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Unit 5: Landmarks Large Numbers September to Early October Grade 4 24 Sessions Inv. # and MA Std Content Objective Key Vocabulary Language Assessment Pacing Name Objective Inv. 1: How 4.N.1, 1. Students will read, write, and sequence numbers to place value, base-ten This is one Review p. 14 for the 6 - 1 hour Much is 4.N.2, 1000. number system, example of a assessment in this sessions 1000? TE p. 4.N.5 sequence, addition, language unit. Complete all 28 - 56 4.N.7, 2. Students will add and subtract multiples of 10, 100, and subtraction, multiple, objective. Please 'Ongoing 4.N.9, 1000. difference, number line, consider your Assessments, 4.N.11 open number line, students' needs Writing 4.N.12, 3. Students will use multiples of 10 and 100 to find the commutative property, when writing your Opportunities, 4.N.16, difference b/w any 3-digit number and 1000. identity property, inverse Portfolio language 4.N.17, operation, landmarks, Opportunities, & End- objectives: 4.M.1, 4. Students will represent addition and subtraction on a rounding, expanded of-Unit Students will use 4.P.2 number line. notation, closer to, Assessments.' content specific between, before, after, Portfolio: SAB p. 9- vocabulary to orally expression, ones, tens, 10, M19 explain their hundreds, thousands thinking. Teacher's Notes: Broken Calculator (Ten Minute Math) reinforces 4.P.2, 4.N.9, 4.N.11, and 4.N.12. Inv. 1.1, make connections between landmark whole numbers and fractional & decimal landmarks, for ex. 25 is 1/4 of 100, 500 is 1/2 of 1000, etc. When assessing students familiarity with the structure of the number system up to the 100's, use base 10 blocks as needed. Be cognizant of Teacher Note # 5 on p. 31 of the teacher's guide. When students are finding numbers in their 1000s book make connections to rounding, for example, if a students states 541 is closer to 500 rather than 600, explain that it is a form of rounding to the nearest 100, and so on. The teacher may want to take this opportunity to reintroduce estimation (4.N.17) as a strategy. SAB p. 3, 11, & 15 reinforce 4.N.11. This is a great time to introduce the place value game "The Greatest." Ask your resource teacher for a copy from the district created math specialist binder. Standard 4.N.1 expects mastery up to 100,000, challenge & differentiate up to that place value when completing any or all of the sessions. Focal Points (connection): Number and Operations CIA Lowell Public Schools Working 3/5/2010 Unit 5: Landmarks Large Numbers September to Early October Grade 4 24 Sessions Inv. # and MA Std Content Objective Key Vocabulary Language Assessment Pacing Name Objective Inv. 2: 4.N.1, 1. Students will add 3 and 4-digit numbers. addition strategies, Portfolio: M23 6 - 1 hour Adding it 4.N.2, expressions, equivalent, sessions Up TE p. 4.N.8, 2. Students will identify, describe and compare addition addition notation, 60 - 93 4.N.9, strategies by focusing on how each strategy starts. subtraction notation, U.S. 4.N.10, standard algorithm, digit, 4.N.11, 3. Students will develop arguments about why addition expanded notation, 4.N.12, expressions are equivalent (e.g., 597 + 375 = 600 + 372) decompose, open number 4.N.13, line, flats, rods, units, 4. Students will use story context and representations to representations, equation, 4.N.14, support explanations about equivalent addition expressions. partial sums, plus 4.N.17, 4.M.1, 5. Students will use clear and concise notation to record 4.P.2, addition and subtraction strategies. 6. Students will understand the meaning of the steps and notation of the U.S. algorithm for addition. 7. Students will find combinations of 3-digit numbers that add to 1000. Teacher's Notes: Broken Calculator (Ten-Minute Math) reinforces 4.P.2, 4.N.9. 4.N.11, 4.N.12. Student activity sheet p. 16-17 develop the understanding of distance and miles for 4.M.1, p. 18 reinforces 4.N.10 & 4.N.17; p. 27 reinforces 4.N.11, 4.N.12; p. 30 reinforces 4.P.2, and p. 32 reinforces 4.N.10, 4.N.11, 4.N.12, & 4.N.13. After playing Close to 1,000 extend the game by having students go back to their recording sheets and write the sums in expanded notation and in words, additional game sheets with this differentiation can be located by your math resource teacher in the district specialist created binder. Continue playing "The Greatest" game. Focal Points (connection): Number and Operations CIA Lowell Public Schools Working 3/5/2010 Unit 5: Landmarks Large Numbers September to Early October Grade 4 24 Sessions Inv. # and MA Std Content Objective Key Vocabulary Language Assessment Pacing Name Objective Inv. 3: 4.N.1, 1. Students will read, write, and sequence numbers to equivalence, place value, 5 - 1 hour Working 4.N.2, 10,000. digit, multiple, equation, sessions with 4.N.5, base-ten number system, Numbers to 4.N.8, 2. Students will understand the structure of 10,000 and power of ten, decompose, 10,000 TE p. 4.N.9, its equivalence to 1,000 10s, 100 100s, and 10 1000s ones, tens, hundreds, 100 - 125 4.N.10, thousands, ten-thousand, 4.N.11, 3. Students will recognize the place value of digits in rows, columns, chunk, 4.N.12, mental math, large numbers. 4.N.13, 4.N.14, 4. Students will add and subtract multiples of 10, 100, and 4.N.17, 1000. 4.M.1, 4.M.2, 5. Students will add 3 and 4-digit numbers. 4.P.2 6. Students will find combinations of 3-digit numbers that add to 1000. Teacher's Notes: Ten-Minute Math Broken Calculator reinforces 4.P.2, 4.N.9. 4.N.11, 4.N.12. During Inv. 3.1, make connections between landmark whole numbers and fractional and decimal landmarks, for example, 2,500 is 1/4 of 10,000, 5,000 = .5 of 10,000, etc. When students are finding numbers in their 10,000s chart make connections to rounding, for example, if a student states 3,218 is between 3,200 and 3,300 they have rounded to the nearest 100, or they could round to the nearest 1000, etc. Student Activity sheet p. 42 reinforces 4.N.10, 4.N.11, 4.N.13. During Inv. 3.4, differentiate by having students convert miles to feet (teacher may use a map of Lowell and simpler problems.) and show the addition another way, this may extend problems up to 5-digit numbers for 4.N.12 and 4.M.2 simple unit conversion. Remember to use horizontal and vertical notation. Play the differentiated game "Close to 10,000". Then extend the game by having students go back to their recording sheets and write the sums in expanded notation and in words. Additional game sheets with this differentiation can be located by your math resource teacher in the district specialist created binder. Continue playing "The Greatest" game. Focal Points (connection): Number and Operations CIA Lowell Public Schools Working 3/5/2010 Unit 5: Landmarks Large Numbers September to Early October Grade 4 24 Sessions Inv. # and MA Std Content Objective Key Vocabulary Language Assessment Pacing Name Objective Inv. 4: 4.N.1, 1. Students will understand the action of subtraction subtraction strategies, Portfolio: SAB p. 55- 7 - 1 hour Subtraction 4.N.2, problems. subtraction situation/story 56, M27, and Unit sessions TE p. 132 - 4.N.5, 2. Students will represent subtraction situations. problems, open number Assessment M29 165 4.N.7, 3. Students will represent addition and subtraction on a line, decompose/break 4.N.8, number line. apart, chunks, landmark, 4.N.9, 4. Students will solve subtraction problems by breaking difference, expression, 4.N.10, numbers apart. take away, minus, 5. Students will find combinations of 3-digit numbers that difference, positive 4.N.11, add to 1000. numbers, negative 4.N.12, 6. Students will identify, describe, and compare subtraction numbers, missing 4.N.13, strategies by focusing on how each strategy starts. addend, comparison, 4.N.14, 7. Students will develop arguments about how the borrowing/regrouping, 4.N.16, U.S. Standard algorithm, differences represented by two subtraction expressions are 4.N.17, related (e.g., 432 - 198 and 432 - 200) inverse, equation, farther, 4.M.1, 8. Students will use story context and representations to plus, 4.M.2, support explanations about related subtraction expressions. 4.P.2 9. Students will add and subtract 3 and 4 digit numbers. 10. Students will solve multi-step addition and subtraction problems. 11. Students will combine positive and negative numbers. Teacher's Notes: Broken Calculator (Ten-Minute Math) reinforces 4.P.2, 4.N.9. 4.N.11, 4.N.12. Encourage students to use the inverse to check their answers. Standard 4.N.1 expects mastery up to 100,000, challenge and differentiate up to that place value when completing any or all of the sessions in these investigations. During Inv. 4.5, introducing Which is Farther?, have students convert miles to feet, this will reinforce 4.M.2 & 4.N.12. Student Activity sheets p. 67 & 68 reinforce 4.N.10 & 4.N.12; p. 69 reinforces 4.N.12; p. 70-71 reinforce 4.N.7 & 4.N.11; p. 73-74 reinforces 4.N.11, 4.N.12, 4.M.1, & 4.M.2. Differentiate sheets 73-74 by having students convert to tons and ounces and show their solutions using those units of measure. Focal Points (connection): Number and Operations CIA Lowell Public Schools Working 3/5/2010 Unit 5: Landmarks & Large Numbers Standards # Description Exhibit an understanding of the base ten number system by reading, modeling, writing, and interpreting whole numbers to at least 100,000; 4.N.1 demonstrating an understanding of the values of the digits; and comparing and ordering the numbers. 4.N.2 Represent, order, and compare large numbers (to at least 100,000) using various forms, including expanded notation, e.g., 853 = 8 x 100 + 5 x 10 + 3. 4.N.5 Recognize classes (in particular, odds, evens; factors or multiples of a given number; and squares) to which a number may belong, and identify the 4.N.7 numbers in those classes. Use these in the solution of problems Select, use, and explain various meanings and models of multiplication and division of whole numbers. Understand and use the inverse 4.N.8 relationship between the two operations. Select, use, and explain the commutative, associative, and identity properties of operations on whole numbers in problem situations, e.g., 37 x 46 = 46 4.N.9 x 37, (5 x 7) x 2 = 5 x (7 x 2). Select and use appropriate operations (addition, subtraction, multiplication, and division) to solve problems, including those involving 4.N.10 money. Know multiplication facts through 12 x 12 and related division facts. Use these facts to solve related multiplication problems and compute related 4.N.11 problems, e.g., 3 x 5 is related to 30 x 50, 300 x 5, and 30 x 500 4.N.12 Add and subtract (up to five-digit numbers) and multiply (up to three digits by two digits) accurately and efficiently. Divide up to a three-digit whole number with a single-digit divisor (with or without remainders) accurately and efficiently. Interpret any 4.N.13 remainders. Demonstrate in the classroom an understanding of and the ability to use the conventional algorithms for addition and subtraction (up to five-digit 4.N.14 numbers), and multiplication (up to three digits by two digits). 4.N.16 Round whole numbers through 100,000 to the nearest 10, 100, 1000, 10,000, and 100,000. Select and use a variety of strategies (e.g., front-end, rounding, and regrouping) to estimate quantities, measures, and the results of whole- 4.N.17 number computations up to three-digit whole numbers and amounts of money to $1000, and to judge the reasonablenes Demonstrate an understanding of such attributes as length, area, weight, and volume, and select the appropriate type of unit for measuring each 4.M.1 attribute. 