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First Steps in
Mathematics
Number
Course Book
FSIM012 | First Steps in Mathematics: Number Course Book © Western Australian Minister for Education 2013. Published by Pearson Canada Inc.© Western Australian Minister
fEducation
Published in Canada by
Pearson Canada Inc.
26 Prince Andrew Place
, ON, M3C 2T8 Text by Sue Willis with Wendy Devlin, Lorraine Jacob, and Kaye Treacy for Steps Professional Development on behalf of the Department of Education and Training, WesternAustralia
Publisher: Debbie Davidson
Director, Pearson Professional Learning: Theresa (Terry) Nikkel Canadian Edition Advisors: Craig Featherstone, Verna Schmidt, Barry OnslowDevelopment House: Pr
onk&AssociatesComposition: Computer Composition of Canada, Inc.
ISBN-13: 978-0-13-201884-5
ISBN-10: 0-13-201884-5
FSIM012 | First Steps in Mathematics: Number Course Book © Western Australian Minister for Education 2013. Published by Pearson Canada Inc. iiiContents
Timetable Example for Number........................................................................ ...................viProfessional Development Messages........................................................................
............viiWhole and Decimal Numbers
Unit 1: Introduction........................................................................Unit 2: From Counting to Partitioning........................................................................
............19Part 1: Counting to Quantifying........................................................................
...........21Part 2: Subitizing to Partitioning........................................................................
..........31Unit 3: From Partitioning to Place Value........................................................................
........37Unit 4: From Fractions to Decimals........................................................................
................57Classroom Research
Unit 5: Task Review........................................................................Operations
Unit 6: From Situation to Operation ........................................................................
...............79Unit 7: Types of Addition and Subtraction Problems.............................................................93
Unit 8: The Meaning of Multiplication and Division ...........................................................109
Computations
Unit 9: Building a Repertoire........................................................................
........................127Conclusion
Unit 10: Developing a Plan........................................................................ ...........................149 FSIM012 | First Steps in Mathematics: Number Course Book © Western Australian Minister for Education 2013. Published by Pearson Canada Inc. iv Diagnostic Tasks........................................................ .......................................................... 163 Diagnostic Tasks Contents........................................................................ ......................... 165WHOLE AND DECIMAL NUMBERS
Counting
More, K-Grade 1........................................................................ Get Me Task, K-Grade 2........................................................................ .............................167Counting Principles, K-Grade 2........................................................................
..................167Ice Cream (Equal Sets), Grades 1-3........................................................................
...........169 Skip Counting, Grades 1-4........................................................................ .........................1701-9 Repeating Sequence, K-Grade 4........................................................................
..........171 Up To and Over 100; Up To and Through the Hundreds, Grades 2-7...............................171Saying the Number Sequence by Ones and Tens, Grades 4-7...........................................174
Partitioning
Subitizing, K-Grade 1........................................................................ .................................175 Animals, Grades 2-4........................................................................ ...................................176How Did You Do It? Grades 3-7........................................................................
................177Whatís Next?
Grades 4-7........................................................................ ............................178Place Value
Dinosaurs,
Grades 2-7........................................................................ .................................18052 Candies, Grades 3-7........................................................................
...............................18243 Candies, Grades 3-7........................................................................
...............................184116 Candies, Grades 3-7........................................................................
.............................186Read, Write, and Say Numbers, Grades 3-7.......................................................................1
88Circle the Biggest,
Grades 6 and up........................................................................ ............190Flexible Numbers,
Grades 6-9........................................................................ ....................192800 Game, Grades 5-7........................................................................
................................195Decimals,
Grades 5-9........................................................................ ..................................197Numbers,
Grades 5-9........................................................................ ..................................201 Money, Grades 5-9........................................................................ .....................................203 FSIM012 | First Steps in Mathematics: Number Course Book © Western Australian Minister for Education 2013. Published by Pearson Canada Inc. vOPERATIONS
Addition and Subtraction
Change Task, Grades 1-7........................................................................ ...........................205 How Much Taller? Grades 4-7........................................................................ ...................208Empty Boxes,
Grades 5-7........................................................................ ..........................210Multiplication and Division
Story Problems, K-Grade 4........................................................................ ........................212 Finding Factors, Grades 5-7........................................................................ .......................215Calculator Number Sentences, Grades 4-7........................................................................
