Angela Escobar
Lesson Plan
Magic Squares 8th
Grade
MAE 4813
3/14/02
Magic Squares
8th Grade Mathematics
Goals-general outcome(s) / Objectives
The students will use
mathematical operations (adding / subtracting / multiplying / dividing) with
integers to solve problems.
The students will analyze
patterns with symbolic rules.
The students will create
patterns with symbolic rules represented as magic squares.
Sunshine State Standards
MA.A. 1.3.4 The students understands that numbers can
be represented in a variety of equivalent forms including integers, fractions,
decimals, percents, scientific notation, exponents, radicals, and absolute
value.
MA.A. 3.3.2 The students select the appropriate
operation to solve problems involving addition, subtraction, multiplication,
and division of rational numbers, ratios, proportions, and percents, including
the appropriate order of operations.
MA.D. 1.3.1 The students describe a wide variety of
patterns, relationships, and functions through models, such as manipulatives,
tables, graphs, expressions, equations, and inequalities.
Materials needed
3 X 3 Grid Paper for each
student (30 copies per class) to create magic squares
Overhead Projector and
Overhead Transparency of Examples used during Closure Activity of Magic Squares
that students must solve missing numbers.
Students will need pencils,
paper, pens, portfolio / 3 Ring Binder
Computer/Lap Top with Power
point software for Power Point Presentation
Internet Access for the links
from within the power point presentation
Dry Erase Board/Markers or
Chalk Board/Chalk
Computer Lab with enough
computers for the class
Internet Access for the
Students
Printer
Teacher Station with LCD
Projector and Screen to Display Internet Activities
Agenda Notebooks
Magic Square Homework
Activities Worksheet
Grouping of students -When the student first come in the classroom they are
in rows all facing forward working independently copying the agenda for the
day. As the transition to the
initiating lesson activity begins the students will move their desks into
groups of three or four (depending on how large the class and what works
best). After the activity they are back
in rows working independently during instruction of the lesson. The students are also working individually in
the computer lab, but may ask for assistance from the students seated next to
them or from the teacher. Once back in
the classroom students are in rows working individually through the example
homework problems during the ending review of the concept.
Time 60 minutes per class period
Motivation Explain to
the students that they will be working in groups today completing a fun
activity dealing with magic and that they will also be going to the computer
lab! This alone will spark their
interest and get them excited. Let the
students know that they will be given challenging projects that even I had to
complete in my own college courses (this always increases their self esteem to
think they can perform at a college level – high expectation bring forth good
results!).
Do Now: I always have an Agenda on the board so that as soon
as the students arrive in the classroom they can copy the activities for that
class period in their Agenda notebooks. They are responsible for completing any
activities that we didn’t finish in class at home. This also serves the purpose so that they will all know what
activities will be taking place during the class period. As soon as the students come into the
classroom this is the first thing they copy down and complete until first
directions are given by the teacher to begin the lesson. It generally looks
something like this:
Math Agenda
Do Now: Review +,
-, X, and / Integers & Order of
Operations
Power Point Presentation / Notes / Questions &
Answers (Magic Squares)
Computer Lab Magic Square Activities
Lesson Review
Review
Homework
Lesson Initiating
Activity: Prior to the lesson on magic
squares it is imparitive that the students know how to add and subtract
integers therefore the students will complete a review of those concepts. Problems similar to the following will be
placed on the board for the students to complete as soon as they come into the
classroom: -4 + 5 –7 – 3 + 9
-2 (-4) – 6 X 1 / 2 + 7
(five problems for the students to practice on their own).
Ask students to volunteer to
come up to the board solving the problems showing each step to the
solution. Review as the students take
notes of the rules for adding, subtracting, multiplying, and dividing integers
(negative X negative = positive, et…)
Next, explain that they will
now use their knowledge to have fun with magic as you direct their attention to
the large screen for a power point presentation of the main lesson.
Lesson procedure
The students are in a
non-group setting all facing forward for an introduction to Magic Squares
through the use of a power point presentation.
The students will take notes and write five questions on a separate
piece of paper as they learn about the history of magic squares, which
originated in China, and what a magic square actually is. (See information that will be put onto
power point slides enclosed). Call on
students also read the information orally. After the presentation explain to
the students that the next step will be that they will pass their questions to
the student sitting beside them as many times as needed so that no one has
their own questions. Using a timer
allow the students three minutes to answer the questions. Instruct the students that once the time is
up you will ask students to volunteer questions and answers they have. Write the questions and answers on an
overhead transparency. Make sure
specific questions about what magic squares are and the history are asked such as: “Explain the ancient Myth
and how it came about relating to magic squares.”, “What regions of the world
were magic squares brought about?”, “What special properties do magic squares
have?”, and “How do you construct a magic square?”. Instruct students to return the questions and answers to the
original student who wrote them. Make
sure all students have notes from the key concepts stated above from the
information given during the power point presentation.
*If power point is not
available it can be completed in a computer lab as well or with copies / packets
of the information for each student.
