Christine Mortlock
Taylor Stoltz
SOL Math Activity Modifications
Math Strand
Patterns, Functions, and Algebra
Name of the Activity
Toothpick and Staircase Patterns
Math SOLs/Grade Level –4 4.15 The student will:
- recognize, create, and extend numerical and
Primary SOL
geometric patterns.
Process Skills or
“Investigative” Skills
TSW use the investigative skills:
Measuring: TSW count how many toothpicks it takes to
make a certain number of squares.
Inferring: TSW infer the pattern that emerges for the
number of toothpicks you have to add to make new
squares based on their observation of how many
toothpicks they add each time they make a new square.
Predicting: TSW guess the outcome of adding three more
toothpicks to the already constructed squares based on the
pattern of how many toothpicks were required for
previous squares.
Communicating: TSW use their words, toothpicks, and
drawings of squares to describe the pattern of how many
toothpicks need to be added to make new squares.
Formulating Hypotheses: TSW state how many toothpicks
they think need to be added to create a certain number of
squares.
Identifying of variables: TSW identify the independent and
dependent variables. Per scenario, the number of
toothpicks is the independent variable. The number of
squares is the dependent variable.
Defining Variables Operationally: TSW explain how to
measure the number of toothpicks and squares.
Describing Relationships Between Variables: TSW
describe the relationship between the number of squares
and number of toothpicks, i.e. that it takes three
toothpicks to make one more square.
Designing Investigations: TSW design an experiment to
figure out how many toothpicks are needed to create a
certain number of squares. TSW use toothpicks as a
material and describe the appropriate steps in the
procedure for testing the number of toothpicks needed.
Experimenting: TSW carry out their investigations by
following the procedures of adding toothpicks to make a
certain number of squares.
Acquiring Data: TSW collect quantitative data by counting
how many toothpicks are needed for each square.
Organizing Data in Tables and Graphs: TSW record their
data in a chart and on the Building Staircases Recording
Sheet.
Analyzing Investigations and Their Data: TSW interpret
the data and formulate a conclusion about how many
toothpicks are needed to create a certain number of
squares based on the data.
Questioning Strategies
Attention Focusing:
● What is this (while pointing to a square made out of
toothpicks)?
Measuring:
● How many toothpicks does it take to make one
square?
● How many to make 2, 3, 4, 5, etc. squares?
Comparison:
● How many toothpicks did you need to make one
square? Did you need more or fewer toothpicks to
make two squares?
● Did you need more or fewer toothpicks to make three
squares or two squares?
Action:
● Try to make a square with five toothpicks. Is it
possible? What about seven? What about eight?
Problem Posing:
● Imagine a cube staircase pattern with six steps. How
many centimeter cubes does the pattern have?
● How would you determine the number of centimeter
cubes needed to build a staircase with any particular
number of steps?
Reasoning:
● How many centimeter cubes would you need to add to
make seven steps?
● How many centimeter cubes would the pattern have
then?
Meta-Cognitive:
● How do you know it takes a certain amount of
toothpicks to make a certain number of squares?
● What do you wonder about number patterns in
nature?
● What have you discovered about number patterns?
Multiple Intelligences
Bodily-Kinesthetic: TSW use toothpicks to make squares
and draw them on their paper to illustrate how many
toothpicks it takes to make the squares. TSW also play the
Number Patterns Game and use a spinner to take turns.
Interpersonal: TSW discuss in pairs and as a class the
pattern for how many toothpicks it takes to make new
squares. TSW play the Number Patterns Game in groups as
well.
Intrapersonal: TSW glue the four toothpicks in their journal
to signify the first square and to use as a reference for
future lessons. TSW write the sequence for how to make
extra squares with toothpicks in their journal. TSW think
about patterns in nature throughout the week and note
them in their science journal.
Spatial-visual: TSW use the toothpicks to create a visual
representation of the pattern of how many toothpicks it
takes to create a certain number of squares.
Logical-mathematical: TSW count the number of
toothpicks is takes to make certain amounts of squares.
