Wilmington University
Pathwise Lesson Plan Format
Teacher/Student
Teacher
Grade:
Subject:
Date:
Website:
Kimberly Kim
K-2
Math- A Matter of Pattern
http://www.sciencenetlinks.com/lessons.cfm?DocID=111
1. Briefly describe the students in this class.
Grade: K-2
Age Range: 5-7
Number of Students: 22
Caucasian: 6
African American: 8
Asian/Pacific Islander: 2
Mexican American: 2
Native American: 1
Other Hispanic: 1
Mixed Race: 2
2. What are your goals for the lesson? What do you want the students to learn?
Students will create and predict patterns formed when making paper snowflakes. Students will
construct understanding that patterns may be predicted based on observation.
3. Why are these goals suitable for this group of students?
Students will explore how shapes can be put together to form repeating sequences or patterns. They
will begin by folding paper and making cuts to create different shapes. They will extend this process
to a multi-folded piece of paper. Students will predict both shapes and patterns that emerge as they
create six-sided snowflakes. The students will also try to predict the pattern of the shape of the entire
snowflake.
By doing this activity, students will begin to develop an appreciation of how elements in a pattern
relate to one another. At this age, students are very concrete and need focused tasks and multiple
representations in order to grasp fundamental concepts. Students will most likely become lost or
uninterested if emphasis is placed on abstract ideas, such as the nature of mathematics.
This lesson is designed to give students multiple representations of pattern using a concrete object
that fascinates them. Students need to develop an understanding of patterns. For future success, they
need to develop the ability to take an initial pattern and extend it to continue the sequence. They need
to be able to do this in a variety of ways: shape, color, sound, and number. This allows students to
construct real meaning of patterns and sequences that are found throughout life.
4. How do these goals support the district’s curriculum, state frameworks, and/or content
standards?
Numeric Reasoning: Students will develop Numeric Reasoning and an understanding of Number
and Operations by solving problems in which there is a need to represent and model real numbers
verbally, physically, and symbolically; to explain the relationship between numbers; to determine
the relative magnitude of real numbers; to use operations with understanding; and to select
appropriate methods of calculations from among mental math, paper-and-pencil, calculators, or
computers.
Numeric Reasoning: Students will develop Numeric Reasoning and an understanding of Number
and Operations by solving problems in which there is a need to represent and model real numbers
verbally, physically, and symbolically; to explain the relationship between numbers; to determine
the relative magnitude of real numbers; to use operations with understanding; and to select
appropriate methods of calculations from among mental math, paper-and-pencil, calculators, or
computers.
Algebraic Reasoning: Students will develop Algebraic Reasoning and an understanding of Patterns
and Functions by solving problems in which there is a need to recognize and extend a variety of
patterns; to progress from the concrete to the abstract using physical models, equations, and graphs;
to describe, represent, and analyze relationships among variable quantities; and to analyze, represent,
model, and describe real-world functional relationships.
Geometric Reasoning: Students will develop Geometric Reasoning and an understanding of
Geometry and Measurement by solving problems in which there is a need to recognize, construct,
transform, analyze properties of, and discover relationships among geometric figures; and to measure
to a required degree of accuracy by selecting appropriate tools and units.
5. How do these goals relate to broader curriculum goals in the discipline as a whole or in other
disciplines?
This lesson is designed to give students multiple representations of pattern using a concrete object
that fascinates them. Students need to develop an understanding of patterns. For future success, they
need to develop the ability to take an initial pattern and extend it to continue the sequence. They need
to be able to do this in a variety of ways: shape, color, sound, and number. This allows students to
construct real meaning of patterns and sequences that are found throughout life.
6. How do you plan to engage students in the content? What will you do? What will the
students do? (include time estimates).
First, have students practice cutting shapes from paper. Have students practice cutting on a piece of
paper that is folded in half. Demonstrate cuts both along the fold and on the non-folded sides. Make
sure that students attempt to predict the shapes they will see when the paper is unfolded. Students
should unfold their paper to determine what shapes emerge from the cuts. (10 min)
After students have practiced cutting their shapes for about ten minutes, have them clear their paper
scraps and discuss their shapes. They should show both the folded and unfolded shapes in their
paper. Talk about the differences in the fold cuts and the cuts along the non-folded area. (5 min)
Next, students should take a piece of paper and make two folds. Students should once again cut
shapes from the folded and non-folded portions of the paper. Have students again predict the shapes
as they cut the paper. Students should also try to guess how many of each of the shapes they will see.
