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Northwest Arkansas Instructional Alignment WORK IN PROGRESS Third Grade Mathematics NCTM Focal # of AR Department of Education Point or Times CONTENT STANDARD/ Objective Task Analysis Essential Vocabulary Materials/Resources Connector Tested Student Learning Expectations (SLE) Enduring Understanding - Successful problem solvers possess a set of core beliefs that support their work: problem solving is important, takes significant time and repeated efforts, and requires reflection. Essential Question - What are the specific strategies that have wide application in attacking problems and can help in problem solving? C.3.4 0 NO.3.3.4 A. Solve simple problems using one operation *use objects, mental computation, paper and pencil, addition Solve simple problems using one operation involving involving addition using a variety of methods and tools and appropriate technology to solve simple addition subtraction addition and subtraction using a variety of methods B. Solve simple problems using one operation and subtraction problems in different ways operation and tools. involving subtraction using a variety of methods and tools tools expanded notation FIRST NINE WEEKS 1. Enduring Understanding - The base 10 number system is based on groups of 10 1a. Essential Question - What strategies can be used to read and compare large numbers? 0 NO.1.3.2 A. Represent whole numbers including thousands *use manipulative to show whole numbers up to and compare Use the place value structure of the base ten number using the place value structure of the base ten including thousands represent system and be able to represent and compare whole number system *use manipulative to compare numbers up to and place value numbers including thousands (using models, B. Compare whole numbers including thousands including thousands thousands illustrations, symbols, expanded notation and problem using the place value structure of the base ten *illustrate to show whole numbers up to and including expanded notation solving) number system thousands models *illustrate to compare whole numbers up to and base ten including thousands period *use symbols to compare whole numbers up to and comma including thousands *use expanded form to write and to compare whole numbers up to and including thousands *solve real-world problems by applying their knowledge of showing and comparing whole numbers up to and including thousands FP.2.1 1 NO.1.3.3 A. Compare 4-digit numbers with and without *identify the thousands place less than Use mathematical language and symbols to compare appropriate technology *introduce the comma in a number greater than and order four-digit numbers with and without B. Order 4-digit numbers with and without appropriate *identify the value of the digits to compare and order 4- equal to appropriate technology (<, >, =) technology digit numbers order *use <, >, = when comparing two 4-digit numbers compare *sequence multiple 4-digit numbers from greatest to least *sequence multiple 4-digit numbers from least to greatest 1 of 18 Northwest Arkansas Instructional Alignment WORK IN PROGRESS Third Grade Mathematics NCTM Focal # of AR Department of Education Point or Times CONTENT STANDARD/ Objective Task Analysis Essential Vocabulary Materials/Resources Connector Tested Student Learning Expectations (SLE) Enduring Understanding - Successfulmethods of computation involveof core beliefs that support their work: problem solving is important, 2. Enduring Understanding - Flexible problem solvers possess a set grouping numbers in a variety of ways takes significant time and repeated efforts, and requires reflection. 2a. Essential Question - What strategies can be used for finding sums and differences? C.3.4 2 NO.3.3.1 A. Discover efficient and accurate methods of *use addition strategies to solve contextual problems sum Develop, with and without appropriate technology, computing in multi-digit addition through 999, using through 999 (strategies may include mental math, difference computational fluency in multi-digit addition and contextual problems: strategies for adding, estimation composing and decomposing, finding benchmark estimation subtraction through 999. of sums, in order to develop computational fluency numbers, compatible numbers, rounding, inverse multi-digit B. Discover efficient and accurate methods of operation) addends computing in multi-digit subtraction through 999, using *use subtraction strategies to solve contextual compatible number contextual problems: strategies for subtracting, problems through 999 (strategies may include mental inverse estimation of differences in appropriate situations, in mouth, composing and decomposing, finding compensatory numbers order to develop computational fluency benchmark numbers, compatible numbers, rounding, C. Show relationships between multi-digit addition and inverse operations) subtraction *illustrate that addition and subtraction are inverse (opposite) operations *use technology to solve contextual problems using addition and subtraction 3. Enduring Understanding - Place value patterns are repeated in large numbers. 