TIPM3 Grades 2 and 3

TIPM3Grades 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 • 2.G. Partition a rectangle into rows and columns of same size squares and count to find the total number of them.

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

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/

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.

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

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.

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.

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.

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.

Lunch

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?

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.

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

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.

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.

Thank you for a great day! See you March 3!

TIPM3 Grades 2 and 3