217COMPUTATIONS
Hide the Jelly Beans, K-Grade 1........................................................................
................219How Many Want Jelly Beans? Grades 1-3........................................................................
220Find the Solutions, Grades 3-7........................................................................
...................223 Buying Apples, Grades 4-7........................................................................ ........................227 Think Boards........................................................................ Planning Masters........................................................................ FSIM012 | First Steps in Mathematics: Number Course Book © Western Australian Minister for Education 2013. Published by Pearson Canada Inc. viTimetable Example for Number
Whole and Decimal Numbers
Unit 1
Introduction
2 hours
Whole and Decimal Numbers
Unit 4
From Fractions to
Decimals
2 hours
Classroom Research
Unit 5
Task Review
1 hour
Operations
Unit 8
The Meaning of
Multiplication and Division
3 hours
Whole and Decimal Numbers
Unit 2
From Counting to Partitioning
Part 1: Counting to Quantifying
Part 2:
Subitizing to Partitioning
2 hours
Operations
Unit 6
From Situation to Operation
1 hour
Computations
Unit 9
Building a Repertoire
2 hours
Whole and Decimal Numbers
Unit 3
From Partitioning to Place Value
2 hours
Operations
Unit 7
Types of Addition and Subtraction
Problems
2 hours
Conclusion
Unit 10
Developing a Plan
1 hour
Units 1-4 Whole and Decimal Numbers
These units use the Key Understandings from Chapter 2 in the Number Sense Resource Book to familiarize you with the
mathematical patterns of our numeration system; what places some children at risk from both a teaching and a learning
point of view; and how to move students along.Units 6-7 Operations
These units use the Key Understandings from Chapter 2 in the Operation Sense Resource Book to familiarize you with
choosing and using operations to mathematically model situations, that is, to use operations and numbers alone to
represent situations. This information is then used to look at what places some children at risk from both a teaching and a
learning point of view, and how to move students along.Unit 8 Computations
This unit uses the Key Understandings from Chapter 3 in the Operation Sense Resource Book to familiarize you with:
building and selecting strategies from a repertoire of computation strategies; what places some children at risk from both
a teaching and a learning point of view; and how to move students along. Unit 5 Classroom Research: Task Review and Unit 10 Conclusion: Developing a PlanThese units use knowledge, experience, and evidence from both the Number Sense and Operation Sense Resource Books
to analyze work samples and plan teaching and learning programs.All units need to be included in the Teacher Course. However, the timetable will be developed in negotiation with the
school or group of participantsFSIM012 | First Steps in Mathematics: Number Course Book © Western Australian Minister for Education 2013. Published by Pearson Canada Inc. viiProfessional Development Messages
These 4 key messages underpin the First Steps in Mathematics ProfessionalDevelopment Resources:
Probably nothing has more impact on students than the personal, professional growth of their teacher.Barth (1990), p. 49