4.M.2 Carry out simple unit conversions within a system of measurement, e.g., hours to minutes, cents to dollars, yards to feet or inches, etc. 4.P.2 sentences that use =, <, >). CIA LPS 3/5/2010 Unit 1: Factors, Multiples, and Arrays Early October - End October Grade 4 14 Sessions Invest Title & MA Std Content Objective Key Vocabulary Language Assessment Pacing Page No. Objective Inv #1: 4.N.1, 1. Students will use arrays to model multiplication multiplication, array/ This is one Review p. 14 for 5 - 1 hour Representing 4.N.2, situations. rectangular arrangement, example of a the assessment in sessions Multiplication 4.N.7, dimensions, 2-dimension, language this unit. Complete with Arrays 4.N.8, 2. Students will break arrays into parts to find the product package, related numbers, objective. Please all 'Ongoing TE Pages 22- 4.N.9, represented by the array. strategy, odd/even, multiple/ consider your Assessments, 47 4.N.10, product, skip counting, factor, students' needs Writing 4.N.11, 3. Students will find the multiples of a number by skip factor pairs, multiplication when writing your Opportunities, & 4.N.12, counting. expression, prime number, language Portfolio composite number, square Opportunities, & 4.P.1, objectives: 4. Students will use arrays to find factors of 2-digit numbers. number, multiplication End-of-Unit 4.P.2, Students will use combination, row, column, Assessments 4.P.4 content specific 5. Students will identify features of numbers, including prime, divide, multiplication Portfolio: SAB p. 2, vocabulary to orally square, and composite numbers. equation, commutative 12, M31 explain their property, associative thinking. 6. Students will identify and learn multiplication combinations property, properties of not yet known fluently. factors, common factors, doubling/halving, decompose 7. Students will use known multiplication combinations to (distributive property) determine the products of more difficult combinations. Teacher's Notes: Standards 4.P.2, and 4.P.4 are addressed during Ten-Minute Math. When making arrays, make connections to related numbers as ways to find other factors for the given multiple, for example, doubling, halving, divisibilty, odd/even. The addition and subtraction in 4.N.12 is practiced and reinforced during Student Activity Book (SAB) practice, as well as, 4.N.10. During Inv. 1 when looking for patterns in the arrays, finding factor pairs, and classifying numbers, make connections to the Identity and Commutative Properties to cover 4.N.9. For those students who are ready, distributive property can be introduced during the discussions about using related multiplication combinations to find more difficult combinations. See page 16 in teacher's guide. Focal Points (addressed): Number and Operations, Algebra (supported): Measurement CIA Lowell Public Schools Working Document 3/5/2010 Unit 1: Factors, Multiples, and Arrays Early October - End October Grade 4 14 Sessions Invest Title & MA Std Content Objective Key Vocabulary Language Assessment Pacing Page No. Objective Inv #2: 4.N.1, 1. Students will use arrays to model multiplication product, multiple, factor, Portfolio: M51 5 - 1 hour Multiplication 4.N.2, situations. "groups of," arrangement, sessions Combinations 4.N.7, equation, image, related TE Pages 54 - 4.N.8, 2. Students will identify and learn multiplication combinations numbers, odd, even, prime, 83 4.N.9, not yet known fluently. composite, doubling, halving, 4.N.10, divisibilty, multiplication, 4.N.11 3. Students will use known multiplication combinations to pattern, expression, 4.N.12 determine the products of more difficult combinations. equations, skip count, 4.P.2, division, strategies, 4.P.3, 4. Students will use determine whether one number is a factor or associative property, 4.P.4 multiple of another. commutative property, distributive property Teacher's Notes: Standards 4.N.8 (in addition to the Investigation), 4.P.2, and 4.P.4 are addressed during Ten-Minute Math. During Inv. 2.1, for students who are ready the associative property, 4.N.9, can be emphasized when discussing related numbers, for example, (2 x 2) x 12 = 48 or 2 x (2 x 12) = 48. During the discussion of strategies for difficult multiplication combinations (p.62-63) and finding factors and multiples (p. 69-70), ask questions that make connections to related numbers, for ex. odd, even, prime, composite, divisibility rules, doubling, and halving, and make connections to the inverse operation. The addition and subtraction in 4.N.12 is practiced and reinforced during Student Activity Book practice, as well as 4.N.10. Standard 4.P.3 can be introduced during the missing factor p. 70 in Inv. 2.3. For those students who are ready, distributive property can be introduced during the discussions about using related multiplication combinations to find more difficult combinations. See page 16 in teacher's guide. During Inv. 2 when looking for patterns in the arrays, finding factor pairs, and classifying numbers, make connections to the identity property to cover 4.N.9. Focal Points (addressed): Number and Operations, Algebra (supported): Measurement CIA Lowell Public Schools Working Document 3/5/2010 Unit 1: Factors, Multiples, and Arrays Early October - End October Grade 4 14 Sessions Invest Title & MA Std Content Objective Key Vocabulary Language Assessment Pacing Page No. Objective Inv #3: 4.N.1, 1. Students will use arrays to model multiplication factors, multiples/product, Portfolio: SAB p. 4- 1 hour Finding 4.N.2, situations. skip counting, doubling and 33-34, Unit sessions Factors 4.N.7, halving, patterns, square Assessment M55- 4.N.8, 2. Students will use arrays to find factors of 2-digit numbers. numbers, landmark, estimate, M56 TE Pages 88- 4.N.9, expressions, equations, 114 4.N.10, 3. Students will find the multiples of a number by skip factor pairs, related numbers, 4.N.11, counting. conjecture, strategies, 4.N.12, divide/division, evenly, 4.P.3 4. Students will identify the factors of a given number. arrays, representations, commutative property, 5. Students will identify all the factors of 100. rectangle, number string, Identity property 6. Students will use knowledge of the factors of 100 to find factors of multiples of 100. 7.Students will use known multiplication combinations to find related multiplication combinations for a given product (e.g., if 4 x 50 = 200, then 8 x 25 = 200). 8. Students will use representations to show that a factor of a number is also a factor of its multiples (e.g., if 25 is a factor of 100, then 25 is also a factor of 300). 9. Students will use the known multiplication combinations to determine the product of more difficult combinations. Teacher Notes: The addition and subtraction in 4.N.12 is practiced and reinforced during Student Activity Book practice, as well as, 4.N.10. Standard 4.P.3 can be introduced during the missing factor p. 70 in Inv. 2.3. For those students who are ready, distributive property can be introduced during the discussions about using related multiplication combinations to find more difficult combinations. See p. 16 in teacher's guide. During Inv. 3 when identifying all the factors of a 100 and multiples of 100 make connections to the Identity property. Focal Points (addressed): Number and Operations, Algebra (supported): Measurement CIA Lowell Public Schools Working Document 3/5/2010 Unit 1: Factors, Multiples, & Arrays Standards # Description 4.N.1 Exhibit an understanding of the base ten number system by reading, modeling, writing, and interpreting whole numbers to at least 100,000; demonstrating an understanding of the values 4.N.2 Represent, order, and compare large numbers (to at least 100,000) using various forms, including 4.N.7 Recognize classes (in particular, odds, evens; factors or multiples of a given number; and squares) to which a number may belong, and identify the numbers in those classes. Use these in the solution of 4.N.8 Select, use, and explain various meanings and models of multiplication and division of whole 4.N.9 Select, use, and explain the commutative, associative, and identity properties of operations on whole 4.N.10 Select and use appropriate operations (addition, subtraction, multiplication, and division) to 4.N.11 Know multiplication facts through 12 x 12 and related division facts. Use these facts to solve related multiplication problems and compute related problems, e.g., 3 x 5 is related to 30 x 50, 300 x 5, and 30 4.N.12 Add and subtract (up to five-digit numbers) and multiply (up to three digits by two digits) accurately and 4.P.1 Create, describe, extend, and explain symbolic (geometric) and numeric patterns, including 4.P.2 4.P.3 4.P.4 Use pictures, models, tables, charts, graphs, words, number sentences, and mathematical notations to interpret mathematical relationships. CIA LPS 3/5/2010 Unit 4: Size, Shape, Symmetry November - Early December Grade 4 20 Sessions Inv. # and Name MA Std Content Objective Key Vocabulary Language Objective Assessment Pacing Inv. 1: Linear 4.M.1, 1. Students will review the lengths of units of area, volume, perimeter, linear This is one example Review p. 14 for 5 - 1 hour Measurement 4.M.2, measure (inches, feet, yards, cm, meters). measurement, inch, foot, yard, of a language the assessment sessions TE p. 22 - 49 4.M.4, centimeter, meter, benchmark, objective. Please in this unit. 4.M.5, 2. Students will use U.S. Standard and Metric millimeter, standard system, consider your Complete all 4.N.1, units to accurately measure length. metric, kilometer, estimate, students' needs 'Ongoing 4.N.2, perimeter, unit, length, when writing your Assessments, 4.N.3, 3. Students will estimate lengths based on expression, equation, hand language objectives: Writing 4.N.4, span Students will use Opportunities, & common units (cm, in., ft. yd. m.). 4.N.5, content specific Portfolio 4.N.6, 4. Students will determine when estimates and vocabulary to orally Opportunities, & 4.N.11, exact measurements are needed. explain their thinking. End-of-Unit 4.N.12, Assessments. 4.N.13, 5. Students will find perimeter using standard units. Portfolio: M13 4.N.14, 4.P.2 6. Students will recognize and explain possible sources of measurement error. 