Growing Patterns with Tiles

Overview

In this fifth lesson of the Linear Patterns and Algebra unit, students build growing patterns with tiles and cubes, record the first terms, and identify the constant increase. They connect concrete models to tables and use the pattern to predict a later figure, building on earlier work with repeating and increasing patterns.

Learning intentions

Students will:

• Build and describe a linear growing pattern using tiles or cubes.
• Record the number of tiles in each figure as a sequence of terms.
• Identify the constant increase between consecutive terms.
• Use a table to predict the number of tiles in a later figure.

Success criteria

• I can build at least the first three figures of a growing pattern.
• I can record the correct number of tiles in each figure.
• I can explain the constant increase using words, numbers, or colour.
• I can use the pattern to predict a later figure and explain how I know.

Curriculum links

• Patterns and Relations — oral and written patterns and their corresponding relations.
• Patterns and Relations — constructing and analysing tables of values from a relation.
• Mathematical processes — communication, connections, mental mathematics and estimation, problem solving, reasoning, and visualization.
• Report card evidence — Knowledge and Understanding, Mental Math, and Problem Solving.

Lesson structure (50 minutes)

1. 0–5 min · Hook and retrieval. Display a visual sequence such as 3, 5, 7, 9 and ask, “What would the tenth term be, and how could you prove it?” Use the opening pattern challenge to show the figures rather than only the numbers. Students quietly notice, write one prediction, then share the change they see; the teacher records “term” and “constant increase” in student-friendly language.

2. 5–12 min · Concrete demonstration. Use a prebuilt starting example from the Mathology hands-on lesson, such as a row that grows by two cubes each time. Colour the original part one colour and the added growth another colour. Students help count Figures 1, 2, and 3 and complete the first three rows of the guided growing-pattern table. The teacher explicitly models: “The terms are 4, 6, 8. The constant increase is 2 because two cubes are added each time.”

3. 12–20 min · Video noticing and discussion. Play a short, suitable segment from the prepared growing-patterns video search results, pausing after examples of tile growth. Students sketch one figure or point to the part that stays the same and the part that grows. Return to the visual examples and discussion prompts and ask: “What stays constant? What changes? How does the table match the model?” Avoid relying on the video for new vocabulary; pause and rephrase each idea using the classroom model.

4. 20–32 min · Guided construction. Give each student tiles or linking cubes and assign one accessible pattern, with a prebuilt Figure 1 available for students who need a starting point. Students build Figures 1–4, use colour-coded growth, and record the number of tiles in the guided growing-pattern table. Circulate and check each model before students continue. Prompt with: “Show me the part that was added,” “How many more than the previous figure?” and “What will Figure 5 look like?”

5. 32–44 min · Independent practice. Students complete the remaining tables on the independent pattern tables. For each pattern, they record the first four terms, identify the constant increase, draw or complete a later figure, and predict a later term such as Figure 6 or Figure 10. Model one example on the worked-example and independent-work instructions before releasing students. Students may use cubes, a number line, or a completed first example as a scaffold.

6. 44–50 min · Evidence checkpoint and exit ticket. Review each student’s model and table for correct terms, constant difference, and a justified prediction. Students complete a brief exit response: “The pattern starts at ___ and increases by ___. Figure 6 has ___ tiles because ___.” Invite one student to explain a solution using the model while others compare their reasoning.

Resources

• the growing-patterns teaching deck
• the guided and independent pattern tables
• Mathology growing-patterns hands-on lesson
• Linking cubes or square tiles in at least two colours
• Small trays or work mats
• Chart paper or whiteboard
• Prepared growing-pattern models
• Short teacher-selected video segment from the growing-patterns search results
• Pencils, coloured pencils, and highlighters

Assessment

• Knowledge and Understanding: Observe whether each student correctly builds Figures 1–4, records the terms, and identifies the constant increase. Document progress as beginning, developing, or secure.
• Mental Math: Listen for efficient counting, skip-counting, and use of the constant increase to find the next term without rebuilding. Record whether the student uses a strategy independently or requires prompting.
• Problem Solving: Assess the exit response and later-figure prediction. Look for a correct answer supported by a model, table, words, or an equation. Note the level of independence and explanation in PowerSchool descriptors.

Differentiation

• Provide prebuilt Figure 1, reduced number ranges, larger cubes, a completed example, and a colour key for students on modified programs or with a math disability.
• Use guided notes with large print, generous spacing, uncluttered tables, and short, numbered instructions. Read directions aloud and allow students to respond by pointing, building, drawing, or speaking before writing.
• Pair students strategically, assigning the roles of builder, counter, recorder, or checker; rotate roles to reduce attention-seeking and keep all four students engaged.
• For students ready for challenge, ask them to predict Figure 20, explain a general rule in words, or design a new pattern with a specified constant increase. Encourage all students to justify predictions using “I notice…” and “I know…” sentence starters.