rationale for third grade instructional guide - lausd. · pdf filerationale for third grade...

Rationale for Third Grade Instructional Guide Organizational Highlights

In Grade Three students deepen their conceptual understanding of place value and the four operations with whole numbers. All of the Number Sense Power Standards are therefore critical as these elements of arithmetic lay the foundation for many future mathematics topics. Students will also estimate, measure, and describe objects in space. They will use patterns to solve problems, represent number relationships, and conduct simple probability experiments.

The mathematics program in the third grade includes the use of manipulatives. All students should have access to concrete objects and/or manipulatives as it enables student to create models which facilitate their understanding of the mathematical concepts being taught. The Lesson Resources in Harcourt Math are identified in the Instructional Guide for each of the content standards. These resources include the use of manipulatives to introduce lessons, math background for teachers, the Problem of the Day, home-school connection activities, and strategies for English learners.

Quarter One

The emphasis during the first quarter of Third Grade is Number Sense. In order to build on the students’ work in second grade, third graders will continue to develop an understanding of place value and comparison of larger numbers, extending into rounding. They will apply this understanding to the operations of addition and subtraction of larger numbers and money amounts. The concept of multiplication will be reviewed and expanded from the end of 2nd grade along with the multiplication facts up to 5. While the 3rd grade measurement and geometry concepts are not difficult in themselves, students can be overwhelmed with too much new information. Therefore, some of these standards are taught each quarter rather than all at the same time. (See page 130 of the Mathematics Framework for California Public Schools)

Quarter Two

Multiplication and division concepts are the focus of this quarter, including the inverse relationship of multiplication and division and the special properties of zero and one. This will build on the students’ work from quarter one. Their work with operations will now include simple multiplication problems with multi-digit numbers by one-digit numbers. Students will also extend their use of numbers into identifying relationships including functional relationships (cost per unit). Measurement and finding perimeter is taught this quarter in order to provide a practical application for students’ work with addition and multiplication.

Quarter Three

Now that 3rd graders have deepened their understanding of number sense, the concept of fractions, equivalency and addition and subtraction of fractions are emphasized in this quarter. The work with multiplication and division will continue and extend to problem solving with money in decimal notation. The students will continue their work in geometry by learning area and volume and attributes of triangles. They will also learn concepts of probability and graphing to record and predict outcomes.

Quarter Four

This quarter provides an opportunity to revisit third grade concepts with which students may have had difficulty. Teachers and coaches can develop instructional plans based on student needs identified in the assessment data. Additional resources such as Marilyn Burns’ material and LUCI investigations can provide a rich experience for students to grasp a deeper understanding of mathematical concepts. Concepts that students will encounter at the beginning of fourth grade such as reading, writing, and rounding large numbers should be emphasized.

LOS ANGELES UNIFIED SCHOOL DISTRICT Third Grade

Mathematics Instructional Guide: Quarter One

NUMBER SENSE INEQUALITIES GEOMETRY Standards: NS1.1 Count, read, and write whole numbers to 10,000. NS1.2 Compare and order whole numbers to 10,000. * NS1.3 Identify the place value for each digit in numbers to 10,000. * NS1.4 Round off numbers to 10,000 to the nearest ten, hundred, and thousand. * NS1.5 Use expanded notation to represent numbers (3,206= 3,000 + 200 + 6). * NS2.1 Find the sum and difference of two whole numbers between 0 and 10,000. * NS 2.2 Memorize to automaticity the multiplication table for numbers between 1 and 10 and 5. NS 2.6 Understand the special properties of 0 and 1 in multiplication and division. * NS 3.3 Solve problems involving addition, subtraction, multiplication, and division of money amounts in decimal notation and multiply and divide money amount in decimal notation by using whole-number multipliers and divisors * AF 1.1 Represent relationships of quantities in the form of mathematical expressions, equations, or inequalities. AF 1.2 Solve problems involving numeric equations or inequalities. AF 1.3 Select appropriate operational and relational symbols to make an expression true. (4___3 = 12) * MG 2.1 Identify, describe, and classify polygons (including pentagons, hexagons, and octagons) MG 2.4 Identify right angles in geometric figures or in appropriate objects and determine whether other angles are greater or less than a right angle. MG 2.5 Identify, describe, and classify common three-dimensional geometric objects (e.g. cube, rectangular solid, prism, pyramid, cone, cylinder). MG 2.6 Identify common solid objects that are components needed to make a more complex solid object. MR 1.0-3.0 Embedded