7. Students will compare different paths that have the same length. Teacher's Notes: Broken Calculator, reinforces 4.P.2, 4.N.1, 4.N.2, 4.N.12, 4.N.14. SAB p. 3 & p. 5 reinforce 4.N.11 & 4.N.12. Students should practice doing simple conversions, 4.M.2. When recording measurements have students record t. same measurement in different ways, e.g. 2 1/4 meters = 2 meters 25 cm = 2.25 meters and 3 1/2 feet = 3 feet 6 inches = 3.5 ft. These differentiations connect to 4.N.3, 4.N.4, 4.N.5, 4.N.6. When exploring Measuring Perimeter make connections & comparisons b/w area & perimeter. Differentiate by having students find area of a desk, etc. Conference w/ your Computer Lab teacher about creating a cheat sheet for the LogoPath Activity. See page 151-153. "Measuring Lengths" (SAB p. 7) can be differentiated by having students complete add'l columns: Simple Unit Conversions, e.g. metric & standard; Record t. same measurement in different ways; Find Area. SAB p. 9 reinforces 4.N.13. Inv. 1.4 Mapping 100 Feet can also be Mapping 100 Yards. Discuss t. relationship. Inv. 1 (measurement) can be supported by Specialists (Art, Gym, Science or Computer teachers). If this is the case, begin t. unit on Inv. 2. Also, Inv. 4 (symmetry) can be supported in Art. CIA Lowell Public Schools Working Document 3/5/2010 Unit 4: Size, Shape, Symmetry November - Early December Grade 4 20 Sessions Inv. # and Name MA Std Content Objective Key Vocabulary Language Objective Assessment Pacing Inv. 2: 4.G.1, 1. Students will define polygons as closed figures polygon, line segment, end Portfolio: M21 5 - 1 hour Polygons of 4.G.2, with line segments as sides, and vertices. point, vertex/vertices, sessions Many Types TE 4.G.3, orientation, side, attribute, p. 54 - 83 4.G.4, 2. Students will classify polygons by attributes angle, trapezoid, equilateral 4.G.5, including number of sides, length of sides, and triangle, scalene triangle, 4.G.9, size of angles. isosceles triangle, acute 4.N.8, triangle, obtuse triangle, 4.N.11, 3. Students will combine polygons to make new equiangular triangle, 4.N.12 polygons. parallelogram, hexagon, prefix, right angle, parallel, acute, 4. Students will recognize number of sides as a obtuse, perpendicular, descriptor of various polygons. intersecting, benchmark, quadrilateral, square, rectangle, 5. Students will develop vocabulary to describe power polygon set, ,2-D,"side length", regular polygon, attributes and properties of quadrilaterals. nonregular, concave, convex, 'gon', 'poly', 6. Students will understand the relationship b/w squares and rectangles. Teacher's Notes: Inv. 2.2, Making Polygons, have students record each # (at least 3 different ex.s of t. # of polygons) on separate pieces of paper. In explore & summary, ask students to count & label t. sides, names, triangles, quadrilaterals, regular vs. nonregular, etc. on each sheet. Differentiate by having students examine & identify which of their polygons are concave and convex. SAB p. 20, "Names for Polygons" can be summarized using a teacher created transparency or chart paper posted for each prefix. Students can go around recording all t. terms they found. For those prefixes that are few, challenge students to search in dictionaries or thesauruses, etc. Summarize the new terms and how they relate to the meaning of the prefix and root words. When playing "Guess My Rule" with all the shape cards make connections to angle terms, for ex. if a student describes an angle > right angle= obtuse, or < 90 degrees = acute. Use benchmarks at this point to determine angle type. Also, encourage students to go beyond just naming a three-sided polygon as a triangle, encourage them to use the specific triangle names. Do the same w/ quadrilaterals. SAB p. 25 reinforces 4.N.8, 4.N.11, 4.N.12. CIA Lowell Public Schools Working Document 3/5/2010 Unit 4: Size, Shape, Symmetry November - Early December Grade 4 20 Sessions Inv. # and Name MA Std Content Objective Key Vocabulary Language Objective Assessment Pacing Inv. 3: 4.G.4, 1. Students will identify a right angle as 90 degrees. angle, degree, right angle, Portfolio: SAB p. 3 - 1 hour Measuring 4.M.5, equilateral triangle, acute angle, 41-43 sessions Angles TE p. 88 - 4.N.1, 2. Students will measure acute angles by relating obtuse angle, benchmark, turn 108 4.N.2, them to 90 degrees. 4.N.3, 4.N.7, 3. Students will use known angles to find the 4.N.11, measure of other angles. 4.N.12, 4.N.14, 4.P.1, 4.P.2 Teacher's Notes: Ten-Minute Math Broken Calculator reinforces standards 4.P.2, 4.N.1, 4.N.2, 4.N.12, 4.N.14. When making right angles and deciding how many degrees make connections to halving, doubling, and fractional numbers, e.g. 45 x 2 = 90, 45 is half of 90, etc. (4.N.3). On Student Activity Book p. 39 -43 & 49, encourage students to record polygon names and angle names. Encourage students to write an equation for Building Angles p. 42 - 43. During the discussion of Smallest Angle, Biggest Angle make connections to benchmarks 180 (half a turn) and 360 ( full turn) degrees and that each unit in the turn is 1 degree. Student Activity Sheets p. 47 & 48 reinforces 4.P.1, 4.N.7, 4.N.11, 4.N.12. CIA Lowell Public Schools Working Document 3/5/2010 Unit 4: Size, Shape, Symmetry November - Early December Grade 4 20 Sessions Inv. # and Name MA Std Content Objective Key Vocabulary Language Objective Assessment Pacing Inv. 4: Finding 4.M.1, 1. Students will make designs with mirror symmetry, symmetrical, mirror Portfolio: SAB p. 7 - 1 hour Area TE p. 112 - 4.M.4, symmetry. symmetry, area, square unit, 70-72, Unit sessions 148 4.M.5, pentagon, irregular polygon, Assessment M27- 4.G.2, 2. Students will find the area of symmetrical designs. decompose, rectangle, triangle, 28 4.G.8, hexagon, equilateral triangle, 4.G.9, 3. Students will understand that the larger the unit of trapezoid, 4.N.1, area, the smaller the number of units needed to parallelogram/rhombus, line of 4.N.2, measure the area. symmetry, standard unit, 4.N.3, nonstandard unit, 4.N.8, 4. Students will divide irregular polygons into two congruent/congruence, 4.N.11, shapes that have equal area. geoboard, array, rows, columns, 4.N.12, length, width 4.N.14, 5. Students will find the area of polygons by 4.P.2 decomposing shapes. 6. Students will find the area of polygons using square units. 7. Students will find the area of rectangles. 8. Students will find the area of triangles in relation to the area of rectangles. Teacher's Notes: Student Activity Sheet p. 53, p. 65 reinforces 4.N.11 & 4.N.12. Make connections to fractions when comparing units of measure during Inv. 4.2, 4.4, 4.5 (4.N.3). Student Activity Sheet p. 60 reinforces 4.N.8, 4.N.11, 4.N.12. To review and reinforce the polygon names, encourage students to name the crazy cake and geoboard figures appropriately, e.g. nonregular hexagon. Ten-Minute Math Broken Calculator reinforces standards 4.P.2, 4.N.1, 4.N.2, 4.N.12, 4.N.14. CIA Lowell Public Schools Working Document 3/5/2010 Unit 4: Size, Shape, and Symmetry Standards # Description Exhibit an understanding of the base ten number system by reading, modeling, writing, and interpreting whole numbers to at least 100,000; demonstrating an understanding of the values of 4.N.1 Represent, order, and compare large numbers (to at least 100,000) using various forms, including 4.N.2 Demonstrate an understanding of fractions as parts of unit wholes, as parts of a collection, and 4.N.3 Select, use, and explain models to relate common fractions and mixed numbers (1/2, 1/3, 1/4, 1/5, 1/6, 4.N.4 Identify and generate equivalent forms of common decimals and fractions less than one whole 4.N.5 Exhibit an understanding of the base ten number system by reading, naming, and writing decimals 4.N.6 Recognize classes (in particular, odds, evens; factors or multiples of a given number; and squares) to which a number may belong, and identify the numbers in those classes. Use these in the solution of 4.N.7 Select, use, and explain various meanings and models of multiplication and division of whole 4.N.8 Know multiplication facts through 12 x 12 and related division facts. Use these facts to solve related multiplication problems and compute related problems, e.g., 3 x 5 is related to 30 x 50, 300 x 5, and 30 x 4.N.11 Add and subtract (up to five-digit numbers) and multiply (up to three digits by two digits) accurately and 4.N.12 Divide up to a three-digit whole number with a single-digit divisor (with or without remainders) 4.N.13 CIA LPS 3/5/2010 Unit 4: Size, Shape, and Symmetry Demonstrate in the classroom an understanding of and the ability to use the conventional algorithms for 4.N.14 Demonstrate an understanding of such attributes as length, area, weight, and volume, and select the 4.M.1 Carry out simple unit conversions within a system of measurement, e.g., hours to minutes, cents to 4.M.2 Estimate and find area and perimeter of a rectangle, triangle, or irregular shape using diagrams, models, 4.M.4 Identify and use appropriate metric and English units and tools (e.g., ruler, angle ruler, graduated (e.g., number of sides, faces, corners, right angles, diagonals, and symmetry) of two- and three- 4.M.5 dimensional geometric shapes. Compare and analyze attributes and other features (e.g., number of sides, faces, corners, right angles, 4.G.1 Describe, model, draw, compare, and classify two- and three-dimensional shapes, e.g., circles, 4.G.2 4.G.3 4.G.4 4.G.5 4.G.8 Predict and validate the results of partitioning, folding, and combining two- and three-dimensional 4.G.9 shapes. Create, describe, extend, and explain symbolic (geometric) and numeric patterns, including multiplication 4.P.1 4.P.2 CIA LPS 3/5/2010 Unit 3: Multple Towers and Division Stories Early December - Middle January Grade 4 20 Sessions Inv. # and Name MA Std Content Objective Key Vocabulary Language Objective Assessment Pacing Resources: Inv. 1: Breaking 4.N.2, 1. Students will develop strategies for multiplication, array, rows, This is one example of Review p. 14 for 5 - 1 hour Apart Multiplication 4.N.7, multiplying that involve breaking apart columns, factor, area, a language objective. the assessment in sessions Problems TE p. 28 - 4.N.8, numbers. product/multiple, equation, Please consider your this unit. Complete 54 4.N.9, break apart/decompose, students' needs when all 'Ongoing 4,N.10, 2. Students will represent a multiplication expanded notation, partial writing your language Assessments, 4.N.11, problem with pictures, diagrams, or models. products/subproduct, objectives: Students Writing 4.N.12, associative property, will use content specific Opportunities, & 4.M.1, 3. Students will review multiplication distributive property, length, vocabulary to orally Portfolio 4.M.2, combinations to 12 x 12. width explain their thinking. Opportunities, & 4.P.2 End-of-Unit 4. Students will use arrays to model Assessments. multiplication. Portfolio: SAB p. 12- 13, M43 Teacher's Notes: Quick Images (Ten-Minute Math) targets standards 4.N.8, 4.N.9, 4.N.11, 4.P.2. Read the Algebraic Connections on p. 16 of this teacher's guide regarding the distributive property. Try to make connections that the product/multiple equals the area of the array (4.M.1 & 4.M.2). When creating Small Arrays for Big Arrays, model how to record the dimensions on the outside of the array, especially if students are posting them on additional sheets of paper or on the board, record the partial products inside each array. For example, 8 x 9 = (4 x 9) + (4 x 9), so the dimension recorded on the outside of the array should read 4 + 4. Encourage students to use parentheses when writing their equations for Small Array/Big Array (Inv. 1.3). It clarifies order of operation for them. Ten-Minute Math, Counting Around the Class, Inv. 1.4, reinforces 4.N.11, 4.P.1, 4.P.2. Focal Points (addressed): Number and Operations, Algebra (connected): Geometry CIA LPS Working Document3/5/2010 Unit 3: Multple Towers and Division Stories Early December - Middle January Grade 4 20 Sessions Inv. # and Name MA Std Content Objective Key Vocabulary Language Objective Assessment Pacing Resources: Inv. 2: Division TE 4.N.2, 1. Students will develop strategies for division, divide, remainder, Portfolio: SAB p. 25- 6 - 1 hour p. 60 - 91 4.N.7, multiplying that involve breaking apart left over, divisor/ factor, 26, M46 sessions 4.N.8, numbers. dimension, 4.N.10, 2. Students will solve division story dividend/product/multiple, 4.N.11, problems. story problem, standard 4.N.12, 3. Students will use and interpret division notation, represent, 4.N.13, notation. multiplication combinations, 4.M.1, 4. Students will solve division problems by rows, sharing, grouping, 4.M.2, making groups of the divisor. quotient, equation, inverse 4.P.1, 5. Students will use known multiplication 4.P.2, combinations to solve division 4.P.3 problems. 