple triangle each time.
Use the rule to find and justify the next part in the pattern.
The next part in the pattern is , because after the there is 1 more purple triangle than before.
Create a rule for the pattern and find the next shape.
Identify what is changing and what is staying the same.
Create a rule based on Step 1.
Start with 1 triangle. Add 1 triangle to the top and 1 triangle to the left side each time.
Use the rule to find and justify the next part in the pattern.
The next part in the pattern is , because 1 triangle is added to the top and 1 triangle is added to the side each time.
Create a rule for the pattern and find the next shape.
Identify what is changing and what is staying the same.
Create a rule based on Step 1.
Add 1 row and 1 column of squares each time, but no square to the top left corner.
Use the rule to find and justify the next part in the pattern.
The next part in the pattern is , because 1 row is added to the bottom and 1 column is added to the side, but there is not a square in the top left corner.
1. What is the next shape in the pattern?
This pattern goes green triangle, purple pentagon, orange cross, red pentagon and then repeats.
The next shape is because the last shape shown is .
2. What is the next shape in the pattern?
b
u
B
This pattern goes B, U, G, 3 , b, u, g, 3 , 3 and then repeats.
The next shape is because the last part of the core shown is .
3. What is the next shape in the pattern?
This pattern goes yellow star, red star, purple star, yellow star, green star, red star.
The next shape is because the last shape shown is .
4. What is the next part in the pattern?
Identify what is changing and what is staying the same:
Rule: Start with 1 blue circle, 1 orange sun and 1 purple sun. Repeat, adding 1 more blue circle each time.
The next part in the pattern is , because after the there is 1 more blue circle than before.
5. What is the next part in the pattern?
Identify what is changing and what is staying the same:
Rule: Start with a green circle in the middle and a purple square above, below, to the left and to the right. Repeat, adding 1 more purple square to the left and right each time.
The next part in the pattern is , because there is a purple square being added to the left and the right each time.
6. What is the next part in the pattern?
Identify what is changing and what is staying the same:
Rule: Start with a row of 1 orange square and 3 orange squares. Repeat, adding a row with 2 more orange squares each time.
The next part in the pattern is , because there is a row of 2 more orange squares being added each time.
Shape problems are a great way to encourage students to sharpen their problem solving skills. Creating a rule and extending patterns requires students to analyze and generalize relationships – an important math skill. Justifying growing patterns in particular is a form of algebraic thinking that can help students create and support valid justifications at an elementary level.
Students as young as Pre-K have the ability to notice and extend simple patterns. Even though this is a 4th grade skill in the Common Core, it is a good idea to introduce patterns and encourage pattern thinking in younger students.
These types of patterns do not typically include fractions or decimals. However, they can be included if used in a way that is not operational (for example in the repeating pattern \frac{1}{2}, \frac{1}{3}, \frac{1}{2}, \frac{1}{3}, \frac{1}{2}, \frac{1}{3} … ). This pattern can be extended without operating.
Yes, decreasing patterns (which are the opposite of growing patterns) involve less and less shapes each time, which would include the use of subtraction in the rule.
At Third Space Learning, we specialize in helping teachers and school leaders to provide personalized math support for more of their students through high-quality, online one-on-one math tutoring delivered by subject experts.
Each week, our tutors support thousands of students who are at risk of not meeting their grade-level expectations, and help accelerate their progress and boost their confidence.
Find out how we can help your students achieve success with our math tutoring programs.
Prepare for math tests in your state with these 3rd Grade to 8th Grade practice assessments for Common Core and state equivalents.
Get your 6 multiple choice practice tests with detailed answers to support test prep, created by US math teachers for US math teachers!