Math Curriculum
I. Overview
Students generally work alone or in small
groups. Students are encouraged to work together and share their
knowledge. We encourage students to communicate their ideas with
each other. Our goal is to have students communicate ideas,
gather information, solve problems and take responsibility for
their own learning. Homework is optional but encouraged.
Students are shown how doing homework benefits them and they are
free to choose whether or not to do it. Emphasis is placed on
learning and understanding as opposed to working to appease the
teacher and/or working to perform well on a test and then
forgetting what has been learned. Aside from the standards
listed, an emphasis is placed on problem solving. On a daily
basis the students are asked to solve problems and clearly
explain the solutions.
As in all subject areas at UCAP, math
classes do not make regular use of a textbook or student
workbook. Instead teachers draw on material from a range of
reference texts, the Internet, other teachers, or from their own
experience. Materials are changed regularly in an effort to
improve curriculum and instruction.
A typical class has an enrolment of 16
students from all three grades. Each student in the class is at
a different point in his/her progress in one of the grade
levels. Each math teacher works as part of four subject
interdisciplinary team and each team is responsible for 65
students. All students in the school loop with teachers on a
team. A challenge of the classes is balancing between group
instruction and individualization. Another primary challenge is
balancing between accelerating students in grade and providing
necessary remediation in basic skills.
II. Content and Assessment
Vocabulary
The students are given a sheet with the
terms and their definitions to study. Students are tested
orally. They should give definitions in their own words. They
could be asked the definitions of the words or they could be
given the definition and asked what word it describes. We
discuss the vocabulary further during tests. We discuss where
the words are useful in real life. Kids test each other first
and when they feel they are ready, the teacher tests them. We
always encourage other students to sit and listen when someone
is being tested so that they can see what it is like as well as
to help them study and become more familiar with the terms. Some
kids like to go to Puzzlemaker.com to make word puzzles using
the definitions. As with all standards we allow the students to
find the study technique that suites them best.
III. Skills and Assessment
Recite the multiplication tables
This is a
simple oral test of the tables. Students usually test each other
before coming to the teacher for the final test. There are many
ways to study for this test. Multiplication.com and other good
sites are used to study the tables. Some students make flash
cards and others fill in a multiplication chart.
Add, subtract, multiply and divide whole numbers
Generally most students have learned these skills prior to
coming to our class. However, there are always a few who have
trouble with division and sometimes multiplication. By making it
a standard we can at least get them to nail down those basic
skills. This is simply a written test of problems.
Add, subtract, multiply and divide positive and negative numbers
The students will be asked to study a set of
numbers called integers. They will explore the concept through
various different models (number lines, observable patterns,
world problems that relate to real world situations). This will
help the student understand how to find the sum, difference,
product, and quotient of positive and negative integers. They
are tested in many different applicable forms in relation to the
real world.
See attached paper titled The Positive and
Negative aspects of Teaching Integers.
Correctly use a ruler to measure and explain
the difference between , , 1/8, 1/ 16
Students will be asked to accurately measure
lines. They may also be given certain measurements and asked to
draw them. We may discuss reduction of fractions i.e. 8/16 = .
We may also compare fractions i.e. Which is greater 7/16 or 5/8
= 10/16. The teacher will sometimes check to see if they realize
that sixteenths are half of eighths. Once again learning this
standard comes from a teacher made packet as well as practice
measuring and discussions about fractions of an inch.
Mentally compute percentages (100%, 75%,
50%, 25%, 20%, 15%, 10%, 5%, 1%)
The students are tested orally and are not
allowed to use paper and pencil. We believe this is one of the
most useful standards. It is easy to show the students where it
useful. We discuss going into stores and seeing signs for 25%
off and being able to figure it out in your head. We talk about
leaving a 15% tip for waiters. Students practice first on paper
to get the concept down and then they practice orally by
quizzing each other.
Correctly use a protractor to measure and draw angles and shapes
The students are tested on this standard by
their knowledge and application of their skills of various
angles and triangles (acute, obtuse, right). In addition these
skills are implemented in the making of pie charts and various
geometrical shapes. Students practice first on paper to visually
see and attain the concepts and then are tested both orally and
in written form.
See attached paper titled Common
misconceptions among students on: The use of a Protractor.