1. Students may get the right answers for the wrong reasons.
2. Good questions and tasks provoke students to show us what
they know and understand.3. Understanding the mathematics helps us make better
professional decisions.4. Seeing the pattern in studentsí responses helps us plan
effective learning experiences. FSIM012 | First Steps in Mathematics: Number Course Book © Western Australian Minister for Education 2013. Published by Pearson Canada Inc. FSIM012 | First Steps in Mathematics: Number Course Book © Western Australian Minister for Education 2013. Published by Pearson Canada Inc. 1 UNIT 1Whole and Decimal
Numbers
INTRODUCTION
Desired Outcomes Participants will
be introduced to the beliefs that underpin First Steps in Mathematics become familiar with the philosophy and rationale that underpins the First Steps in MathematicsResource Books and professional learning process
begin to learn about the structure of the DiagnosticMap: Number in the Emergent, Matching, and
Quantifying phases
Unit Contents
Classroom Planning Aid............................................3 Beliefs about Teaching and Learning ......................4 Professional Decision Making...................................5Making Professional Decisions about Student
Sarah's Story...........................................................6 Searching for Patterns.............................................14Diagnostic Task: Up To and Over 100 &
Up To and Through the Hundreds........................14 Student Work Samples..........................................15 Bridging to Practice .............................................18 FSIM012 | First Steps in Mathematics: Number Course Book © Western Australian Minister for Education 2013. Published by Pearson Canada Inc. 2Related Reading First Steps in Mathematics:
Number Sense Resource Book
Chapter 1: An Overview of First Steps in
Mathematics
Beliefs about Teaching and Learning
Learning Mathematics: Implications for
the ClassroomUnderstanding the Elements of First
Steps in Mathematics
How to Read the Diagnostic Map
Chapter 2: Whole and Decimal Numbers
Key Understanding 4, pp. 52-63
Diagnostic Map: Number
Emergent phase
Matching phase
Quantifying phase
Suggestions for Further Reading
Munns, P. "Children's beliefs about counting." In
Teaching and Learning Early Number, edited by
Ian Thompson. Open University Press,
Philadelphia, 1998.
Willis, S. "Numeracy and
Outcomes in the Early
Years."
Every Child, 5(1), Autumn 1999.
FSIM012 | First Steps in Mathematics: Number Course Book © Western Australian Minister for Education 2013. Published by Pearson Canada Inc. 3Classroom Planning Aid
Two low-achieving students:
Student 1___________________________ Student 2 ____________________________ KeyUnderstanding(s) Mathematical
Focus Sample Learning
Activities Focus Questions Observations
Anecdotes
concept e.g., a dot point in KU diagnostic tasks post taskTwo average-achieving students:
Student 1___________________________ Student 2 ____________________________ KeyUnderstanding(s) Mathematical
Focus Sample Learning
Activities Focus Questions Observations
Anecdotes
concept diagnostic tasks post taskTwo high-achieving students:
Student 1___________________________ Student 2 ____________________________ KeyUnderstanding(s) Mathematical
Focus Sample Learning
Activities Focus Questions Observations
Anecdotes
concept diagnostic tasks post task FSIM012 | First Steps in Mathematics: Number Course Book © Western Australian Minister for Education 2013. Published by Pearson Canada Inc. 4Beliefs about Teaching and Learning
First Steps in Mathematics
FSiM) is underpinned by the following beliefs. Indicate the extent to which you currently share these beliefs by checking the appropriate box.1. Learning is improved if the whole school has a shared understanding of the
mathematics outcomes, and a commitment to achieving them. agree disagree2. All students can be successful learners of mathematics.
agree disagree3. Learning is not simply about the transfer of knowledge from one person to another.
agree disagree4. Students need to construct thei
r own knowledge in their own way. agree disagree5. If all students are to succeed to the best of their ability in achieving mathematics
outcomes, differentiated instruction will be not only possible but necessary. agree disagree6. Teaching cannot be reduced to a set of instructions about what to do in any given
situation. agree disagree7. Robust learning that focuses on students achieving mathematics outcomes fully and in
depth is essential for long-term sustained learning. agree disagree8. A focus on short-term performance or procedural knowledge places students at risk of
not progressing in later years.agree disagree FSIM012 | First Steps in Mathematics: Number Course Book
© Western Australian Minister for Education 2013. Published by Pearson Canada Inc. 5Professional Decision Making
Components of Professional Decision Making
Professional Development Cycle
Number Sense Resource Book, p. 16
Discussion
How do you currently make professional decisions about mathematics, pedagogy, and students?quotesdbs_dbs14.pdfusesText_20[PDF] pearson my lab
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