Ask them if the shapes will repeat in a pattern. Make sure that students spend time in thinking both
about the shape themselves and the pattern they create as they cut out shapes. (10 min)
Tell students that they will make a six-sided snowflake using paper you have provided for them.
Show students how to fold paper to create a six-sided snowflake. You can refer to the Snowflakes
page on the KinderArt website to see how to make a six-sided snowflake. (5 min)
As students fold their paper, stop them at each fold and ask them what shape they see. Have students
discuss the shapes. This will also help to make sure that students are folding the paper in the correct
way. After students have folded their paper, assign each student to a partner and have the partners
check each others folds to make sure they are correct. (10 min)
Say to students, "Now we are going to cut out a paper snowflake. You want to make sure that you do
not cut completely along a side where there is a fold. Cut out different shapes."
Encourage students to cut out different shapes in their snowflakes. Make sure to remind students that
they are to keep their snowflakes folded. After the students have had about ten minutes to cut out
their snowflakes, have them set aside their scissors. (10 min)
Ask students: (5 min)
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What shapes have you cut into your snowflake?
Do you think that they will be the same shape when you unfold the paper? Why or why not?
Do you think that you will see the shape one time or more than once? Why?
Allow students to unfold two folds of their snowflakes. Demonstrate how they are to unfold it. Make
sure to instruct students to not completely unfold the snowflake.
Ask students: (5 min)
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What happened to the shapes that you cut along the fold?
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Is it the beginning of a pattern?
Do you expect that the shape will repeat more? Why or why not?
Based on the shape and pattern of the folded snowflake, are you able to predict what will be
the pattern of the whole snowflake?
Have students look at their folded snowflakes and sketch the shapes they think they will see when
they completely unfold their paper snowflake. Allow students to unfold one more fold of their
snowflakes. Have them revise their drawings. Next, students should completely unfold their
snowflakes. (5 min)
Ask students: (10 min)
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How is the snowflake like your drawing?
How is the snowflake different than your drawing?
What shapes do you see?
Can you see a pattern?
Is there more than one pattern in the flake?
How is your snowflake like that of a student near you?
How is your snowflake different than theirs?
Pick one pattern on your snowflake. What would be the next three shapes that would come if
the pattern were to continue? Compare your pattern to that of a student near you.
Have students go to the Six-sided Snowflake activity on the ExploreLearning website. Here, students
are able to create a six-sided snowflake online. As they create the snowflake, they are able to
simultaneously watch the actual pattern emerge. (10 min each)
Ask students: (10 mins)
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How is the snowflake you created different than you what expected it to be?
How is the snowflake similar to what you expected?
How quickly were you able to see a pattern in the snowflake?
Is the pattern simpler or more complex than your paper snowflake?
Do you think that you could re-create your pattern by memory?
Would using this program before cutting a paper snowflake be useful? How?
In an effort to incorporate technology, students will have the opportunity to go on the computer and
experience http://www.internet4classrooms.com/skills-1st-mathbuilders.htm. They will have the
opportunity to try different approaches to patterning. This will also be useful if they are having
difficulty with finding patterns in snowflakes therefore giving them a way to rebuild self esteem
through other approaches.
7. What difficulties do students typically experience in this area, and how do you
plan to anticipate these difficulties?
 I expect students to have difficulty with naming their shapes. Therefore, we will review
shapes in the beginning as a warm up.
 I expect some students to have difficulty with the 6 fold. I will rely on their peers to help
them.
 I expect some students to have difficulty deciphering patterns. I will individually work with
them to better point out patterns and the main idea of repetition.
8. What instructional materials or other resources, if any, will you use?
Materials:
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pictures of snowflakes - there are printable images at the Wilson A. Bentley website
string, 6-8 inches in length
paper - you may want to use origami paper since it is thinner than regular paper and it is
already square in shape.
pre-cut snowflakes\
Snowflake images from the Wilson A. Bentley website
http://www.snowflakebentley.com/snowflakes.htm
9. How did you plan to assess student achievement of the goals? What procedures
will you use? (Attached any tests or performance tasks, with accompanying scoring
guides or rubrics.)
Divide students into groups of four. Distribute a pre-cut six-sided snowflake to each group. Each
group should cut its snowflake in half. Collect one half of each of the group's snowflakes and put
them on a table. Allow each group to find the match to its snowflake half.
Discuss with students how they knew that each of their snowflake halves were matches. Have the
students point out patterns that helped them to identify their missing half.
10. How do you plan to use the results of the assessment?
I will utilize these results as a way to determine an overall grade for pattern comprehension along
with other related approaches.