| Description |
1 online resource : illustrations |
| Contents |
Opportunities to Build a Foundation for Proportional Thinking. Kindergarten : Counting and comparing equal groups ; Decomposing numbers into equal groups ; Comparing measurements relatively -- Grade 1 : Adding and subtracting using equal groups ; Multiples of ten ; Measuring with units ; Introducing halves and quarters -- Grade 2 : Introducing multiplication ; Creating groups of tens and hundreds ; Decomposing into units to add and subtract ; Measuring with units ; Relating money units ; Creating fractions of wholes -- Focusing on Proportional Thinking. Grade 3 : Interpreting a number as units of another number ; Interpreting multiplication as a unit change ; Recognizing proportional thinking in multiplication/division properties ; Measuring with units ; Graphing using scale -- Grade 4 : Making multiplicative comparisons ; Interpreting fraction equivalence using multiplicative comparisons ; Ordering fractions ; Interpreting decimals as ratios ; Converting measurements by changing units ; Relating angle measurements -- Grade 5 : Comparing pattern growth ; Comparing powers of ten ; Comparing decimals using proportional reasoning ; Interpreting a fraction as a division ; Interpreting fraction multiplication in terms of unitizing ; Interpreting fraction division in terms of unitizing : Measurement conversion ; Using proportional reasoning to explore volume -- Grade 6 : Concept of ration ; Equivalent rations ; Unit rate ; Percent ; Converting measurement units ; Relating fraction division to proportional reasoning ; Using equations to express proportional relationships -- Grade 7 : Exploring proportionality numerically ; Exploring proportionality algebraically ; Describing fractions as decimals ; Circle measurement ratios ; Volume and surface area ratios ; Predicting likelihood -- Grade 8 : Using exponent situations to build on proportional reasoning -- Connection proportional relationships to linear equations -- Using proportional reasoning in solving equations ; Similarity -- Volume ratios -- Data relationships |
| Summary |
Although proportional reasoning is not formally introduced as a topic in the Common Core and other mathematics curricula until 6th grade, introducing its fundamental ideas in the early grades helps students develop essential skills in ratios, percentages, and other proportional representations when they reach the upper grades. The author takes this complex subject and crafts examples and questions that help teachers see the larger purpose in teaching concepts, such as unitizing, and how that understanding is essential for more complex ideas, such as ratios. Teachers and vertical teams can see how the concepts can build year after year. This new resource by well-known professional developer Marian Small suggests questions that are both interesting for students and useful for providing diagnostic information to teachers. Chapters are organized by grade level (K-8) around the Common Core State Standards for Mathematics to help teachers use the resource more easily |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Print version record |
| Subject |
Mathematics -- Study and teaching (Primary)
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Mathematics -- Study and teaching (Elementary)
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Mathematics -- Study and teaching (Middle school)
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Mathematics teachers -- Training of.
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EDUCATION -- Elementary.
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Mathematics -- Study and teaching (Elementary)
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Mathematics -- Study and teaching (Middle school)
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Mathematics -- Study and teaching (Primary)
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Mathematics teachers -- Training of
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| Form |
Electronic book
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| ISBN |
9780807773826 |
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0807773824 |
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