Elementary Mathematics Pacing Guide Grade 3

Transcription

1 Elementary Mathematics Pacing Guide Grade 3 FCPS Program of Studies (POS): The state of Virginia provides schools with a standards based curriculum to support student learning. These Standards, Benchmarks, and Indicators (SBIs) are measurable learning goals that are embedded in Fairfax County Public School s Program of Studies. FCPS has ensured that the content in the FCPS Mathematics Program of Studies is organized within and across grade levels to support students mathematical understanding by providing SBIs which provide a context, a bridge or an enhancement to the SBI s. SBIs were also created to be used to differentiate instruction for advanced learners. Elementary Mathematics Instructional Sequence (EMIS): The PreK 12 Mathematics Office designed an Elementary Mathematics Instructional Sequence (EMIS) that is aligned with the new standards. The new instructional sequence provides teachers with the tools needed to offer students the opportunity to access an advanced mathematics curriculum as they develop the cognitive skills to be successful. Advanced mathematics extensions will be available for students as early as kindergarten and will build a strong foundation in mathematics. Tools, such as the Mathematics POS Inventory, the Mathematics Behaviors Rubric, and performance tasks, will be available in ecart to assist with the differentiation process. Assessments, such as unit assessments and standards assessments will be available in Horizon for teachers to use as formative assessments throughout the year. An elearnit course is available to provide more information about the Elementary Mathematics Instructional Sequence. FCPS Pacing Guides: The State of Virginia recognizes five student goals to support the mathematics content. They include: becoming mathematical problem solvers, communicating mathematically, reasoning mathematically, making mathematical connections, and using mathematical representations to model and interpret practical situations. These five goals support students learning of the mathematics content and appear in conjunction with the SBI s in FCPS mathematics pacing guide documents. The FCPS Mathematics office used research based resources and the support from focus groups of FCPS teachers to create instructional units within the mathematics pacing guides. There are nine weeks in each quarter eight weeks are designated for instruction, leaving one week (five days) for teachers to integrate assessment throughout the quarter. Six weeks of instruction are included in quarter four due to SOL testing. There are two or three units per quarter and each unit has a suggested sequence and time table. In general, Number and Number Sense, Computation, and Algebra concepts are taught during the first half of the school year. These concepts are embedded, reinforced, and built upon in the second half of the school year when students are working on Measurement, Geometry, and Probability and Statistics concepts. Advanced Mathematics Pacing Guides: There is no separate pacing guide for Advanced Mathematics. The pacing guide teachers will use to teach Advanced Mathematics is the grade level pacing guide.

2 Elementary Mathematics Pacing Guide Grade 3 This pacing guide contains four tools for teacher use: Unit Overview Chart: This chart provides a year long look at the grade level units to be taught in each quarter. Correlated Standards Chart: This chart shows the correlation of the standards taught within a given unit. Grade level standards are listed as well as correlated above and below grade level standards. Correlated Indicators Chart: This chart provides a more in depth look at the correlations within a given unit. All indicators (essential, expected, and extended) are listed for a given unit. The above grade level indicators are included. This chart should be used to provide differentiation during mathematics instruction. POS Framework Document: This document provides teachers with information to understand the standard. Teacher notes and vocabulary related to each standard are listed. Pacing Guide Features: indicators: Indicators from the VDOE Standards of Learning document. indicators: Indicators added by the FCPS Program of Studies to provide a context, a bridge, or an enhancement to the SBIs. Indicators: Indicators added by the FCPS Program of Studies generally used to differentiate instruction for advanced learners (Honors). Directly Correlated Standards: Standards that build on above and below grade level standards. Indirectly Correlated Standards: Standards that do not directly connect to or build on above and below grade level standards. Indirectly correlated standards are indicated on the pacing guide with the following symbol,. Resources: There are two types of resource materials which can be used for instructional use. They include: 1. ecart Resources These are public domain or FCPS produced resources that can be found in ecart. These resources include lessons and other teacher tools to support EMIS. Search by indicator to locate ecart resources. 2. Print Resources These are resources that have been provided to schools to support instruction. These resources cannot be included in ecart due to copyright laws. A chart listing alignments between print resources and grade level standards may be found in ecart. Alignments between textbook and grade level standards are included in this chart. Complete a grade level search in ecart to locate the print resource alignment.

3 Table of Contents Grade 3 Grade 3 Unit Overview 1 Quarter 1 Units Unit 1: Building Relationships...3 Unit 2: Adding and Subtracting Whole Numbers.6 Unit 3: Fraction Concepts and Computation 9 Quarter 2 Units Unit 4: Multiplication and Division..12 Unit 5: All About Patterns..14 Quarter 3 Units Unit 6: Customary and Metric Measurement.18 Unit 7: Shapes and Figures 21 Unit 8: Measuring Temperature and Money 24 Quarter 4 Units Unit 9: Measuring Time 26 Unit 10: Graphs Galore.28 Unit 11: What are the Chances?...31 Mathematics POS Framework Grade 3.33 Mathematics POS Framework Grade 4.64 *Use the bookmark button to the left of your PDF document to navigate to different parts of the electronic version of the pacing guide.

