OPM1501 - Orientation To Intermediate Phase Mathematics (OPM1501NOTES)
Exam (elaborations)
OPM1501 NOTES (ASSIGNMENTS & EXAM)
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Course
OPM1501 - Orientation To Intermediate Phase Mathematics (OPM1501NOTES)
Institution
University Of South Africa (Unisa)
THIS DOCUMENT HAS MOST USEFUL NOTES TO HELP YOU WITH SOLVING OPM1501 QUESTIONS. PLEASE DO NOT JUST COPY AND PASTE FOR I KNOW THAT THERE ARE A LOT OF QUESTIONS WHICH HAVE BEEN ANSWERED BY THE LECTURE. MAKE SURE YOU READ AND UNDERSTANT.
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mary became excited about these patterns and calls a friend to tell her about them can you help mary to describe to her friend how she moved the triangle to make each pattern is there more than one
Written for
University of South Africa (Unisa)
OPM1501 - Orientation To Intermediate Phase Mathematics (OPM1501NOTES)
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Order Number 2-179
ISBN 978-1-58324-246-9
H I J K L 17 16 15 14 13
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, CONTENTS
Contents ............................................................................................. 3
Foreword ............................................................................................ 4
What are Base Ten Blocks?................................................................ 5
Base Ten Blocks ................................................................................. 6
A Guide to Using Base Ten Blocks in the Classroom ........................ 7
Challenging the Step-by-Step Approach ........................................... 8
Towards Mathematical Abstraction .................................................... 9
Before Base Ten 10–21
Before Introducing Base Ten Blocks ................................................ 12
99 and Over ...................................................................................... 13
Trading Board (Tens and Ones) ........................................................ 14
Progress Chart ................................................................................. 15
Count Down ................................................................................16–17
Expanding the Number Experience.................................................. 18
Mix and Match.............................................................................19–21
Trading Games 22–41
Discovering Base Ten Blocks ........................................................... 24
Base Ten Trading Board—1.............................................................. 25
Trading Games in Tens Land .......................................................26–27
Base Ten Trading Board—2.............................................................. 28
Trading to 100 .............................................................................29–30
Breaking a Flat ................................................................................. 31
Base Ten Challenges ........................................................................ 32
Longs and Minis ............................................................................... 33
Match and Collect Cards ................................................................. 34
Make My Number ........................................................................35–36
Mix and Match—Base Ten ..........................................................37–38
Renaming Numbers.....................................................................39–40
Hundreds and Thousands ................................................................ 41
Developing Computational Skills 42–79
Double and Split ..........................................................................44–46
Place Value—1 ................................................................................. 47
Place Value—2 ................................................................................. 48
Arrow Math ..................................................................................49–50
Decimal Fractions............................................................................. 51
Base Ten Decimal Fraction Trading Board—1.................................. 52
Trading with Decimal Fractions ........................................................ 53
Base Ten Decimal Fraction Trading Board—2.................................. 54
Decitrade .......................................................................................... 55
Addition .......................................................................................56–57
Addition without Regrouping............................................................ 58
Operations Board ............................................................................. 59
Addition with Regrouping ................................................................. 60
Spinner ............................................................................................. 61
Subtraction ..................................................................................62–63
Subtraction without Decomposition ................................................. 64
Subtraction with Decomposition ...................................................... 65
Subtraction Numerals....................................................................... 66
Multiplication—1 .............................................................................. 67
Multiplication—2 .........................................................................68–69
Base Ten Blocks ............................................................................... 70
Sharing Time .................................................................................... 71
Division ........................................................................................72–73
Checking Your Work ......................................................................... 74
The Block Game ............................................................................... 75
Percent ........................................................................................76–78
Adding Tenths and Hundredths........................................................ 79
Measuring with Base Ten Blocks 80–87
Comparing Lengths .....................................................................82–83
Make a Meter ................................................................................... 84
Make a Square Meter ....................................................................... 85
One in a Million ................................................................................. 86
All Wrapped Up .............................................................. 87
Correlation to Key Standards ......................................... 88
Glossary ......................................................................... 92
3
, Foreword
For many decades, educators have recommended the
use of manipulative materials to assist young children in
their learning of mathematics. The advocacy of educators
such as Maria Montessori, Zoltan Dienes and Catherine Stern
encourages a wide acceptance of the use of manipulative
materials, especially in elementary school classrooms. Once,
it was felt that simply giving students manipulatives to use in
mathematics lessons would be enough to develop an understanding
of mathematical concepts. This is not true. Manipulatives in and of
themselves do not teach—skilled teachers do.
How will I know whether the students are learning anything?
This series—Developing Mathematics—is designed to help
Observe the students as they work with the manipulatives. Don’t worry
teachers who are trying to make the most of students’ experiences
if they solve a problem in a way different from what you expected.
with manipulatives. It is better to use a few well-chosen manipulative
Ask questions. Encourage students to explain their thoughts or write
materials rather than an array of bits and pieces so students will have
about their experience.
an adequate supply of pieces. We recommend a lot of a little rather than
a little of a lot when it comes to working with manipulatives. Nothing is
What evidence can I show that students are learning?
more frustrating than not having enough to finish creating a design or
building that masterpiece. It is also important that sufficient materials are Some teachers are concerned about the lack of written evidence
available to allow models to be left on display in the classroom. to substantiate learning when manipulatives form a large part
of the lesson. There are several ways a student might record
Why use manipulatives? his/her findings:
When used as part of a well thought-out lesson, manipulatives can help • writing about the experience,
students understand difficult concepts. The key to good use of manipulatives • sketching or drawing any models produced,
is for teachers to have a clear goal in mind. This will help maintain the intention • photographing any models produced,
of the lesson and focus responses to any questions asked during the lesson. • presenting to students in other classrooms and
Teachers will have a clear idea of what to look for when observing students using • maintaining a learning journey log book.
manipulatives. Actually, when preparing this type of learning evidence,
We have observed how students experiment with ideas willingly. If satisfaction students have a wonderful opportunity to reinforce their
with an idea is not achieved, students will seek another solution. We do not see this own learning.
happening as frequently when students are expected to work with abstract statements
such as equations and written problems. How do I manage the use of manipulatives?
The skilled use of manipulatives will enhance mathematics outcomes. Poor use many be Some teachers worry that students will only play with
detrimental to student attainment. This series of books is designed to ensure skilled use the manipulatives and not pay attention, or worse
of manipulatives in the classroom. still, begin to throw the material around. These are
genuine fears which will decrease as experience,
Is there a difference between a mathematics manipulative and a mathematics both by the students and teacher, increases.
teaching aid? The first time you introduce a manipulative,
We believe there is a big difference between the two types of materials. allow time for the students to explore it. Set
A child can interact with and even take control of a good mathematical manipulative; whereas some simple rules and limits for the way the
a teaching aid tends to control the learning experience. Too often, a teaching aid is used as a material is used and enforce these early
telling support rather than a learning support and experience has taught us that “telling” is not on. Students will soon learn to respect the
a very successful method of teaching mathematical ideas. material. Throughout this book, we present
management ideas. We encourage you to
4 adopt them as your own.
BaseTen03-09.indd 4 7/10/06 11:19:51
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