The Office for Mathematics, Science, and Technology Education
K–5 Technology Passport:
Curriculum Applications of Squeak in Mathematics,
Science, Art, Language Arts, and Social Science
Kathleen Harness, Enrichment Specialist
Office for Mathematics, Science, and Technology Education
K – 5 Technology Passport
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Preface
This K-5 Technology Passport uses Squeak to give elementary students a
functional, accessible introduction to programming. Squeak is an objectoriented programming language invented and developed by Alan Kay and
his colleagues at Viewpoints Research Institute. The K-5 Technology
Passport lessons were developed at the University of Illinois UrbanaChampaign in the Office for Mathematics, Science, and Technology
Education.
The K-5 Technology Passport is a curriculum that will give students a solid
foundation in computer logic, critical thinking, and problem solving. The
lessons apply Squeak in mathematics, art, science, language arts, and social
science. The lessons introduce programming to children for modeling and
visualization of scientific and mathematical concepts and other interesting
applications.
Squeak is a multi-media authoring tool and the projects students make will
be a source of pride to them, their teachers and their parents. The lessons can
be applied for many purposes far beyond these examples. The Squeak
lessons are based on projects, useful as examples, but students will create
their own versions. We invite you to introduce your students to Squeak.
Curriculum Consultants
Science: Dr. Barbara Hug: Asst. Professor, College of Education,
University of Illinois
Mathematics: Dr. George Reese, Director of the Office for Mathematics, Science,
and Technology Education (MSTE), University of Illinois; Kathleen Smith,
Mathematics Instructor, University of Illinois; Avigail Snir, Mathematics
Curriculum Specialist (MSTE)
Computer Science: Dr. Lenny Pitt, Professor Computer Science, University
of Illinois
Squeak Software Source
www.squeakland.org for Squeak software free and open source
www.squeakcmi.org for additional resources, lesson plans and projects
The Office for Mathematics, Science, and Technology Education
University of Illinois Urbana-Champaign
K – 5 Technology Passport
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University of Illinois Urbana-Champaign
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K – 5 Technology Passport
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Mathematics
Number Slate: Fractions and Decimals
Fourth and Fifth Grade Levels
Introduction
This lesson uses the computer screen as a place for students to create a set of
numbers to play with and to think about order, chaos, and patterns. The
number slate can be in used graphs, charts, and reports. Students add math
symbols for multiplication and division. The symbols for Dollars and cents
can be added to the set.
The student is the calculator.
The computer screen is a good place for experiments with Magic Squares.
The number slate will be useful in experiments to create and solve Sudoku
and other math puzzles.
Topic: Students use the set of numbers and symbols they began as Math
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University of Illinois Urbana-Champaign
K – 5 Technology Passport
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Number Play K-1 and Math Number Play 2-3 projects and modify it to suit
purposes during their upper grade level years.
These tools can be used to explore and develop mathematical relationships
and ideas without the use of pencil and paper. Students add math symbols
for percents and fractions and experiment with the challenge of magic
squares, and Sudoku puzzles.
Time Frame: 30 minutes for one lesson
Description: Students will use the numbers and symbols on slate of
numbers on maker buttons for an unlimited supply of numbers to explore
mathematics. They can use this supply for counting, sequencing, and
creating many patterns in numbers.
Vocabulary: Add, subtract, equals, multiply, divide, dollars, cents, decimal,
percent, value, counting, number names, zero, nothing, pattern, duplicate,
copy, set, sequence, above, below, beside, before, left, right, upper, lower,
edge, near, up, down, between, almost, add, subtract, equals, exactly
Criteria for Core Curriculum Outcome Evaluation:
Adds, subtracts, multiplies, and divides with numbers from the slate
Includes Dollar and cents signs on their slate
Includes decimal point, fraction line and percent sign on the slate
Makes sequences and other patterns of numbers
Makes a playfield grid of appropriate size
Makes magic squares with single digit numbers
Creates and Solves Sudoku puzzles
Criteria for Squeak Programming Outcome Evaluation:
Knows how to open Squeak, publish and find projects
Knows how to change the color of the world screen and of playfields
Knows how to use a playfield as a place like a slate for convenient
expression of mathematical ideas
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University of Illinois Urbana-Champaign
K – 5 Technology Passport
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Teacher Information
Goals: Students use the slates of numbers they drew to experiment with and
to explore many mathematical ideas with fractions and decimals. They use
the numbers to visualize sets, sequences and other patterns.
Lesson 1 (30 minutes)
In this lesson students use the paint tool to draw the extra symbols they will
use in math curriculum for Fourth and Fifth grade.
Show students an example of a Magic Square and ask them to make one
using a playfield as a basic grid.
Make a grid on a playfield:
1. Open the Supplies flap, drag out a playfield and put it on the screen.
2. Alt click on the playfield, then click on the red menu button to open a list
of options.