6. Students will make sense of remainders in terms of the problem context. 7. Students will represent a division problem with pictures, diagrams, or models. 8. Students will create a story problem to represent a division expression. Teacher's Notes: Counting Around the Class (Ten-Minute Math) reinforces 4.N.11, 4.P.1, 4.P.2. As you go through the division story problems always try to identify with students if it is a sharing or grouping division problem. Identify with students how divisor is synonymous with factor and vice versa, as well as, dividend is to product is to multiple. You may use the nmemonic that the standard notation for division (i.e. the house), is an adaptation of the array for that problem. Ten-Minute Math, Quick Images, targets standards 4.N.8, 4.N.9, 4.N.11, 4.P.2. Encourage students to use a circle or square to write their equations for the "Missing Factors/Quotient." Continue to make the connection that the product/multiple equals the area of the array (4.M.1 & 4.M.2). Focal Points (addressed): Number and Operations, Algebra (connected): Geometry CIA LPS Working Document3/5/2010 Unit 3: Multple Towers and Division Stories Early December - Middle January Grade 4 20 Sessions Inv. # and Name MA Std Content Objective Key Vocabulary Language Objective Assessment Pacing Resources: Inv. 3: Multiplying 4.N.1, 1. Students will review multiplication multiple, factor, mulitply, Portfolio: SAB p. 37- 4 - 1 hour Tens TE p. 94 - 120 4.N.7, combinations to 12 x 12. sequence, visual 38, M48-49, SAB p. sessions 4.N.8, 2. Students will multiply multiples of 10. representation, 42-43, M50 4.N.11, 3. Students will understand the effect of mutliplication 4.N.12, multiplying by a multiple of 10 (e.g., situations/story problems, 4.N.14, describing the relationship b/w 3 x 4 & 3 x multiple towers, landmarks 4.M.5, 40). multiples, equation, 4.P.1, 4 Students will find multiples of 2-digit expression 4.P.2 numbers. 5. Students will describe a sequence of multiples in order to predict other multiples. 6. Students will represent a multiplication problem with pictures, diagrams, or models. 7. Students will compare a visual representation of multiplication situations. Notes: Counting Around Class reinforces 4N11, 4P1, 4P2. Connect multiple towers to mathematical expressions, ex. ask How many multiples have we counted? Multiple 27 is expressed 3 x 9 or 9 multiples of 3 have been counted. Inv. 3.1, when looking at list of multiples of 3 look for patterns, ex. the sum of digits in the multiples of 3 is always 3, 6, or 9. Therefore, the number is a multiple of 3 or divisible by 3. Apply this same thinking to other numbers when counting around the room & record multiples. Apply thinking of looking for patterns when creating multiple towers. Touch on measurement (4.M.5) when students are creating their own multiple towers, measure evenly sized sections. SAB p. 39 & 40 reinforce 4N8 & 4N11. Inv. 3.2 the idea of "Adding a Zero" is discussed. Use the term "ATTACHING A ZERO" instead, adding a zero will not change the sum. For ex. 4 x 4 = 24 & 40 x 6 = 240, but 24 + 0 is not 240. We want students to see pattern of attaching zero! Encourage students to make drawings, use grid paper, etc. to show what happens to arrays as we multiply by 10s. As students become fluent with 2-digit x 1-digit multiplication differentiate & solve 2 x 2 & 3 x 2 multiplication. Focal Points (addressed): Number and Operations, Algebra (connected): Geometry CIA LPS Working Document3/5/2010 Unit 3: Multple Towers and Division Stories Early December - Middle January Grade 4 20 Sessions Inv. # and Name MA Std Content Objective Key Vocabulary Language Objective Assessment Pacing Resources: Inv. 4: Strategies 4.N.1, 1. Students will determine the effect on the double, halve, factor, Portfolio: SAB p. 57- 5 - 1 hour for Multiplication 4.N.2, product when the factor is doubled or product/multiple, strategies, 58, Unit sessions TE p. 124 - 150 4.N.8, halved. cluster, expanded notation, Assessment M51- 4.N.9, partial 52 4.N.10, 2. Students will represent a products/subproducts, 4.N.11, multiplication or division problem with equivalent expression, 4.N.12, pictures, diagrams, or models. inverse operation, array, big 4.P.1, & small array, cluster 4.P.2, 3. Students will develop strategies for problems, length, width, multiplying that involve breaking apart dimensions, area, equation, numbers. divide, distributive property 4. Students will use arrays to model multiplication. Teacher's Notes: Quick Images (Ten-Minute Math) targets standards 4.N.8, 4.N.9, 4.N.11, 4.P.2. For students, who are still struggling seeing the arrays, you may try drawing in the hash marks along the length and width during, Inv.4.2. Record the products inside the array. Continue to make connections to area. As students become fluent with 2-digit by 1-digit multiplication differentiate by challenging them to try 2 by 2 and 3 by 2 multiplication. Students who master doubling and halving may try to experiment with tripling and quadrupling. Ten-Minute Math, Counting Around the Class, reinforces 4.N.11, 4.P.1, 4.P.2. Students who are flexible with using and explaining their strategies for multiplication and division should be exposed to the standard algorithms. Students compare the standard algorithm for multiplication with partial products/distributive property. If students are not ready for the standard algorithms they will have additional opportunities to master them during Unit 8: How Many Packages? How Many Groups? Focal Points (addressed): Number and Operations, Algebra (connected): Geometry CIA LPS Working Document3/5/2010 Unit 3: Multiple Towers & Division Stories Standards # Description Exhibit an understanding of the base ten number system by reading, modeling, writing, and interpreting whole numbers to at least 100,000; demonstrating an understanding of the values of the digits; and comparing and 4.N.1 ordering the numbers. Represent, order, and compare large numbers (to at least 100,000) using various forms, including expanded notation, 4.N.2 Recognize classes (in particular, odds, evens; factors or multiples of a given number; and squares) to which a number 4.N.7 Select, use, and explain various meanings and models of multiplication and division of whole numbers. 4.N.8 Select, use, and explain the commutative, associative, and identity properties of operations on whole numbers in problem 4.N.9 Select and use appropriate operations (addition, subtraction, multiplication, and division) to solve problems, 4.N.10 Know multiplication facts through 12 x 12 and related division facts. Use these facts to solve related multiplication 4.N.11 4.N.12 Divide up to a three-digit whole number with a single-digit divisor (with or without remainders) accurately and 4.N.13 Demonstrate in the classroom an understanding of and the ability to use the conventional algorithms for addition and 4.N.14 subtraction (up to five-digit numbers), and multiplication (up to three digits by two digits). Demonstrate an understanding of such attributes as length, area, weight, and volume, and select the appropriate type of 4.M.1 Carry out simple unit conversions within a system of measurement, e.g., hours to minutes, cents to dollars, yards to feet 4.M.2 or inches, etc. Identify and use appropriate metric and English units and tools (e.g., ruler, angle ruler, graduated (e.g., number 4.M.5 of sides, faces, corners, right angles, diagonals, and symmetry) of two- and three-dimensional geometric shapes. Create, describe, extend, and explain symbolic (geometric) and numeric patterns, including multiplication patterns like 3, 4.P.1 4.P.2 4.P.3 CIA LPS 3/5/2010 Unit 6: Fraction Cards Decimal Squares Mid January - Mid February Grade 4 20 Sessions Inv. # and MA Std Content Objective Key Vocabulary Language Objectives Assessment Pacing Name Inv. 1: 4.N.1, 1. Students will find fractional parts of a rectangular fraction, denominator, This is one example of Review p. 14 for 7 - 1 hour Parts of 4.N.2, area. numerator, rectangular a language objective. the assessment in sessions Rectangle 4.N.3, 2. Students will interpret the meaning of the numerator area, half, fourths, Please consider your this unit. TE p. 20 - 4.N.4, and denominator of a fraction. thirds, sixths, eighths, students' needs when Complete all 62 4.N.5, 3. Student will identify relationships b/w unit fractions unit fraction, multiple, writing your language 'Ongoing 4.N.7, when one denominator is a multiple of another (e.g. equivalent fraction, objectives: Students Assessments, 4.N.8, halves and fourths, thirds and sixths). fraction notation, whole, will use content specific Writing sum, estimate, square vocabulary to orally Opportunities, & 4.N.12, 4. Students will identify equivalent fractions. unit, divide/division, explain their thinking. Portfolio 4.N.18, 5. Students will find fractional parts of a group (e.g. of congruent, halving, Opportunities, & 4.M.1, objects, people, etc.) doubling, groups of, End-of-Unit 4.M.4, 6. Student will write, read, and apply fraction notation. dimensions, length, Assessments. 4.P.2 7. Students will compare the same fractional parts of width, row, columns, Portfolio: M12, different sized wholes. combinations, greater SAB p. 19-21 8. Students will use representations to add fractions that than >, less than <, sum to one. equal to = 9. Students will add fractions with the same and related denominators (e.g., halves, fourths, and eights; thirds and sixths) 10. Students will estimate sums of fractions. Teacher's Notes: Practicing Place Value reinforces 4N1, 4N2, 4N12, 4P2. While discussing 1/2s & 1/4s show notation w/ symbols & words, for ex. 1/4 of a 4 x 6 rectangle is 6 or 1/4 of 24 = 6 or 1/4 x 24 = 6 or 24/4 = 6, etc. This will reinforce 4N8. Continue this throughout unit. Be aware that the same area ≠ congruent figures. Use Math Note # 3 p. 27 in guide. Inv. 1.1 p. 29, record 1/4 + 3/4 = 4/4 = 1, continue this throughout the unit. SAB p. 2, p. 8, p. 17 reinforce 4.N.12. Standard 4N4 calls for mastery of the following fractions: 1/2, 1/3, 1/4, 1/5, 1/6, 1/8, 1/10, 1/12, 1 1/2. Find these fractional parts of wholes when appropriate, for ex. when finding fractions of the 5 x 12 rectangle, 8ths would not work. Continue this throughout the unit. SAB p. 15, differentiate by having students write an equivalent equation, for example 1/2 of 24 = 24/2 = 1/2 x 24. Be aware of common misconception when adding fractions with unlike denominators (ex. 1/2 + 2/6 ¹ 3/8). Use models to clarify why this doesn't work. During Inv. 1.7, More or Less Than 1? encourage students to write inequalities using the > & < signs when deciding, for ex. 1/2 + 3/4 > 1, etc., this will continue to extend 4P2. Focal Points (addressed): Number and Operations CIA Lowell Public Schools Working Document 3/5/2010 Unit 6: Fraction Cards Decimal Squares Mid January - Mid February Grade 4 20 Sessions Inv. # and MA Std Content Objective Key Vocabulary Language Objectives Assessment Pacing Name Inv. 2: 4.N.3, 1. Students will interpret the meaning of the numerator numerator, Portfolio: M23 6 - 1 hour Ordering 4.N.4, and denominator of the fraction. denominator, fraction, sessions Fractions 4.N.5, rectangular area, TE p. 68 - 4.N.10, 2. Students will represent fractions greater than one. equivalent fractions, 97 4.N.12, landmarks, number 4.N.18, 3. Students will find fractional parts of a rectangular line, fraction cards, 4.M.1, area. greater than, less than, 4.M.2, "strategies for comparing fractions", 4.M.4, 4. Students will identify equivalent fractions. greater than, less than, 4.P.2, equal to, conjecture, 4.D.1, 5. Students will order fractions and justify their order mixed number 4.D.2, through reasoning about fraction equivalencies and 4.D.3 relationships. 