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Fractions, Percentages, Decimals and Proportions: A Learning- Teaching Trajectory for Grade 4, 5 and 6

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Fractions, Percentages, Decimals and Proportions: A Learning- Teaching Trajectory for Grade 4, 5 and 6

4.85 47,889 ratings · 6,256 reviews
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Overview: This book describes the field of fractions, percentages, decimals and proportions. It shows the relations between these topics, and how they can be taught in a way that emphasizes these relations.. The book also describes the need for change in the way we teach mathematics. The authors argue for a shift in emphasis from acquired skill to understanding. First and foremost, students should grasp the underlying concepts. Placing less high demands on the skill level of students in the use of formal procedures can set free time that can be invested in in-depth understanding.

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Pages 164
Publisher Sense Publishers
Published January 1, 2008
ISBN 16897220
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Els Feijs
About the Author
Els Feijs
10,349 Followers

Els Feijs is a writer and avid reader based in the Pacific Northwest. Before pursuing writing full-time, they spent over a decade working in education. When not working on their next book, Els Feijs can usually be found hiking with their dog or trying out new coffee shops in their neighborhood.

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Mary Perez
Mary Perez August 19, 2024
Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Mary Moore
Mary Moore October 24, 2025
Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
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Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
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A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
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Melissa Thomas August 13, 2024
Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
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I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Eric Miller
Eric Miller November 12, 2024
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Joshua Wilson August 22, 2024
I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
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Melissa Wright March 04, 2024
Not entirely to my refined tastes. Certain acts were fascinating, while others felt like a slight endeavor to complete. Suitable if your reading queue is empty.
Richard Flores
Richard Flores August 01, 2024
Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
Sandra Phillips
Sandra Phillips October 07, 2025
Excellent, though slightly flawed. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall.
Andrew Evans
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I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. Quite impressive overall.
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I thoroughly enjoyed the elegance of it. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall.
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Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
Joseph Turner
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Took a moment to build, but the payoff was spectacular. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A wonderful companion for a quiet weekend.
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Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
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Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
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I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
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Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
Jennifer Perez
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I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. A solid 4 stars from me.
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An acceptable diversion. Certain acts were fascinating, while others felt like a slight endeavor to complete. Perhaps more aligned with a different audience's tastes.
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Honestly one of the most premium reading experiences lately. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
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Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
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I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers.
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Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
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A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. Quite impressive overall.
Donna Martinez
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An acceptable diversion. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Unlikely to reread, but a reasonable expenditure of time.
Patricia  Parker
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Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
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Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
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I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
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Absolutely brilliant. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
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Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
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A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend.
Joshua Wilson
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Ryan Smith October 15, 2025
Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
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Jessica Scott June 20, 2024
Excellent, though slightly flawed. A brilliant concept executed with flair. Just a few pacing choices I would change. A solid 4 stars from me.
Joseph Collins
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Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
Richard Gomez
Richard Gomez July 20, 2024
A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
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A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
Susan Taylor
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Excellent, though slightly flawed. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
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Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
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Took a moment to build, but the payoff was spectacular. The protagonist was compelling, though some subplots felt slightly overshadowed. I would highly recommend this to discerning readers.
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A very strong entry. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel.
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Patricia Parker July 29, 2025
Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
Emily Campbell
Emily Campbell July 19, 2024
A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall.
