TIPM3

Grades 2 and 3

February 15

Monica Hartman

Agenda

Homework and Lesson SharingHomework and Lesson Sharing

Geometric Measurement – relating area to Geometric Measurement – relating area to multiplication and additionmultiplication and addition

Geometry – reason with shapes and attributes Geometry – reason with shapes and attributes Fractions.Fractions.

Perimeter and Area ProblemPerimeter and Area Problem

Geometry

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

Geometric Measurement

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

3.MD.6 Measure area by counting unit squares3.MD.6 Measure area by counting unit squares

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

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

Stacking the Facts

Using the area model to provide meaning for Using the area model to provide meaning for multiplicationmultiplication

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

Geometry

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

Geometry

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

Chart the Parts

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

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

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

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

Geoboard Fractions

Make a large square on the Geoboard. Make a large square on the Geoboard.

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

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

Are all the parts congruent?Are all the parts congruent?

Record two different ways on your Geoboard paperRecord two different ways on your Geoboard paper

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

Geoboard Fractions

Make a large rectangle on the Geoboard. Make a large rectangle on the Geoboard.

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

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

Are all the parts congruent?Are all the parts congruent?

Record two different ways on your Geoboard paper.Record two different ways on your Geoboard paper.

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

Puzzle Makers

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

Trade your puzzle with your partners at the tableTrade your puzzle with your partners at the table

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

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

Label your pieces with the fraction name.Label your pieces with the fraction name.

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

4 cm

8 cm

4 cm

Perimeter = 16 cmArea = 16 square centimeters

Perimeter = 24 cmArea = 32 square centimeters

How would you respond to this student?

Three Possible Responses

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

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

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

Chinese Teachers Approach1. Justifying the students’ claim as correct (16/72).1. Justifying the students’ claim as correct (16/72).

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

Second Level of understanding: Identifying the possibilitiesSecond Level of understanding: Identifying the possibilities

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

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

Teaching With Curriculum Focal Points

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

The Distributive Property (3.OA.5)The Distributive Property (3.OA.5)

Strengthening Fluency Through Connections Strengthening Fluency Through Connections (65 – 67)(65 – 67)

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

Planning Together and Learning

from Children’s WorkDesign a lesson that you will teach in the next Design a lesson that you will teach in the next few weeks. Use the TLC Protocol.few weeks. Use the TLC Protocol.

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

See you March 3!

Thank you for a great

day!