TSW determine the pattern of how many toothpicks are
needed to make new squares, how many toothpicks it
would take to make a certain number of squares, and how
many squares can be built with a certain number of
toothpicks. TSW will make T Charts and use the Building
Staircases Recording Sheet to build a staircase model.
Linguistic: TSW write the pattern of toothpicks needed to
create a certain number of squares in their journals. TSW
read the book, Fibonacci Zoo, and talk about number
patterns in different contexts.
Literacy Strategies
The class will read the Fibonacci Zoo together. They will
create a class book using photographs of other patterns
they observe in nature. They will take a nature walk to take
photographs of petals and leaves that exhibit number
patterns and glue the photographs in a class book. They
will write a story that goes along with the photographs.
Editorial Review from Children's Literature - Tina Chan
“Eli and his father are at the Fibonacci Zoo, where Eli
documents the number and type of animals he sees.
Animals include an alligator, bison, camel, dolphin,
elephant, flamingo, gorilla, and hippopotamus. Eli realizes
a number pattern occurs. Although the pattern is
unnamed, the Fibonacci sequence, named after a
mathematician who discovered the pattern in 1202, is
covered in the back. The sequence begins with number
one, and each number in the pattern is the sum of the
previous two numbers. The book ends with asking how
many animals would be in the next exhibit. Large text and
color illustrations make this educationally entertaining
book appropriate for young readers. Mathematical
sequences are shown as the story progresses. The back of
the book has educational and fun activities among them a
number pattern quiz, using Fibonacci numbers in nature,
and matching pictures of animals to its description; some
of these are also illustrated. Reviewer: Tina Chan; Ages 7
to 10.”
Script for teaching the lesson:
Chrissy: Hey, Taylor, what you got there?!
Taylor: Oh, these are just my toothpicks. I carry them wherever I go. Never know when you
might need ‘em.
Chrissy: Oh, cool, Taylor. Do you think we might play with them while we’re waiting around? I
love building things.
Taylor: Um, I guess….
Chrissy: Ok, awesome, I want to build a square.
Taylor: Ok, here are four tooth picks. You can build a square with four toothpicks. That’s all you
get.
Chrissy: Oh, thanks. Nice. A square. Do you want me to add another square to this so you can
have a square too?
Taylor. Um, I guess.
Chrissy: Ok, let’s see how many toothpicks I need to make a second square.
One…
Two…
Three…
I need just three. Wow, before I needed to have four toothpicks and now I only need three.
How many toothpicks do I have in all? Oh, I have 7!
Taylor: Wow, Chrissy that’s cool. Can I try building another square too. Let’s see if I only need
three too.
One….
Two…
Three…
Yes!
Chrissy: How many to total toothpicks do you have, Taylor?
Taylor: I have ten now.
Chrissy: So we started out with four toothpicks, then we had seven, then we had ten. How
many do you think we will have if we need to make a fourth square?
Taylor: Hrm .. Chrissy, it looks like there’s a pattern here. It seems for every additional square
you make you add three toothpicks.
Chrissy: Wow, Taylor, that’s neat. Patterns are really interesting aren’t they?
Points to Bring up During the Presentation
The point of this activity is to highlight patterns and how to recognize and express patterns.
Each student has their own toothpicks to build squares. Each student records how many
toothpicks are necessary for that number of squares in a table. Encourage students to predict
how many toothpicks are necessary for a certain number of squares. Encourage students to
look for a pattern for how many toothpicks are necessary after they’ve built several squares.
As a class try to come up with a mathematical algebraic formula that expresses the pattern--->
[(n 3) + 1] where n is the number of squares
You can use licorice instead of toothpicks for this activity! (The kids will have something to eat
after. :))
The lesson can be extended with another activity involving centimeter cubes. Students are
given their own centimeter cubes and figure out the number of cubes needed for a certain
number of steps. They record the number of cubes to make a step and they look for the pattern
as they add one step after the other.
To help students get practice identifying patterns, the students can play the Number Pattern
Game. They have to identify number patterns in a series of numbers to move their piece
forward in the game.