Lesson 7 — Growing Patterns

Summary

Learners tell a growing pattern from a repeating one, then build growing patterns — staircases that add one more each step. They learn to say how a pattern grows: what changes from one step to the next.

Objectives

• Identify and extend growing patterns and describe how the pattern changes from one step to the next. (D05.S2.02.01)

Connection

Some patterns repeat — day and night, bead colors on a necklace — and some patterns grow. A plant grows one leaf, then two, then three; steps of a staircase rise one at a time; a tower grows a block taller each time you add one. When you see how a pattern grows, you can predict what comes next — and prediction is how people plan a garden, build a staircase, or guess tomorrow’s weather.

Materials

• About 30 small objects (counters, seeds, pebbles, blocks)
• Paper or slate and a drawing tool

Preparation

• Give each learner or pair about 30 objects.
• Prepare a repeating pattern and a growing pattern to compare.
• Plan to model building a growing staircase as a worked example.

Facilitator note

This lesson is written to the learner (“you”). It builds on Grade 1’s repeating patterns and introduces growing patterns — the new idea is describing change, not just repetition. Start by recalling a repeating pattern, then contrast it with a staircase that grows. Teach building and describing a growing pattern as a worked example (philosophy §13): “one block, then two, then three — it grows by one each step.” Patterns are found in every culture — in woven cloth, in songs, in the steps of a dance — and naming the change is a kind of poetry about structure. No one’s speed at seeing a pattern measures their smartness; noticing is a skill that grows with practice, at each learner’s own pace. For learners who are Deaf or hard of hearing, build with objects and point to each change; for learners who are blind or low-vision, build patterns by touch and feel each row grow. A learner who does not speak shows the change by pointing or adding the next step.

Procedure

1. Gather — recall repeating patterns (5 min). Last year you made repeating patterns: red, blue, red, blue — the same thing over and over. Say one repeating pattern you remember. Today we meet a different kind: patterns that grow.
2. Worked example — a growing staircase (10 min). Build a staircase with blocks: one block, then two blocks, then three, then four. Look at it. Is it repeating? No — it grows. How does it grow? Each step has one more than the step before. Say it: “it grows by one each step.”
3. Build your own (15 min). Use your objects to build a growing staircase. Start with one, then two, then three, then four. Say how it grows. Now try a pattern that grows by two: two, four, six, eight. How is it different?
4. Draw and label (8 min). Draw one growing pattern. Draw an arrow and write how it changes from one step to the next (“add one more,” “add two more”).
5. Check with a partner (5 min). Trade patterns. A friend says how your pattern grows and adds the next step. Do you agree? Talk it through kindly if not.
6. Close (2 min). A growing pattern is change you can see coming. When you can say how it grows, you can guess what comes next — and that is the start of prediction.

Differentiation

• Support: Build only the “add one” staircase and say “one more” for each step.
• Support (motor): Use large blocks and have a partner place them while the learner directs and describes.
• Extension: Build a pattern that grows by three, or a staircase that grows on both sides, and describe the change.

Assessment

• Formative (observation): Can the learner build a growing pattern and describe how it changes from one step to the next?
• Formative (self): Can the learner add the next step and check it matches the rule?

Home connection

At home, build a growing staircase with stones, beans, or toys and tell a grown-up how it grows each step.

Resources

• Clements, D. H., & Sarama, J. (2014). Learning and Teaching Early Math: The Learning Trajectories Approach (2nd ed.). Routledge. (Growing patterns and describing change from one term to the next.)