4 Quarter 1 Grade 3 Unit Overview Unit Name Suggested Time Frame Standard Correlating Standard MTH.G3.1 Read, write, and identify place value of six 1.5 weeks numbers 9,999 digit numerals; round and compare whole or less Unit 1 Building Relationships Unit 2 Adding and Subtracting Whole Numbers Unit 3 Fraction Concepts and Computation 2.5 weeks 4 weeks MTH.G3.4 Estimate solutions to and solve single step and multistep problems involving the sum or difference of two whole numbers, each 9,999 or less, with or without regrouping MTH.G3.3 Name, write, model fractions (including mixed numbers) and compare fractions having like and unlike denominators MTH.G3.7Add and subtract proper fractions having like denominators of 12 or less MTH.G4.1 Identify, compare, and round whole numbers expressed through millions MTH.G4.3 Read, write, represent, identify, round, and compare decimals MTH.G4.4 Estimate sums, differences, products, and quotients of whole numbers and solve single step and multistep problems MTH.G4.2 Compare/order fractions, represent equivalent forms MTH.G4.5 Solve problems involving addition/subtraction of fractions and decimals, and determine common multiples and factors Quarter 2 Unit 4 Multiplication and Division Unit 5 All About Patterns 5.5 weeks 2.5 weeks Assessment: ecart Window 1 MTH.G3.2 Recognize/use inverse relationships to MTH.G4.4 Estimate sums, differences, products, and complete basic fact sentences. quotients of whole numbers and solve single step and MTH.G3.5 Recall the multiplication and division facts multistep problems through the twelves table MTH.G3.6 Represent multiplication and division and solve multiplication problems MTH.G3.19 Recognize, describe, and extend a variety of MTH.G4.15 Recognize, create and extend numerical and patterns geometric patterns MTH.G3.20 Investigate and identify identity and MTH.G4.16 Demonstrate meaning of equality and commutative properties for addition and multiplication investigate associative property for addition and multiplication Assessment: MOY (optional) Page 1

5 Grade 3 Unit Overview Unit Name Suggested Time Frame Standard Correlating Standard MTH.G3.9 Estimate and use U.S. Customary and metric units to measure length, liquid volume, weight/mass, and area and perimeter MTH.G3.10 Measure to determine perimeter and count to determine area Unit 6 Customary & Metric Measurement 4 weeks MTH.G4.6 Estimate and measure weight/mass and identify equivalent measurements between units within U.S. customary/metric systems MTH.G4.7 Estimate and measure length and identify equivalent measurements between units within U.S. customary/metric systems MTH.G4.8.Estimate and measure liquid volume and identify equivalent measurements between units within U.S. customary/metric systems Quarter 3 Unit 7 Shapes and Figures 3 weeks MTH.G3.14 Identify, describe, compare, and contrast attributes of geometric figures (circle, square, rectangle, triangle, cube, rectangular prism, square pyramid, sphere, cone, and cylinder) MTH.G3.15 Identify and draw representations of points, line segments, rays, angles, and lines MTH.G3.16 Identify and describe congruent and noncongruent plane figures There is not a correlated standard in the above grade level. Use an extended indicator at the current grade level to deepen student(s) mathematical knowledge or spend additional time teaching concepts already reviewed. MTH.G4.10 Identify and describe points, lines, line segments, rays, angles, and intersections MTH.G4.11 Investigate congruence and recognize images after transformations MTH.G4.12 Define polygon and identify polygons with 10 or fewer sides Unit 8 Measuring Temperature and Money 1 week MTH.G3.8 Count money, compare values, and make change MTH.G3.13 Read temperature to the nearest degree from a Celsius thermometer and a Fahrenheit thermometer MTH.G4.5 Solve problems involving addition/subtraction of fractions and decimals and determine common multiples and factors Use an extended indicator at the current grade level to deepen student(s) mathematical knowledge or spend additional time teaching concepts already reviewed. Quarter 4 Unit 9 Measuring Time Unit 10 Graphs Galore 1.5 weeks 2.5 weeks Assessment: ecart Window 2 MTH.G3.11 Tell time to the nearest minute, using analog and digital clocks/ Determine elapsed time over a 12 hour period MTH.G3.12 Identify equivalent periods of time, including relationships among days, months, and years, as well as minutes and hours MTH.G4.9 Determine elapsed time in hours and minutes within a 12 hour period Use an extended indicator at the current grade level to deepen student(s) mathematical knowledge or spend additional time teaching concepts already reviewed. MTH.G3.17 Collect/organize data and construct/ interpret MTH.G4.14 Collect, organize, display, and interpret data data in graphs (line plot, a picture graph, or a bar graph) from a variety of graphs Unit 11 What are the Chances? 2 weeks MTH.G3.18 Investigate and describe the concept of probability as chance and list possible results of a given situation Assessment: Grade level SOL MTH.G4.13 Predict likelihood of outcomes and represent probability as a number between 0 and 1, inclusive Page 2

6 Mathematics Grade 3 Unit 1: Building Relationships Suggested Time Frame: 1.5 weeks Correlated Standards Grade Level Below Standards Current Grade Level Standards Grade Level Above Standards MTH.G2.1 The student will a) read, write, and identify the place value of each digit in a three digit numeral, using numeration models; b) round two digit numbers to the nearest ten; and c) compare two whole numbers between 0 and 999, using symbols (>, <, or =) and words (greater than, less than, or equal to). MTH.G3.1 The student will a) read and write six digit numerals and identify the place value and value of each digit; b) round whole numbers, 9,999 or less, to the nearest ten, hundred, and thousand; and c) compare two whole numbers between 0 and 9,999, using symbols (>, <, or =) and words (greater than, less than, or equal to). MTH.G4.1 The student will a) identify orally and in writing the place value for each digit in a whole number expressed through millions; b) compare two whole numbers expressed through millions, using symbols (>, <, or =); and c) round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. Indirect Correlation MTH.G4.3 The student will a) read, write, represent, and identify decimals expressed through thousandths; b) round to the nearest whole number, tenth, and hundredth; c) compare and order decimals; and d) given a model, write the decimal and fraction equivalents. Page 3

