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TIPM3 Grades 2 and 3. February 15 Monica Hartman. Agenda. Homework and Lesson Sharing Geometric Measurement – relating area to multiplication and addition Geometry – reason with shapes and attributes Fractions. Perimeter and Area Problem. Geometry.

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TIPM3Grades 2 and 3

February 15

Monica Hartman


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Agenda

  • Homework and Lesson Sharing

  • Geometric Measurement – relating area to multiplication and addition

  • Geometry – reason with shapes and attributes Fractions.

  • Perimeter and Area Problem


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Geometry

  • 2.G. Partition a rectangle into rows and columns of same size squares and count to find the total number of them.


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Geometric Measurement

  • 3.MD.5 Recognize area as attribute of plane figures and understand concept of area measurement

  • 3.MD.6 Measure area by counting unit squares

  • 3.MD.7 Relate area to the operations of multiplication and division

  • 3.MD.8 Solve real world and mathematical problems involving perimeters of polygons


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Stacking the Facts

  • Using the area model to provide meaning for multiplication

  • Follow the directions of the instructor as you use the materials for this activity/


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Geometry

  • 2.G.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.


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Geometry

  • 3.G.2 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.


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Chart the Parts

  • Learning Goal : To partition shapes into two, three, and four equal shares.

  • Each person at the table will choose one of the shapes from the blue sheet of six shapes. You need four of the chosen shape.

  • Leave one shape alone; fold the other shapes to make two, three, or four equal parts. Cut on the fold.

  • Glue the original shape in the top left corner of a sheet of construction paper. Glue the three cut-up shapes back together under the original shape.


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Geoboard Fractions

  • Make a large square on the Geoboard.

  • Show how you can divide that square into two equal parts.

  • How many ways can you divide the square into equal parts?

  • Are all the parts congruent?

  • Record two different ways on your Geoboard paper

  • What is the area and perimeter of your shapes? Label them.


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Geoboard Fractions

  • Make a large rectangle on the Geoboard.

  • Show how you can divide that triangle into two equal parts.

  • How many ways can you divide the rectangle into equal parts?

  • Are all the parts congruent?

  • Record two different ways on your Geoboard paper.

  • What is the area and perimeter of your shapes? Label them.


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Puzzle Makers

  • Make the puzzles found in the envelopes on your table.

  • Trade your puzzle with your partners at the table

  • Trace your shape on a piece of paper, then cut out your shape.

  • Make a puzzle by cutting the shape into two, three, or four equal pieces.

  • Label your pieces with the fraction name.

  • Give your puzzle and the paper with the traced shape to your partners to make.



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The Relationship Between Perimeter and Area

Imagine one of your students comes to class very excited. She tells you that she figured out a theory that you never told the class. She explains that she has discovered that as the perimeter of a rectangle increases, the area also increases. She shows you this picture to prove what she is doing.

4 cm

8 cm

4 cm

4 cm

Perimeter = 16 cm

Area = 16 square centimeters

Perimeter = 24 cm

Area = 32 square centimeters

How would you respond to this student?


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Three Possible Responses

  • 1. Divert the student from pursuing ideas outside the scheduled curriculum.

  • 2. Be responsible for evaluating the truth of the student’s claim.

  • Engage the student in exploring the truth of the claim.


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Chinese Teachers Approach

  • 1. Justifying the students’ claim as correct (16/72).

    • First Level of Understanding: Disproving the claim (50 of 72)

    • Second Level of understanding: Identifying the possibilities

    • Third Level of Understanding: Clarifying the conditions by exploring the numerical relationships between perimeter and area and elaborating on the possibilities

      • Explaining the conditions (Proof by using the distributive property. *Ma, Liping (1999).Knowing and Teaching Elementary Mathematics


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Teaching With Curriculum Focal Points

  • Applications of Composing and Decomposing Polygons (page 60 – top of page 63)

    • The Distributive Property (3.OA.5)

  • Strengthening Fluency Through Connections (65 – 67)

  • Demonstrate the Distributive Property with a rectangle made from the grid paper.


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Planning Together and Learning from Children’s Work

  • Design a lesson that you will teach in the next few weeks. Use the TLC Protocol.

  • Be prepared to share what you learned during the last session.


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Thank you for a great day!

See you March 3!


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