Attribute Blocks and 2D Shape Attributes – Comprehensive Study Notes

Attribute Blocks and 2D Shape Attributes – Study Notes

Overview of activity and focus
  • Use attribute blocks to discuss mathematical attributes of 2D shapes (squares, hexagons, circles, triangles; also rectangles as needed).
  • Primary goal: identify and compare mathematical attributes beyond color, such as size, thickness/thinness, number of sides, side length equality, folding/symmetry, corners, and angle types.
  • Classroom workflow described:
    • On the whiteboard (or Lumio screen), project several shapes/blocks and have students sort or group by a chosen attribute.
    • Use a text tool to capture students’ ideas and entries, while ignoring color to focus on mathematical attributes.
    • Move from concrete shapes to abstract concepts like symmetry, parallelism, and angle classification.
  • Students compare shapes with different properties (e.g., a triangle vs. a rectangle vs. a circle) to discuss what makes each shape unique by attribute.
Key concepts and definitions
  • Mathematical attributes to consider (beyond color):
    • Size: large vs. small (relative size comparisons)
    • Thickness/thinness of the shape’s border (if applicable)
    • Number of sides: e.g., 3 (triangle), 4 (quadrilateral), 6 (hexagon)
    • Side length equality: whether all sides are equal (regular polygons) or not
    • Corners meet up / folding: whether a shape can be folded to match up corners
    • Angles: acute, right, obtuse
    • Parallel sides: presence/absence of parallel sides (triangles typically lack parallel sides; rectangles and squares have parallel sides; circles have none in the typical sense)
    • Symmetry: lines of symmetry; whether the shape can map onto itself via reflection
    • Lines of symmetry (examples):
    • Triangle: 3 lines of symmetry
    • Square: 4 lines of symmetry (two diagonals plus vertical/horizontal cuts)
    • Rectangle: 2 lines of symmetry (vertical and horizontal, assuming non-square rectangle)
    • Circle: infinitely many lines of symmetry
    • Hexagon (regular): 6 lines of symmetry (3 through opposite sides and 3 through opposite vertices)
  • Angle definitions (in degrees):
    • Acute: heta < 90^ ext{o}
    • Right: heta=90extoheta = 90^ ext{o}
    • Obtuse: heta > 90^ ext{o}
  • Relationship between attributes and shapes (examples):
    • A shape can have multiple attributes at once (e.g., a large red hexagon has attributes: large, hexagon, red, polygon with all sides equal).
    • “And” vs. “Or” logic in clues:
    • “I am a hexagon or I am blue” means the shape satisfies at least one of the conditions (or both).
    • “I am circle and blue” means the shape must satisfy both conditions simultaneously.
  • Sorting and seriation concepts:
    • Seriation: ordering objects by a particular attribute (e.g., from smallest to largest).
    • Reverse seriation: ordering in the opposite direction (e.g., largest to smallest).
    • Use skip counting to quantify groups after ordering (e.g., 3, 6, 9 balloons).
Practical activity notes and problem walkthroughs
  • Problem 3, Part 1 (3A): determine based on clues
    • Clue: I am blue. I am not large. I am a triangle (inferred from angles and lack of obtuse angle).
    • Student conclusion example: a small blue triangle.
    • Teaching note: ensure students distinguish color and size clues; use the “not large” cue to deduce small.
  • Problem 3, Part 2 (3B): multiple possibilities due to OR clue
    • Clue: I am a hexagon or I am blue; I am large; I am a polygon with all equal sides.
    • Possible solutions discussed:
    • Large red hexagon (fits both sides: large, hexagon, polygon with all equal sides)
    • Large blue hexagon (fits both OR and large/equal-sides criteria)
    • Why multiple solutions can exist: OR allows overlap; a shape can satisfy one or both conditions.
  • Problem 4: attributes and combinations
    • Part a: blocks that are four-sided and large
    • Solutions discussed: large square, large rectangle (color unspecified)
    • Part b: blocks that are red or are square
    • Interpretation: any red shape or any square, regardless of color, size
    • Examples considered: large circle, large rectangle, triangle, square, hexagon, etc. Red shapes of any type also qualify.
    • Important nuance: OR can yield many valid shapes; color and type can combine depending on entries.
  • Practical guidance for students on OR/AND interpretation (five a/b exercises):
    • Part a emphasizes identifying blocks with certain attributes (e.g., large and red) using AND logic.
    • Part b emphasizes using OR logic to identify blocks that satisfy at least one attribute; students should consider that a single block can satisfy both attributes if applicable.
  • Five a and five b discussion prompts
    • Five a: compile a list of mathematical attributes for the attribute blocks and 2D shapes (e.g., size, number of sides, symmetry, parallelism, angle types, side equality, folding potential).
    • Five b: interpret statements about shapes and predict which blocks satisfy the statements (e.g., not quadrilateral, triangle and large, all sides equal or quadrilateral, circle/blue with OR semantics).
    • Emphasis on parsing “not,” “and,” and “or” correctly in statements and using separate clauses for different interpretation tasks.
  • Venn diagram (Problem 6) exercise with Regions A, B, C
