Students will learn to analyze a pattern and identify the rules for the pattern. They will also learn how to represent those rules.
Main Curriculum Tie:
Mathematics - 5th Grade
Standard 2 Objective 1
Identify, analyze and determine a rule for predicting and extending numerical patterns involving operations whole numbers, decimals, and fractions.
For the class:
For each pair:
For each student:
- Quack and Count, by Kieth Baker; ISBN 0-15-292858-8
- Family Math in the Middle School Years, by Virginia Thompson and
Karen Mayfield-Ingram; ISBN 0-912511-29-X
- Hundred Number Board Activities Grades 4-5, by Cindy Barden;
- Navigating through Algebra in Grades 3-5, by Gilbert J. Cuevas and
Karol Yeatts; ISBN 0-87353-500-6
- Ordinary Mary’s Extraordinary Deed, by Emily Pearson;
Background For Teachers:
When students develop an understanding of patterns, they begin to
create and discover a reasoning of how patterns grow, repeat, continue, or
are solved. This is when students need added encouragement to promote
discovery of ‘rules for the pattern.’ When a student understands how to
represent the ‘rule for the pattern,’ s/he begins to develop a sense that the
rule can be applied several times, and in many different ways. This gives
the student prior knowledge so s/he becomes a flexible problem solver
and realizes that there is a solution.
Intended Learning Outcomes:
2. Become mathematical problem solvers.
3. Reason mathematically.
4. Communicate mathematically.
Invitation to Learn
Choose one or both of the following activities to get students to think
about patterns and how to describe them.
What’s the Rule?
Explain how to play a game called What’s the Rule?
- Two students who have
something in common are chosen to come
to the front of the classroom. For example, what they have in
common, or the ‘rule,’ may be that both students have blue tennis
- The rest of the class or audience needs to think about what the
rule may be. A student from the class or audience is called on,
who in turns calls on another student from the audience who they
think follows the rule.
- If the student called on does not fit the rule,
then s/he must stand
off to the side of the classroom. If s/he follows the rule, then s/he
joins the two at the front of the classroom.
- Have the class continue taking
turns naming other students in the
audience who they think follow the rule until all students who
follow the rule have been named.
Some examples of rules to use: all boys or all girls, wearing
something in their hair, wearing short or long-sleeved shirts,
wearing shorts or long pants, wearing a watch, has short or long
hair, wearing glasses, etc.
Ordinary Mary’s Extraordinary Deed
Read Ordinary Mary’s Extraordinary Deed. As you read the book,
begin to write on the board the rule for how many people are exchanging
good deeds. An example of this is:
1 person = 5 deeds
5 people = 25 deeds
25 people = 125 deeds
What is the Rule? (If n = number of people, then n x
5, or 5n, = the
number of deeds.)
Question: How many deeds will be exchanged with 50 people?
When finished, determine how many good deed exchanges would
take place in the classroom if each student exchanged five deeds.
- Give at least 30 toothpicks
to each student. Have students
make a square using the toothpicks, telling how many
toothpicks they used. Students add another square at the lower
right corner. How many toothpicks were used? Continue this
until four squares are made. Record the information given on
1 square = 4 toothpicks
2 squares = 8 toothpicks
3 squares = 12 toothpicks
4 squares = 16 toothpicks
Ask students if they see a pattern in the
numbers written on the
board. Ask for explanations. The pattern they are seeing can
be described with a rule. The rule is square x 4 = toothpick or
n x 4 = y (use a variety of symbols to represent this rule).
make triangles. Add one triangle at a time to the
lower left vertex of the previous triangle. Continue until they
come up with the rule.
Give each student several square, triangle, rhombus,
trapezoid pattern blocks. Have them complete the first section of
the Growing Patterns worksheet. Model how to complete the
worksheet using one of the shapes and going across the row.
complete the second section by making a pattern
using three to five pattern blocks (e.g., square, hexagon, square,
hexagon). Call on select students to tell what their pattern is.
student answers. Have them tell how they decided on the
rule for their pattern.
Hand out the What’s
The Rule? I worksheet to
each pair of
students. Have each pair solve what numbers come next in the
pattern and state the rule. Students may use pattern blocks to help
them visualize the growing pattern. (Answers: Steamship n + 2,
Pattern Path 2x + 2, Drawbridge n - 1, Suns n x 6, Fish & Fins
n x 2, and Building Flowers n x 4.)
For an extra challenge, give each
student a What’s
The Rule? II worksheet. Have them add, subtract,
and multiply to find the missing numbers. Read Quack
and Count. As the
book is read,
show students that numbers can be added or subtracted from each
other to find a pattern.
- Give each student a What’s The Rule? III worksheet.
create their own patterns and rules on their worksheet. Exchange
with classmates to solve when finished.
- Create an art project where
the pattern in the design grows as it
- Make quilt blocks using pattern blocks and display them in the
- Design a tiled floor. Use a 2” x 2” square as the main pattern
piece. Have students determine how many pattern pieces are
needed for a certain size of floor.
- Have students take home extra
What’s The Rule? II and What’s
The Rule? III worksheets and complete them with a family
- Conduct a Family Math Night at school. Invite students and
family members to come in the evening to experience the fun of
the math activities used in the lesson.
- Have students write a summary of what they learned
in their math
journals. Draw patterns and write what the rule is as an example.
- Have students
play concentration with the Match The Rule
Kagan, S. (1994). Cooperative Learning.
Resources for Teachers, Inc.
A student who is off task and misbehaving is usually a student
wanting attention. In a cooperative learning atmosphere, each student is
repeatedly included in a group of students working as a team to achieve
the goal of being a successful individual.
Created Date :
Jan 27 2006 08:56 AM