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Sir Cumference and the Isle of Immeter

Sir Cumference and the Isle of Immeter

Author: Tammy Long
Description:

Reinforce previously mastered concepts of area and perimeter of squares and rectangles.  Construct formulas.  Apply similar reasoning to explore the concepts of area and circumference of circles.  Construct formulas.  Explore the concept of what pi represents.  Extend lesson to use concepts with fractions and decimals.

Assess working knowledge with pretest and post test.  Have students reflect on the activity and knowledge gained.

Using literature to teaching the concept that area is always multiplying two measurements.  Showing how that looks in the real world for both rectangles and circles.  Using knowledge of perimeter of rectangles to extend the concept to the circumference of a circle.  

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Tutorial

TEKS and Content Standards

Math

§111.27.8.C Expressions, equations, and relationships. The student applies mathematical process standards to develop geometric relationships with volume. The student is expected to:  use models to determine the approximate formulas for the circumference and area of a circle and connect the models to the actual formulas.

§111.27.9.B Expressions, equations, and relationships. The student applies mathematical process standards to solve geometric problems. The student is expected to:  determine the circumference and area of circles

English

§110.19.7  Reading/Comprehension of Literary Text/Literary Nonfiction. Students understand, make inferences and draw conclusions about the varied structural patterns and features of literary nonfiction and provide evidence from text to support their understanding. Students are expected to describe the structural and substantive differences between an autobiography or a diary and a fictional adaptation of it.

§110.19.10.C  Reading/Comprehension of Informational Text/Expository Text. Students analyze, make inferences and draw conclusions about expository text and provide evidence from text to support their understanding. Students are expected to use different organizational patterns as guides for summarizing and forming an overview of different kinds of expository text;

Source: Tammy Long

Prerequisite Skills

All: basic operations including carrying, borrowing, multi-digit multiplying, and long division.  General concept of area and perimeter.

6th: basic operations with fractions

7th: basic operations with decimals

Source: Tammy Long

Materials/Supplies/Technology

Sir Cumference and the Isle of Immeter book (or YouTube reading of book), graph paper, 20 square tiles per student (or group if class is too large), scissors, math journal books, dry erase board or ELMO, and handouts:

     Area and Perimeter pretest,  Inners and Edges (2 pages of questions), Perimeter Recording Sheet, Area and Perimeter post test. One Eighths circle per student, one Sixteenths circle per student,  Area of a Circle sheets (2 pages), and  Perimeter and Area sheet.

Source: Tammy Long

Pre-reading Activity

Show the cover and ask what the students think the book is about.  Recall the previous books in the series.  Have them distinguish between old and new characters in this story.  Have them write their responses in their journal.

Pass out the handout with vocabulary words and the rules written out of the game Inners and Edges played in the game.  Have students define in their journal in their own words the five vocabulary words they should already know: inners, edges, area, perimeter, length, and width.

Have the students play Inners and Edges while you circulate and check journals for understanding.  Have a math dictionary available and help those that need it in finding accurate definitions. 

Source: Tammy Long

During Reading Activity

The first read through will be silently at the tables.  The teacher may differentiate for various level of readers by allowing buddy reading or listening to the book on CD with headphones.

Since the assignment’s main objective is to strengthen working knowledge of area and perimeter of rectangles and relate it to area and circumference of a circle, the second read through will be  orally with the students following along with copies at their tables.  In this way reading is supported and valued even within the mathematics classroom.

Have 20 square tiles per student at the tables to build the shapes as you read together.  Also have 8th and 16th circles for them to cut out and manipulate while mimicking the story.  Stop at key points, asking purposeful questions and journaling important ideas:

What is meant by inners?  Edges?  (page 5) Can we translate this word phrase in to a mathematical one?  Remember phrases are not complete sentence, but a chunk of information both in words and numbers. (page 5) What do you think the door will look like that matches the riddle?   (page 6)  What would you call Radius’ comment about the sea serpent?  (foreshadowing)  (page 8) Was your prediction correct?  Would yours also work?  Why or why not?  Be sure to emphasize that the inners (area) can ALWAYS be found by multiplying two measurements.  Repeat this every time an area is found.  (page 15) How will they be able to find the inners (number of square tiles) inside the circular floor of a tower?  (have students discuss with each other a few minutes and write their predictions in their journal.  (page 17) Compare their predictions to Per’s method.  Again emphasize that she is multiplying two measurements ( ½ the circumference and the radius).  (page 24)  Point out how “peel” is used.  Based on context, what is it’s meaning?  (ringing of a bell)  

Source: Tammy Long

Read Aloud

Having an audio version of the book for struggling readers or to help with comprehension helps with ELL students and various learning styles. Differentiation is key to keeping students engaged and progressing toward literacy in both math and reading.