Dates** Standard # Concepts Harcourt Additional Resources

NS 1.1 NS 1.2 NS 1.3 NS 1.4 NS 1.5

Place value to 10,000; Rounding; Comparing and Ordering Numbers

Lesson Resources 2A-12B Lessons 1.1 – 1.5 Lesson Resources 18A-30B Lesson 2.1 – 2.6

About Teaching Mathematics, Marilyn Burns: • Digit Place, p. 176 • Understanding Place Value, p. 181-182 Place Value Models; Number Line Activities

NS 2.1

Adding and Subtracting Greater Numbers

Lesson Resources 36A-46B: Lessons 3.1-3.6 Lesson Resources 54A-62B: Lessons 4.1 –4.4

About Teaching Mathematics, Marilyn Burns: • Acting Out Add./Subtract. Stories, p. 164 • Number Sums, p.125-132

Key: Power Standard * Assessed Standard Strikethrough: Topic not taught or assessed this quarter ** Dates to be determined at school site

LAUSD Mathematics ProgramInstructional Guide, Grade 3

Quarter One, 2003-2004



NUMBER SENSE INEQUALITIES GEOMETRY Dates** Standard # Concepts Harcourt Additional Resources

AF 1.1 AF 1.2 AF 1.3

Expressions, Equations, Inequalities

Lesson Resources:68AB: Lesson 4.6 Lesson Resources: 84 AB: Lesson 5.3

Patterns, Functions, and Algebra from About Teaching Mathematics, M. Burns pp 112-124

NS 3.3 Adding and Subtracting Money

Lesson Resources 82A-88B: Lessons 5.2 – 5.5

NS 2.2NS 2.6 AF 1.1

Multiplication Concepts and Facts; Zero and One in Multiplication; Missing Factors

Lesson Resources 114J-122B: Lessons 7.1-7.4 Lesson Resources 132A-134B: Lessons 8.1-8.2, 8.4-8.5

The Raccoon Problem and How Many Animals? From 50 Problem-Solving Lessons, M. Burns pp 31-32, pp 47-48 Multiplication Lessons from About Teaching Mathematics, M. Burns pp. 194-203 Lessons for Introducing Multiplication Grade 3 , M. Burns

MG 2.5 MG 2.6 MG 2.4

Three-dimensional Objects Solid Objects Classification of Angles

Lesson Resources 362A-372B Lessons 21.1-21.4

Geoboards; Lessons in Measurement, About Teaching Mathematics, M. Burns pp. 46-58






NUMBER SENSE INEQUALITIES GEOMETRY Dates** Standard # Concepts Harcourt Additional Resources

MG 2.1 Identify Polygons Lesson Resources 380A-380D Lesson 22.1

Geoboards; Lessons in Measurement, About Teaching Mathematics, M. Burns pp. 46-58

A S S E S S M E N TE N R I C H M E N T / R E T E A C H I N G




LOS ANGELES UNIFIED SCHOOL DISThird Grade

Mathematics Instructional Guide: Quart

MULTIPLICATION FACTS AND CONCEPTS FUNCTIONAL RELATIONSHIPSStandards: * NS 2.2 Memorize to automaticity the multiplication table for numbers between 1 and 10. * NS 2.3 Use the inverse relationship of multiplication and division to compute and check results. * NS 2.4 Solve simple problems involving multiplication of multi-digit numbers by one-digit numbers NS 2.6 Understand the special properties of 0 and 1 in multiplication and division. NS 2.8 Solve problems that require two or more of the skills. * AF 1.2 Solve problems involving numeric equations or inequalities. AF 1.4 Express simple unit conversions in symbolic form. AF 1.5 Recognize and use the commutative and associative properties of multiplication. * AF 2.1 Solve simple problems involving a functional relationship between two quantities. AF 2.2 Extend and recognize a linear pattern by its rule. * MG 1.1 Choose the appropriate tools and units (Metric and US) and estimate and measure length, liqu* MG 1.3 Find the perimeter of a polygon with integer sides. MG 1.4 Carry out simple unit conversions within a system of measurement. * MG 2.1 Identify, describe, and classify polygons (including pentagons, hexagons, and octagons) * MG 2.3 Identify attributes of quadrilaterals (parallelogram, rectangle, square)

Dates** Standard # Concepts Harcourt

NS 2.8 MG 1.4

Solving Multi-step Problems/Time

Lesson Resources 94A-100B Lesson 6.1- 6.4

NS 2.2NS 2.6 NS 2.8 AF 1.2 AF 1.5 AF 2.1 AF 2.2

Understand/Practice Multiplication Facts; Zero and One in Multiplication Find the Rule Extend a Pattern



TRICT

er Two

PLANE GEOMETRY MEASUREMENT

(3,671 x 3 = )

id volume, and weight/mass of given objects.