Barbara Reyes
Barbara Reyes March 19, 2024
Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
Ashley Gonzalez
Ashley Gonzalez September 07, 2024
A very strong entry. It held my rapt attention, even when certain twists were telegraphed. A solid 4 stars from me.
Michael Walker
Michael Walker December 22, 2024
Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
Karen Rivera
Karen Rivera August 29, 2025
Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
Steven Gomez
Steven Gomez March 26, 2025
Excellent, though slightly flawed. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend.
Susan Walker
Susan Walker November 29, 2024
Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
Ashley Torres
Ashley Torres September 22, 2024
A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
Robert Jackson
Robert Jackson October 07, 2025
Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
Elizabeth King
Elizabeth King August 28, 2025
Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
Gary Robinson
Gary Robinson June 21, 2025
A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
Richard Carter
Richard Carter June 21, 2024
A very strong entry. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel.
Thomas Diaz
Thomas Diaz July 06, 2025
A very strong entry. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A solid 4 stars from me.
Emily Clark
Emily Clark April 11, 2025
A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
Ashley Flores
Ashley Flores April 20, 2024
I find myself somewhat conflicted. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Perhaps more aligned with a different audience's tastes.
Sarah White
Sarah White October 09, 2025
Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
Rebecca Wilson
Rebecca Wilson February 26, 2025
An acceptable diversion. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Perhaps more aligned with a different audience's tastes.
Kenneth Gomez
Kenneth Gomez July 29, 2024
It was adequate. It verged on repetitive in the second act. A more concise edit would have served it well. Suitable if your reading queue is empty.
Lisa Robinson
Lisa Robinson November 10, 2024
I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
William Walker
William Walker November 24, 2025
I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
Betty Phillips
Betty Phillips March 04, 2024
Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem.
Thomas Brown
Thomas Brown March 23, 2025
I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
Christopher Nguyen
Christopher Nguyen March 23, 2025
Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
Donald White
Donald White December 17, 2025
A decent, if standard, experience. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Suitable if your reading queue is empty.
William Walker
William Walker March 14, 2025
A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend.
Carol Baker
Carol Baker June 12, 2025
Honestly one of the most premium reading experiences lately. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
Jacob Lee
Jacob Lee July 15, 2025
A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A solid 4 stars from me.
Karen  Davis
Karen Davis June 05, 2024
Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
Eric Torres
Eric Torres January 31, 2024
Took a moment to build, but the payoff was spectacular. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
Melissa Rivera
Melissa Rivera July 10, 2025
I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
Karen Rivera
Karen Rivera June 08, 2025
Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem.
Thomas Brown
Thomas Brown May 19, 2025
Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
Gary Williams
Gary Williams August 15, 2025
Excellent, though slightly flawed. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
Elizabeth Young
Elizabeth Young March 07, 2025
Absolutely brilliant. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
Elizabeth King
Elizabeth King June 27, 2025
I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
Daniel  Parker
Daniel Parker October 25, 2024
Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
Ryan Williams
Ryan Williams April 16, 2024
Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
Nancy Carter
Nancy Carter June 20, 2024
I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Brian Campbell
Brian Campbell October 19, 2025
Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
Kenneth Evans
Kenneth Evans August 22, 2024
A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
Laura Phillips
Laura Phillips July 13, 2024
Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
Jessica Nelson
Jessica Nelson January 05, 2024
A very strong entry. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel.
Betty Allen
Betty Allen September 18, 2024
Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
Ashley Perez
Ashley Perez May 07, 2025
Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
Sarah Taylor
Sarah Taylor July 22, 2025
I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
Sharon Rivera
Sharon Rivera July 02, 2025
I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
Steven Gomez
Steven Gomez September 13, 2025
A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers.
Kevin Allen
Kevin Allen July 20, 2025
Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
Lisa Garcia
Lisa Garcia November 06, 2025
Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
Daniel Lopez
Daniel Lopez July 18, 2024
A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
Cynthia Wright
Cynthia Wright December 25, 2025
Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
Melissa Adams
Melissa Adams March 03, 2025
Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
Linda Jones
Linda Jones January 29, 2024
Absolutely brilliant. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
Melissa Harris
Melissa Harris February 12, 2024
A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. A solid 4 stars from me.
Kimberly Baker
Kimberly Baker May 17, 2025
Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Michael Moore
Michael Moore January 22, 2024
Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
James Jackson
James Jackson June 25, 2024
I find myself somewhat conflicted. It verged on repetitive in the second act. A more concise edit would have served it well. Perfectly average.
Matthew Hall
Matthew Hall July 17, 2024
A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Steven Rivera
Steven Rivera August 05, 2025
A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
Steven Hill
Steven Hill January 05, 2024
Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Donna Martinez
Donna Martinez September 29, 2025
I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
Daniel  Parker
Daniel Parker June 04, 2024
Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Brian Smith
Brian Smith September 19, 2025
A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Ryan Young
Ryan Young January 06, 2025
Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
Jennifer Thomas
Jennifer Thomas December 11, 2025
A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
Susan Reyes
Susan Reyes June 14, 2024
It was adequate. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. A fair 3 stars.
Paul Taylor
Paul Taylor July 29, 2025
Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
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