Geometric Pattern Growth

Overview

In Lesson 14 of 26, students distinguish linear growth from non-linear growth by building and comparing geometric patterns with matchsticks, tiles, and pictures. They connect concrete changes to tables, graphs, and written relations, building on prior work with patterns and tables of values.

Learning intentions

Students will:

• Identify whether a geometric pattern grows linearly or non-linearly.
• Build figures and record the number of objects in each term.
• Compare first differences to justify a classification.
• Represent a pattern using pictures, a table, and a graph.
• Practise independently using Mathology and Mathletics.

Success criteria

• I can build and extend a geometric pattern.
• I can record the number of objects in each figure in a table.
• I can identify whether the growth is linear or non-linear.
• I can justify my answer by comparing the differences between terms.

Curriculum links

• Patterns and Relations — oral and written patterns and their corresponding relations.
• Patterns and Relations — constructing tables of values, graphing relations, and analysing graphs.
• Mathematical processes — communication, connections, problem solving, reasoning, visualization, and technology.
• Report card evidence — Knowledge and Understanding, Mental Math and Estimation, and Problem Solving.

Lesson structure (50 minutes)

1. 0–5 min · Attention hook and retrieval. Teacher displays two side-by-side picture patterns in the geometric pattern introduction deck: one pattern adding the same number of tiles each time and one pattern growing by increasingly larger amounts; ask, “Which pattern would be easier to predict, and why?” Students silently choose, sketch the next figure, then share one observation. Teacher briefly revisits the terms term, difference, linear growth, and non-linear growth using visual examples and dyslexia-friendly large print.

2. 5–13 min · Explicit teaching with concrete models. Teacher builds a matchstick pattern, such as squares in a row, while modelling: figure number, total matchsticks, and first differences. Record a table on the board and explain that constant first differences indicate linear growth. Then model a tile pattern that forms square figures, highlighting that the differences change. Students build along with the teacher, repeat the language aloud, and use gestures for “same change” and “changing change.”

3. 13–23 min · Guided investigation. Teacher provides pairs of students with matchsticks, square tiles, and simplified picture patterns. Students build the first three or four figures, count carefully, and record results on the geometric pattern growth worksheet. They calculate the changes between consecutive terms and compare their tables with another pair. Teacher circulates and asks: “What changed from Figure 1 to Figure 2?” “Did the change stay the same?” “How does your table prove your classification?”

4. 23–29 min · Video and discussion. Teacher plays a short, age-appropriate geometric-patterns video selected from the provided search results, pausing before examples are classified. Students use a visual two-column prompt in the geometric pattern introduction deck to record one example of linear growth and one example of non-linear growth. After viewing, students explain their choices using the sentence frame: “This is ___ because the differences ___.”

5. 29–38 min · Sorting and collaborative practice. Teacher gives each pair a small set of pattern examples and the sequence rule cards for sorting support. Students classify examples as linear or non-linear, place them in two groups, and select one example from each group to justify. For each selected pattern, students identify the first differences and predict the next term. Teacher pauses for a quick whole-group check, correcting the misconception that any repeating or visually straight-looking pattern must be linear.

6. 38–46 min · Independent practice and evidence checkpoint. Teacher assigns selected Mathology questions followed by an appropriate Mathletics activity, using the visual instructions in the geometric pattern introduction deck. Students independently classify two new patterns on the geometric pattern growth worksheet and justify one classification by comparing differences. Students who finish early write a general rule for a linear pattern, such as “multiply the figure number by the constant growth and adjust by the starting value.”

7. 46–50 min · Plenary and exit evidence. Teacher asks students to hold up a card or point to “linear” or “non-linear” for one final pattern, then invites two students to explain their reasoning. Students complete the worksheet exit prompt: “A pattern has totals 5, 9, 13, 17. Is it linear or non-linear? Explain using the differences.” Collect work and note each student’s level of independence and mathematical language.

Resources

• the geometric pattern introduction deck
• the geometric pattern growth worksheet
• Matchsticks
• Square tiles or linking cubes
• Printed geometric picture patterns
• the sequence rule cards
• Board or chart paper and coloured markers
• Teacher-selected geometric-patterns video
• Mathology materials
• Mathletics-enabled devices

Assessment

• Knowledge and Understanding: Observe whether students correctly build figures, complete tables, identify first differences, and classify linear versus non-linear growth. Record evidence in PowerSchool using indicators such as “identifies constant change” and “represents a relation in a table.”
• Mental Math and Estimation: Listen for efficient counting, skip-counting, and mental comparison of changes between terms. Note whether students can predict a nearby term without recounting every object.
• Problem Solving: Use the independent checkpoint to document whether students classify two patterns and justify one with mathematical evidence. Look for a clear claim, accurate differences, and a connection between the table and classification.

Differentiation

• Provide pre-built Figures 1 and 2, colour-code each new addition, use smaller figures, and offer a partially completed table for students with foundational gaps or a math disability.
• Use large, uncluttered, dyslexia-friendly print; read instructions aloud; provide symbols and pictures beside key words; allow students to respond orally before writing.
• Pair students strategically, assigning roles such as builder, counter, recorder, or checker, and use a visible timer and short teacher check-ins to support distractible learners.
• For extension, students create a geometric pattern with either constant or changing differences, represent it in a table, and write a general rule or explain why a rule is not linear.