Source: Kirk Framke

Post Reading Activity

Pass out the questions sheet “Sir Cumference and the Isle of Immeter: Inners and Edges” included at the end of this write up.  Have students answer together at their tables. Circulate and notice students that are struggling or have misconceptions about the key concepts.

Pass out the “Perimeter Recording Sheet” and have the students build the rectangles and fill out the sheet.  Continue stressing area (the number of tiles used to make the shape) is found by multiplying two measurements.  (The area can be found in these simple shapes by counting.  But multiplying is really just fast adding.  We also need a procedure for when the measurements are too big or complicated as in decimals and fractions.)

Display the “Circles Overhead” and have the students calculate the area of the Papa circle, Mama circle, and baby circle.  Continue pointing out that the area is still just multiplying two measurements.  Have students dictate how as you model the first circle.  Be sure they  realize you must cut the circumference in half before multiplying.

Have students add definitions to their math journals for the following terms: circumference, radius, diameter, and pi.  Include the formulas for area, perimeter, and circumference.

Source: Tammy Long

Comprehension Strategies

Questioning step.

After reading a selection, students make a note of questions they have about the material.  Together they attempt to answers each of these questions.

Clarifying step

If an answer cannot be found, or the teacher notices a misconception, the group seeks to find correct answers before continuing.

Summarizing step

Once a solid base has been established with the correct information, the students decide what information is relevant to their task at hand.

Predicting step

Using the newly acquired knowledge, the students make predictions about what is coming up.

Adding to the line of questioning in the previous section, the teacher could opt to split the reading up into two sections: Up to page 15 about rectangles and Reread page 15 to the end of the book for applying the concepts to circles.

Have the students stop at page 15 and answer questions.  aHHUse the page of questions for the questioning step as well as any questions the students wrote down in their journals.  Allow students to discuss with each other to come to a consensus.

Circulate and be available for clarifying.  Be sure the main concepts are correct about area and perimeter.  When possible guide them back to the reading to discover the answers.

As a class discuss the main ideas (area and perimeter).  Include in the discussion that you could find each by counting the tiles and their edges.  See if they can come to the conclusion that the method Per and Radius use is faster.  Together translate the strategy from words into a mathematical formula.  Note this would not only be faster but useful for larger numbers and measurements using fractions and decimals.  Keep stressing area is multiplying two measurements.  Always, always, ALWAYS!  If they haven’t already noticed, point out the difference in units for perimeter (linear: adding up lengths) and area (units squared: two measurements multiplied).

Using these ideas, see if they can make a prediction about how Per and Radius will solve the next riddle about the circular tower.  How can they measure the circle floor in square tiles?  Have them discuss at their tables and journal their predictions.

Source: Tammy Long

Independent Reading and Reader Response

Even a math teacher can promote independent reading.  The teacher can have a reading corner for students to feel more comfortable reading than a desk as well as allowing time for reading.  If the math assignment of the day has been completed, the teacher should encourage students pick what book they’d like to read independently, providing assistance as needed.  The teacher could offer alternative assignments for certain key concepts that are literature based.  For example, “It’s Probably Penny” is a great introduction into probability.  The teacher could have a starter list of selections about math concepts covered in class.  The teacher could enlist the school librarian on helping the students find titles.  If the Reading or English teachers are amicable, they could collaborate to work on the same book for both classes.  The same could be done for History, Science, Music, Art, and even sports.  Getting the students writing is also an important component in the math classroom.  Vocabulary is critical for understanding mathematical concepts.  Higher order thinking requires analysis and responses.  Those responses will need to be shared, further analyzed, and revised as necessary.  The function of math is to have problem solving strategies at your disposal.  Being able to convey those strategies through writing helps solidify the procedures for life long workable knowledge.

Source: Tammy Long

Encouraging Further Reading

To further extend the Sir Cumference and the Isle of Immeter lesson, the teacher has several options.  The teacher should have already introduced the characters in the first book of the series: Sir Cumference and the First Round Table.  Various books relating to area and perimeter could be available in the classroom throughout the unit: Spaghetti and Meatballs for All, A Monster Book of Dimensions.  To encourage reading beyond the unit and even the class, books on math in general should be introduced to the students.  Mysterious Patterns: Finding Fractals in Nature not only shows the importance of math in recent discoveries like cell phone antennae and diagnosis of precancerous growths, it tells the story of Mandelbrot following his true self even when the rest of the math community did not recognize him. Math and reading are all around us and a key function in every life.  Modeling the importance of both for students will make a significant impact on them

Source: Tammy Long

Questions

Answer these questions as you read the book. Have graph paper ready for drawing the shapes when instructed to do so.

Source: Cindy Neuschwander