Last updated: 8/15/2021

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Grade 3 - Geometry

  Subject:   Mathematics (NYS P-12 Common Core)
  Grade:   Elementary, 3rd Grade
  Unit Title:  

Grade 3 - Geometry

  Approx. Number of Weeks:  

1-10 weeks

Unit Summary:

Properties of  2-dimensional shapes. 

Develop understanding of rectangular arrays and of area.

Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

Reason with shapes and their attributes.

Next Generation Skills Addressed:
   Collaboration & Communication
   Creativity & Innovation
   Critical Thinking & Problem Solving
   Research & Information Fluency
   Social & Emotional Intelligence

1. What will students know and be able to do?

Standards:



3.MD.5 - Recognize area as an attribute of plane figures and understand concepts of area measurement.

3.MD.6 - Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).

3.MD.7 - Relate area to the operations of multiplication and addition.

3.MD.8 - Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

3.G.1 - Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

3.G.2 - Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.


Essential Understandings:


Students will understand that…

Plane figures have attributes that can be used to solve problems.

  

Essential Questions:


How can I describe objects in my world precisely?

Possible ways to scaffold the question:

  • What do you need to describe objects? (e.g. tools, strategies, units, common attributes)
  • What relationships do you see among the attributes?

Students will know:


Area is an attribute of 2-dimensional shapes that expresses the size of the 2-dimensional surface.

  

Students will be able to:


Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

Recognize area as an attribute of plane figures and understand concepts of area measurement. (3.MD.5)

a. A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area.

b. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.

Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).  Use pattern blocks and grid paper.

Relate area to the operations of multiplication and addition. (3.MD.6)

a. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.

b. Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.

c. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a x b and a x c.

For Example,

4 x 15 = (4 x 10 ) + ( 4 x 5 )

Use area models to represent the distributive property in mathematical reasoning.

d. Recognize area as additive.

Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.

Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

Solve real world and mathematical problems involving perimeters of polygons, (3.MD.8)

 --including finding the perimeter given the side lengths,

 --finding an unknown side length,

 -- and drawing rectangles with the same perimeter and different areas

 --or with the same area and different perimeters.

Geometry

Reason with shapes and their attributes.

Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g.,quadrilaterals). (3.G.1)

Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

Partition shapes into parts with equal areas. (3.G.2)

Express the area of each part as a unit fraction of the whole.

For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

 

Color Code Key: Gaps, Major Clusters, Supporting Clusters, Additional Clusters

2. How will we – and they – know?

Authentic Performance Task:


Common Benchmark Assessment:




3. What learning activities will students participate in?

Learning Activities:


Discipline Specific Considerations:


Vocabulary – Specialized and High Frequency

sides, angles, plane figure, unit square, square unit, polygons, perimeter, area, attribute, rhombus, rectangle, quadrilateral, polygons, regular, irregular

Misconception Alerts:

A square is a special rectangle. (true)

Diamond is not a mathematical term. (true)

Students need experience with irregular polygons.

Common Core State Standards:  Standards for Mathematical Practice

Standard 1:    Make sense of problems and persevere in solving them

Standard 2:    Reason abstractly and quantitatively

Standard 3:    Construct viable arguments and critique the reasoning of others

Standard 4:    Model with Mathematics

Standard 5:    Use appropriate tools strategically

Standard 6:   Attend to precision

Standard 7:  Look for and make use of structure

Standard 8:  Look for and express regularity in repeated reasoning

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