3a. Essential Question - How are place value patterns repeated in large numbers? C.3.4 0 NO.1.3.1 A. Identify equivalent representations for the same *break apart whole numbers into smaller units equivalent Recognize equivalent representations for the same whole numbers *put a set of numbers together to form a whole whole number whole number and generate them by composing and B. Generate equivalent representations for the same number place value decomposing numbers whole number using composing and decomposing *show whole numbers in expanded form, standard digit numbers form, and written form, and recognize that they are expanded form equivalent standard form written form ones tens hundreds thousands compose decompose 0 Review: NO.1.3.2 A. Represent whole numbers including thousands *use manipulatives to show whole numbers up to and compare Use the place value structure of the base ten number using the place value structure of the base ten including thousands represent system and be able to represent and compare whole number system *use manipulatives to compare numbers up to and place value numbers including thousands (using models, B. Compare whole numbers including thousands including thousands thousands illustrations, symbols, expanded notation and problem using the place value structure of the base ten *illustrate to show whole numbers up to and including expanded notation solving) number system thousands models *illustrate to compare whole numbers up to and base ten including thousands period *use symbols to compare whole numbers up to and comma including thousands *use expanded form to write and to compare whole numbers up to and including thousands *solve real-world problems by applying their knowledge of showing and comparing whole numbers up to and including thousands 4. Enduring Understanding - Currency amounts can be grouped and exchanged to solve problems. 4a. Essential Question - Why is it important to represent currency amounts in different ways? 0 M.13.3.5 Identify the value of money up to $10 *state the value of bills ($1, $5, $10) dollar bill Determine the value of money up to $10 *state the value of coins dime *count coins (count by 50's, 25's, 10's, 5's, 1's) nickel *sort money to prepare to count penny *count money, begin with the largest value quarter half dollar value 2 of 18 Northwest Arkansas Instructional Alignment WORK IN PROGRESS Third Grade Mathematics NCTM Focal # of AR Department of Education Point or Times CONTENT STANDARD/ Objective Task Analysis Essential Vocabulary Materials/Resources Connector Tested Student Learning Expectations (SLE) 1 OR A. Identify change with the least possess a set of core beliefs that support change Enduring Understanding - Successful problem solvers amount of currency in *recognize the relationship between cost and their M.13.3.6 decimal problem solving is important, work: point Apply money concepts in contextual situations up to contextual situations up to $10.00 *determine change with the least amount of currency dollar sign takes B. Compare money up to $10.00 in reflection. $10.00 significant time and repeated efforts, and requires contextual *compare values of money up to $10 cost situations *develop strategies for solving money problems in change context 5. Enduring Understanding - Multiplication and division can be accomplished through addition and subtraction of partial products. 5a. Essential Question - How can multiples be used to solve problems? C.3.4 1 NO.3.3.5 A. Solve problems using estimation strategies *use front-end estimation, rounding, under-estimation, estimate Use estimation strategies to solve problems and judge B. Judge the reasonableness of the answer over-estimation to solve problems reasonable the reasonableness of the answer. *judge the reasonableness of the answer 3 of 18 Northwest Arkansas Instructional Alignment WORK IN PROGRESS Third Grade Mathematics NCTM Focal # of AR Department of Education Point or Times CONTENT STANDARD/ Objective Task Analysis Essential Vocabulary Materials/Resources Connector Tested Student Learning Expectations (SLE) Enduring Understanding - Successfultime is the measure of the a set of core beliefs that support their work: problem solving is important, 6. Enduring Understanding - Elapsed problem solvers possess duration of an event. takes significant time and repeated efforts, and requires reflection. of time and time of day? 6a. Essential Understanding - What is the difference between length 0 M.12.3.1 Identify the number of days in a month, days in a year *use strategies to determine the number of days in a day Determine the number of days in a month, days in a and identify the number of weeks in a year month week year and identify the number of weeks in a year. *identify the days in a year and a leap year month *identify the number of weeks in a year year leap year 0 M.12.3.2 Identify that 60 minutes equals 1 hour and that a day *recognize that 60 minutes equals one hour A.M. (Ante-Meridian) Recognize that 60 minutes equals 1 hour and that a is divided into A.M. and P.M. *recognize that a day is divided into A.M. and P.M. P.M. (Post-Meridian) day is divided