7 Mathematics Grade 3 Unit 1: Building Relationships Suggested Time Frame: 1.5 weeks Grade 3 Indicators MTH.G3.1.a.1 Investigate and identify the place and value for each digit in a six digit numeral, using Base 10 manipulatives (e.g., Base 10 blocks). MTH.G3.1.a.2 Use the patterns in the place value system to read and write numbers. MTH.G3.1.a.3 Read six digit numerals orally. Correlated Indicators Grade 4 Indicators MTH.G4.1.a.1 Identify and communicate, both orally and in written form, the place value for each digit in whole numbers expressed through the one millions place. MTH.G4.1.a.2 Read whole numbers through the one millions place that are presented in standard format, and select the matching number in written format. MTH.G3.1.a.4 Write six digit numerals that are stated verbally or written in words. MTH.G3.1.b.1 Round a given whole number, 9,999 or less, to the nearest ten, hundred, and thousand. MTH.G3.1.b.2 Solve problems, using rounding of numbers, 9,999 or less, to the nearest ten, hundred, and thousand. MTH.G3.1.c.1 Determine which of two whole numbers between 0 and 9,999 is greater. MTH.G3.1.c.2 Determine which of two whole numbers between 0 and 9,999 is less. MTH.G3.1.c.3 Compare two whole numbers between 0 and 9,999, using the symbols >, <, or =. MTH.G3.1.c.4 Use the terms greater than, less than, and equal to when comparing two whole numbers. MTH.G3.1.a.5 Represent whole numbers on an open number line. MTH.G3.1.c.5 Order a group of no more than six whole numbers between 0 and MTH.G4.1.a.3 Write whole numbers through the one millions place in standard format when the numbers are presented orally or in written format. MTH.G4.1.b.1 Identify and use the symbols for greater than, less than, and equal to. MTH.G4.1.b.2 Compare two whole numbers expressed through the one millions, using symbols >, <, or =. MTH.G4.1.c.1 Round whole numbers expressed through the one millions place to the nearest thousand, ten thousand, and hundred thousand place. MTH.G4.3.a.1 Investigate the ten to one place value relationship for decimals through thousandths, using Base 10 manipulatives (e.g., place value mats/charts, decimal squares, Base 10 blocks, money). MTH.G4.3.a.2 Represent and identify decimals expressed through thousandths, using Base 10 manipulatives, pictorial representations, and numerical symbols (e.g., relate the appropriate drawing to 0.05). MTH.G4.3.a.3 Identify and communicate, both orally and in written form, the position and value of a decimal through thousandths. For example, in 0.385, the 8 is in the hundredths place and has a value of MTH.G4.3.a.4 Read and write decimals expressed through thousandths, using Base 10 manipulatives, drawings, and numerical symbols. Page 4

8 MTH.G4.3.b.1 Round decimals to the nearest whole number, tenth, and hundredth. MTH.G4.3.c.1 Compare the value of two decimals, using the symbols <, >, =. MTH.G4.3.c.2 Order a set of decimals from least to greatest or greatest to least. MTH.G4.3.d.1 Represent fractions for halves, fourths, fifths, and tenths as decimals through hundredths, using concrete objects (e.g., demonstrate the relationship between the fraction and its decimal equivalent 0.25). MTH.G4.3.d.2 Relate fractions to decimals, using concrete objects (e.g., 10 by 10 grids, meter sticks, number lines, decimal squares, decimal circles, money [coins]). MTH.G4.3.d.3 Write the decimal and fraction equivalent for a given model (e.g., = 0.25 or 0.25 = ). MTH.G4.1.a.4 Represent whole numbers on a number line. MTH.G4.3.a.5 Represent decimal numbers on a number line. MTH.G3.1.a.6 Use and represent numbers through hundred thousands in various contexts, including estimation of relative sizes of amounts or distances (e.g., $385,204 might buy a small house in Northern Virginia). MTHG4.3.a.6 Use and represent numbers through millions in various contexts, including estimation of relative sizes of amounts or distances (e.g., 310,989,822 is the population of the United States of America). MTH.G3.1.a.7 Explore other bases such as base 5 and base 8. MTH.G3.1.b.3 Use strategies to estimate quantities (i.e., the number of items in a collection). Page 5

9 Mathematics Grade 3 Unit 2: Adding and Subtracting Whole Numbers Suggested Time Frame: 2.5 weeks Correlated Standards Grade Level Below Standards Current Grade Level Standards Grade Level Above Standards MTH.G2.5 The student will recall addition facts with sums to 20 or less and the corresponding subtraction facts. MTH.G2.6 The student, given two whole numbers whose sum is 99 or less, will a) estimate the sum; and b) find the sum, using various methods of calculation. MTH.G2.7 The student, given two whole numbers, each of which is 99 or less, will a) estimate the difference; and b) find the difference, using various methods of calculation. MTH.G2.9 The student will recognize and describe the related facts that represent and describe the inverse relationship between addition and subtraction. MTH.G2.21 The student will solve problems by completing numerical sentences involving the basic facts for addition and subtraction. The student will create story problems, using the numerical sentences. Indirect Correlation MTH.G3.4 The student will estimate solutions to and solve single step and multistep problems involving the sum or difference of two whole numbers, each 9,999 or less, with or without regrouping. MTH.G4.4 The student will a) estimate sums, differences, products, and quotients of whole numbers; b) add, subtract, and multiply whole numbers; c) divide whole numbers, finding quotients with and without remainders; and d) solve single step and multistep addition, subtraction, and multiplication problems with whole numbers. *This standard is also referenced in unit 4. Page 6