6. Students will compare fractions to the landmarks 0, 1/2, 1, 2. 7. Students will represent fractions using a number line. Teacher's Notes: Quick Survey reinforces 4D1, 4D2, & 4D3. In Inv. 2.1, Fractions > 1, encourage students to write inequalities using the > & < signs, for ex. 1/2 + 3/6 + 4/8 > 1, etc. This will cont. to extend 4P2. ALERT! SAB P. 26, FOR THIS UNIT IS PRINTED INCORRECTLY, IT SHOULD SHOW 1 WHOLE RECTANGLE w 3/4 SHADED OF ANOTHER. GIVE STUDENTS A COPY OF t. TEACHER'S MASTER P. 19 OR HAVE STUDENTS MAKE t. CORRECTION IN THEIR BOOKS. SAB p.28, p.34, reinforces 4N12, differentiation may be done by having students do simple conversions (4.M.2). When comparing fractions for ordering, create a list of student strategies, for ex., "One piece missing" compare t. size of t. missing piece. The smaller t. piece, t. larger the fraction. With "like denominators" compare numerators, etc. Begin this strategy chart w/ Missing Piece & it leave posted to add to in the future. When playing "Capture Fractions", Students can differentiate by recording the expressions & equations using the > & < symbols, for ex. 2/3 < 1 3/4, etc. On SAB p. 38, encourage students to use the > and < symbols as opposed to just circling. SAB p. 40 reinforces 4.N.10 & 4.N.12. Focal Points (addressed): Number and Operations CIA Lowell Public Schools Working Document 3/5/2010 Unit 6: Fraction Cards Decimal Squares Mid January - Mid February Grade 4 20 Sessions Inv. # and MA Std Content Objective Key Vocabulary Language Objectives Assessment Pacing Name Inv. 3: 4.N.1, 1. Students will identify every day uses of fractions and decimal, fraction, 10ths, Portfolio: SAB p. 7 - 1 hour Working 4.N.3, decimals. 100ths, area, 57-58, Unit sessions with 4.N.4, equivalence, estimate, Assessment M31 Decimals 4.N.5, 2. Students will read and write 10ths and 100ths. sums, multiples, mixed TE p. 104 - 4.N.6, number, decimal 137 4.N.7, 3. Students will represent 10ths and 100ths as part of an notation, equations 4.N.10, area. 4.N.12, 4.N.14, 4. Students will order decimals and justify their order through 4.N.17, reasoning about representations and meanings of the 4.N.18, numbers. 4.P.2, 4.M.1, 5. Students will identify decimal and fraction 4.M.4 equivalence. 6. Students will use representations to combine 10ths and 100ths. 7. Students will estimate sums of decimal numbers. 8. Students will add decimal numbers that are multiples of 0.1 and 0.25 (e.g., 2.3 + 3.25) Teacher's Notes: Practicing Place Value (Ten-Minute Math) reinforces 4.N.1, 4.N.6, and 4.N.12. SAB p. 46 , p. 49 reinforce 4.N.12. During Inv. 3.2, "Decimal Compare" differentiate by having students record the fraction notation for each decimal card. During Inv. 3.3, "Fill Two", differentiate by having students record the equivalent fraction equations for example, 0.45 + 0.1 + 0.35 = 0.9, similarly, 45/100 + 1/10 + 35/100 = 9/10, this extends to 4.N.18. With SAB p. 55 & 59 encourage students to use the greater than, less than, or equal to symbols as opposed to circling the greater decimal. SAB p. 60 reinforces 4.N.12, 4.N.17, 4.N.10. Focal Points (addressed): Number and Operations CIA Lowell Public Schools Working Document 3/5/2010 Unit 6: Fraction Cards & Decimal Squares Standards # Description Exhibit an understanding of the base ten number system by reading, modeling, writing, and interpreting whole numbers to at least 100,000; 4.N.1 demonstrating an understanding of the values of the digits; and comparing and ordering the numbers. 4.N.2 Represent, order, and compare large numbers (to at least 100,000) using various forms, including expanded notation, e.g., 853 = 8 x 100 + 5 x 10 + 3. Demonstrate an understanding of fractions as parts of unit wholes, as parts of a collection, and as locations on the number line 4.N.3 Select, use, and explain models to relate common fractions and mixed numbers (1/2, 1/3, 1/4, 1/5, 1/6, 1/8, 1/10, 1/12, and 11/2), find equivalent 4.N.4 fractions, mixed numbers, and decimals, and order fractions. 4.N.5 Identify and generate equivalent forms of common decimals and fractions less than one whole (halves, quarters, fifths, and tenths). 4.N.6 Exhibit an understanding of the base ten number system by reading, naming, and writing decimals between 0 and 1 up to the hundredths. Recognize classes (in particular, odds, evens; factors or multiples of a given number; and squares) to which a number may belong, and identify the 4.N.7 numbers in those classes. Use these in the solution of problems. Select, use, and explain various meanings and models of multiplication and division of whole numbers. Understand and use the inverse 4.N.8 relationship between the two operations. 4.N10 Select and use appropriate operations (addition, subtraction, multiplication, and division) to solve problems, including those involving money. 4.N.12 Add and subtract (up to five-digit numbers) and multiply (up to three digits by two digits) accurately and efficiently. Demonstrate in the classroom an understanding of and the ability to use the conventional algorithms for addition and subtraction (up to five-digit 4.N.14 numbers), and multiplication (up to three digits by two digits). Select and use a variety of strategies (e.g., front-end, rounding, and regrouping) to estimate quantities, measures, and the results of whole- 4.N.17 number computations up to three-digit whole numbers and amounts of money to $1000, and to judge the reasonablenes 4.N.18 Use concrete objects and visual models to add and subtract common fractions. Demonstrate an understanding of such attributes as length, area, weight, and volume, and select the appropriate type of unit for measuring each 4.M.1 attribute. 4.M.2 Carry out simple unit conversions within a system of measurement, e.g., hours to minutes, cents to dollars, yards to feet or inches, etc. 4.M.4 Estimate and find area and perimeter of a rectangle, triangle, or irregular shape using diagrams, models, and grids or by measuring. 4.D.1 Collect and organize data using observations, measurements, surveys, or experiments, and identify appropriate ways to display the data. 4.D.2 Match a representation of a data set such as lists, tables, or graphs (including circle graphs) with the actual set of data. Construct, draw conclusions, and make predictions from various representations of data sets, including tables, bar graphs, pictographs, line 4.D.3 graphs, line plots, and tallies. 4.P.2 sentences that use =, <, >). CIA LPS 3/5/2010 Unit 2: Describing The Shape of the Data End February - Middle March Grade 4 17 Sessions Invest Title & MA Std Content Objective Key Vocabulary Language Assessment Pacing Page No. Objective Invest #1 4.D.1, 1. Students will organize ordered, numerical data to describe a data data, data set, This is one Review p. 14 5 - 1 hour Landmarks 4.D.2, set. numerical data, list, example of a for the sessions in the Data 4.D.3, 2. Students will desribe the shape of the data set; where the data are spread, language assessment in 4.M.2, spread out or concentrated, what the highest and lowest values are, repesentation, bar objective. Please this unit. TE pages 22- 4.M.5, what the range is, and what the outliers are. graph, line plot, consider your Complete all 50- 4.N.2 3. Students will describe what values are typical or atypical in a data range, median, students' needs 'Ongoing 4.N.11 set. mode, outlier, typical, when writing Assessments, 4.N.12 4. Students will use a line plot to represent ordered numerical data. atypical, your language Writing 4.P.2 interpret/analyze, Opportunities, 5. Students will determine the range of a data set. objectives: order, organize, & Portfolio 6. Students will use U.S. standard units to measure lengths longer than Students will use shape of data, Opportunities, the measuring tool. content specific standard unit, length, & End-of-Unit 7. Students will record and keep track of data. vocabulary to expression, equation, Assessments 8. Students will represent 2 sets of data in order to compare them. orally explain their landmark, frequency Portfolio: SAB 9. Students will consider how well a data representation communicates to an thinking. p. 7, M7-8 audience. 10. Students will describe and interpret data that compare two groups. 11. Students will develop arguements based on data. 12. Students will find the median of a data set. 13. Students will use medians to compare groups. 14. Students will consider what information a median does and does not provide. Notes: 10-Minute Math covers 4P2 & 4N12 with writing, solving equations, addition, and subtraction. When having students describe the shape of date they should use correct terminology, as opposed to referring to "bumps, clumps, & holes", mathematicians prefer "mean, median, mode, outlier, range, frequency, and typical." SAB p. 1 targets 4N11. Prior to start of Inv. 1.2, consider a mini-lesson on proper use of measuring tools. Another form of differentiation may be to use measurements to the nearest whole in. or 1/2 in. through the height data collection. Inv. 1.2 & 1.3 students who are ready may convert inches to feet (4M2) as a form of differentiation. In session 1.3, please consider the sensitivity around the HW "How Many Cavities?" You may substitute w/ a more appropriate question since you will need data for the assessment in Inv. 1.5 or use the one provided in the M pages. When comparing heights, Inv. 1.4, have students represent data in more than one way as a form of differentiation. Daily practice p 8 & 9 in SAB cover 4N11 & 4P2. SAB p. 29 reinforces 4N11, 4N12. Focal Points (supported): Number and Operations, Algebra (connected): Data Analysis Lowell Public Schools Working Document [Date] Unit 2: Describing The Shape of the Data End February - Middle March Grade 4 17 Sessions Invest Title & MA Std Content Objective Key Vocabulary Language Assessment Pacing Page No. Objective Invest #2 4.D.1, 1. Students will develop and revise a survey question. survey, numerical Portfolio: SAB 7 - 1 hour Using Data 4.D.2, 2. Students will record and keep track of a set of data. data, , categorical p.34-35 sessions To Compare 4.D.3 3. Students will represent two sets of data in order to compare them. data, line plot, bar 4.P.2, 4. Students will consider how well a data representation communicates to an graph, conclusion, TE pages 56- 4.N.11, audience. value, data sets, 90 4.N.12, 5. Students will compare two sets of data by using the shape and represent, shape, 4.N.13 spread of the data. spread, median, 6. Students will draw conclusions based on data. range, outliers, 7. Students will develop arguments based on data. expression, equation, 8. Students will use a line plot to represent ordered numerical data. frequency, typical 9. Students will use medians to compare groups. 