美国加州教材 Illinois Mathconnects 4.pdf

AuthorsAltieri Balka Day Gonsalves Grace Krulik Malloy Molix-Bailey Moseley Mowry Myren Price Reynosa Santa Cruz Silbey VielhaberAbout the CoverFractions and decimals and the relationship between fractions and decimals are featured topics in Fourth grade.On the cover,the pitcher is wearing a fraction.It is equ ivalent to 0.5.Have students find the other fraction on the cover that is equivalent to 0.5.Copyright 2009 by The McGraw-Hill Companies,Inc.All rights reserved.Except as permitted under the United States Copyright Act,no part of this publication may be reproduced or distributed in any form or by any means,or stored in a database or retrieval system,without prior permission of the publisher.Send all inquiries to:Macmillan/McGraw-Hill8787 Orion PlaceColumbus,OH 43240-4027ISBN:978-0-02-107481-5MHID:0-02-107481-X Illinois Math Connects,Grade 4Printed in the United States of America.1 2 3 4 5 6 7 8 9 10 058/055 16 15 14 13 12 11 10 09 08 07iiiStart SmartChapter1Use Place Value to Represent Whole Numbers G4-FP8CChapter2Solve Addition and Subtraction ProblemsG4-FP4C,G4-FP8CChapter3 Organize,Display,and Interpret Data G4-FP7CChapter4 Apply Multiplication and Division Facts G4-FP1Chapter5 Describe Algebraic Patterns G4-FP4C,G4-FP1Chapter6 Multiply by One-Digit Numbers G4-FP1Chapter7 Multiply by Two-Digit Numbers G4-FP1Chapter8 Divide by One-Digit Numbers G4-FP8CChapter9Identify and Describe Geometric FiguresG4-FP6C,G4-FP5CChapter10Understand and Develop Spatial ReasoningG4-FP5CChapter11Measure Length,Area,and TemperatureG4-FP3,G4-FP5CChapter12 Measure Capacity,Weight,and Volume G4-FP3,G4-FP5CChapter13 Describe and Compare Fractions G4-FP2,G4-FP8CChapter14 Use Place Value to Represent Decimals G4-FP2,G4-FP8CChapter15 Add and Subtract Decimals G4-FP2,G4-FP8C Looking Ahead to Next Year Problem-Solving Projectsand ConnectionsSee page iv for key.ivThe Curriculum Focal Points identify key mathematical ideas for this grade.They are not discrete topics or a checklist to be mastered;rather,they provide a framework for the majority of instruction at a particular grade level and the foundation for future mathematics study.The complete document may be viewed at www.nctm.org/focalpoints.G4-FP1Number and Operations and Algebra:Developing quick recall of multiplication facts and related division facts and fluency with whole number multiplicationStudents use understandings of multiplication to develop quick recall of the basic multiplication facts and related division facts.They apply their understanding of models for multiplication(i.e.,equal sized groups,arrays,area models,equal intervals on the number line),place value,and properties of operations(in particular,the distributive property)as they develop,discuss,and use efficient,accurate,and generalizable methods to multiply multidigit whole numbers.They select appropriate methods and apply them accurately to estimate products or calculate them mentally,depending on the context and numbers involved.They develop fluency with efficient procedures,including the standard algorithm,for multiplying whole numbers,understand why the procedures work(on the basis of place value and properties of operations),and use them to solve problems.G4-FP2Number and Operations:Developing an understanding of decimals,including the connections between fractions and decimals Students understand decimal notation as an extension of the base-ten system of writing whole numbers that is useful for representing more numbers,including numbers between 0 and 1,between 1 and 2,and so on.Students relate their understanding of fractions to reading and writing decimals that are greater than or less than 1,identifying equivalent decimals,comparing and ordering decimals,and estimating decimal or fractional amounts in problem solving.They connect equivalent fractions and decimals by comparing models to symbols and locating equivalent symbols on the number line.G4-FP3Measurement:Developing an understanding of area and determining the areas of two-dimensional shapesStudents recognize area as an attribute of two-dimensional regions.They learn that they can quantify area by finding the total number of same-sized units of area that cover the shape without gaps or overlaps.They understand that a square that is 1 unit on a side is the standard unit for measuring area.They select appropriate units,strategies(e.g.,decomposing shapes),and tools for solving problems that involve estimating or measuring area.Students connect area measure to the area model that they have used to represent multiplication,and they use this connection to justify the formula for the area of a rectangle.KEYG4-FP1Grade 4 Focal Point 1G4-FP2Grade 4 Focal Point 2G4-FP3Grade 4 Focal Point 3G4-FP4CGrade 4 Focal Point 4ConnectionG4-FP5CGrade 4 Focal Point 5ConnectionG4-FP6CGrade 4 Focal Point 6ConnectionG4-FP7CGrade 4 Focal Point 7ConnectionG4-FP8CGrade 4 Focal Point 8ConnectionvG4-FP4CAlgebra:Students continue identifying,describing,and extending numeri