10 Mathematics Grade 3 Unit 2: Adding and Subtracting Whole Numbers Suggested Time Frame: 2.5 weeks Grade 3 Indicators MTH.G3.4.a.1 Determine whether an estimate or an exact answer is an appropriate solution for practical addition and subtraction problem situations involving single step and multi step problems. MTH.G3.4.a.2 Determine whether to add or subtract in practical problem situations. MTH.G3.4.a.3 Estimate the sum or difference of two whole numbers, each 9,999 or less, when an exact answer is not required. Correlated Indicators Grade 4 Indicators MTH.G4.4.a.1 Estimate whole number sums, differences, products, and quotients. MTH.G4.4.a.2 Refine estimates by adjusting the final amount, using terms such as closer to, between, and a little more than. MTH.G4.4.b.1 Determine the sum or difference of two whole numbers, each 999,999 or less, in vertical and horizontal form with or without regrouping, using paper and pencil, and using a calculator. MTH.G3.4.a.4 Add or subtract two whole numbers, each 9,999 or less. MTH.G3.4.a.5 Solve practical problems involving the sum of two whole numbers, each 9,999 or less, with or without regrouping, using calculators, paper and pencil, or mental computation in practical problem situations. MTH.G3.4.a.6 Solve practical problems involving the difference of two whole numbers, each 9,999 or less, with or without regrouping, using calculators, paper and pencil, or mental computation in practical problem situations. MTH.G3.4.a.7 Solve single step and multi step problems involving the sum or difference of two whole numbers, each 9,999 or less, with or without regrouping. MTH.G3.4.a.8 Estimate and add three or more addends (two and three digit numbers). MTH.G3.4.a.9 Evaluate alternative addition and subtraction algorithms used in other countries for efficiency and accuracy. MTH.G4.4.b.2 Estimate and find the product of two whole numbers when one factor has two digits or fewer and the other factor has three digits or fewer, using paper and pencil and calculators. MTH.G4.4.c.1 Estimate and find the quotient of two whole numbers, given a one digit divisor and a two or three digit dividend. MTH.G4.4.d.1 Solve single step and multistep addition, subtraction, and multiplication problems using whole number operations. MTH.G4.4.d.2 Verify the reasonableness of sums, differences, products, and quotients of whole numbers using estimation. MTH.G4.4.c.2 Interpret the remainder in problem solving settings. MTH.G4.4.d.3 Solve single step and multistep division problems using whole number operations. MTH.G4.4.d.4 Evaluate the traditional multiplication and division algorithms and invented algorithms used by peers for efficiency and accuracy. MTH.G3.4.a.10 Use given information to create story problems involving whole numbers. Explain solution strategies. Page 7

11 Page 8

12 Mathematics Grade 3 Unit 3: Fraction Concepts and Computation Suggested Time Frame: 4 weeks Correlated Standards Grade Level Below Standards Current Grade Level Standards Grade Level Above Standards MTH.G2.3 The student will a) identify the parts of a set and/or region that represent fractions for halves, thirds, fourths, sixths, eighths, and tenths; b) write the fractions; and c) compare the unit fractions for halves, thirds, fourths, sixths, eighths, and tenths. No correlated standard. Indirect Correlation MTH.G3.3 The student will a) name and write fractions (including mixed numbers) represented by a model; b) model fractions (including mixed numbers) and write the fractions' names; and c) compare fractions having like and unlike denominators, using words and symbols (>, <, or =). MTH.G3.7 The student will add and subtract proper fractions having like denominators of 12 or less. MTH.G4.2 The student will a) compare and order fractions and mixed numbers; b) represent equivalent fractions; and c) identify the division statement that represents a fraction. MTH.G4.5 The student will a) determine common multiples and factors, including least common multiple and greatest common factor; b) add and subtract fractions having like and unlike denominators that are limited to 2, 3, 4, 5, 6, 8, 10, and 12, and simplify the resulting fractions, using common multiples and factors; Page 9

13 Mathematics Grade 3 Unit 3: Fraction Concepts and Computation Suggested Time Frame: 4 weeks Grade 3 Indicators MTH.G3.3.a.1 Name and write fractions (including mixed numbers) represented by a model to include halves, thirds, fourths, eighths, tenths, and twelfths. MTH.G3.3.b.1 Use concrete materials and pictures to model at least halves, thirds, fourths, eighths, tenths, and twelfths. MTH.G3.3.c.1 Compare fractions using the terms greater than, less than, or equal to and the symbols (<, >, and =). Comparisons are made between fractions with like denominators, using models, concrete materials and pictures. MTH.G3.3.c.2 Compare fractions using the terms greater than, less than, or equal to and the symbols (<, >, and =). Comparisons are made between fractions with unlike denominators, using models, concrete materials and pictures. Correlated Indicators Grade 4 Indicators MTH.G4.2.a.1 Compare and order fractions having denominators of 12 or less, using manipulative models and drawings, such as region/area models. MTH.G4.2.a.2 Compare and order fractions with like denominators by comparing number of parts (numerators) (e.g., < ). MTH.G4.2.a.3 Compare and order fractions with like numerators and unlike denominators by comparing the size of the parts (e.g., < ). MTH.G4.2.a.4 Compare and order fractions having unlike denominators of 12 or less by comparing the fractions to benchmarks (e.g., 0,, or 1) to determine their relationships to the benchmarks or by finding a common denominator. MTH.G4.2.a.5 Compare and order mixed numbers having denominators of 12 or less. MTH.G3.7.a.1 Demonstrate a fractional part of a whole, using region/area models (e.g., pie pieces, pattern blocks, geoboards, drawings); set models (e.g., chips, counters, cubes, drawings); and length/measurement models (e.g., nonstandard units such as rods, connecting cubes and drawings). MTH.G3.7.a.2 Name and write fractions and mixed numbers represented by drawings or concrete materials. MTH.G3.7.a.3 Represent a given fraction or mixed number, using concrete materials, pictures, and symbols. For example, write the symbol for one fourth and represent it with concrete materials and/or pictures. MTH.G3.7.a.4 Add and subtract with proper fractions having like denominators of 12 or less, using concrete materials and pictorial models representing area/regions (circles, squares, and rectangles), length/measurements (fraction bars and strips), and sets (counters). MTH.G4.2.a.6 Use the symbols >, <, and = to compare the numerical value of fractions and mixed numbers having denominators of 12 or less. MTH.G4.2.b.1 Represent equivalent fractions through twelfths, using region/area models, set models, and measurement models. MTH.G4.2.c.1 Identify the division statement that represents a fraction (e.g., means the same as 3 divided by 5). MTH.G4.5.a.1 Find common multiples and common factors of numbers. MTH.G4.5.a.2 Determine the least common multiple and greatest common factor of numbers. MTH.G4.5.b.1 Use least common multiple and/or greatest common factor to find a common denominator for fractions. MTH.G4.5.b.2 Add and subtract with fractions having like denominators whose denominators are limited to 2, 3, 4, 5, 6, 8, 10, and 12, and simplify the Page 10