Additional Resources

Multiplication Lessons from About Teaching Mathematics, pp 194–203 Lessons for Introducing Multiplication Grade 3 (by M. Burns) Patterns, functions, and Algebra from About Teaching Mathematics, M. Burns pp 112-124


Quarter Two, 2003-2004


Mathematics Instructional Guide: Quarter Two

MULTIPLICATION FACTS AND CONCEPTS FUNCTIONAL RELATIONSHIPS PLANE GEOMETRY MEASUREMENT Dates** Standard # Concepts Harcourt Additional Resources

NS 2.3 Relate Multiplication and Division; Fact Families


Division Lessons from About Teaching Mathematics pp 215 - 222 Sharing 50 Cents and The Game of Leftovers from 50 Problem-Solving Lessons pp. 49-50, pp. 81-84

NS 2.4 Multi-digitMultiplication

Lesson Resources 290F – 300B Lessons 17.1 – 17.4

Multiplication Lessons from About Teaching Mathematics, pp 194–203

MG 2.1 Polygons Lesson Resources 380A-382B Lesson 22.1

MG 2.3 Quadrilaterals Lesson Resources 402A-404B Lessons 23.3-23.4

MG 1.1MG 1.4 AF 1.4

Measurement; Unit Conversion

Lesson Resources 420A – 450B Lessons 24.1-24.6 Lessons 25.1-25.5

Lessons in Measurement from About Teaching Mathematics by M. Burns pp. 46-58

MG1.3 Perimeter Lesson Resources 456AB Lessons 26.1-26.2




Quarter Two, 2003-2004


Mathematics Instructional Guide: Quarter Three

NUMBER SENSE FUNCTIONAL RELATIONSHIPS GEOMETRY PROBABILITY Standards: * NS 2.4 Solve simple problems involving multiplication of multi-digit numbers by one-digit numbers (3,671 x 3= ____) NS 2.5 Solve division problems in which a multi-digit number is divided evenly by a one-digit number. NS 2.7 Determine the unit cost when given the total cost and number of units. NS 2.8 Solve problems that require two or more number sense skills. * NS 3.1 Compare fractions represented by drawings or concrete materials to show equivalency and to add and subtract simple fractions in context. * NS 3.2 Add and subtract simple fractions * NS 3.3 Solve problems involving addition, subtraction, multiplication, and division of money amounts in decimal notation and multiply and divide money amounts in decimal notation by using whole-number multipliers and divisors * NS 3.4 Know and understand that fractions and decimals are two different representations of the same concept * AF 2.1 Solve simple problems involving a functional relationship between two quantities (e.g. find the total cost of multiple items given the cost per unit) * MG 1.2 Estimate or determine the area and volume of solid figures by covering them with squares or by counting the number of cubes that would fill them. * MG 2.2 Identify attributes of triangles (two equal sides for isosceles, three equal sides for equilateral, right angle for right triangle SDAP 1.1 Identify whether common events are certain, likely, unlikely, or probable. * SDAP 1.2 Record the possible outcomes for a simple event and systematically keep track of the outcomes when the event is repeated many times. * SDAP 1.3 Summarize and display the results of probability experiments in a clear and organized way (e.g. bar graph or a line plot) SDAP 1.4 Use the Results of probability experiments in a clear and organized way (e.g. bar graph or line plot). MR 1.0-3.0 Embedded Dates** Standard # Concepts Harcourt Additional Resources

NS 2.7 NS 2.8 AF 2.1

Find Unit Cost Lesson Resources 224AB Lesson 13.4

SDAP 1.1SDAP 1.2 SDAP 1.3 SDAP 1.4

Identify Events: Certain to Impossible; Record and Display Results of Probability Experiments