into A.M. and P.M. 0 M.13.3.2 Tell time to the nearest 1-minute intervals *identify that each mark on a clock represents one minute hand Tell time to the nearest 1-minute intervals. minute according to the minute hand hour hand *count by ones and fives to determine time second hand *identify that there are sixty minutes in one hour *read a clock to the nearest one-minute interval 0 M.13.3.3 Express time to the half hour and quarter hour using *define quarter as related to time, not money quarter hour Express time to the half hour and quarter hour using the terms half-past, quarter after, quarter until *identify that four quarters equals one whole (as half hour the terms half-past, quarter after, quarter until related to fractions) quarter until *use quarter after, quarter until, and half past when quarter of expressing time quarter to 0 M.13.3.1 Use a calendar to determine elapsed time from month *read a calendar from month to month (forward and week Use a calendar to determine elapsed time from month to month backward) month to month. *develop the strategy that every time you move up or year down a square you move a week or seven days leap year *determine elapsed time by reading a calendar calendar elapsed 0 M.13.3.4 Identify elapsed time in contextual situations to five- *determine what the unknown is elapsed Determine elapsed time in contextual situations to five- minute intervals *determine the amount of time that has passed starting time minute intervals. between a starting time and an ending time to the ending time nearest five minutes analog clock *determine how to figure out the ending time when digital clock given the starting time to the nearest five minutes *develop strategies for finding various unknowns (counting by 5s, counting to the next hour, adding an hour) 4 of 18 Northwest Arkansas Instructional Alignment WORK IN PROGRESS Third Grade Mathematics NCTM Focal # of AR Department of Education Point or Times CONTENT STANDARD/ Objective Task Analysis Essential Vocabulary Materials/Resources Connector Tested Student Learning Expectations (SLE) SECOND NINE set of core Enduring Understanding - Successful problem solvers possess a WEEKS beliefs that support their work: problem solving is important, takes significant time and repeated efforts, and requires reflection. 1. Enduring Question - Multiplication and division are inverse operations. 1a. Essential Question - What is the relationship among factors, products, and quotients? C.1.3 1 NO.2.3.2 Determine if a 3-digit number is even or odd *identify the digit in the one's place and determine if even Apply number theory. *determine if a 3-digit number the 3-digit number is even or odd based on the digit in odd is even or odd the one's place (no matter the other digits) number theory *identify the patterns for even (0,2,4,6,8) *identify the patterns for odd (1,3,5,7,9) FP.3.1 0 NO.2.3.1 A. Show the commutative property of multiplication *use arrays, groups and area models to show the commutative property of Develop an understanding of the commutative and using objects commutative property of multiplication multiplication identity properties of multiplication using objects. B. Show the identity properties of multiplication using *make arrays and groups to show the identity property identity property of objects of multiplication multiplication *commutative property of multiplication - Ex. 2x4=4x2 array *identity property of multiplication - Ex. 2x1=2 5 of 18 Northwest Arkansas Instructional Alignment WORK IN PROGRESS Third Grade Mathematics NCTM Focal # of AR Department of Education Point or Times CONTENT STANDARD/ Objective Task Analysis Essential Vocabulary Materials/Resources Connector Tested Student Learning Expectations (SLE) Enduring UnderstandingHow can models for multiplication be used toof core beliefs that support their work: problem solving is important, 1b. Essential Question - - Successful problem solvers possess a set divide? FP.3.1 1 takes A. Model, represent requires reflection. NO.2.3.4 significant time and repeated efforts, andand explain division as *identify/describe when you know the number in each division MEASUREMENT: Model, represent and explain division as measurement set and the total but not how many sets, that is partitive division *Apply to price (Ex. Pies cost measurement and partitive division including equal B. Model, represent and explain division as partitive division as measurement measurement division $4 each. How many pies can groups, related rates, price, rectangular arrays (area division *identify/describe when you know how many sets and remainder you buy for $28?) model), combinations and multiplicative comparison. NOTE: INCLUDE REPEATED SUBTRACTION the total but not how many in each set, that is partitive inverse operation *Apply to rate (Ex. Ellen walks division *apply to price, rate, rate 3 miles an hour. How many and multiplicative comparison (see last column) hours will it take her to walk 15 *use rectangular arrays and combinations to show miles?) division in these two forms *Apply to multiplicative *explain how a remainder may impact an answer in a comparison (Ex. The