3rd Grade Operations and Algebraic Thinking Interpret the products of whole numbers as repeated addition up to 100 EL 1 (3.OA.1) (3.2.2) SCORE Skill Level Description Sample Tasks 4.0 In addition to Score 3.0, in-­‐depth inferences and applications that go beyond what was taught. 3.5 In addition to score 3.0 performance, in-­‐depth inferences and applications with partial success. The student: 3.OA.1 /3.2.2 Interprets and explains the products of whole numbers as repeated addition up to 100. The student exhibits no major errors or omissions. 3.0 2.5 2.0 1.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content There are no major errors or omissions regarding the simpler details and processes as the student: • Recognizes or recalls specific terminology, such as: o repeated addition, array, multiplication, factor, groups, product • Performs basic processes, such as: o grouping manipulatives or making an array. However, the student exhibits major errors or omissions regarding the more complex ideas and processes. Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content 5 X 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 X 7. ( 7 + 7 + 7 + 7 + 7 = 5 X 7 = 35 ) Student solves problems involving repeated addition using manipulatives. For example, “Sally had five bags of apples with seven apples in each bag. How many apples does she have all together?” Given manipulatives students can demonstrate understanding. 1.0 With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Students apply and create a real life word problem involving repeated addition of equal groups. For example, student writes, “Sally had five bags of apples with seven apples in each bag. How many apples does she have all together?” 3rd Grade EL2-­‐ Operations and Algebraic Thinking Interpret whole-­‐number quotients of whole numbers and understand division of whole numbers as equal groupings EL 2 (3.OA.2) (3.2.3) SCORE Skill Level Description In addition to Score 3.0, in-­‐depth inferences and 4.0 applications that go beyond what was taught. 3.5 3.0 2.5 2.0 1.5 1.0 0.5 In addition to score 3.0 performance, in-­‐depth inferences and applications with partial success. The student: 3.OA.2/3.2.3 Interprets whole-­‐number quotients of whole numbers and understands division of whole numbers as equal groupings *Comment-­‐CCSS interprets division as partitioning and groups as shares. The student exhibits no major errors or omissions. No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content There are no major errors or omissions regarding the simpler details and processes as the student: • Recognizes or recalls specific terminology, such as: o Division, partitioning, whole number, quotient, dividend, divisor, equal shares. • Performs basic processes, such as: o Partitioning, manipulatives into equal groups. However, the student exhibits major errors or omissions regarding the more complex ideas and processes. Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes. With help, a partial understanding of the 2.0 content but not the 3.0 content Sample Tasks A student applies and creates a word problem and explains the rational involving partitioning objects into equal groups. For example, student writes, “Sally partitioned 40 apples into 5 bags. How many apples were in each bag?” Interpret 40/5 as the number of objects in each share when 40 objects are partitioned equally into 5 shares, or as a number of shares when 40 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or number of groups can be expressed, as 40/5 is 5 groups of 8. Given 30 manipulatives, a student can share them in 6 equal groups and determine how many manipulatives are in each of the 5 groups. For example, X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X 3rd Grade SCORE 4.0 Solve multiplication and division word problems within 100 using symbols for unknown numbers EL 3 (3.OA.3) (3.2.2, 3.2.3) Skill Level Description Sample Tasks In addition to Score 3.0, in-­‐depth inferences and applications that go beyond what was taught. -­‐A child solves equations with a symbol for the 3.5 In addition to score 3.0 performance, in-­‐depth inferences and applications with partial success. 3.0 The student: 3.OA.3/3.2.2, 3.2.3 Solves multiplication and division word problems within 100 using symbols for unknown numbers Solves word problems using multiplication and division within 100 (e.g., use drawings and equations with a symbol for the unknown number to represent the problem) (Standard: 3.OA.3) *Comment-­‐ Indiana Academic Standards represents multiplication as repeated addition and the division is represented as repeated subtraction until June of 2014. The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Using drawings, arrays and equations with a symbol for the unknown number students represent multiplication and division problems. Sally has 8 boxes of markers. There are 4 markers in each box. How many markers in all? For example, 8 X 4 = ? There are 32 markers. If 4 children share them, how many will each child get? For example, 32/4 = ? 2.0 There are no major errors or omissions regarding the simpler details and processes as the student: recognizes or recalls specific terminology, such as: array, multiplication, factor, product, division, partitioning, whole number, quotient, equal share, equation, groups, symbol, unknown, column, row, dividend, and divisor. Performs basic processes, such as: sharing and partitioning objects into equal groups However, the student exhibits major errors or omissions regarding the more complex ideas and processes. •Given manipulatives, students can create an array showing 4 equal groups of 8 manipulatives. •Given 32 manipulatives a student can share them in 4 equal groups. