



Visible Thinking in Mathematics is a series of eleven supplementary books that promotes critical and creative thinking in mathematics. It is designed to help make thinking visible by providing the child with opportunities to think, explore and reflect.
While practice leads to better performance, practice without contextual and conceptual understanding prevents the child from thinking critically and creatively. In this series, instead of learning procedures and formulas by rote, the child masters concepts through:
 Thinking routines: functional questions to direct the child's thinking on key concepts and cultivate the child's thinking skills.
 Parallel questions: consecutive mathematical problems with the same context but different key words to highlight differences between problems; ensuring that the child understands and retains concepts and skills better.
This approach not only instills in the child mathematical skills but also inspires discipline in thinking and greater motivation for learning.
Additional support is provided to the child through Notes. Notes present opportunities for parents and teachers to clarify misconceptions, simplify difficult concepts and address areas of difficulty for the child.
Above extract from Preface of Visible Thinking in Mathematics (reproduced with the permission of the publishers).
Answers are in the back of each book.
Note: This series has not been revised for U.S. usage. Currency images in the money chapters at the lower levels are Singapore coins and bills. Also, only metric measurement units are used.
Visible Thinking in Math 3A
Contents
Chapter 1
Numbers To 10 000
Number Notation And Place Value
Reading And Writing Numbers In Words
Comparing And Ordering Numbers
Number Patterns
Chapter 2
Addition And Subtraction Within 10 000
Addition Without Regrouping
Addition With Regrouping
Subtraction Without Regrouping
Subtraction With Regrouping
Chapter 3
Word Problems Involving Addition And Subtraction
Word Problems
More Word Problems (1)
More Word Problems (2)
Chapter 4
Multiplication And Division By 6, 7, 8 And 9
Multiplication And Division By 6
Multiplication And Division By 7
Multiplication And Division By 8
Multiplication And Division By 9
More Multiplication And Division By 6, 7, 8 And 9
Chapter 5
Multiplication And Division
Multiplication Without Regrouping
Multiplication With Regrouping
Division Without Regrouping
Division With Regrouping
Word Problems Involving Four Operations Using Models
Number Patterns Involving Gaps And Intervals
Chapter 6
Mental Calculations
Addition Of 2Digit Numbers
Subtraction Of 2Digit Numbers
Mental Multiplication
Mental Division
Answers
Samples
Click here to view samples for Visible Thinking in Mathematics 3A.
Sample includes:
 Chapter 6 Mental Calculations  Addition of 2Digit Numbers (p. 143145)
 Mental Calculations  Mental Multiplication (p. 149)
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Our recommendation:
This is a good supplementary series for reteaching students who need additional guidance. The books emphasize the pictorial stage and helping students to move from the pictorial stage to the abstract or contextual stage. They include questions the teacher can ask the student to get them to think about the concepts, as well as teaching tips for the teacher that include common errors.
They would be useful in the classroom for teachers as a differentiation tool to use when working with students who need additional help, or for homeschoolers whose students need additional practice, discussion, and visual aids before moving to the abstract stage or before doing some of the more challenging material.
Includes some model drawing sooner than appropriate, as well as recording steps for strategies that would normally be a mental math strategy for more capable students, but this can be useful for those students who need more guidance through those particular strategies. It should not be used as a substitute for the Primary Mathematics, particularly for more capable students, but rather as a reteaching tool. There are detailed answers in the back.








