MSIS #4 – Geometry

Back in Shanghai again for the fourth institute! Moving past the vast, unmanageable resources such as Engage & adapting to our students and classes. General and random notes and thoughts.

Geo-metry: measurement of the Earth

A balanced brain –> numerical, verbal, spatial

What is Geometry

  • study of shapes
  • relationships between objects
  • connection of mathematics to the physical world
  • dimensions (point, line, plane,
  • space
  • logic / reasoning
  • making / defending conjectures

Connection of geometry to number & algebra

  • bar models – multiplication area models
  • number lines – Cartesian plane
  • distribute property
  • tables to graphs
  • composing & decomposing (shapes like numbers & expressions)

Data – clumps, bumps and holes

Van Hiele Levels

  1. Identify – name
  2. Draw – create
  3. Describe – characteristics
  4. Analyze – properties, examples & counterexamples
  5. Classify / categorize

Language: informal to formal + Picture


  • benchmarks or referents are essential
  • Number is discrete, measurement is continuous
  • Estimation is essential
  • an approximation with tools (i.e. nearest kilogram)
  • measurement conversion similar to common denominator (must have same to compare / work with)

Resource Reminder – spend 5 minutes on LearnZillion to see how they unpack the standard.


Day 2

Justification – Give problems more ambiguity. Justification involves explaining why certain mathematical decisions were made.

PreK-2 Progressions of Measurement

  • Describe and compare measurable attributes
  • Measure lengths indirectly and by iterating length units
    • Order first (G1) then measure (G2)
    • G1: express length as whole number of length units spanning with no gaps or overlaps. End to end
    • G2: measure with different units, estimate lengths, how much longer is one than another
  • Relate addition and subtraction to length
    • PreK – directly compare, “more of / less of”
    • G2 – using number lines
  • Tell & write time (G1-G2) Note: G2 begins with money as well (not quite sure what that has to do with time)
  • Classify objects and count the number of objects in each
    • PreK – sort
    • K – classify & count
  • Represent and interpret data
    • PreK: Compare categories (greater than / less than…)
    • G1 – Organize, represent and interpret data with up to 3 categories
    • G2 – generate measurement data. Make line plots of whole number units


  • Identify & describe shapes
    • PreK – match like shapes, group by attributes, correctly name
    • K – Describe objects using their name s and relative positions, identify shapes as 2-dimensional (flat) or 3-dimensional (solid)
  • Analyze, compare, create & compose shapes
    • PreK – describe 3d objects
    • K – analyze & compare 2D / 3D shapes, model shapes by building, compose simple shapes to form larger shapes
    • G1-distinguish between defining attributes (e.g. triangles are closed & 3D) versus non-defining attributes (color, orientation, size…)
      • build shapes
      • draw shapes
      • compose 2D shapes or 3D shapes to make composite shapes
      • Partition circles & rectangles (halves, fourths, quarters)
    • G2-Recognize & draw shapes with specified attributes
      • partition rectangles into rows & columns. Count to find total number
      • partition circles & rectangles into shares. Describe, and recognize part:whole

Notes looking from 3 to 7

  • Rectangles are hammered in the lower grades. 2D, 3D. Area. Volume.
  • Circles pop up in 7th but have not been discussed since 2nd grade. Wow! Students might not know these key vocabulary terms.
  • Angles have not been discussed since 4th grade
  • Triangles are worked on in 6th
  • Scale drawings are new – build upon ratios

Big Middle School Ideas

  • Circles (pi)
    • Pizza is 78% of the pizza box
  • Pythagorean Theorem (G8)
  • Using formulas (generalization of relationships)
    • Why do they work?
  • Surface Area
  • Transformations – Scale
  • Congruence & Similarities (G8)
  • Lines & Angles
    • Begin becoming more precise of justification

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