Patterns and SequencesActivities & Teaching Strategies
Active learning turns abstract ideas like symmetry and sequence rules into concrete experiences. Hands-on folding, building, and predicting let students test their hunches and revise them in real time, which builds lasting understanding faster than worksheets alone.
Learning Objectives
- 1Identify and describe the rule for a given number sequence, distinguishing between additive and multiplicative patterns.
- 2Predict the next three terms in an increasing or decreasing number sequence based on its identified rule.
- 3Classify 2D shapes and patterns based on their lines of symmetry.
- 4Determine the order of rotational symmetry for given 2D shapes.
- 5Create a repeating pattern using geometric shapes and articulate its rule.
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Pairs: Symmetry Folding Challenge
Provide students with assorted 2D shapes cut from paper. In pairs, they fold shapes to identify lines of symmetry and record the number of lines per shape. Then, they test rotational symmetry by spinning shapes on pins and noting the smallest angle for full rotation.
Prepare & details
What is a repeating pattern, and how do you find the rule that describes it?
Facilitation Tip: During the Symmetry Folding Challenge, circulate with a small mirror to confirm each fold line; students often miss partial symmetry without immediate feedback.
Setup: Wall space or tables arranged around room perimeter
Materials: Large paper/poster boards, Markers, Sticky notes for feedback
Small Groups: Pattern Rule Hunt
Give groups attribute blocks or number cards forming repeating patterns. Students discuss and write the core unit and repeating rule, then extend the pattern by five terms. Groups share one prediction with the class for verification.
Prepare & details
How do you identify whether a number pattern is increasing or decreasing?
Facilitation Tip: For the Pattern Rule Hunt, hand each group a set of colored tiles and a single blank rule card; this forces them to agree on wording before moving on.
Setup: Wall space or tables arranged around room perimeter
Materials: Large paper/poster boards, Markers, Sticky notes for feedback
Whole Class: Sequence Prediction Relay
Write a starting number sequence on the board. Teams line up; first student adds the next term based on the rule whispered by the teacher, then runs back for the next teammate. Correct sequences win points; discuss rules afterward.
Prepare & details
Can you continue a given pattern and predict a term further along in the sequence?
Facilitation Tip: In the Sequence Prediction Relay, pause after each turn to ask, 'What made you choose that next number?' to keep reasoning visible.
Setup: Wall space or tables arranged around room perimeter
Materials: Large paper/poster boards, Markers, Sticky notes for feedback
Individual: Create Your Pattern
Students design an original repeating pattern or increasing number sequence on grid paper, write the rule, and include three missing terms for a partner to fill. Swap and check work using the described rule.
Prepare & details
What is a repeating pattern, and how do you find the rule that describes it?
Setup: Wall space or tables arranged around room perimeter
Materials: Large paper/poster boards, Markers, Sticky notes for feedback
Teaching This Topic
Start with physical tools—folding paper, tiles, number cards—so students experience the concept before labeling it. Avoid rushing to abstract symbols; instead, let students use their own language first. Research shows that students who verbalize patterns out loud before writing them down develop stronger reasoning skills.
What to Expect
You will see students describe patterns precisely, justify symmetry claims with tools, and revise rules when peers challenge them. Successful moments include accurate folding lines, clear rule statements, and confident sequence predictions backed by evidence.
These activities are a starting point. A full mission is the experience.
- Complete facilitation script with teacher dialogue
- Printable student materials, ready for class
- Differentiation strategies for every learner
Watch Out for These Misconceptions
Common MisconceptionDuring Symmetry Folding Challenge, watch for students who assume every shape has exactly one line of symmetry.
What to Teach Instead
Have students fold a square and a rectangle, then compare the number of lines; prompt them to explain why the square has four and the rectangle has two, using the fold lines they created.
Common MisconceptionDuring Pattern Rule Hunt, watch for students who assume all patterns repeat every two items.
What to Teach Instead
Give each group a set of colored cubes with a repeating unit of three (e.g., red, blue, green); ask them to describe the core unit before extending the sequence.
Common MisconceptionDuring Sequence Prediction Relay, watch for students who assume number sequences always increase by addition.
What to Teach Instead
After teams predict the next term in a doubling sequence, ask them to explain their rule in words and defend it to another team using the tiles or cards they used to build it.
Assessment Ideas
After Symmetry Folding Challenge, hand out a quick sheet with a parallelogram, a kite, and a regular hexagon. Ask students to draw all lines of symmetry and state the order of rotational symmetry for each shape.
During Pattern Rule Hunt, give each student the exit ticket with Sequence A: 3, 6, 9, 12, ... and Sequence B: 2, 4, 8, 16, ... Ask them to write the rule for each and predict the next two numbers in Sequence B.
After Create Your Pattern, display a complex tile pattern on the board. Ask, 'What is the smallest repeating unit?' and 'How can you describe the rule so someone else could build the same pattern?' Circulate and listen for precise language and shared reasoning.
Extensions & Scaffolding
- Challenge: Provide a sequence where the rule shifts mid-pattern (e.g., 2, 4, 8, 16, 32, 64, 128, 256, 129, 258…). Ask students to identify the change point and explain why the rule breaks.
- Scaffolding: Give students a partially drawn pattern with every third tile missing; they reconstruct the repeating unit first.
- Deeper exploration: Introduce a pattern that combines shape and number, such as triangle, 3; square, 4; pentagon, 5; then ask students to predict the 10th term and justify their answer.
Key Vocabulary
| Symmetry | A property of a shape or pattern where one part is a mirror image of another part. It means the shape can be divided into two identical halves. |
| Line of Symmetry | A line that divides a shape into two identical, mirror-image halves. Folding the shape along this line would make the two halves match exactly. |
| Rotational Symmetry | A property where a shape looks the same after being rotated by a certain angle around its center. The order of rotational symmetry is the number of times it matches itself during a full 360-degree turn. |
| Repeating Pattern | A sequence of elements that occurs over and over again in a predictable order. The pattern unit is the smallest set of elements that repeats. |
Suggested Methodologies
Planning templates for Mathematics
5E Model
The 5E Model structures lessons through five phases (Engage, Explore, Explain, Elaborate, and Evaluate), guiding students from curiosity to deep understanding through inquiry-based learning.
Unit PlannerMath Unit
Plan a multi-week math unit with conceptual coherence: from building number sense and procedural fluency to applying skills in context and developing mathematical reasoning across a connected sequence of lessons.
RubricMath Rubric
Build a math rubric that assesses problem-solving, mathematical reasoning, and communication alongside procedural accuracy, giving students feedback on how they think, not just whether they got the right answer.
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