10. Students will consider what information a median does or does not provide. 11. Students will describe the shape of a set of data; where the data are spread out or concentrated, what the highest and lowest values are, what the range is, and what the outliers are. Teacher's Notes: Ten Minute Math covers 4.P.2 and 4.N.12 with writing, solving equations, addition, and subtraction. When students are playing Broken calculator, make connections to expanded notation (4.N.2). Students may represent their data in more than one way as a form of differentiation and may write several statements describing and comparing their data in detail. Teachers need to be attentive to the various typs of survey questions student create for their assessment, e.g. students may develop numerical questions around measurement. Be aware of the measurement standards that survey question connects with. SAB p. 18, 19 supports 4.N.11. Page 22 of the daily practice in the SAB reinforces 4.N.13; p. 23, 24, 36 reinforces 4.N.11. Focal Points (supported): Number and Operations, Algebra (connected): Data Analysis Lowell Public Schools Working Document [Date] Unit 2: Describing The Shape of the Data End February - Middle March Grade 4 17 Sessions Invest Title & MA Std Content Objective Key Vocabulary Language Assessment Pacing Page No. Objective Invest #3 4.D.1, 1. Students will associate the word probability with how likely will is to occur. probability, likely, Portfolio: SAB 5 - 1 hour Finding & 4.D.2, likelihood, unlikely, p.49-50,Unit sessions Comparing 4.D.3, 2. Students will arrange events along a line representing the range of event, certain, Assessment Probabilities4.D.4, certain to impossible. definate, impossible, M18-21 4.D.6, possible, range, TE pages 94- 4.N.2, 3. Students will use numbers from 0-1 as measures of probability. trials, experimental 119 4.N.3, probability, shape, 4.N.7, 4. Students will associate verbal descriptions of probability with spread, data, predict, 4.N.11, numeric descriptions. maybe, chance, 4.N.12, often, not often 4.P.2 5. Students will compare the expected probability of an event with the actual results of repeated trials of that event. 6. Students will compare two sets of data by using the shape and spread of the data. Teacher's Notes: Ten Minute Math covers 4.P.2 and 4.N.12 with writing, solving equations, addition, and subtraction. When students are playing Broken Calculator, make connections to expanded notation (4.N.2). SAB. pgs. 39, 46, 48, 51 reinforces 4.N.11, p. 48 also reinforces 4.N.7. Focal Points (supported): Number and Operations, Algebra (connected): Data Analysis Lowell Public Schools Working Document [Date] Unit 2: Describing the Shape of the Data Standards # Description Represent, order, and compare large numbers (to at least 100,000) using various forms, including expanded notation, e.g., 4.N.2 Demonstrate an understanding of fractions as parts of unit wholes, as parts of a collection, and as locations on 4.N.3 the number line. Recognize classes (in particular, odds, evens; factors or multiples of a given number; and squares) to which a number may 4.N.7 Know multiplication facts through 12 x 12 and related division facts. Use these facts to solve related multiplication problems 4.N.11 4.N.12 Divide up to a three-digit whole number with a single-digit divisor (with or without remainders) accurately and 4.N.13 efficiently. Interpret any remainders. Carry out simple unit conversions within a system of measurement, e.g., hours to minutes, cents to dollars, yards to feet or 4.M.2 inches, etc Identify and use appropriate metric and English units and tools (e.g., ruler, angle ruler, graduated (e.g., number of 4.M.5 sides, faces, corners, right angles, diagonals, and symmetry) of two- and three-dimensional geometric shapes. Collect and organize data using observations, measurements, surveys, or experiments, and identify appropriate ways to 4.D.1 display the data 4.D.2 Construct, draw conclusions, and make predictions from various representations of data sets, including tables, 4.D.3 Represent the possible outcomes for a simple probability situation, e.g., the probability of drawing a red marble from a bag 4.D.4 containing three red marbles and four green marbles. Classify outcomes as certain, likely, unlikely, or impossible by designing and conducting experiments using concrete objects 4.D.6 such as counters, number cubes, spinners, or coins. 4.P.2 inequalities (mathematical sentences that use =, <, >). CIA LPS 3/5/2010 Unit 9: Penny Jars Plant Growth Middle March - Middle April Grade 4 15 Sessions Inv. # and MA Std Content Objective Key Vocabulary Language Assessment Pacing Name Objectives Inv. 1: 4.D.1, 4.D.2, 1. Students will interpret the points and shapes of a graph in terms axis/axes, This is one Review p. 16 2 - 1 hour Looking at 4.D.3, of the situation the graph represents. horizontal, vertical example of a for the sessions Graphs 4.N.7, graph, points, language assessment in TE p. 24 - 4.N.11, 2. Students will find the difference b/w two values on a line graph. shape, difference, objective. this unit. 39 4.N.12, value, quantity, Please consider Complete all 4.N14, 3. Students will discriminate b/w features of a graph that represent highest, lowest, your students' 'Ongoing 4.N.17, quantity and those that represent changes in quantity. range, constant, needs when Assessments, 4.P.4 relative, gradually, writing your Writing interpret, zero language Opportunities, speed, slanted, Portfolio objectives: increase, Opportunities, & Students will use decrease, steadily, End-of-Unit content specific diagonal, gradual Assessments. vocabulary to slope, steep slope, orally explain jagged their thinking. Teacher's Notes: PRIOR TO STARTING INV. 1, PLANT LIMA BEANS YOU WILL NEED FOR MEASURING & COLLECTING DATA FOR USE DURING INV. 3 (SEE TEACHER'S GUIDE P. 13-15). Ten-Minute Math, Quick Survey, reinforces 4.D1, 4.D.2, & 4.D.3. During Inv. 1.1, to extend to standard 4.D.2, have students create a table for each city to show the temperatures for each day. Student Activity Sheet p. 11, reinforces 4.N.7 & 4.N.11. To reduce unit, review all sessions (especially as connected to the Unit Assessment). Some can be combined or condensed. Focal Points (supported): Numbers and Operations, Algebra CIA Lowell Public Schools Working Document 3/5/2010 Unit 9: Penny Jars Plant Growth Middle March - Middle April Grade 4 15 Sessions Inv. # and MA Std Content Objective Key Vocabulary Language Assessment Pacing Name Objectives Inv. 2: 4.D.1, 4.D.2, 1. Students will identify pts. in a graph w/ corresponding values in a Portfolio: SAB p. 8 - 1 hour Penny 4.D.3, 4.P.2, table & interpret t. numerical info. 21-22, p.35-37, sessions Jars and 4.P.4, 4.P.6, 2. Students will plot points on a coordinate grid to represent a M28-30 Towers 4.N.1, 4.N.2, situation in which one quantity is changing in relation to another. TE p 46 - 4.N.7, 3. Students will compare situations by describing the differences in 102 4.N.10, their graphs. 4.N.13, 4. Students will describe the relative steepness of graphs or parts of 4.N.14, graphs in terms of different rates of change. 4.N.16, 5. Students will use tables to represent the relationship b/w two 4.N.17 quantities in a situation of constant change & describe their relationship. 6. Students will interpret #s in a table in terms of t. situation they represent. 7. Students will find t. value of one quantity in a situation of constant change, given t. value of t. other. 8. Students will represent a situation of constant change. 9. Students will write an arithmetic expression using symbolic letter notation to represent and find t. value of one quantity in terms of t. other. 10. Students will make rules that relate one variable to another. Notes: Closest Estimate (Ten Minute Math) addresses 4N1, 4N2, 4N11, 4N16, 4N17. Inv. 2.1, Share Representations, connects to order of operations when writing expressions, ex. 4 + (6 x 9). SAB p. 14, 29, 49, 55 reinforces 4N10, 4N14. Inv. 2.2, Start with 2 & Add 3, have students express rules in oral, written, & symbolic expression. Continue this throughout the unit. When creating tables consider the zero/starting round. It will come up in Inv.2.4. SAB p. 19, 48 reinforces 4N13. 10-Min. Math Quick Survey reinforces 4D1, 4D2, 4D3. Inv. 2.3, Round 20, record the most efficient arithmetic expression in the calculation column, refer to it as an arithmetic expression, connect to order of operations. In this unit introduce the term method, use synonmously with strategy. SAB p. 24 reinforces 4N14. During Inv. 2.4, Matching Tables & Graphs, emphasize the reasonableness of connecting the pts, refer to T.N. #1 on pg. 70. Inv.2.5, Single & Double Tower, consider extending the rule to floors 20 & 100 . For students who struggle with keeping track of the number of windows, a suggestion is to insert an extra column for writing the arithmetic expressions, just like the calculation column in Round 20. SAB p.38 reinforces 4N17, 4N14. Focal Points (supported): Numbers and Operations, Algebra CIA Lowell Public Schools Working Document 3/5/2010 Unit 9: Penny Jars Plant Growth Middle March - Middle April Grade 4 15 Sessions Inv. # and MA Std Content Objective Key Vocabulary Language Assessment Pacing Name Objectives Inv. 3: 4.P.4, 1. Students will identify points in a graph with corresponding values points, graph, Portfolio: SAB p. 5 - 1 hour Collecting 4.P.6, in a table and interpret the numerical information in terms of the corresponding 60, Unit sessions and 4.D.1, 4.D.2, situation the graph represents. value, table, Assessment Analyzing 4.D.3, 2. Students will plot points on a coordinate grid to represent a numerical M37-39 Measurem 4.M.5, situation in which one quantity is changing in relation to another. information, plot, ents TE 4.M.2, 3. Students will describe the relative steepness of graphs or parts of points, coordinate 106 - 131 4.N.1, graphs in terms of different rates of change. graph, quantity, 4.N.2, 4. Students will compare situations by describing the differences in change, relative 4.N.8, their graphs. steepness, rate of 4.N.10, change, difference, 5. Students will interpret the points and shapes of a graph in terms 4.N.11, relationship, of the situation the graph represents 4.N.12, constant change, 6. Students will compare tables, graphs, and situations of constant 4.N.13, arithmetic change with those of non-constant change. expression, 4.N.14, 7. Students will use tables to represent the relationship b/w two plotting, x-axis, y- 4.N.15, quantities in a situation of constant change. axis, horizontal 4.N.16, 8. Students will write an arithmetic expression for finding the value axis, vertical axis. 4.N.17 of one quantity in terms of the other in a situation of constant relative steepness, change. steadily, decrease, 9. Students will measure in centimeters. increase Teacher's Notes: Ten-Minute Math, Quick Survey, reinforces 4.D1, 4.D.2, & 4.D.3. Ten-Minute Math, Closest Estimate, reinforces 4.N.1, 4.N.2, 4.N.11, 4.N.16, 4.N.17. Prior to Inv. 3.1, review metric system of measurement, make connection to the base-ten number system, fraction and decimal notation, and strategies for measuring accurately. Differentiate by having students record heights in mm and cm, when appropriate, to reinforce 4.M.2 and to record the measurements to the nearest half and whole. Differentiate by having students represent plant growth data using different representations, e.g. bar graphs. Student Activity Sheets p. 61-61, 65 reinforce 4.N.10, 4.N.11, 4.N.12,4.N.14. Student Activity Sheets p.64 & 72 reinforce 4.N.8, 4.N.11, 4.N.12, 4.N.13, 4.N.14, 4.N.15. Add a calculation/expression column to the sheet Removing Pennies from a Penny Jar for students who struggle seeing the change everytime. Focal Points (supported): Numbers and Operations, Algebra CIA Lowell Public Schools Working Document 3/5/2010 Unit 9: Penny Jars & Plant Growth Standards # Description Exhibit an understanding of the base ten number system by reading, modeling, writing, and interpreting whole numbers to at least 100,000; 4.N.1 demonstrating an understanding of the values of the digits; and comparing and ordering the numbers. Represent, order, and compare large numbers (to at least 100,000) using various forms, including expanded notation, e.g., 853 = 8 x 100 + 5 x 10 + 3. 