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes. With help, a partial understanding of the 2.0 content but not the 3.0 content 1.0 0.5 Operations and Algebraic Thinking unknown number for multiplication and division problems. -­‐There are 4 children and they have 8 markers each, how many markers in all? For example, 4 X 8 = N There are 32 markers. Each child will receive 8 markers. If N children share them, how many children will receive markers? For example, 32/ N = 8 3rd Grade Operations and Algebraic Thinking Demonstrates knowledge and understanding of fact families including fluently multiplies and divides within 100 EL 4 (3.OA.7) (3.2.5, 3.2.4, 3.3.4) SCORE Skill Level Description Sample Tasks 4.0 In addition to Score 3.0, in-­‐depth inferences and applications that go beyond what was taught. 3.5 In addition to score 3.0 performance, in-­‐depth inferences and applications with partial success. The student: 3.OA.7/ 3.2.5, 3.2.4, 3.3.4 Demonstrates knowledge and understanding of fact families o Fluently multiplies and divides within 100, using strategies such as the inverse relationship between multiplication and division. o Demonstrates knowledge and understanding of fact families. *Comment-­‐ By the end of grade 3, CCS 3.OA.7 requires students know from memory all products of two one-­‐digit numbers (facts within 100). The student exhibits no major errors or omissions. 3.0 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content 2.0 There are no major errors or omissions regarding the simpler details and processes as the student: • Recognizes or recalls specific terminology, such as: o factor, product, dividend, divisor, quotient, fact families, inverse relationship, commutative and associative, symbol. • Performs basic processes, such as: o grouping manipulatives or making an array. However, the student exhibits major errors or omissions regarding the more complex ideas and processes. Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes. •Given manipulatives, students create an array showing 6 equal groups of 7 and then share them in 7 equal groups of 6. •Given 42 manipulatives, a student can share them in 6 equal groups and then share them in 7 equal groups. With help, a partial understanding of the 2.0 content but not the 3.0 content 1.5 1.0 0.5 Knows and uses the inverse relationship between multiplication and division facts, such as 6 X 7=42, 42/6=7. If one knows that 8 X 5=40, one also knows 40/5=8 as an example of properties of operations. Math Fact Apps and websites ie. Websites: www.mrnussbaum.com http://oswego.org/ocsd-­‐
web/games/mathmagician/cathymath.html 3rd Grade Number and Operations in Base Ten Identify any number up to 1,000 in various combinations of hundreds, tens, and ones EL 5 (3.NBT) (3.1.4) SCORE 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 Skill Level Description In addition to Score 3.0, in-­‐depth inferences and applications that go beyond what was taught. In addition to score 3.0 performance, in-­‐depth inferences and applications with partial success. The student: 3.NBT/ 3.1.4 Identify any number up to 1,000 in various combinations of hundreds, tens, and ones The student exhibits no major errors or omissions. No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content There are no major errors or omissions regarding the simpler details and processes as the student: Use place value understanding to round whole numbers to the nearest 100. • Recognizes or recalls specific terminology, such as: o place value terms (ones, tens, hundreds, etc.) o chart • Performs basic processes, such as: o Regrouping base ten blocks into hundred, tens, ones number representation However, the student exhibits major errors or omissions regarding the more complex ideas and processes. Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes. With help, a partial understanding of the 2.0 content but not the 3.0 content Sample Tasks • Complete the chart to represent 3 thousands, 12 hundreds, 69 tens, 11 ones Thousands Hundreds Tens Ones • Complete the chart to represent 4 hundreds, 13 tens, and 5 ones Hundreds Tens Ones • Using place value blocks, complete the chart to represent 4 hundreds, 13 tens, and 5 ones Hundreds Tens Ones 3rd Grade Number and Operations in Base Ten Use place value understanding to round whole numbers to the nearest 10 and 100 EL 6 (3.NBT.1) (3.1.6) SCORE Skill Level Description Sample Tasks 4.0 In addition to Score 3.0, in-­‐depth inferences and applications that go beyond what was taught. 3.5 In addition to score 3.0 performance, in-­‐depth inferences and applications with partial success. The student: 3.NBT.1/ 3.1.6 Uses place value understanding to round whole numbers to the nearest 10 and 100 Use place value understanding to round whole numbers to the nearest 10 and 100. The student exhibits no major errors or omissions. No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content 3.0 2.5 2.0 1.5 1.0 0.5 Students round to any given place value in a whole number or decimal. There are no major errors or omissions regarding the simpler details and processes as the student: Use place value understanding to round whole numbers to the nearest 100. • Recognizes or recalls specific terminology, such as: o rounding, actual value/worth, place value position, place value terms (ones, tens, hundreds, etc.) • Performs basic processes, such as: o rounding However, the student exhibits major errors or omissions regarding the more complex ideas and processes. Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes. With help, a partial understanding of the 2.0 content but not the 3.0 content • Round 3,126 to the nearest 100. • Round 3,126 to the nearest 10. • Given a two digit number students round to the nearest ten. • Given a three digit number students round to the nearest hundred. Number and Operations in Base Ten Fluently add and subtract multi-­‐digit numbers within 1000 with and without regrouping EL 7 (3.NBT.2) (3.2.1) SCORE 4.0 Skill Level Description In addition to Score 3.0, in-­‐depth inferences and applications that go beyond what was taught. Sample Tasks 4,726 + 5,117 = 9,843 9,843 – 4,726 = 5,117 4,726 9,843 + 5,117 -­‐ 4,726_ 9,843 5,117 3.5 In addition to score 3.0 performance, in-­‐depth inferences and applications with partial success by: 3.0 The student: 3.NBT.2/3.2.1 Adds and subtracts multi-­‐digit numbers within 1000 with and without regrouping o Fluently adds and subtracts within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. *Fluency is the ability to compute math facts and problem solve with automaticity and confidence. *Comment-­‐ 3.NBT.2 includes a range of algorithms for addition and subtraction. The student exhibits no major errors or omissions. 726 + 117 = 843 843 – 726 = 117 726 843 + 117 -­‐ 726_ 843 117 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content 2.5 2.0 There are no major errors or omissions regarding the simpler details and processes as the student: • Recognizes or recalls specific terminology, such as: o digit, base ten, place value position, actual value/worth, ones, tens, hundreds, thousands, sum, difference, regrouping, algorithm • Performs basic processes, such as: o addition, subtraction, regrouping, subtracting across zeros, (properties of operations) •Using base-­‐ten blocks, students can perform properties of operations. However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 1.5 1.0 0.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes. With help, a partial understanding of the 2.0 content but not the 3.0 content 3rd Grade SCORE 4.0 3.5 3.0 2.5 2.0 Numbers and Operations-­‐ Fractions Understand fractions as equal parts of a whole or sets of objects *EL 8 (3NF.1) (3.1.9) Skill Level Description In addition to Score 3.0, in-­‐depth inferences and applications that go beyond what was taught. In addition to score 3.0 performance, in-­‐depth inferences and applications with partial success. The student: 3NF.1/3.1.9 Understands fractions as equal parts of a whole or sets of objects o Understands a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction c/b as the quantity formed by c parts of size 1/b. o Uses and identifies correct names for numerators and denominators. The student exhibits no major errors or omissions. No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content There are no major errors or omissions regarding the simpler details and processes as the student: • Recognizes or recalls specific terminology, such as: o partition, unit fraction, composed, equal parts, fraction, numerator, denominator, part, whole, halves, thirds, fourths, sixths, and eighths. • Performs basic processes, such as: o naming fractions, and partitioning. However, the student exhibits major errors or omissions regarding the more complex ideas and processes. Sample Tasks Compares fractions with common denominators, numerators, and/or mixed fractions. Student uses the understanding of fractions to draw, label and explain the following: •The quantity ¼ represents 1 part of a whole divided into 4 equal parts. •The quantity ¾ represents 3 parts of a whole divided into 4 equal parts. •In the quantity ¾ 3 represents the numerator. •In the quantity ¾ 4 represents the denominator. •Student identifies the fraction shaded/unshaded when given an illustration of a fraction. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content 1.0 With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes. With help, a partial understanding of the 2.0 content but not the 3.0 content 0.5 *(Footnote: Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.) 3rd Grade Measurement and Data Tell and write time to the nearest minute EL 9 (3.MD.1a) (3.5.9) SCORE Skill Level Description 4.0 In addition to Score 3.0, in-­‐depth inferences and applications that go beyond what was taught. 3.5 In addition to score 3.0 performance, in-­‐depth inferences and applications with partial success. The student: 3.MD.1 Part 1/3.5.9 Tells and writes time to the nearest minute. The student exhibits no major errors or omissions. 3.0 Sample Tasks Student tells and writes the time in multiple ways. For example, 9:57 is the same as 3 minutes until ten. •Given an analog clock a student can tell and write the time to the nearest minute. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content 2.0 There are no major errors or omissions regarding the simpler details and processes as the student: • Recognizes or recalls specific terminology, such as: o o’clock, half past, quarter past, quarter-­‐until, minutes until/minutes past, analog, digital, colon, minute hand, hour hand, • Performs basic processes, such as: o counting by fives up to 55, knowing how many minutes in an hour. • However, the student exhibits major errors or omissions regarding the more complex ideas and processes. •Given an analog clock a student can tell and write the time to the nearest 5 minutes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content 1.0 With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content 3rd Grade SCORE Measurement and Data Solve word problems involving addition and subtraction of time intervals in minutes EL 10 (3.MD.1b) (3.5.9) Skill Level Description Sample Tasks 4.0 In addition to Score 3.0, in-­‐depth inferences and applications that go beyond what was taught. 3.5 In addition to score 3.0 performance, in-­‐depth inferences and applications with partial success. The student: 3.MD.1 Part 2/3.5.9 Solves word problems involving addition and subtraction of time intervals in minutes 3.0 o Measures time intervals in minutes.