14 resulting fraction using common multiples and factors. MTH.G4.5.b.3 Add and subtract with fractions having unlike denominators whose denominators are limited to 2, 3, 4, 5, 6, 8, 10, and 12, and simplify the resulting fraction using common multiples and factors. MTH.G4.5.b.4 Solve problems that involve adding and subtracting with fractions having like and unlike denominators whose denominators are limited to 2, 3, 4, 5, 6, 8, 10, and 12, and simplify the resulting fraction using common multiples and factors. MTH.G3.3.b.2 Generate equivalent expressions for the same quantity [e.g., one case of cola = 24 cans = 2 (12 packs) = 4 (6 packs) = 12 (pairs) = 3 (8 packs)]. MTH.G3.3.c.3 Use partitioning to determine "how much more" when comparing fractions. MTH.G3.7.a.5 Create and solve word problems involving adding and subtracting fractions having like denominators. MTH.G4.5.b.5 Estimate the sum and difference of fractions with like and unlike denominators which are limited to 2, 3, 4, 5, 6, 8, 10, and 12. MTH.G4.2.a.7 Use partitioning to determine "how much more" when comparing fractions. MTH.G4.2.b.2 Generate equivalent expressions for the same quantity [e.g., 1 case of cola = 24 cans = 2 (12 packs) = 4 (6 packs) = 3 (8 packs)]. MTH.G4.5.b.6 Estimate, add, and subtract mixed numbers with like and unlike denominators limited to 2, 3, 4, 5, 6, 8, 10, 12. MTH.G3.7.a.6 Add and subtract with proper fractions having unlike denominators whose denominators are limited to 2, 4, 8 or 2, 3, 6, 12. Page 11

15 Mathematics Grade 3 Unit 4: Multiplication and Division Suggested Time Frame: 5.5 weeks Correlated Standards Grade Level Below Standards Current Grade Level Standards Grade Level Above Standards No correlated standard. MTH.G3.2 The student will recognize and use the inverse relationships between addition/subtraction and multiplication/division to complete basic fact sentences. The student will use these relationships to solve problems. MTH.G3.5 The student will recall multiplication facts through the twelve s table, and the corresponding division facts. MTH.G3.6 The student will represent multiplication and division, using area, set, and number line models, and create and solve problems that involve multiplication of two whole numbers, one factor 99 or less and the second factor 5 or less. MTH.G4.4 The student will a) estimate sums, differences, products, and quotients of whole numbers; b) add, subtract, and multiply whole numbers; c) divide whole numbers, finding quotients with and without remainders; and d) solve single step and multistep addition, subtraction, and multiplication problems with whole numbers. *This standard is also referenced in unit 2. Indirect Correlation Page 12

16 Mathematics Grade 3 Unit 4: Multiplication and Division Suggested Time Frame: 5.5 weeks Grade 3 Indicators MTH.G3.2.a.1 Use the inverse relationships between addition/subtraction and multiplication/division to solve related basic fact sentences. For example, = 8 and 8 3 = ; 4 x 3 = 12 and 12 4 =. MTH.G3.2.a.2 Write three related basic fact sentences when given one basic fact sentence for addition/subtraction. For example, given = 8, solve the related facts + 5 = 8, 8 = 5, and 8 5 =. MTH.G3.2.a.3 Write three related basic fact sentences when given one basic fact sentence for multiplication/division. For example, given 3 x 2 = 6, solve the related facts x 3 = 6, 6 3 =, and 6 = 3. MTH.G3.5.a.1 Recall and state the multiplication and division facts through the twelve s table. MTH.G3.5.a.2 Recall and write the multiplication and division facts through the twelve s table. MTH.G3.6.a.1 Model multiplication, using area, set, and number line models. Correlated Indicators Grade 4 Indicators MTH.G4.4.a.1 Estimate whole number sums, differences, products, and quotients. MTH.G4.4.a.2 Refine estimates by adjusting the final amount, using terms such as closer to, between, and a little more than. MTH.G4.4.b.1 Determine the sum or difference of two whole numbers, each 999,999 or less, in vertical and horizontal form with or without regrouping, using paper and pencil, and using a calculator. MTH.G4.4.b.2 Estimate and find the product of two whole numbers when one factor has two digits or fewer and the other factor has three digits or fewer, using paper and pencil and calculators. MTH.G4.4.c.1 Estimate and find the quotient of two whole numbers, given a one digit divisor and a two or three digit dividend. MTH.G4.4.d.1 Solve single step and multistep addition, subtraction, and multiplication problems using whole number operations. MTH.G3.6.a.2 Model division, using area, set, and number line models. MTH.G3.6.a.3 Solve multiplication problems, using the multiplication algorithm, where one factor is 99 or less and the second factor is 5 or less. MTH.G3.6.a.4 Create and solve word problems involving multiplication where one factor is 99 or less and the second factor is 5 or less. MTH.G3.6.a.5 Estimate the product of two whole numbers, where one factor is 99 or less and the second factor is 5 or less. MTH.G3.6.a.6 Evaluate the traditional multiplication algorithms and invented algorithms used by peers for efficiency and accuracy. MTH.G4.4.d.2 Verify the reasonableness of sums, differences, products, and quotients of whole numbers using estimation. MTH.G4.4.c.2 Interpret the remainder in problem solving settings. MTH.G4.4.d.3 Solve single step and multistep division problems using whole number operations. MTH.G4.4.d.4 Evaluate the traditional multiplication and division algorithms and invented algorithms used by peers for efficiency and accuracy. Page 13