    • Setup: Regions describe combinations of attributes (e.g., A: large or; B: does not have right angles; C: does not have parallel sides).
    • Region 5 (inside-out) shapes that fit A ∧ B ∧ not(C) logic
    • Given shapes: large circle, large triangle fit region 5 (A and B; C false).
    • Region 2 (A ∧ B) overlap: large hexagon (does not have right angles) fits.
    • Region 6 (B ∧ C): small circle (or small triangle) fits because not right angles and not parallel sides.
    • Region 4 (A ∧ C): empty (no shapes fit due to prior constraints in this activity).
    • Region 1 (A only): large square fits.
    • Region 3 (not large and not right angles): small hexagon fits.
    • Region 7 (not large and not parallel sides): discussed as potentially empty in some configurations; shapes considered were circles/triangles but may conflict with other regions.
    • Region 8 (not large, right angles, parallel sides): small square and small rectangle.
  • Additional practice problems and resources
    • Problems 1, 3, 4, 8, 10, 11 on pages 97–98 to complete; optional PDF submission in assignment folder.
    • Page 99 provides a picture of attribute blocks; page 100 lists different attributes.
    • Page 99–100 resources are useful for students without printed blocks; includes shapes and attributes for reference.
  • Perusal (reading) on developing early number concepts and number sense
    • Three prompts to respond to after reading: identify parts of the learning progression or numeracy that students typically find difficult.
    • How to respond in the assignment portal: box the relevant learning progression and comment in the right-hand box.
    • Common focus areas include counting, solving problems using concrete objects, understanding unit composition, and decomposing numbers (e.g., 5 as 2+3 or 1+4).
  • Classroom logistics and workflow reminders
    • The instructor plans to begin with addition/subtraction strategies in the next session.
    • Students should submit hard copy or PDF of the activity problems and complete the perusal prompts.
    • For meetings, email the instructor with preferred times; Zoom links will be provided.
Connections to foundational principles and real-world relevance
  • Seriation and quantity understanding underpin number sense and physical reasoning about size, order, and grouping in everyday contexts (e.g., arranging objects by size, comparing sets).
  • Attribute analysis of shapes supports geometric thinking, including recognizing regular vs. irregular shapes, symmetry, and properties that persist under transformations (folding, rotation, reflection).
  • Logical reasoning with AND/OR conditions mirrors real-world decision-making and problem solving (e.g., product filtering by multiple attributes, eligibility criteria).
  • Venn diagrams as visualization tools help students reason about overlap and exclusive properties, a foundational skill for probability, set theory, and data interpretation.
  • Emphasizing process over color helps students focus on mathematical structure, a key practice in early geometry and number sense.
Formulas and numerical references (LaTeX)
  • Lines of symmetry:
    • Triangle: extsymmetrylines=3ext{symmetry lines} = 3
    • Square: extsymmetrylines=4ext{symmetry lines} = 4
    • Rectangle: extsymmetrylines=2ext{symmetry lines} = 2
    • Circle: extlinesofsymmetry=extinfiniteext{lines of symmetry} = ext{infinite}
    • Hexagon (regular): extlinesofsymmetry=6ext{lines of symmetry} = 6
  • Angle types (in degrees):
    • Acute: heta < 90^ ext{o}
    • Right: heta=90extoheta = 90^ ext{o}
    • Obtuse: heta > 90^ ext{o}
  • Seriation and skip counting examples:
    • Smallest to largest ordering (seriation) followed by counting steps, e.g., balloons ordered smallest to largest and counted by threes: 3,6,9, …3, 6, 9, \,…
Tips for studying and exam preparation
  • Focus on internalizing the definitions of each attribute and how to identify them in different shapes (e.g., recognizing lines of symmetry without counting degrees).
  • Practice with OR and AND logic through concrete examples: create your own clue sets and determine all shapes that satisfy them.
  • Familiarize yourself with Venn diagram region labeling and reasoning about overlaps; practice mapping attributes to regions logically.
  • Use the problem-set structure (3A, 3B, 4A, 4B, 5A, 5B, 6) to simulate exam-style questions: read clues, determine applicable shapes, justify reasoning.
  • Review perusal activities and learning progressions to articulate how students typically experience difficulty and how to address it with concrete tasks.
  • Remember the workflow: sort by attributes, document observations, discuss interpretations, and then apply to more complex statements and diagrams.
Quick references to course materials mentioned
  • Attribute blocks and shapes on page 99 (list of attributes) and page 100 (additional attributes).
  • Problems on pages 97 and 98: focus problems 1, 3, 4, 8, 10, 11 for five-a/ five-b activities.
  • Lumio-based activity setup (projection of attribute blocks) to support sorting and discussion.
  • Developmental reading: developing early number concepts; perusal prompts and reflection in the assignment portal.

If you’d like, I can convert these notes into notecards or create a targeted study guide focusing specifically on problem types (3A/3B, 4A/4B, 5A/5B, 6) with example solutions and common student misconceptions.