Activity 01
Inquiry Circle: Fill the Outline
Provide each pair with a large outline shape (hexagon, trapezoid, rectangle) drawn on paper. Students use pattern blocks to fill the outline completely, try at least two different combinations, and record each combination's recipe (e.g., '2 triangles and 1 square'). Pairs share their combinations with another pair and discuss whether any of the same combinations were found.
How many triangles does it take to build a single square?
Facilitation TipFor Fill the Outline, provide clear outlines and pattern blocks so the goal of gap-free coverage is visible to every student.
What to look forProvide students with a large rectangle drawn on paper. Ask them to draw lines to divide it into two triangles. Then, ask them to draw lines to divide it into four smaller squares. Check if they can successfully decompose the rectangle in two different ways.
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Activity 02
Think-Pair-Share: Triangle Factory
Give each student exactly four equilateral triangles. Ask them to build every different shape they can by joining edges. Students share their shapes with a partner and together name as many of the resulting shapes as possible. The class discusses which combinations made recognizable shapes and which didn't, and why.
Can we use different shapes to build the exact same larger design?
Facilitation TipDuring Triangle Factory, model how to rotate and flip triangles before combining them to prevent rigid thinking about orientation.
What to look forHold up a hexagon shape made from pattern blocks. Ask students to hold up the number of triangles it would take to make the same hexagon. Then, ask them to hold up the number of rhombuses it would take. Observe their responses to gauge understanding of different compositions.
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Activity 03
Stations Rotation: Shape Builder Challenge
Each station has a target shape card (a larger shape drawn with a dotted outline) and a set of specific smaller shapes. Students fill the target using only the given shapes, record the combination, and note whether a second combination is possible. Rotate every 8 minutes.
Design a new shape by combining two or more basic shapes.
Facilitation TipIn Shape Builder Challenge, circulate with a timer to keep groups focused on testing multiple solutions within the rotation time.
What to look forPresent students with a large square outline and a collection of pattern blocks. Say, 'Your challenge is to fill this square using only triangles and rhombuses. Work with a partner to find a way. Be ready to explain how your shapes fit together and why your design works.'
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Activity 04
Gallery Walk: Recipe Wall
After each group completes a composition task, they post their shape recipe on the wall (drawing plus list of shapes used). Students do a gallery walk to find and star any combinations different from their own, then return to try recreating one new combination they saw.
How many triangles does it take to build a single square?
What to look forProvide students with a large rectangle drawn on paper. Ask them to draw lines to divide it into two triangles. Then, ask them to draw lines to divide it into four smaller squares. Check if they can successfully decompose the rectangle in two different ways.
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Generate Complete Lesson→A few notes on teaching this unit
Teach this topic by starting with concrete materials like pattern blocks so students feel the fit of shapes before moving to drawings. Avoid early reliance on worksheets that show pre-drawn compositions, as these limit students' spatial testing. Research shows that students who manipulate shapes develop stronger partitioning skills, which supports later work in area and fractions.
Successful learning shows when students combine shapes precisely without gaps or overlaps and explain how their pieces form the larger shape. They should also rotate and flip pieces intentionally to test different arrangements.
Watch Out for These Misconceptions
During Collaborative Investigation: Fill the Outline, watch for students who insist only identical shapes can be combined to make a new shape.
Model combining two different shapes (e.g., a triangle and a square) to fill a hexagon outline. Then, during the investigation, ask partners to deliberately try building with mixed pieces and name their new shapes.
During Station Rotation: Shape Builder Challenge, watch for students who leave gaps between shapes and cannot detect the error.
Provide pattern blocks that must physically touch without gaps. Circulate and ask students to point to where their shapes meet and to check their partner’s work for gaps before moving to the next station.
During Think-Pair-Share: Triangle Factory, watch for students who treat a triangle in different orientations as different shapes.
Use pattern blocks to physically flip and rotate triangles while naming the shape and counting sides each time. Then, during the pair work, ask students to rebuild their designs using rotated triangles and explain why the shape name stays the same.
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