17 Mathematics Grade 3 Unit 5: All About Patterns Suggested Time Frame: 2.5 weeks Correlated Standards Grade Level Below Standards Current Grade Level Standards Grade Level Above Standards MTH.G2.20 The student will identify, create, and extend a wide variety of patterns. MTH.G3.19 The student will recognize and describe a variety of patterns formed using numbers, tables, and pictures, and extend the patterns, using the same or different forms. MTH.G4.15 The student will recognize, create, and extend numerical and geometric patterns. MTH.G2.22 The student will demonstrate an understanding of equality by recognizing that the symbol = in an equation indicates equivalent quantities and the symbol indicates that quantities are not equivalent. Indirect Correlation MTH.G3.20 The student will a) investigate the identity and the commutative properties for addition and multiplication; b) identify examples of the identity and commutative properties for addition and multiplication; and c) write number sentences to represent equivalent and nonequivalent mathematical relationships. MTH.G4.16 The student will a) recognize and demonstrate the meaning of equality in an equation; and b) investigate and describe the associative property for addition and multiplication. Page 14

18 Mathematics Grade 3 Unit 5: All About Patterns Suggested Time Frame: 2.5 weeks Grade 3 Indicators MTH.G3.19.a.1 Recognize repeating and growing numeric and geometric patterns (e.g., skip counting, addition tables, and multiplication tables). Correlated Indicators Grade 4 Indicators MTH.G4.15.a.1 Describe geometric and numerical patterns, using tables, symbols, or words. MTH.G3.19.a.2 Describe repeating and growing numeric and geometric patterns formed using numbers, tables, and/or pictures, using the same or different forms. MTH.G3.19.a.3 Extend repeating and growing patterns of numbers or figures using concrete objects, numbers, tables, and/or pictures. MTH.G3.20.a.1 Investigate the identity property for addition and determine that when the number zero is added to another number or another number is added to the number zero, that number remains unchanged. Examples of the identity property for addition are = 2; = 5. MTH.G3.20.a.2 Investigate the identity property for multiplication and determine that when the number one is multiplied by another number or another number is multiplied by the number one, that number remains unchanged. Examples of the identity property for multiplication are 1 x 3 = 3; 6 x 1 = 6. MTH.G3.20.a.3 Recognize that the commutative property for addition is an order property. Changing the order of the addends does not change the sum (5 + 4 = 9 and = 9). MTH.G3.20.a.4 Recognize that the commutative property for multiplication is an order property. Changing the order of the factors does not change the product (2 3 = 3 2). MTH.G4.15.a.2 Create geometric and numerical patterns, using concrete materials, number lines, tables, and words. MTH.G4.15.a.3 Extend geometric and numerical patterns, using concrete materials, number lines, tables, and words. MTH.G4.16.a.1 Recognize and demonstrate that the equal sign (=) relates equivalent quantities in an equation. MTH.G4.16.a.2 Write an equation to represent equivalent mathematical relationships (e.g., 4 3 = 2 6). MTH.G4.16.a.3 Recognize and demonstrate appropriate use of the equal sign in an equation. MTH.G4.16.b.1 Investigate and describe the associative property for addition as (6 + 2) + 3 = 6 + (2 + 3). MTH.G4.16.b.2 Investigate and describe the associative property for multiplication as (3 x 2) x 4 = 3 x (2 x 4). MTH.G3.20.b.1 Identify examples of the identity and commutative properties for addition and multiplication. MTH.G3.20.c.1 Write number sentences to represent equivalent mathematical relationships (e.g., 4 x 3 = 14 2). Page 15

19 MTH.G3.20.c.2 Write number sentences to represent nonequivalent mathematical relationships (e.g., 4 x ). MTH.G3.19.a.4 Create patterns using numbers, tables, and/or pictures. MTH.G3.19.a.5 Recognize and describe even and odd patterns of multiplication (e.g., odd x odd = odd; even x odd = even; even x even = even). MTH.G3.19.a.6 Find simple addition, subtraction, and multiplication function rules (e.g., multiply by 5) given input and output data (e.g., input is 5, output is 25; input is 7, output is 35). MTH.G4.15.a.4 Find function rules using a combination of two of the four operations (e.g., times 2, add 1) given input and output data (e.g., input 5, output 11; input 7, output 15). Page 16

20 Page 17

21 Mathematics Grade 3 Unit 6: Customary and Metric Measurement Suggested Time Frame: 4 weeks Correlated Standards Grade Level Below Standards Current Grade Level Standards Grade Level Above Standards MTH.G3.9 The student will estimate and use U.S. Customary and metric units to measure a) length to the nearest inch, inch, foot, yard, MTH.G2.11 The student will estimate and measure a) length to the nearest centimeter and inch; b) weight/mass of objects in pounds/ounces and kilograms/grams, using a scale; and c) liquid volume in cups, pints, quarts, gallons, and liters. centimeter, and meter; b) liquid volume in cups, pints, quarts, gallons, and liters; c) weight/mass in ounces, pounds, grams, and kilograms; and d) area and perimeter. MTH.G4.6 The student will a) estimate and measure weight/mass and describe the results in U.S. Customary and metric units as appropriate; and b) identify equivalent measurements between units within the U.S. Customary system (ounces, pounds, and tons) and between units within the metric system (grams and kilograms). MTH.G4.7 The student will a) estimate and measure length, and describe the result in both metric and U.S. Customary units; and b) identify equivalent measurements between units within the U.S. Customary system (inches and feet; feet and yards; inches and yards; yards and miles) and between units within the metric system (millimeters and centimeters; centimeters and meters; and millimeters and meters). No correlated standard. Indirect Correlation MTH.G3.10 The student will a) measure the distance around a polygon in order to determine perimeter; and b) count the number of square units needed to cover a given surface in order to determine area. MTH.G4.8 The student will a) estimate and measure liquid volume and describe the results in U.S. Customary units; and b) identify equivalent measurements between units within the U.S. Customary system (cups, pints, quarts, and gallons). There is not a correlated standard in the above grade level. Use an extended indicator at the current grade level to deepen student(s) mathematical knowledge or spend additional time teaching concepts already reviewed. Page 18