Solves word problems involving addition
and subtraction of time intervals in
minutes.
Student represents time intervals within word problems mentally without manipulatives and answers and explains in writing. Student represents time intervals within word problems in a variety of ways. For example: Tonya wakes up at 6:45 a.m., it takes her 5 minutes to shower, 15 minutes to get dressed and 15 minutes to eat breakfast. What time will she be ready for school? The student exhibits no major errors or omissions. 2.5 2.0 1.5 1.0 0.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content There are no major errors or omissions regarding the simpler details and processes as the student: • Recognizes or recalls specific terminology, such as: o analog, digital, half past, half hour, minutes, minute hand, start time, end time, hour, hour hand, a.m., p.m., elapsed time, time intervals. • Performs basic processes, such as: o adding and subtracting hour intervals, counting by fives up to 55. However, the student exhibits major errors or omissions regarding the more complex ideas and processes. Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes With help, a partial understanding of the 2.0 content but not the 3.0 content Given manipulatives such as clock models, students will demonstrate time intervals by the hour to solve word problems. 3rd Grade Measurement and Data Measure lengths to the nearest half-­‐inch using rulers marked in halves and fourths of an inch EL 11 (3.MD.4a) (3.5.1) SCORE Skill Level Description Sample Tasks 4.0 In addition to Score 3.0, in-­‐depth inferences and applications that go beyond what was taught. 3.5 3.0 2.5 2.0 1.5 Given standard rulers, a student measures to the nearest fourth and eighth of an inch. In addition to score 3.0 performance, in-­‐depth inferences and applications with partial success. The student: Given a ruler with quarter and half 3.MD.4 Part 1/3.5.1 Measures lengths using rulers inch markings, a student measures marked with halves and fourths of an inch. lengths to nearest half of an inch. *Comment-­‐ CCSS specifies using rulers marked in halves and fourths of an inch. The student exhibits no major errors or omissions. No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content There are no major errors or omissions regarding the simpler details and processes as the student: • Recognizes or recalls specific terminology, such as: standard, object, unit, halves, inch, ruler, length, and measure. • Performs basic processes, such as: using a ruler to measure length. However, the student exhibits major errors or omissions regarding the more complex ideas and processes. Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Given a ruler with half-­‐inch markings, a student knows how to align the ruler correctly and measure correctly to the nearest inch. 1.0 With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content 3rd Grade Measurement and Data Solve real world and mathematical problems involving perimeters of polygons EL 12 (3.MD.8a) (3.5.3) SCORE 4.0 In addition to Score 3.0, in-­‐depth inferences and applications that go beyond what was taught. 3.5 In addition to score 3.0 performance, in-­‐depth inferences and applications with partial success. The student: 3.MD.8 Part 1/3.5.3 Solves real world and mathematical problems involving perimeters of polygons o Solves real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths finding an unknown side length. o 3.5.3 Find the perimeter of a polygon. *Comment-­‐ Extension of IAS 3.5.3. CCSS emphasizes connection between area and perimeter; this is moved from IAS Grade 4 (4.5.6). The student exhibits no major errors or omissions. No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content There are no major errors or omissions regarding the There are no major errors or omissions regarding the simpler details and processes as the student: • Recognizes or recalls specific terminology, such as: o length, unknown, measurement units, calculate, adjacent, rectangular, perimeter, polygon • Performs basic processes, such as: o linear measurement, metric and standard measurement. However, the student exhibits major errors or omissions regarding the more complex ideas and processes. Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content 3.0 2.5 2.0 1.5 1.0 0.5 Skill Level Description With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes. With help, a partial understanding of the 2.0 content but not the 3.0 content Sample Tasks Given a rectangular bulletin board with 4 unknown sides, student calculates perimeter to apply border. Given the measurement of adjacent sides of a rectangular bulletin board, student determines the lengths of the unknown sides and calculates the perimeter to apply border. Student finds the perimeter of a polygon by counting unit segments and by adding given lengths of sides.