giraffe is real-world situation 18 feet tall.The kangaroo is 6 feet tall. The giraffe is how many times taller than the kangaroo?) PARTITIVE: *Apply to rate (Ex. Ellen walked 15 miles.It took her 5 hours. If she walked the same speed the whole way, how far did she walk in one hour?) *Apply to price (Ex. Jan bought 7 pies. She spent a total of $28. If each pie cost the same amount, how much did one pie cost?) *Apply to multiplicative comparison (Ex. The giraffe is 18 feet tall. She is 3 times as tall as the kangaroo. How tall is the kangaroo?) FP.3.1 0 A.4.3.2 Use skip-counting patterns to multiply NOTE: *practice skip counting by any given number up to ten multiples of numbers Relate skip-counting patterns to multiplication. INCLUDE REPEATED ADDITION *relate skip counting to repeated addition skip counting . *use skip counting as a strategy for multiplication 6 of 18 Northwest Arkansas Instructional Alignment WORK IN PROGRESS Third Grade Mathematics NCTM Focal # of AR Department of Education Point or Times CONTENT STANDARD/ Objective Task Analysis Essential Vocabulary Materials/Resources Connector Tested Student Learning Expectations (SLE) 1c. Essential Question - - Successful problem used to learn basic multiplication and division facts? Enduring UnderstandingWhat strategies can besolvers possess a set of core beliefs that support their work: problem solving is important, FP.4.1;C.4.5 3 takes A. Discover efficient requires reflection. NO.3.3.3 significant time and repeated efforts, and and accurate methods of *develop and use strategies for multiplying and product OR-1 Develop, with and without appropriate technology, computing in multiplication, using contextual dividing numbers factor computational fluency in multiplication and division problems: strategies for multiplying, estimation of *perform operations in more than one way divisor using contextual problems products, in order to develop computational fluency *estimate products and quotients in appropriate dividend B. Discover efficient and accurate methods of situations quotient computing in division, using contextual problems: *show the relationship between multiplication and doubles strategies for division, estimation of quotients in division. multiple appropriate situations, in order to develop *solve contextual problems involving multiplication computational fluency and division with and without appropriate technology C. Show relationships between multiplication and division FP.3.1 0 NO.3.3.2 A. Discover efficient and accurate methods of *develop multiplication strategies (strategies may product Develop with and without appropriate technology, computing basic number combinations for include arrays, skip counting, repeated addition, factor fluency with basic number combinations for multiplication facts (10 x 10) in order to develop derived facts (using a fact you know, figure out a fact divisor multiplication and division facts (10 x 10) computational fluency you don't know), doubles, patterns) with and without dividend B. Discover efficient and accurate methods of appropriate technology quotient computing basic division facts (100 / 10) in order to *develop division strategies (strategies may include doubles develop computational fluency using repeated subtraction, multiplication (inverse multiple operation)), knowing multiplication facts, arrays, fact family) with and without appropriate technology 1d. Essential Question - What strategies are used to estimate products and quotients? C.3.4 1 Review: NO.3.3.5 A. Solve problems using estimation strategies *use front-end estimation, rounding, under-estimation, estimate Use estimation strategies to solve problems and judge B. Judge the reasonableness of the answer over-estimation to solve problems reasonable the reasonableness of the answer *judge the reasonableness of the answer 2. Enduring Understanding - Relationships between numbers can be described by generalizations. 2a. Essential Question - How can a pattern be generalized? C.3.1 1 A.4.3.5 Evaluate the relationship between sets of numbers, *find one-step rules involving sets of numbers in Determine the relationship between sets of numbers and use that to select the rule various forms (charts, lists) by selecting the rule *apply the rule to the set of numbers 3. Enduring Understanding - Symbolic notation is used to represent mathematical relationships. 