Contents
Introduction
Working Mathematically
Computation
Principles of Mathematics Teaching
Working through a Syllabus
Strategies for encouraging syllabus-related investigations
7
7
8
10
12
12
Posing and Solving Problems
Organising Problem Posing
Posing problems for middle and upper primary students
Posing Problems on Specific Mathematical Topics
Scaffolding Problem Writing
Sharing Students’ Problems
13
13
16
18
19
Investigating
The Investigation Process
Beginning an investigation
The language students use to explain ideas
Writing a definition
Searching for patterns
Posing questions
Group Work
Establishing working groups
Bringing groups together
It All Adds Up! Engaging 8-to-12-Year-Olds in Math Investigations
© 1999 Math Solutions
20
20
20
21
22
22
23
23
23
3
Report Writing
Note making
Making diagrams
Modelling report writing
Reviewing an Investigation
24
24
26
26
28
Addition
Single-digit Addition Strategies
Addition Chains
Adding Two-digit Numbers
Mental addition
Written addition
Spreadsheet addition
Addition Practice through Investigations
Adding Larger Numbers
Adding Decimals
Triangular Numbers
Fibonacci Numbers
Pascal’s Triangle
29
33
34
34
35
39
40
42
43
44
48
49
Multiplication
Investigating Sequences of Multiples
Multiples of nine
Reducing numbers
Multiples of four
Multiples of five and twenty-five
Zero as a multiple
Multiples and angles
Multiples of eight
Common multiples
4
It All Adds Up! Engaging 8-to-12-Year-Olds in Math Investigations
© 1999 Math Solutions
51
51
55
55
58
59
62
62
64
Multiplication Strategies
Doubling
Multiplying by single-digit numbers
The standard algorithm
Multiplying by eleven
Multiplying by numbers greater than eleven
Multiples of ninety-nine
Square Numbers
Square number problems
Square number investigations
Rectangular Numbers
Factors
Linking factors with square numbers
Linking factors with the binary sequence
Factors and angles
Introducing prime numbers
‘Maths Party’ activity
Measuring Area and Volume
Cubic Numbers
Multiplying Decimals
Permutations and Factorials
66
66
67
69
71
74
78
79
81
84
88
89
92
94
94
95
96
96
97
100
101
Subtraction
Subtraction Contexts
Finding differences
Taking away
Single-digit Subtraction Strategies
Subtracting Larger Numbers
Estimation
Mental subtraction
Written subtraction
It All Adds Up! Engaging 8-to-12-Year-Olds in Math Investigations
© 1999 Math Solutions
105
105
106
106
107
107
108
110
5
Subtraction Practice through Investigations
Negative Numbers
Subtracting Decimals
Pyramid Numbers
112
114
119
119
Division
Division Contexts
Fractions
Quotition division
Partition division
Percentages
Multiplication tables
Division Strategies
Dividing by single-digit numbers
Making sense of division answers
Making sense of calculator answers to division
Divisibility
Divisibility by five and ten
Divisibility by other single-digit numbers
Divisibility by eleven
Divisibility by twelve
Division with Decimals
Linking fractions and decimals
Why do some decimals repeat infinitely?
Percentages
Percentage calculation devices
Conclusion
120
120
121
121
121
122
122
122
126
127
129
129
130
130
131
132
133
136
138
138
140
Posing Questions in View of the Mathematics Teaching Principles 144
6
It All Adds Up! Engaging 8-to-12-Year-Olds in Math Investigations
© 1999 Math Solutions