Activity 01
Pairs: Two-Shape Tiling Design
Provide pairs with cut-outs of two shapes, like squares and triangles. They design a tiling pattern on A4 paper, rotating shapes as needed. Pairs explain their design to the class, noting any gaps found during testing.
Analyze how repeating geometric shapes create a pattern.
Facilitation TipFor the Pairs: Two-Shape Tiling Design activity, give each pair exactly one square and one equilateral triangle cut-out so they discover how rotations help interlock shapes.
What to look forProvide students with a worksheet showing several patterns. Ask them to circle the repeating unit in each pattern and draw the next two shapes in the sequence. This checks their ability to identify and extend patterns.
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Activity 02
Small Groups: Prediction and Test Stations
Set up stations with shape sets: one tessellates, one does not. Groups predict outcomes, then test by arranging shapes on mats. They record reasons for success or failure and rotate stations.
Design a tiling pattern using a combination of two different shapes.
Facilitation TipAt the Prediction and Test Stations, place a timer for three minutes at each station so groups stay focused on testing one hypothesis before moving on.
What to look forGive each student a card with two different shapes (e.g., a square and a triangle). Ask them to draw one way these two shapes could be combined to start a tiling pattern on a small grid. This assesses their design and tiling prediction skills.
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Activity 03
Whole Class: Pattern Extension Chain
Display a starting pattern on the board. Students add one shape each in turn, predicting the next fit. Class discusses adjustments if gaps appear, creating a large shared tessellation.
Predict whether a given set of shapes can tile a surface without gaps or overlaps.
Facilitation TipDuring the Pattern Extension Chain, stand at the back of the room to scan the entire chain so you can spot where students break the pattern and guide them to correct it immediately.
What to look forPresent students with a collection of cut-out shapes (squares, triangles, hexagons). Ask: 'Which of these shapes can tile a flat surface by themselves? How can you tell?' Guide them to explain why the angles at the vertices must add up to 360 degrees.
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Activity 04
Individual: Personal Mosaic Creator
Give each student grid paper and shape tracers. They create a tiling artwork using at least two shapes, then colour it. Share one prediction they tested during creation.
Analyze how repeating geometric shapes create a pattern.
What to look forProvide students with a worksheet showing several patterns. Ask them to circle the repeating unit in each pattern and draw the next two shapes in the sequence. This checks their ability to identify and extend patterns.
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Generate Complete Lesson→A few notes on teaching this unit
Experienced teachers start with physical cut-outs before any drawing, because moving shapes reveals angle gaps faster than abstract calculations. They avoid showing only completed tessellations and instead let students struggle to fit pieces, then facilitate a class discussion where the class corrects mistakes together. Research shows that peer feedback during tiling builds stronger spatial vocabulary and precision.
By the end of these activities, every student will confidently predict whether shapes tile, justify their answers with angle sums, and design a simple two-shape pattern on grid paper with no overlaps or empty spaces. Their notebooks should show neat sketches with repeating units clearly marked.
Watch Out for These Misconceptions
During Pairs: Two-Shape Tiling Design, watch for students who assume any two regular shapes will tile together. Redirect them by asking, 'Do the angles at each vertex add up to 360 degrees?' and let them physically test before continuing.
During Prediction and Test Stations, provide a checklist with angle sums for each shape so students compare their predictions against the actual fit of cut-outs at the station.
During Small Groups: Prediction and Test Stations, watch for students who accept tiny gaps as acceptable tiling. Redirect them by giving a ruler to measure the gap and asking, 'Is this space covered by any shape? If not, what is missing?'
During the Whole Class: Pattern Extension Chain, stop the chain at a gap and ask the class to calculate how much area is missing before continuing the pattern.
During Individual: Personal Mosaic Creator, watch for students who arrange shapes only in straight rows. Redirect them by showing a curved rangoli pattern and asking, 'Can the same shapes curve around a circle too?'
During Pairs: Two-Shape Tiling Design, provide a set of tangram pieces and ask pairs to find at least one curved or radial arrangement before returning to straight-line tiling.
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