3a. Essential Question - How are symbols used to represent mathematical relationships including operations, equality, and inequality? C.3.1 2 A.5.3.1 Select and/or write number sentences (equalities) to *define the equal sign to mean that the equation is equation Select and/or write number sentences (equalities) to find the unknown in problem-solving contexts balanced ("same as") balance find the unknown in problem-solving contexts involving two-digit times one-digit multiplication using *write number sentences that can be used to solve a equal sign involving two-digit times one-digit multiplication using appropriate labels word problem label appropriate labels. *use appropriate labels place value C.3.1; C.5.1 2 A.5.3.2 Express mathematical relationships using equalities *explain and understand the symbols (<, >, =, ≠) greater than Express mathematical relationships using equalities and inequalities *evaluate expressions on both sides less than and inequalities. *use symbols to compare the expressions equal to Ex. *decide whether an equality or inequality is true or not equal to 4 x 9 ___ 36 - 3 false true *compare numbers in expressions using symbols false *supply numbers that make given equalities or expression inequalities true equality inequality C.5.1 2 A.5.3.3 Use a symbol to represent an unknown quantity in a *use a symbol to represent an unknown number symbol Use a symbol to represent an unknown quantity in a number sentence involving contextual situations and *identify the unknown strategy number sentence involving contextual situations and find the value *solve for the unknown using a mathematical strategy unknown find the value. value Ex. number sentence 2 x Δ = 16 7 of 18 Northwest Arkansas Instructional Alignment WORK IN PROGRESS Third Grade Mathematics NCTM Focal # of AR Department of Education Point or Times CONTENT STANDARD/ Objective Task Analysis Essential Vocabulary Materials/Resources Connector Tested Student Learning Expectations (SLE) 0 Write problem solvers possess a of core information from story problem Enduring Understanding - Successful equations for contextual problems involving set*identify vital beliefs thatasupport their NO.2.3.3 work: problem solving is important, symbols Use conventional mathematical symbols to write multiplication using conventional mathematical *use strategies to solve a story problem by writing an equations takes for contextual problems and repeated efforts, and requires reflection. equation that represents a multiplication story. equationssignificant timeinvolving symbols contextual problems multiplication. 8 of 18 Northwest Arkansas Instructional Alignment WORK IN PROGRESS Third Grade Mathematics NCTM Focal # of AR Department of Education Point or Times CONTENT STANDARD/ Objective Task Analysis Essential Vocabulary Materials/Resources Connector Tested Student Learning Expectations (SLE) THIRD NINE set of core Enduring Understanding - Successful problem solvers possess a WEEKS beliefs that support their work: problem solving is important, takes significant time and repeated efforts, and requires shows relationships. 1. Enduring Understanding - Organization of information reflection. 1a. Essential Question - What are some ways to organize data? C.3.3 0 A.6.3.1 Complete a chart or table to organize given *using the information given, identify the rule to chart Complete a chart or table to organize given information and use the chart to identify relationships complete the chart or table table information and to understand relationships and and explain the results *explain how you arrived at your result using words explain the results. and/or pictures *use a chart or table to describe relationships (change from January to July in a given chart, etc.) C.3.3 2 DAP.14.3.1 A. Design a survey question after being given a topic *describe a frequency table, line plot, bar graph, and survey Design a survey question after being given a topic B. Collect, organize, display and describe simple data pictograph data and collect, organize, display and describe simple using frequency tables or line plots, pictographs and *identify what a survey is frequency table data using frequency tables or line plots, pictographs bar graphs *design a question from the given topic line plot and bar graphs. *collect and sort data pictograph *decide how to display data key (on a pictograph) *organize and display data using a frequency table, bar graph line plot, pictograph, and bar graph organize *label and title graph or table correctly (vertical and display horizontal labels, values, key) tally mark *apply data procedure with frequency tables, line plots, pictographs, and bar graphs. 1b. Essential Question - How can the elements of a graph help people to understand and to interpret the data? C.3.3 2 Review: DAP.14.3.1 A. Design a survey question after being given a topic *describe a frequency table, line plot, bar graph, and survey Design a survey question after being given a topic B. Collect, organize, display and describe simple data pictograph data and collect, organize, display and describe simple using frequency tables or line plots, pictographs and *identify what a survey is frequency table data using frequency tables or line plots, pictographs bar graphs *design a question from the given topic line plot and bar graphs. *collect and sort data pictograph *decide how to display data key (on a pictograph) *organize and display data using a frequency table, bar graph line plot, pictograph, and bar graph organize *label and title graph or table correctly (vertical and display horizontal labels, values, key) tally mark *apply data procedure with frequency tables, line plots, pictographs, and bar graphs C.3.3 0 DAP.15.3.2 Match a set of data with a graphical representation of *compare data with a graphical representation (Does graphical representation Match a set of data with a graphical representation of the data the graph represent the data?) data the data. *choose the appropriate graph to represent a given set of data C.3.3 0 DAP.16.3.1 Make predictions for a given set of data *make predictions for a particular set of data by prediction Make predictions for a given set of data extending charts and graphs certain impossible possible C.3.3 0 A.7.3.1 Identify the change over time *identify change as related to time vs. money difference Identify the change over time. *use given information to identify the distinction compare between two or more events over a longer period of time 1c. Essential Question - How does changing the scale affect how data is communicated? 