22 Mathematics Grade 3 Unit 6: Customary and Metric Measurement Suggested Time Frame: 4 weeks Grade 3 Indicators MTH.G3.9.a.1 Estimate and use U.S. Customary and metric units to measure lengths of objects to the nearest of an inch, inch, foot, yard, centimeter, and meter. Correlated Indicators Grade 4 Indicators MTH.G4.6.a.1 Determine an appropriate unit of measure (e.g., ounce, pound, ton, gram, kilogram) to use when measuring everyday objects in both metric and U.S. Customary units. MTH.G3.9.b.1 Estimate and use U.S. Customary and metric units to measure liquid volume to the nearest cup, pint, quart, gallon, and liter. MTH.G3.9.c.1 Estimate and use U.S. Customary and metric units to measure the weight/mass of objects to the nearest ounce, pound, gram, and kilogram. MTH.G3.9.d.1 Estimate and use U.S. Customary and metric units to measure area and perimeter. MTH.G3.10.a.1 Measure each side of a variety of polygons and add the measures of the sides to determine the perimeter of each polygon. MTH.G3.10.b.1 Determine the area of a given surface by estimating and then counting the number of square units needed to cover the surface. MTH.G3.9.a.2 Identify objects whose lengths are greater than or less than a meter. MTH.G3.9.d.2 Find perimeter and area in problem solving settings. MTH.G4.6.a.2 Estimate and measure objects in both metric and U.S. Customary units (e.g., ounce, pound, ton, gram, or kilogram) to the nearest appropriate measure, using a variety of measuring instruments. MTH.G4.6.a.3 Record the mass of an object including the appropriate unit of measure (e.g., 24 grams). MTH.G4.6.b.1 Identify equivalent measurements between units within the U.S. Customary system (ounces, pounds, and tons). MTH.G4.6.b.2 Identify equivalent measurements between units within the metric system (grams and kilograms). MTH.G4.7.a.1 Determine an appropriate unit of measure (e.g., inch, foot, yard, mile, millimeter, centimeter, and meter) to use when measuring everyday objects in both metric and U.S. Customary units. MTH.G4.7.a.2 Estimate the length of everyday objects (e.g., books, windows, tables) in both metric and U.S. Customary units of measure. MTH.G4.7.a.3 Measure the lengths of objects in both metric and U.S. Customary units, measuring to the nearest inch (,, ), foot, yard, mile, millimeter, centimeter, or meter, and record the length including the appropriate unit of measure (e.g., 24 inches). MTH.G4.7.a.4Compare estimates of the length of objects with the actual measurement of the length of objects. MTH.G4.7.b.1 Identify equivalent measurements between units within the U.S. Customary system (inches and feet; feet and yards; inches and yards; yards and miles) and between units within the metric system (millimeters and Page 19

23 centimeters; centimeters and meters; and millimeters and meters). MTH.G4.8.a.1 Determine an appropriate unit of measure (cups, pints, quarts, gallons) to use when measuring liquid volume in U.S. Customary units. MTH.G4.8.a.2 Estimate the liquid volume of containers in U.S. Customary units of measure to the nearest cup, pint, quart, and gallon. MTH.G4.8.a.3 Measure the liquid volume of everyday objects in U.S. Customary units, including cups, pints, quarts, and gallons, and record the volume including the appropriate unit of measure (e.g., 24 gallons). MTH.G4.8.b.1 Identify equivalent measures of volume between units within the U.S. Customary system (cups, pints, quarts, and gallons). MTH.G3.9.a.3 Identify personal benchmarks for a meter. MTH.G4.8.a.4 Explore volume using nonstandard units. Page 20

24 Mathematics Grade 3 Unit 7: Shapes and Figures Suggested Time Frame: 3 weeks Correlated Standards Grade Level Below Standards Current Grade Level Standards Grade Level Above Standards MTH.G3.14 The student will MTH.G4.12 The student will identify, describe, compare, and contrast a) define polygon; and characteristics of plane and solid geometric figures b) identify polygons with 10 or fewer sides. (circle, square, rectangle, triangle, cube, rectangular prism, square pyramid, sphere, cone, and cylinder) by identifying relevant characteristics, including the number of angles, vertices, and edges, and the number and shape of faces, using concrete models. MTH.G2.15 The student will a) draw a line of symmetry in a figure; and b) identify and create figures with at least one line of symmetry. MTH.G2.16 The student will identify, describe, compare, and contrast plane and solid geometric figures (circle/sphere, square/cube, and rectangle/rectangular prism). No correlated standard. No correlated standard. Indirect Correlation MTH.G3.15 The student will identify and draw representations of points, line segments, rays, angles, and lines. MTH.G3.16 The student will identify and describe congruent and noncongruent plane figures. MTH.G4.10 The student will a) identify and describe representations of points, lines, line segments, rays, and angles, including endpoints and vertices; and b) identify representations of lines that illustrate intersection, parallelism, and perpendicularity. MTH.G4.11 The student will a) investigate congruence of plane figures after geometric transformations, such as reflection, translation, and rotation, using mirrors, paper folding, and tracing; and b) recognize the images of figures resulting from geometric transformations, such as translation, reflection, and rotation. Page 21