Graphing in the Classroom from About Teaching Mathematics, pp75-78

NS 2.4NS 3.3

Multi-digit Multiplication Multiplying Money

Lesson Resources 292A-318B Lessons 17.1 – 18.6

Lessons for Introducing Multiplication Grade 3 by M. Burns



Quarter Three, 2003-2004


Mathematics Instructional Guide: Quarter Three

NUMBER SENSE FUNCTIONAL RELATIONSHIPS GEOMETRY PROBABILITY Dates** Standard # Concepts Harcourt Additional Resources NS 2.5

Division


MG 2.2

Identify Attributes of Triangles


Geoboards

MG 1.2 Area and Volume of Solid Figures


NS 3.1NS 3.2

Fraction Concepts Add and Subtract Fractions

Lesson Resources 480A-492B Lessons 27.1-27.4 Lesson Resources 502A-514B Lessons 28.1-28.5

Fraction Activities from About Teaching Mathematics, M. Burns pp 233-237 Fraction Lessons from 50 Problem Solving Lessons Geoboards, Color Tiles, Cuisenaire Rods, Fraction Tiles, Fraction Circles, Fraction Kit

NS 3.4NS 3.3

Decimals and Fractions Relating Fractions and Decimals to Money


Decimals on a Grid from About Teaching Mathematics, M. Burns pp 240-241




Quarter Three, 2003-2004


Mathematics Instructional Guide: Quarter Four

NUMBER SENSE FUNCTIONAL RELATIONSHIPS GEOMETRY PROBABILITY Standards: * NS 1.3 Identify the place value for each digit in numbers to 10,000. * NS 1.5 Use expanded notation to represent numbers (e.g., 3,206 = 3,000 + 200 + 6 ). * NS 2.3 Use the inverse relationship of multiplication and division to compute and check results. * NS 2.4 Solve simple problems involving multiplication of multi-digit numbers by one-digit numbers (3,671 x 3 = ). * NS 3.2 Add and subtract simple fractions (e.g. determine that 1/8 + 3/8 is the same as 1/2) * NS 3.3 Solve problems involving addition, subtraction, multiplication, and division of money amounts in decimal notation and multiply and divide money amounts in decimal notation by using whole-number multipliers and divisors. * AF 1.1 Represent relationships of quantities in the form of mathematical expressions, equations, or inequalities. * AF 2.1 Solve simple problems involving a functional relationship between two quantities (e.g. find the total cost of multiple items given the cost per unit). * MG 1.2 Estimate and determine the area and volume of solid figures by covering them with squares or by counting the number of cubes that would fill them. * MG 1.3 Find the perimeter of a polygon with integer sides. * MG 2.1 Identify, describe, and classify polygons. * MG 2.2 Identify the attributes of a triangle. * MG 2.3 Identify the attributes of a quadrilateral. * SDAP 1.2 Record the possible outcomes for a simple event and systematically keep track of the outcomes when the event is repeated many times. * SDAP 1.3 Summarize and display the results of probability experiments in a clear and organized way (e.g. bar graph or a line plot) MR 1.0-3.0 Embedded Dates** Standard # Concepts Harcourt Additional Resources

SDAP 1.2 SDAP 1.3

Probability Graphing

Lesson Resources: 236A-260B Lessons 14.1 - 15.6

NS 1.3NS 1.5

Place Value; Expanded Notation

Lesson Resources 2A -12B Lesson Resources 18A-30B

See Additional Resources from Quarters One through Three.

NS 2.3NS 2.4

Relate Multiplication and Division

Lesson Resources 146A-172B

NS 3.2 Add and Subtract Fractions Lesson Resources 502A-514B



Quarter Four, 2003-2004


Mathematics Instructional Guide: Quarter Four

NUMBER SENSE FUNCTIONAL RELATIONSHIPS GEOMETRY PROBABILITY Dates** Standard # Concepts Harcourt Additional Resources

NS 3.3 Solving Problems involving Money and Decimal Notation

Lesson Resources 316 AB Lesson Resources 520A-538B

AF 1.1

Expressions, Equations, Inequalities

Lesson Resources 68AB and 84AB

AF 2.1 Find Unit Cost Lesson Resources 224AB Lesson Resources 316AB Lesson Resources 430A-432B

MG 1.2 Area and Volume of Solid Figures

Lesson Resources 464AB

MG 2.1MG 2.2 MG 2.3

Polygons Attributes of Triangles and Quadrilaterals

Lesson Resources: 382AB Lesson Resources: 396A-409B

A S S E S S M E N TE N R I C H M E N T / R E T R A I N I N G



Quarter Four, 2003-2004

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