9 of 18 Northwest Arkansas Instructional Alignment WORK IN PROGRESS Third Grade Mathematics NCTM Focal # of AR Department of Education Point or Times CONTENT STANDARD/ Objective Task Analysis Essential Vocabulary Materials/Resources Connector Tested Student Learning Expectations (SLE) C.3.3 2 Read problem solvers possess a of core beliefs that pictograph Enduring Understanding - Successful and interpret pictographs and bar graphs in set*identify and count symbols on asupportintheir work: a pictograph) DAP.15.3.1 key (on problem solving is important, Read and interpret pictographs and bar graphs in which symbols or intervals are greater than one intervals greater than one using the key symbol takes significant time and repeated efforts, and requires reflection. *find information on a bar graph by counting in which symbols or intervals are greater than one. vertical label intervals greater than one (2's, 5's, 10's, etc.) horizontal label *identify that a half symbol represents half of the value pictograph on a pictograph bar graph *read and interpret pictographs and bar graphs in which symbols or intervals are greater than one 1d. Essential Question - How can the next step in a pattern be found? C.4.1 3 A.4.3.4 A. Use repeating numeric or geometric patterns to *extend a variety of numeric and geometric patterns repeating patterns Use repeating and growing numeric or geometric solve problems *differentiate between a repeating and a growing growing patterns patterns to solve problems. B. Use growing numeric or geometric patterns to solve pattern extend problems 0 A.4.3.1 Count forward and backward when given a number *count forward and backward by any given number to forward Count forward and backward when given a number less than or equal to 1000 1000 in written or oral form backward less than or equal to 1000 _____, 399, _____, _____ 0 A.4.3.3 Identify a number that is more or less than any whole *skip count by multiples of ten from any number more Identify a number that is more or less than any whole number up to 1000 using multiples of ten and/or 100 forward and backward (Ex. 23, 33, 43, 53, etc.) with less number up to 1000 using multiples of ten and/or 100 objects such as 100s charts multiple *skip count by multiples of one hundred from any whole number number forward and backward (Ex. 114, 214, 314, 414, etc.) with objects such as numbers charts 10 of 18 Northwest Arkansas Instructional Alignment WORK IN PROGRESS Third Grade Mathematics NCTM Focal # of AR Department of Education Point or Times CONTENT STANDARD/ Objective Task Analysis Essential Vocabulary Materials/Resources Connector Tested Student Learning Expectations (SLE) Enduring Understanding - Successful problem solvers possess a set of for communicating measurements. problem solving is important, 2. Enduring Understanding - Standard units provide common language core beliefs that support their work: takes significant time and repeated efforts, and requires reflection. 2a. Essential Question - How are units of measure related? 1 M.12.3.4 A. Show the relationship between linear measurement *identify how many inches are in a foot and in a yard, foot Demonstrate the relationship among different B. Show the relationship between units of capacity feet in a yard using tools (rulers, etc.) inch standard units. C. Show the relationship between units of weight *identify how many cups are in a pint, how many pints yard in a quart, and how many quarts in a gallon using cup materials pint *identify how many ounces are in a pound using quart materials ounce *identify the abbreviations for the standard units or pound measurement length *apply measurement relationships in context capacity weight/mass standard units of measurement linear measurement (measuring a straight line) 0 M.12.3.5 Create and complete a conversion table to show *create a conversion table convert Create and complete a conversion table (from larger relationships between units of measurement in the *use a conversion table conversion table unit to smaller unit) to show relationships between same system (LARGER UNIT TO SMALLER UNIT) *change feet to inches using multiplication units of measurement in the same system. *change yards to feet using multiplication Ex. Change feet to inches using multiplication *change yards to inches using multiplication *change pints to cups using multiplication *change quarts to pints using multiplication *change gallons to quarts using multiplication *change pounds to ounces using multiplication *read and use the mathematics references sheet in Benchmark released items 3. Enduring Understanding - Perimeter is a one-dimensional measure (perimeter surrounds); area is a two-dimensional measure (area covers); volume is a three-dimensional measure (volume fills in). 