# 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

Measurement

• 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

Geometry

• 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