3. Click on ‘make graph paper’.
4. On-screen directions ask what size to make the grid. The basic grid size is
eight which is a very small size for the typical size of numbers on most
students’ number slates. Give students time to experiment with sizes.
5. The on-screen directions require a choice of background color and a
palette of colors opens. Click to choose.
6. The directions next ask that a line color be chosen. The paint palette opens
again; click to choose.
7. Give students time to experiment with size of the grid, and colors of lines
and backgrounds. Give students time to make a Magic Square, or two.
Publish this project: There is no need to change the name of the project this
is the final version students can use in math lesson ideas and for casual play.
Extend Lesson 1 (additional time required)
There are many ways to use this Squeak project in math class or as a source
of numbers for other Squeak projects in Science, Language Arts and Social
Sciences.
1. Grids can be made for Sudoku puzzles. Perhaps they are easier to make
than they are to solve.
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University of Illinois Urbana-Champaign
K – 5 Technology Passport
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2. Students who drew their numbers as Kindergarteners or First Graders will
enjoy seeing their early work. The number slate is just a source of numbers
the student is the calculator.
3. Use the set of numbers for experimenting with mathematical concepts,
groups, and tens, some may be revealed more easily due to the colors
students have chosen.
4. Practice math facts or applications of word problems and or rate, speed
and distance formulas.
5. Show the smallest value number that will fit on the screen. Tell the
number with the correct words.
6. Show the largest value number that will fit on the screen. Tell the number
with the correct words.
7. What is a good monthly salary? How much is that per day, per week and
per year? What is the daily salary if annual income is $1,000,000? Show
your work.
Student Information
Show students an example screen if an LCP projector is available or use a
computer and show examples to small groups.
Standards
Mathematics
Illinois Performance Standards
Fourth Grade
6A, 6C Percents
6A, 6B Decimals
Fifth Grade:
6B, 6C Division
6A, 6B, 6C, 6D Fractions and Rations
6A, 6B, 6C, 6D Decimals and Percents
National Educational Technology Standards (NETS)
1. Basic operations and concepts
Students are proficient in the use of technology.
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University of Illinois Urbana-Champaign
K – 5 Technology Passport
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3. Technology productivity tools
Students use technology tools to enhance learning, increase productivity, and
promote creativity.
Students use productivity tools to collaborate in constructing technologyenhanced models, prepare publications, and produce other creative works
4. Technology communications tools
Students use a variety of media and formats to communicate information and
ideas effectively to multiple audiences.
Squeak Help:
See Appendix A
Resources:
www.squeakcmi.org
http://en.wikipedia.org/wiki/Sudoku
This article is about the logic puzzle. For the disease, see Sodoku.
A sudoku puzzle...
...and its solution numbers marked in red
Sudoku (数独 sūdoku?) listen (help·info) is a logic-based number placement puzzle. The
objective is to fill a 9x9 grid so that each column, each row, and each of the nine 3x3
boxes contains the digits from 1 to 9. The puzzle setter provides a partially completed
The Office for Mathematics, Science, and Technology Education
University of Illinois Urbana-Champaign
K – 5 Technology Passport
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grid.
Completed Sudoku puzzles are a type of Latin square, with an additional constraint on the
contents of individual regions. Leonhard Euler is sometimes cited as the source of the
puzzle, based on his work with Latin squares[1].
The modern puzzle was invented by an American, Howard Garns, in 1979 and published
by Dell Magazines under the name "Number Place"[2]. It became popular in Japan in
1986, when it was published by Nikoli and given the name Sudoku. It became an
international hit in 2005.
http://mathworld.wolfram.com/MagicSquare.html
Recreational Mathematics > Magic Figures > Magic Squares
Foundations of Mathematics > Mathematical Problems > Unsolved Problems
Algebra > Linear Algebra > Matrices > Matrix Types
Magic Square
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University of Illinois Urbana-Champaign
K – 5 Technology Passport
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A magic square is a square array of numbers consisting of the distinct positive integers 1, 2,
...,
arranged such that the sum of the numbers in any horizontal, vertical, or main diagonal
line is always the same number (Kraitchik 1952, p. 142; Andrews 1960, p. 1; Gardner 1961,
p. 130; Madachy 1979, p. 84; Benson and Jacobi 1981, p. 3; Ball and Coxeter 1987, p. 193),
known as the magic constant
If every number in a magic square is subtracted from
, another magic square is obtained
called the complementary magic square. A square consisting of consecutive numbers starting
with 1 is sometimes known as a "normal" magic square.
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The Office for Mathematics, Science, and Technology Education
University of Illinois Urbana-Champaign
K – 5 Technology Passport
The Office for Mathematics, Science, and Technology Education
University of Illinois Urbana-Champaign
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