Students will learn how to see patterns by understanding how things work together.
Eye Spy a Pattern
For each pair:
Hundreds Board Patterns
For each student:
Patterns and Patterns Galore
For each group:
- Math for All Seasons, by Greg Tang; ISBN 0-439-44440-3
- Ten Little
Rabbits, by Virginia Grossman; ISBN 0-87701-552-X
- A Problem Solving Approach
to Mathematics for Elementary School
Teachers, by Rick Billstein; ISBN 0-201-52565-8
- Hundred Number Board Activities Grades 4-5, by Cindy Barden;
- Math Grades 4-6, The Best of The Mailbox Magazine;
- Math on Call, by Great Source; ISBN 0-669-45770-1
Background for Teachers
Students look for understandable ways to make sense out of what
they are learning. If they are directed and encouraged into seeing and
understanding how things work together, then they are seeing and
understanding patterns. Helping students understand and communicate
the connection and relationship in patterns enables them to understand
strategies for problem solving in a variety of ways.
It is beneficial for students to play games, learn, and work together.
This practice encourages the lowest to the highest achieving students to
engage in active and social learning. Many cooperative learning research
studies have proven that when students work together they practice and
experience a variety of social skills.
Give students some background information by explaining to them
that Blaise Pascal was a French mathematician, philosopher, and scientist
who studied number patterns and lived from 1623 to 1662. Leonardo
Fibonacci was an Italian mathematician who studied number patterns and
lived from 1180 to 1250.
Intended Learning Outcomes
2. Become mathematical problem solvers.
3. Reason mathematically.
Invitation to Learn
Choose one or both of the following activities to get the students
thinking about patterns and how to describe them.
Spy A Pattern
- Tell the students that you Spy
a Pattern in the classroom (choose
a pattern visible for all students to see, e.g., repeating tiles on the
ceiling, bricks on the wall, a group of shelves, etc.).
- Students are the
detectives and they are to guess what you have
chosen for the pattern by asking questions. When one or more
students have guessed the pattern, have them tell the class what it
is and explain how they guessed it.
- Have the students sing a song
with a growing pattern such as
BINGO, I Knew an Old Lady Who Swallowed a Fly,
Theres a Hole in the Bottom of the Sea, or The Green Grass
Grew All Around.
- Ask the students to listen for patterns as they are singing
rhythm or beat of the song, letters or words increasing or
decreasing, lyrics repeat, etc.).
- After the song is over, have the students
explain the patterns they
heard and write these on the board.
Eye Spy a Pattern
- Give an Eye Spy a Pattern worksheet to each pair.
- Each pair studies a pattern in the first column, then, discuss
possible solution(s) to the corresponding question in the second
column. Solve and talk about one pattern at a time.
- Give the students time
to figure out each solution. If needed, give
clues as to what the solution(s) may be. Guide students to look
for patterns by adding, subtracting, looking at the numbers
diagonally, top to bottom, right to left, etc.
- When time is up, choose
groups to come to the front of the
classroom and explain the solution(s) to an assigned pattern.
- Ask questions
like, What is the rule for the next pattern? Is there
more than one pattern? What patterns do we see in the world
Answers for Eye Spy a Pattern worksheet:
- N; Reading
left to right and top to bottom, the letters are the first letters in the
number words 1-9.
- 1 9 36 84 126 126 84 36 9 1. Answers will vary. Yes.
- 12345 X 9 + 6 =
111111. Yes, it will work until you add 10.
- 89, 144, 233. Answers will
- D, A (Beginning in the top left corner, the pattern consists of A,
AB, ABC, ABCD; B,
BC, BCD, BCDA; etc.)
Hundreds Board Patterns
- Hand each student a Hundreds
- Have students follow the directions below. After
each direction is
given, have the students describe the pattern.
- Underline all multiples of
2 with red.
- Circle all multiples of 3 with blue.
- Draw a purple box around each
multiple of 6.
- Cross out all multiples of 9 with orange.
- Draw a yellow triangle
around each multiple of 5.
- Multiples of 2 are found in alternating columns.
- All multiples of
3 are also multiples of 2.
- Multiples of 6 are multiples of both 2 and
- Multiples of 9 are also multiples of 3.
- The sum of the digits for
all multiples of 9 (except 99) is 9.
- The multiples of 6 are also multiples
- 90 is a multiple of 2, 3, 5, 6, and 9.
- All multiples of 5 end in
5 or 0.
- Discuss the correlation between multiplication and patterns.
Explain how multiplication is repeated addition, while division is
Patterns and Patterns Galore
Divide students into teams of two to four. Give each team a
Hundreds Board handout and a set of number tiles. Explain how to
play a game called Patterns and Patterns Galore.
- Place the number tiles face
down on the table next to the Hundreds Board handout.
- Each player
draws 10 number tiles and places them face up in
front of them on the table.
- Player 1 places any number pattern or sequence
of numbers on
the Hundreds Board using any of his/her 10 number tiles. A
pattern or sequence may be horizontal, vertical, or diagonal. A
pattern or sequence may be any length, but may go in one
direction only. Player one does not draw additional tiles at this
- Player 2 adds any number pattern or sequence of numbers to what
is already on the board. If a player cannot add on or start a new
number pattern or sequence, s/he draws 2 tiles from the pile and
play moves on to the next player.
- Players continue taking turns adding
number tiles to existing
number patterns and sequences, starting new ones when needed,
or drawing two tiles from the pile.
- The first player to place all of his/her
tiles on the board wins.
- Have each team show and discuss the various patterns
Ask students if they see any patterns that continue with a rule
(e.g., 10, 20, 30, 40, the rule is n x 10).
Read picture books on counting
to the students (e.g., Math for All
Seasons and Ten Little Rabbits). Have students describe patterns
they hear and see in the illustrations.
- Have students do the Patterned
Names activity at home with
family, using a family members name. Compare and contrast
differences and what is alike between all name patterns created.
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.
- Students write a summary and draw examples of their
of patterns in their math journals.
- Go on a walking field trip around the
school. Have students spy
patterns they see and describe how they repeat, grow, or continue.
- As a
class, assign each letter of the alphabet a different solid color
or colored pattern. Then, hand each student a piece of graph
paper. Have the students write each letter of their first name very
lightly across the first row of graph squares (one letter per graph
square). Repeat this seven times, moving to the next row each time. Cut out
the square that is created with the letters. Color
each letter the assigned color or pattern. Have the students
describe patterns they see. Display the students work around the
Example: If possible, have the students create their Patterned
Name Square using a keyboarding program.
Patterned Name Square
Variation: Delete or add one column and one row, see what
pattern is created. Discuss the changes and new patterns that
are seen. Have the students explain in detail how the pattern
will repeat and grow and how many graph squares will be
needed to create their name two or more times.
Kagan, S. (1994). Cooperative learning. Resources for Teachers, Inc. ISBN
Cooperative learning promotes higher achievement than competitive
and individualistic learning structures across all age levels, subject areas,
and almost all tasks. Studies have demonstrated that when students are
allowed to work together, they experience an increase in a variety of
social skills. Students become more able to solve problems that demand
cooperation for a solution, are better able to take the role of the other,
are generally more cooperative on a variety of measures, such as willingness
to help and reward others.