4.N.2 Recognize classes (in particular, odds, evens; factors or multiples of a given number; and squares) to which a number may belong, and identify the 4.N.7 numbers in those classes. Use these in the solution of problems. Select, use, and explain various meanings and models of multiplication and division of whole numbers. Understand and use the inverse 4.N.8 relationship between the two operations. Select and use appropriate operations (addition, subtraction, multiplication, and division) to solve problems, including those involving 4.N.10 money. Know multiplication facts through 12 x 12 and related division facts. Use these facts to solve related multiplication problems and compute related 4.N.11 problems, e.g., 3 x 5 is related to 30 x 50, 300 x 5, and 30 x 500. 4.N.12 Add and subtract (up to five-digit numbers) and multiply (up to three digits by two digits) accurately and efficiently. Divide up to a three-digit whole number with a single-digit divisor (with or without remainders) accurately and efficiently. Interpret any 4.N.13 remainders. Demonstrate in the classroom an understanding of and the ability to use the conventional algorithms for addition and subtraction (up to five-digit 4.N.14 numbers), and multiplication (up to three digits by two digits). Demonstrate in the classroom an understanding of and the ability to use the conventional algorithm for division of up to a three-digit whole number 4.N.15 with a single-digit divisor (with or without remainders). 4.N.16 Round whole numbers through 100,000 to the nearest 10, 100, 1000, 10,000, and 100,000. Select and use a variety of strategies (e.g., front-end, rounding, and regrouping) to estimate quantities, measures, and the results of whole- 4.N.17 number computations up to three-digit whole numbers and amounts of money to $1000, and to judge the reasonablenes 4.D.1 Collect and organize data using observations, measurements, surveys, or experiments, and identify appropriate ways to display the data. 4.D.2 Match a representation of a data set such as lists, tables, or graphs (including circle graphs) with the actual set of data. Construct, draw conclusions, and make predictions from various representations of data sets, including tables, bar graphs, pictographs, line 4.D.3 graphs, line plots, and tallies. 4.M.2 Carry out simple unit conversions within a system of measurement, e.g., hours to minutes, cents to dollars, yards to feet or inches, etc. Identify and use appropriate metric and English units and tools (e.g., ruler, angle ruler, graduated (e.g., number of sides, faces, corners, 4.M.5 right angles, diagonals, and symmetry) of two- and three-dimensional geometric shapes. 4.P.2 (mathematical sentences that use =, <, >). Use pictures, models, tables, charts, graphs, words, number sentences, and mathematical notations to interpret mathematical relationships. 4.P.4 4.P.6 Determine how change in one variable relates to a change in a second variable, e.g., input-output tables. CIA LPS 3/5/2010 Unit 8: How Many Packages? How Many Groups? End April - Middle May Grade 4 16 Sessions Inv. # and MA Std Content Objective Key Vocabulary Language objectives Assessment Pacing Name Inv. 1: 4.N.1, estimation, multiplication, 1. Students will estimate solutions to 2-digit multiplication This is one example Review p. 14 for 5 - 1 hour Multiplication 4.N.2 problems. landmark, multiple, factor, of a language the assessment in sessions with 2-Digit 4.N.7, product/solution, objective. Please this unit. Numbers 4.N.8, 2. Students will multiply by multiples of 10. subproduct/partial product, consider your Complete all TE p. 24 - 58 4.N.11, expression, cluster, division, students' needs 'Ongoing 4.N.12, 3. Students will solve 2-digit multiplication problems by array, 'groups of', estimate, when writing your Assessments, 4.N.14, breaking a problem into smaller parts and combining the sub over-estimate, under-estimate, language objectives: Writing 4.N.16, products. magnitude,strategy, break Students will use Opportunities, & 4.N.17 apart/decompose, expanded content specific Portfolio notation, distributive property, vocabulary to orally Opportunities, & 4. Students will use story problems represented by a chunk, arithmetic, big array, explain their thinking. End-of-Unit multiplication expression to keep track of parts of the smaller array Assessments. problem. Portfolio: SAB p. 5-6, 14-15 5. Students will represent a multiplication or division problem with pictures, or diagrams, including arrays, and pictures of groups. Teacher's Notes: Ten-Minute Math, Closest Estimate, reinforces 4.N.1, 4.N.2, 4.N.11, 4.N.16, 4.N.17. StandardS 4.N.12 and 4.N.14 expect students to master 3 by 2 digit multiplication. Differentiate 'Closest Estimate' to include these types of problems. SAB p. 2 and 16 reinforce 4.N.12 & 4.N.14. When solving 2 by 2 digit multiplication make connections to the distributive property, order of operations, and array models to help studenSt make sense of the partial products. When students are drawing arrays for their multiplication problems encourage those who are struggling to use their grid paper as well as drawing the abstract representations. We want students to be able to draw the abstract models without all the square units. SAB p. 7 reinforces 4.N.8, 4.N.11, 4.N.12, 4.N.14, 4.N.17. SAB p. 10 reinforces 4.N.12 & 4.N.14. Ten-Minute Math, Counting Around the Class, reinforces standards 4.N.11, 4.P.1, 4.P.2. To reduce unit, review all sessions (especially as connected to the Unit Assessment). Some can be combined or condensed. Focal Points (addressed): Number and Operations, Algebra CIA Lowell Public Schools Working Document 3/5/2010 Unit 8: How Many Packages? How Many Groups? End April - Middle May Grade 4 16 Sessions Inv. # and MA Std Content Objective Key Vocabulary Language objectives Assessment Pacing Name Inv. 2: 4.N.1, 1. Students will solve 2-digit multiplication problems by multiplication, landmark, Portfolio: SAB p. 5 - 1 hour Strategies for 4.N.2, changing one factor to create an easier problem. multiple, factor, 71-72,M19 sessions Multiplication 4.N.7, 2. Students will use a story problem represented by a product/solution, TE p. 62 - 84 4.N.8, multiplication expression to keep track of parts of the subproduct/partial product, 4.N.9, problem. expression, cluster, division, 4.N.10, 3. Students will represent a multiplication or division problem array, 'groups of', subtract, 4.N.11, with pictures or diagrams, including arrays and pictures of rounding, distributive property, 4.N.12, groups. related number/problems, 4.N.14, cluster 4. Students will solve 2-digit multiplication problems by 4.N.16, breaking a problem into smaller parts and combining the sub 4.N.17, products. 4.P.1, 5. Students will multiply multiples of 10. 4.P.2, 4.P.4 Teacher's Notes: Ten-Minute Math, Closest Estimate, reinforces 4.N.1, 4.N.2, 4.N.11, 4.N.16, 4.N.17. SAB p. 21 reinforces 4.P.4, 4.N.10, 4.N.11. SAB p. 28 reinforces 4.N.8, 4.N.9, 4.N.12, & 4.N.14. When solving 2 by 2 digit multiplication make connections to the distributive property, order of operations, and array models to help students make sense of the partial products. When students are drawing arrays for their multiplication problems encourage those who are struggling to use use their grid paper as well as drawing the abstract representations. We want students to be able to draw the abstract models without all the square units. SAB p. 29 reinforces 4.N.7, 4.N.11, 4.N.12, & 4.N.14. SAB p. 30 reinforces 4.N.8 & 4.N.11. Ten-Minute Math, Counting Around the Class, reinforces 4.N.11, 4.P.1, 4.P.2. SAB p. 33 reinforces 4.N.11 & 4.N.12. Focal Points (addressed): Number and Operations, Algebra CIA Lowell Public Schools Working Document 3/5/2010 Unit 8: How Many Packages? How Many Groups? End April - Middle May Grade 4 16 Sessions Inv. # and MA Std Content Objective Key Vocabulary Language objectives Assessment Pacing Name Inv. 3: 4.N.1, 1. Students will solve 2-digit multiplication problems by divisor/factor, quotient, Portfolio: SAB p. 6 - 1 hour Solving 4.N.2, breaking a problem into smaller parts and combining the sub dividend, division, 44-45, Unit sessions Division 4.N.7, products. multiplication, 'groups of', Assessment M21- Problems TE 4.N.8, remainder, left over, 22 p. 88 - 111 4.N.9, 2. Students will solve 2-digit multiplication problems by expression, multiples, 4.N.11, changing one factor to create an easier problem. estimate, landmark number, 4.N.12, extra, strategies, doubling, 4.N.13, 3. Students will solve division problems by breaking the halving, rounding, standard 4.N.14, notation, inverse problem into parts. 4.N.15, 4.N.16, 4. Students will use multiples of 10 to solve division 4.N.17, problems. 4.P.1, 4.P.2 5. Students will use relationships b/w multiplication and division to solve division problems. 6. Students will represent a multiplication or division problem with pictures or diagrams including arrays and pictures of groups. 7. Students will use a story problem represented by a multiplication or division expression to keep track of parts of the problem. Teacher's Notes: Ten-Minute Math, Closest Estimate, reinforces 4.N.1, 4.N.2, 4.N.11, 4.N.16, 4.N.17. SAB p. 39 and 49 reinforce 4.N.12, 4.N.16, & 4.N.17. SAB p. 46 reinforces 4.N.1 & 4.N.12. Differentiate by having students record remainders using fraction notation. SAB p. 47 reinforces 4.N.7, 4.N.11, & 4.N.12. SAB p. 48 reinforces 4.N.8, 4.N.13, 4.N.12, & 4.N.15. Ten-Minute Math, Counting Around the Class, reinforces 4.N.11, 4.P.1, 4.P.2. SAB p. 33 reinforces 4.N.11 & 4.N.12. SAB p. 53 reinforces 4.N.12, 4.N.14, &4.P.2. Investigation 3 goes beyond our standard when teaching division of 3 digit by 2 digit. 