TIME ALLOTMENT: Three 1 hour lessons
SUBJECT MATTER: Mathematics: algebraic thinking, proportions
National Council of Teachers of Mathematics Principles and Standards for School Mathematics, Grades 3-5, http://standards.nctm.org
Tell your own story of why you have a beaded section of a broken necklace. Use real objects and visual representations that model how the children will explain their work. Explain that we will watch a video showing some young mathematicians working together on a similar problem.
The complete Mathline website with ideas for many math topics.
National Council of Teachers of Mathematics website http://www.nctm.org
site for female mathematicians http://www.agnesscott.edu/
PREP FOR TEACHER
This video is for teachers and students alike. As teachers view it they can focus on the pre-assessment and interview sections and the verbal prompts used by the teacher to elicit responses and analyze responses for understanding.
View the beginning of “Bead-dazzled”. Here the teacher demonstrates and talks about the interview process. (about 3 ½ minutes). Skip until you see the outside of a school. The next section shows how the teacher sets up the class with a personal story to entice the students. Students will see a model of other students’ classroom behavior, interest in the lesson, and methods of working.
Preview the video
for your understanding and to know where your pause points will be for
your students. Cue the video. Write the steps to the lesson on the board
so the students will know what is expected of them during this lesson.
(Introduction, The problem, Methods for solving and sharing) Prepare the
PRIOR KNOWLEDGE This lesson should follow previous multiple experiences with many kinds of patterns.
Step 2: View the video. Your questioning and explanations throughout the video will provide the FOCUS FOR MEDIA INTERACTION. Say, “Let’s see how this class works together to solve their problem.” PLAY showing how the students use drawing, discussing, numbers and writing to solve their problem.
STOP and ask what your students saw happening in the classroom. SKIP to the spot where a group of 3 girls and 1 boy work through the problem together.
PAUSE before the teacher talks about the 6 packs of beads. Ask what they saw happening in the group. Point out how they all wrote on their pads using numbers.
the segment showing the problem-solvers using drawings. PAUSE and
point that out. PLAY through the segment that shows the teacher
explaining the next step until after the students explain their work at
the board. STOP. Ask what your students saw on the group’s paper
taped on the board. Did they notice how well the students explained their
Step 3: Use
mathematicians’ names as you form groups. Some suggestions are; Fibonacci,
Pythagoras, Euclid, Archimedes, Pascal, Descartes, Gauss, Boole. (We study
historical figures in mathematics throughout the year. They come alive
through their fascinating stories.) Don’t forget to include women who
contributed to math.
Step 4: In your problem, the original necklace contained 20 beads (2 colors) and 5 are left from the broken necklace. Can you recreate the whole necklace from these 5 beads? Discuss the problem. Volunteers will explain their reasoning. Hand out pre-made packages of beads that contain either 2, 4, or 5 beads of 2 different colors. Each group gets one package so that different groups have different numbers of beads. Groups will answer the question: How many packs of beads will it take to make the original 20 bead necklace? Hand out chart paper and markers to each group. Check each group’s progress. One member of each group will present their solution at the board using their chart paper. Introduce the words, “ 1 package is to 2 beads as blank packages is to 20 beads, or 1 package is to 4 beads as blank is to 20, or 1 package is to 5 beads as blank is to 20.”
Step 2: What is the cost of our necklace? Explain that a pack of 4 beads costs $4, a pack of 8 beads costs $5, and a pack of 12 beads costs $7 dollars. They will determine the cost of their necklace. Using the same procedures as the previous problem, each group will present their conclusions and reasoning.
POST VIEWING ACTIVITIES
Step 1: Students will look for patterns in nature and in the manmade world. Take a walk around your community and, using a digital camera or Polaroid, let students take photos of any patterns they see, (at least one for each student).
The student will decide if his pattern repeats (not all will) and will draw and describe the pattern in his math journal.
Student will apply their knowledge of: ____ is to _____ as _____ is to _____ in their descriptions.
Students will present
their work at the board.
Step 2: Make
a mural of the photos and students’ charts. Student Assessment: Read the
math journals for improved understanding.
Let the students work independently on this however you wish. They must make a repeating pattern and they must calculate how many beads they will need to complete a 5” beaded section. Make a class quilt with repeating patterns.
Students can use proportional reasoning to determine how many pieces of each color they will need.
For additional lesson plans and ideas relating to this topic and many others try TeacherSource at PBS Online! You will find activities, lesson plans, teacher guides and links to other great educational web sites! Search the database by keyword, grade level or subject area! Mathline and Scienceline are also great resources for teachers seeking teaching tips, lesson plans, assessment methods, professional development, and much more!
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