Write numbers in words and digits
The students are given a written test where
they are given numbers and asked to write them out in words and
on the back they are given numbers in word form and asked to
write them out in digits. They learn this standard by studying
place value charts and practicing on worksheets. They learn
where to place the hyphens and commas. This skill may be helpful
later in life with check writing.
Compute elapsed time, read a clock, identify
s of an hour
Students are tested orally on their ability
to tell time and understand quarter past and quarter of.
They are tested in written form for their ability to compute
elapsed time. Again, they learn this skill from drill and
practice. Elapsed time is often a source of difficulty for many
students. We discuss 24 hours in a day and the difference
between A.M. and P.M.
Graph points on a Coordinate Plane
The test for this standard could be as
simple as: Given a list of coordinates, draw the graph or
picture. It could also be: Draw a picture and then list the
coordinates used to make that picture so that someone else can
draw your picture. Another test could be: Given a drawing, list
coordinates of the same drawing in a different quadrant. This
leads to discussion of Translation, Rotation, and Reflection.
Students practice this standard by drawing different graphs from
a book of coordinates. Actually most students learn this
standard from other students. This is one of the most fun
standards for many students.
Add, subtract, multiply, and divide decimal numbers
Students are given a written test of each of
the four operations. They use handouts to learn the rules of
each of the operations. However we always emphasize making sense
of the facts before turning to the rules. We suggest that they
estimate an answer that makes sense first then compute the
correct answer. If they really understand decimal numbers then
they can make good estimates. If they do not understand decimals
they will be lost as to what a good estimate is and this tells
us that it is a waste for them to learn rules to find and answer
that means nothing to them.
Compute any percentage and solve percentage
problems (9 is 8% of __, 7 is __% of 38)
The students have already learned how to
mentally compute some simple percentages. Now they will learn to
compute more difficult percentages using a calculator. As in the
examples above, the missing information could be the percent or
it could be some other number. The trick is simply knowing when
to divide and when to multiply to find the answer. I try not to
give rules but rather, we want them to discover for themselves
what works and what makes sense. The test is simply a written
test of problems with a few word problems.
Convert between fractions, decimals, and percentages
This test can be either written or oral.
Sometimes we have students take a written test to show that they
can convert from one to the other and other times we just have
students explain to us how it all works and how they are related
and ask for some examples. We made a packet that explains this
topic and offers examples. As always we have a discussion with
the student, either during his/her work or during the test,
about their relationship and when it is useful to convert from
one to the other.
Create and analyze pie charts and other types of charts and
graphs
Once students know how to use a protractor
and compass and are able to convert between fractions, decimals
and percents, they can now apply all of this knowledge by
creating pie charts. For a test they are asked to make up a
survey and graph the results in a pie chart. Sometimes we ask
questions to see if there is an understanding of the steps
involved or simply a memorization of random steps.
Add, subtract, multiply, and divide fractions and mixed numbers
Written test of about 25 difficult problems.
We made up a packet titled Everything you need to know about
Fractions. It contains lots of drill and practice. We try to
discuss this with them as they go through it in order to make
sense of all the crazy rules. This can be a tough skill for many
middle school students.
Compute area and perimeter of polygons; and area and
circumference of circles
There is no written test for this standard.
There is usually lots of conversation during the working of this
packet. The packet that we made is filled with directions,
examples, practice, and application. The application aspect is
where the students usually ask for help. We have managed to find
some interesting application problems that generate some good
discussion. During these discussions we can begin to see whether
or not the student understands the concepts being taught.
Compute volume of solid shapes (cube,
rectangular solid, sphere, cylinder)
At the end of this packet, which we have put
together, a student may be asked to construct two different
rectangular solids that have the same volume. A student may be
asked to construct a cylinder and find the volume and then
construct a rectangular solid that has the same volume. Again
lots of discussion occurs during the working of the packet.
Algebra I curriculum
The next nine standards are all Algebra I.
Basically they are nothing more than chapters in a text book. By
completing these chapters or packets, the student will have
completed an entire Algebra I course. There is a written test at
the completion of each packet. As usual there is plenty of time
for discussion throughout the packet. We can usually tell if a
student will do well on the test before they even take it.