4N13 calls for mastery fro 3 digit by 1 digit. Please be flexible when teaching this investigation and emphasize the 3 by 1 digit division and use the 3 by 2 digit division for differentiation. Focal Points (addressed): Number and Operations, Algebra CIA Lowell Public Schools Working Document 3/5/2010 Unit 8: How Many Packages? How Many Groups? Standards # Description Exhibit an understanding of the base ten number system by reading, modeling, writing, and interpreting whole numbers to at 4.N.1 least 100,000; demonstrating an understanding of the values of the digits; and comparing and ordering the numbers. Represent, order, and compare large numbers (to at least 100,000) using various forms, including expanded notation, e.g., 853 = 8 x 4.N.2 100 + 5 x 10 + 3. Recognize classes (in particular, odds, evens; factors or multiples of a given number; and squares) to which a number may belong, 4.N.7 and identify the numbers in those classes. Use these in the solution of problems. Select, use, and explain various meanings and models of multiplication and division of whole numbers. Understand and use 4.N.8 the inverse relationship between the two operations. Select, use, and explain the commutative, associative, and identity properties of operations on whole numbers in problem situations, 4.N.9 e.g., 37 x 46 = 46 x 37, (5 x 7) x 2 = 5 x (7 x 2). Select and use appropriate operations (addition, subtraction, multiplication, and division) to solve problems, including those 4.N.10 involving money. Know multiplication facts through 12 x 12 and related division facts. Use these facts to solve related multiplication problems and 4.N.11 compute related problems, e.g., 3 x 5 is related to 30 x 50, 300 x 5, and 30 x 500. Add and subtract (up to five-digit numbers) and multiply (up to three digits by two digits) accurately and efficiently. 4.N.12 Divide up to a three-digit whole number with a single-digit divisor (with or without remainders) accurately and efficiently. 4.N.13 Interpret any remainders. Demonstrate in the classroom an understanding of and the ability to use the conventional algorithms for addition and subtraction (up 4.N.14 to five-digit numbers), and multiplication (up to three digits by two digits). Demonstrate in the classroom an understanding of and the ability to use the conventional algorithm for division of up to a three-digit 4.N.15 whole number with a single-digit divisor (with or without remainders). 4.N.16 Round whole numbers through 100,000 to the nearest 10, 100, 1000, 10,000, and 100,000. Select and use a variety of strategies (e.g., front-end, rounding, and regrouping) to estimate quantities, measures, and the results of whole-number computations up to three-digit whole numbers and amounts of money to $1000, and to judge the 4.N.17 reasonablenes Create, describe, extend, and explain symbolic (geometric) and numeric patterns, including multiplication patterns like 3, 30, 300, 4.P.1 3000, …. 4.P.2 inequalities (mathematical sentences that use =, <, >). Use pictures, models, tables, charts, graphs, words, number sentences, and mathematical notations to interpret mathematical 4.P.4 relationships. CIA LPS 3/5/2010 Unit 7: Moving Between Solids Silhouttes Middle May - June Grade 4 14 Sessions Inv. # and MA Std Content Objective Key Vocabulary Language Assessment Pacing Name Objectives Inv. 1: 4.G.1, 1. Students will describe attributes of geometric prism, cube, cylinder, solid, This is one example Review p. 14 for 4 - 1 hour Geometric 4.G.2, solids. vertex/vertices, edge, face, of a language the assessment sessions Solids TE p. 20 - 4.G.3, geometric, attributes, objective. Please in this unit. 43 4.G.9, 2. Students will name geometric solids. silhouttes, 2-D, 3-D, consider your Complete all 4.N.1, triangular, circular, shape, students' needs 'Ongoing 4.N.3, 3. Students will understand how 3-D solids project visualize, figure, when writing your Assessments, 4.N.4, silhouettes with 2-D shapes (e.g., how a cone can perspective, rectangle, language Writing 4.N.6, produce triangular and circular silhouettes.) rectangular prism, triangle, Opportunities, objectives: 4.N.10, octagonal prism, Portfolio Students will use 4.N.11, 4. Students will decompose images of 3-D shapes hemisphere, cone, Opportunities, & content specific 4.N.12, and then recombine them to make a given structure. hexagonal prism, square End-of-Unit vocabulary to orally 4.N.13, prism, sphere, arrangement Assessments. explain their thinking. 4.N.18, 5. Students will visualize what 3-D figures look Portfolio: SAB p. 4.P.2 like from different perspectives. 5, M14 Teacher's Notes: Ten-Minute Math reinforces place value, standards 4.N.1, 4.N.6, 4.N.12. SAB p. 2 reinforces 4.N.6 & 4.P.2. SAB p. 3, reinforces 4.N.13, 4.N.3, 4.N.10, 4.N.11. SAB p. 8 relates to standards 4.N.3 and 4.N.4 SAB p. 14 reinforces standards 4.N.10, 4.N.18; p. 15 reinforces 4.N.4 & 4.P.2 Focal Points (supported): Number and Operations, Algebra (connected): Geometry CIA Lowell Public Schools Working Document 3/5/2010 Unit 7: Moving Between Solids Silhouttes Middle May - June Grade 4 14 Sessions Inv. # and MA Std Content Objective Key Vocabulary Language Assessment Pacing Name Objectives Inv. 2: Make 4.G.1, 1. Students will recognize how components of 3-D volume, fill-up, cube, mental Portfolio: SAB p. 5 - 1 hour and Visualizing 4.G.2, cube buildings come together to form a whole model, visualize, silhouette, 30, M16-17 sessions Cube Bldgs. TE 4.G.3, building. perspective, faces, edge, p. 48 - 72 4.G.7, vertex/vertices, layer, area, 4.G.9, 2. Students will find the volume of cube buildings. square units, cubic units, 4.M.1, top/bird's eye view, front, 4.N.1, 3. Students will draw silhouettes of 3-D cube buildings right side, flip (reflection), 4.N.3, from different perspectives. turn (rotation), slide 4.N.4, (translation) 4.N.5, 4. Students will interpret different silhouettes of an 4.N.6, object, both to form a mental model and to build a 4.N.10, whole object. 4.N.11, 4.N.12 5. Students visualize what 3-D figures look like 4.N.13, from different perspectives. 4.N.18 Teacher's Notes: Ten-Minute Math reinforces place value, standards 4.N.1, 4.N.6, 4.N.12. SAB p. 19 reinforces 4.N.13, 4.N.3, 4.N.10, 4.N.11; p. 24 reinforces 4.N.18; and p. 25, 31, and 32 reinforce standards 4.N.4 & 4.N.6. During Inv. 2.2, p. 57, include the terms from standard 4.G.7, when describing the configurations. Standard 4.M.1 area can be extended for those students who are ready by asking them to find surface area of their buildings, this is another form of differentiation. Standard 4.N.5 is reinforced with Student Activity sheet p. 34. Focal Points (supported): Number and Operations, Algebra (connected): Geometry CIA Lowell Public Schools Working Document 3/5/2010 Unit 7: Moving Between Solids Silhouttes Middle May - June Grade 4 14 Sessions Inv. # and MA Std Content Objective Key Vocabulary Language Assessment Pacing Name Objectives Inv. 3: 4.G.1, 1. Students will find the number of cubes (volume) rectangular prism, volume, Portfolio: SAB p. 5 - 1 hour Understanding 4.G.2, that will fit into the box made by a given pattern. cubes, box, congruent, 39-42, 45, Unit sessions Volume TE p. 4.M.1, pattern/net, layer, strategy, Assessment M23- 76 - 96 4.M.4, 2. Students design patterns for boxes that hold a decompose, dimensions, 25 4.N.1, given number of cubes (volume). silhoutte, 3-D, perspective, 4.N.3, length, width/depth, 4.N.4, 3. Students will see that cubes filling a rectangular height/tall, congruent, 4.N.6, prism can be decomposed into congruent layers. top/bird's eye view, front, 4.N.10, right side, box pattern/net, 4.N.12, 4. Students will develop a strategy for determining the rows, array, 4.N.18, volume of rectangular prisms. algorithm/notation (l x w x 4.P.1, h), doubling 4.P.2 5. Students will double the number of cubes for a given box and consider how that changes the dimensions of the original box. 6. Students will draw silhouettes of 3-D cube buildings from different perspectives. 7. Students will find the volume of cube buildings. Teacher's Notes: Ten-Minute Math in Inv. 3.1 reinforces place value (standards 4.N.1, 4.N.6, 4.N.12). SAB p. 36, reinforces 4.N.18.; p. 37, 43 reinforces standards 4.N.6 and 4.P.2. Ten-Minute Math in Inv. 3.2 reinforces place value (standards 4.N.6, 4.N.12). When completing the activity "Doubling the Number of Cubes" Student Activity Sheet p. 47, consider your students who are ready for this and those who are not, also, consider recording the doubling results on a chart so that students can easily follow the change or pattern, 4.P.1. Student Activity Sheet p. 49 reinforces standards 4.N.3, 4.N.4 & 4.N.10. Focal Points (supported): Number and Operations, Algebra (connected): Geometry CIA Lowell Public Schools Working Document 3/5/2010 Unit 7: Moving Between Solids & Silhouttes Standards # Description Exhibit an understanding of the base ten number system by reading, modeling, writing, and interpreting whole numbers to at least 4.N.1 100,000; demonstrating an understanding of the values of the digits; and comparing and ordering the numbers. 4.N.3 Demonstrate an understanding of fractions as parts of unit wholes, as parts of a collection, and as locations on the number line. Select, use, and explain models to relate common fractions and mixed numbers (1/2, 1/3, 1/4, 1/5, 1/6, 1/8, 1/10, 1/12, and 11/2), find 4.N.4 equivalent fractions, mixed numbers, and decimals, and order fractions. Identify and generate equivalent forms of common decimals and fractions less than one whole (halves, quarters, fifths, and tenths). 4.N.5 Exhibit an understanding of the base ten number system by reading, naming, and writing decimals between 0 and 1 up to the hundredths. 4.N.6 Select and use appropriate operations (addition, subtraction, multiplication, and division) to solve problems, including those 4.N.10 involving money. Know multiplication facts through 12 x 12 and related division facts. Use these facts to solve related multiplication problems and compute 4.N.11 related problems, e.g., 3 x 5 is related to 30 x 50, 300 x 5, and 30 x 500. 4.N.12 Add and subtract (up to five-digit numbers) and multiply (up to three digits by two digits) accurately and efficiently. Divide up to a three-digit whole number with a single-digit divisor (with or without remainders) accurately and efficiently. 4.N.13 Interpret any remainders. 4.N.18 Use concrete objects and visual models to add and subtract common fractions. Demonstrate an understanding of such attributes as length, area, weight, and volume, and select the appropriate type of unit for measuring 4.M.1 each attribute. Estimate and find area and perimeter of a rectangle, triangle, or irregular shape using diagrams, models, and grids or by measuring. 4.M.4 Compare and analyze attributes and other features (e.g., number of sides, faces, corners, right angles, diagonals, and symmetry) of two- and 4.G.1 three-dimensional geometric shapes. Describe, model, draw, compare, and classify two- and three-dimensional shapes, e.g., circles, polygons—especially triangles and 4.G.2 quadrilaterals—cubes, spheres, and pyramids. 4.G.3 Recognize similar figures. Describe and apply techniques such as reflections (flips), rotations (turns), and translations (slides) for determining if two shapes are 4.G.7 congruent. 4.G.9 Predict and validate the results of partitioning, folding, and combining two- and three-dimensional shapes. Create, describe, extend, and explain symbolic (geometric) and numeric patterns, including multiplication patterns like 3, 30, 300, 3000, …. 4.P.1 4.P.2 (mathematical sentences that use =, <, >). CIA LPS 3/5/2010

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language: | English |

pages: | 40 |

OTHER DOCS BY maclaren1

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