Next, explain to the students
that they will be taken to the computer lab where they will complete Internet
activities relating to what they have learned about magic squares. Once the students arrive at the computer lab
instruct them to follow the directions you give them as they follow the steps
on the projector screen from the teacher’s station. The first thing they will do is long on to the following website:
http://www.allmath.com/magicsquare.asp Instruct the students to individually
complete activities with magic squares that have 3, 4, and 5 rows/columns. While the students are completing the
activity circulate, assist, and ask students questions relating to the activity
to make sure they comprehend the lesson.
Also ask some students to print out their activities to add to their
portfolios. After the students have
been timed taking about ten minutes to complete the activities go through them
as a class. The students are following along as you are asking questions such
as the following: Activity 1 “What characteristics about this magic square do
you notice? “What was the result at the
end of the activity?” “What was the
difference between completing a magic square with 3 columns & rows and with
5?”.
Next, the students will put
their creativity to use by creating and solving actual problems from the
website: http://www.grogono.com/magic/
relating to magic
squares. Explain to the students that
they will have ten minutes to create and solve the given problems. Circulate and assist students as they
complete problems. Review the problems
on the projector screen asking the students some questions like the following:
“What formula did you use to solve the problem”, “What numbers did you
substitute for each row/column?”, “Use the dry erase board to show step by step
procedure to solve the problem”. Make
sure that students are also told that they are required to copy the problems
and solve them in their class notes section of their three ring binders. Instruct students to exit and turn off the
computers for the next activity will be completed back in the classroom as a
closure activity to the lesson.
Closure
Back in the classroom hand
out blank 3 X 3 grids and have students work in pairs to create their own magic
squares. Put a few of the following
magic squares on a transparency for the students to then solve:
|
-16 |
|
-2 |
|||
|
8 |
-6 |
20 |
|||
|
-10 |
-12 |
4 |
|||
|
|
22 |
-17 |
|||
|
0 |
-6 |
-12 |
|||
|
5 |
-34 |
11 |
|||
Review the lesson taught
about magic squares, what they are, the history, how to solve, and how to
create them asking the students high level questions throughout the review.
Review adding and subtracting
integers and go over examples from the homework that will be assigned (see
worksheet at the end of this lesson).
Extension—
The 8th grade math
curriculum has a wonderful website: www.hbschool.com/elab
that correlates to their textbook in which they can complete activities where
they must solve the missing integer in magic squares. If students have Internet at home or access at school in the
library in the morning before school, after school, during lunch, or at tutoring
they can complete the activities and print them out for extra credit. Students love the opportunity to earn extra
credit!!
Assessment—
Throughout all the activities I always have a class
roster in which I can check off that a student has shown to me they have
comprehended the concept and proved so by successfully completing the given
activity and/or when they demonstrate and answer any posed questions relating
to the concept. Also students will be
assessed through their individual homework and results of any post test
given.
Homework
Review and thoroughly explain
the homework practice worksheet on magic squares.
(See homework activity sheet
at the end of the lesson plan). If time
permits allow students to begin in class, although I usually never have extra
time for my students to begin their homework in class! Ask if students have any questions regarding
what they are asked to complete.
Release students accordingly at the end of the period.
Accommodations—
What modifications could be made to the lesson for
students with learning disabilities or L.E.P. students? For ESE/LEP students some suggestions would
be to actually give them a copy of the notes/slides of the power point
presentation, pair the students up with students who are strong in the subject
area, make sure those students are seated at the front of the classroom/nearest
to the teacher. Give the students extra
assistance and support during group/individual activities. Require the students to complete one of the
Internet activities instead of two and three activities. Pair up students during individual
activities such as the one at the computer lab. Have the Internet activities printed out as a hard copy for the
students to have also with step by step directions printed for them in large
print if needed. Allow students more
time to complete assignments, shorten assignments, and give students pictures
and diagrams of each activity problems.
Assess students through work completed in portfolios or during assigned
activities and/or during verbal responses.
Reflections—done after the lesson is taught. What went well? What needs
to be changed for the next time?
I will let you know when I actually teach the lesson and
get the results!!!
Homework Activity Sheet
Activities to Uncover the Magic
|
Name _______________________ |
|
1. Using the magic square shown at right, answer the following questions: a. What order is the
magic square? Explain your answer. |
|
2. In India, around 1500 A.D., 4-by-4 magic squares were constructed for particular purposes. For example, to soothe a crying child, a fourth-order magic square with a magic constant of 84 was prescribed.
a. If you were traveling in India around 1500 A.D., you would want to construct a fourth-order magic square with a magic constant of 34 to protect you on your travels. Do so using the numbers 1-16.
b. If you were a warrior in India around 1500 A.D., you would need to construct a fourth-order magic square with a magic constant of 64 for protection. Construct this square using 7 as the smallest number and 25 as the largest number.
3. Construct your own magic square with the following 3 X 3 Grid *for a challenge add extra rows & columns….
Magic Squares
3 X 3 Grid
4.) Solve the missing places in the
magic squares below:
|
-1 |
48 |
10 |
|
30 |
19 |
|
|
28 |
-10 |
39 |
|
20 |
-2 |
12 |
|
2 |
|
18 |
|
8 |
22 |
0 |
|
-1 |
48 |
10 |
|
30 |
19 |
|
|
28 |
-10 |
39 |