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Big Idea Geometry: Spatial sense
and geometric relationships are a means to solve problems and make
sense of a variety of phenomena.
Big Idea Measurement: Measurement is a tool to
quantify a variety of phenomena. |
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4.2 A.
Geometric Properties |
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Descriptive Statement: This includes identifying,
describing and classifying standard geometric object, describing and
comparing properties of geometric objects, making conjectures
concerning them, and using reasoning and proof to verify or refute
conjectures and theorems. Also included here are such concepts as
symmetry, congruence, and similarity. |
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Essential Questions |
Enduring Understandings |
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- How can spatial relationships be described by
careful use of geometric language?
- How do geometric relationships help in solving problems and/or
make sense of phenomena? |
- Geometric properties can be used to construct
geometric figures. (4.5D1; 4.5D2; 4.5E3)
- Geometric relationships provide a means to make sense of a variety
of phenomena. |
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Areas of Focus/Cumulative Progress Indicators |
Comments and Examples |
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By the end of Grade 2: |
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1. Identify and describe spatial relationships among objects in
space and their relative shapes and sizes.
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Inside/outside, left/right, above/below, between
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Smaller/larger/same size, wider/ narrower, longer/shorter
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Congruence (i.e., same size and shape)
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2.
Use concrete
objects, drawings, and computer graphics to identify, classify, and describe
standard three-dimensional and two-dimensional shapes.
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Vertex, edge,
face, side
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3D figures – cube,
rectangular prism, sphere, cone, cylinder, and pyramid
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2D figures –
square, rectangle, circle, triangle
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Relationships
between three- and two-dimensional shapes (i.e., the face of a 3D shape is a 2D
shape)
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3.
Describe, identify and create instances of line symmetry. |
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4.
Recognize,
describe, extend and create designs and patterns with geometric objects of
different shapes and colors. |
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4.2
B. Transforming Shapes |
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Descriptive Statement: This includes identifying,
describing and classifying standard geometric object, describing and
comparing properties of geometric objects, making conjectures
concerning them, and using reasoning and proof to verify or refute
conjectures and theorems. Also included here are such concepts as
symmetry, congruence, and similarity. |
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Essential Questions |
Enduring Understandings |
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- What situations can be analyzed using
transformations and symmetries? (4.5E1; 4.5E2; 4.5E3) |
- Shape and area can be conserved during
mathematical transformations.. |
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Areas of Focus/Cumulative Progress Indicators |
Comments and Examples |
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By the end of Grade 2: |
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1.
Use simple shapes
to make designs, patterns, and pictures.
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2.
Combine and
subdivide simple shapes to make other shapes. |
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4.2 C. Coordinate Geometry |
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Descriptive Statement: Coordinate geometry provides an
important connection between geometry and algebra. It facilitates
the visualization of algebraic relationships, as well as an
analytical understanding of geometry. |
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Essential Questions |
Enduring Understandings |
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- How can geometric/algebraic relationships best
be represented and verified? (4.5C2; 4.5D2; 4.5E1; 4.5E2; 4.5F5) |
- Reasoning and/or proof can be used to verify or
refute conjectures or theorems in geometry (4.5D1; 4.5D3; 4.5D4;
4.5D5; 4.5F5)
- Coordinate geometry can be used to represent and verify
geometric/algebraic relationships. |
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Areas of Focus/Cumulative Progress Indicators |
Comments and Examples |
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By the end of Grade 2: |
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1.
Give and follow
directions for getting from one point to another on a map or grid. |
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4.2 D. Units Of Measurement |
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Descriptive Statement: Measurement helps describe our
world using numbers. An understanding of how we attach numbers to
real-world phenomena, familiarity with common measurement units
(e.g., inches, liters, and miles per hour), and a practical
knowledge of measurement tools and techniques are critical for
students' understanding of the world around them. |
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Essential Questions |
Enduring Understandings |
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- How can measurements be used to solve problems?
(4.5A6) |
- Everyday objects have a variety of attributes,
each of which can be measured in many ways.
-What we measure affects how we measure it.
(4.5A4; 4.5A6)
- Measurements can be used to describe, compare, and make sense of
phenomena. |
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Areas of Focus/Cumulative Progress Indicators |
Comments and Examples |
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By the end of Grade 2: |
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1.
Directly compare
and order objects according to measurable attributes.
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Attributes –
length, weight, capacity, time, temperature
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2.
Recognize the need
for a uniform unit of measure. |
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3.
Select and use
appropriate standard and non-standard units of measure and standard measurement
tools to solve real-life problems.
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Length – inch,
foot, yard, centimeter, meter
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Weight – pound,
gram, kilogram
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Capacity – pint,
quart, liter
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Time – second,
minute, hour, day, week, month, year
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Temperature –
degrees Celsius, degrees Fahrenheit
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4.
Estimate measures. |
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4.2 E. Measuring Geometric Objects |
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Descriptive Statement: This area focuses on applying the
knowledge and understandings of units of measurement in order to
actually perform measurement. While students will eventually apply
formulas, it is important they develop and apply strategies that
derive from their understanding of the attributes. In addition to
measuring objects directly, students apply indirect measurement
skills, using, for example, similar triangles and trigonometry. |
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Essential Questions |
Enduring Understandings |
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- How can measurements be used to solve problems?
(4.5A6) |
- Everyday objects have a variety of attributes, each of which can
be measured in many ways.
- What we measure affects how we measure it. (4.5A4; 4.5A6)**
- Measurements can be used to describe, compare, and make sense of
phenomena. |
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Areas of Focus/Cumulative Progress Indicators |
Comments and Examples |
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By the end of Grade 2: |
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1.
Directly
measure the perimeter of simple two-dimensional shapes. |
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2.
Directly measure
the area of simple two-dimensional shapes by covering them with squares.
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