25 Mathematics Grade 3 Unit 7: Shapes and Figures Suggested Time Frame: 3 weeks Grade 3 Indicators MTH.G3.14.a.1 Identify models and pictures of plane geometric figures (circle, square, rectangle, and triangle) and solid geometric figures (cube, rectangular prism, square pyramid, sphere, cone, and cylinder) by name. MTH.G3.14.a.2 Identify and describe plane geometric figures by counting the number of sides and angles. MTH.G3.14.a.3 Identify and describe solid geometric figures by counting the number of angles, vertices, edges, and by the number and shape of faces. MTH.G3.14.a.4 Identify characteristics of solid geometric figures (cylinder, cone, cube, square pyramid, and rectangular prism). MTH.G3.14.a.5 Compare and contrast characteristics of plane and solid geometric figures (e.g., circle/sphere, square/cube, triangle/square pyramid, and rectangle/rectangular prism), by counting the number of sides, angles, vertices, edges, and the number and shape of faces. MTH.G3.14.a.6 Compare and contrast characteristics of solid geometric figures (i.e., cube, rectangular prism, square pyramid, sphere, cylinder, and cone) to similar objects in everyday life (e.g., a party hat is like a cone). Correlated Indicators Grade 4 Indicators MTH.G4.12.a.1 Define and identify properties of polygons with 10 or fewer sides. MTH.G4.12.b.1 Identify polygons by name with 10 or fewer sides in multiple orientations (rotations, reflections, and translations of the polygons). MTH.G4.10.a.1 Identify and describe representations of points, lines, line segments, rays, and angles, including endpoints and vertices. MTH.G4.10.b.1 Understand that lines in a plane can intersect or are parallel. Perpendicularity is a special case of intersection. MTH.G4.10.b.2 Identify practical situations that illustrate parallel, intersecting, and perpendicular lines. MTH.G4.11.a.1 Recognize the congruence of plane figures resulting from geometric transformations such as translation, reflection, and rotation, using mirrors, paper folding and tracing. MTH.G4.11.b.1 Recognize the images of figures resulting from geometric transformations such as translation, reflection, or rotation. MTH.G3.15.a.1 Identify examples of points, line segments, rays, angles, and lines. MTH.G3.15.a.2 Draw representations of points, line segments, rays, angles, and lines, using a ruler or straightedge. MTH.G4.12.a.2 Identify a figure as open or closed and identify plane figures as polygons or nonpolygons. MTH.G4.11.b.2 Build tessellations with congruent shapes using transformations. MTH.G3.16.a.1 Identify examples of congruent and noncongruent figures. Verify their congruence by laying one on top of the other using drawings or models. MTH.G3.16.a.2 Determine and explain why plane figures are congruent or noncongruent, using tracing procedures. Page 22

26 MTH.G3.14.a.7 Construct solid shapes (cube, rectangular prism, cone, and cylinder) using concrete materials (e.g., straws, clay). MTH.G3.15.a.3 Compare and contrast points, line segments, rays, and angles. MTH.G4.10.a.2 Compare and contrast points, line segments, rays, and angles including endpoints and vertices. MTH.G4.10.a.3 Sort angles and describe sorting rule. Page 23

27 Mathematics Grade 3 Unit 8: Measuring Temperature and Money Suggested Time Frame: 1 week Correlated Standards Grade Level Below Standards Current Grade Level Standards Grade Level Above Standards MTH.G2.10 The student will a) count and compare a collection of pennies, nickels, dimes, and quarters whose total value is $2.00 or less; and b) correctly use the cent symbol ( ), dollar symbol ($), and decimal point (.). MTH.G3.8 The student will determine, by counting, the value of a collection of bills and coins whose total value is $5.00 or less, compare the value of the bills and coins, and make change. MTH.G4.5 The student will c) add and subtract with decimals; and d) solve single step and multistep practical problems involving addition and subtraction with fractions and with decimals. MTH.G2.14 The student will read the temperature on a Celsius and/or Fahrenheit thermometer to the nearest 10 degrees. Indirect Correlation MTH.G3.13 The student will read temperature to the nearest degree from a Celsius thermometer and a Fahrenheit thermometer. Real thermometers and physical models of thermometers will be used. There is not a correlated standard. Use an extended indicator at the current grade level to deepen student(s) mathematical knowledge, or spend additional time reviewing concepts already taught. Page 24

28 Mathematics Grade 3 Unit 8: Measuring Temperature and Money Suggested Time Frame: 1 week Grade 3 Indicators MTH.G3.8.a.1 Count the value of collections of coins and bills up to $5.00. MTH.G3.8.a.2 Compare the values of two sets of coins or bills, up to $5.00, using the terms greater than, less than, and equal to. MTH.G3.8.a.3 Make change from $5.00 or less. MTH.G3.13.a.1 Read temperature to the nearest degree from real Celsius and Fahrenheit thermometers and from physical models (including pictorial representations) of such thermometers. Correlated Indicators Grade 4 Indicators MTH.G4.5.c.1 Add and subtract with decimals through thousandths, using concrete materials, pictorial representations, and paper and pencil. MTH.G4.5.d.1 Solve single step and multistep problems that involve adding and subtracting with fractions and decimals through thousandths. MTH.G4.5.c.2.Estimate the sum and difference of decimals to thousandths by using models, pictorial representations, and paper and pencil MTH.G3.8.a.4 Count the value of collections of coins and bills up to $ MTH.G3.8.a.5 Find and record a variety of ways to show a given amount of money ($10.00 or less). MTH.G3.8.a.6 Compare the values of two sets of coins or bills, up to $10.00, using the terms greater than, less than, and equal to. MTH.G3.8.a.7 Make change from $10.00 or less. MTH.G3.8.a.8 Create and solve single step and multistep problems using addition, subtraction, multiplication, and/or division with amounts of money. MTH.G4.5.d.2 Use given information to create story problems with fractions and with decimals. Explain solution strategies. Page 25