3a. Essential Question - What strategies can be used to find area, perimeter, and volume of a shape or region? C.2.2; FP.4.3 OR-1 M.13.3.10 Find the perimeter of a figure by measuring the length *identify that perimeter is the distance around a figure perimeter Find the perimeter of a figure by measuring the length of the sides *measure a side and label the side with that length of the sides. measurement side *find perimeter by adding the length of ALL the sides (even if there is an unknown side) C.3.2 0 M.13.3.11 Find the area of any region counting squares and half- *identify that area is the measurement of the interior of area Find the area of any region counting squares and half- squares a figure square squares. *contrast square units with units. square unit *recognize that each square represents one square grid unit array *combine half square units into whole square units using grid paper, square tiles, pictures to find the area of any region FP.5.3 1 M.13.3.12 Discover strategies for finding the volume of *recognize a rectangular prism and a cube using rectangular prism Develop strategies for finding the volume (cubic units) rectangular prisms and cubes using models models cube of rectangular prisms and cubes using models. *contrast units, square units, and cubic units cubic unit *use models and pictorial representations of models volume *develop strategies to find volume by counting cubes that may or may not be seen 4. Enduring Understanding - A three-dimensional figure can be analyzed in terms of its two-dimensional parts. 4a. How are one-, two-, or three-dimensional shapes described and classified? 11 of 18 Northwest Arkansas Instructional Alignment WORK IN PROGRESS Third Grade Mathematics NCTM Focal # of AR Department of Education Point or Times CONTENT STANDARD/ Objective Task Analysis Essential Vocabulary Materials/Resources Connector Tested Student Learning Expectations (SLE) FP.5.3 1 of core beliefs that Enduring Understanding - Successful problem solvers possess a set*identify 3-D solids (G.8.2.1) support their work: problem solving G.8.3.1 A. Compare and contrast 3-D solids by investigating faces is important, Compare, contrast and build 3-D solids by the number of faces, edges, and vertices on models *use 3-D models to show faces, edges, and vertices edges takes significant faces, and repeated Build 3-D solids by investigating reflection. *count the faces, edges, and vertices on each 3-D investigating the number of timeedges, and vertices B.efforts, and requires the number of vertices on models. faces, edges and vertices on models model solids *compare/contrast the faces, edges, and vertices of all three-dimensional (3-D) 3-D models rectangular prism *build a 3-D solid using the number of faces, edges, cone and vertices given sphere cube cylinder properties FP.3.3 0 G.8.3.2 Identify regular polygons with at least 4 sides *identify a polygon regular polygon Identify regular polygons with at least 4 sides. *know the definition of a regular polygon (equal sides, square equal angles) regular pentagon *identify square, regular pentagon, regular hexagon, regular hexagon and regular octagon regular octagon properties FP.3.3 0 G.11.3.1 Replicate a three-dimensional model composed of *provide a model built from cubes for students to 3-D model Replicate a three-dimensional model composed of cubes when given a physical model replicate replicate cubes when given a physical model. sides vertices faces visualization 5. Enduring Understanding - Changing the position of an object does not affect its attributes. 5a. Essential Question - What strategies can be used to check for symmetry? FP.3.3 1 G.9.3.1 Draw one or more lines of symmetry in a polygon *apply congruency and symmetry (G.9.2.1) congruent Draw one or more lines of symmetry in a polygon. *identify one of more lines of symmetry in a polygon symmetry *draw one or more lines of symmetry in a polygon lines of symmetry 6. Enduring Understanding - Objects can be described and compared using geometric attributes. 6a. Essential Question - How can objects be represented and compared using geometric attributes? FP.3.3 3 G.11.3.2 Identify which new figure will be formed by combining *identify figures by name combining Determine which new figure will be formed by and subdividing models of existing figures *combine figures to make new figures subdividing combining and subdividing models of existing figures. *take apart an existing whole figure into its parts visualization properties 6b. Essential Question - How are points, lines, line segments, and rays related? 0 G.8.3.3 A. Identify line, line segment and ray using *identify the definition of a line, a line segment, and a line Identify and draw line, line segment and ray using appropriate labels ray by using examples line segment appropriate labels. B. Draw line, line segment and ray using appropriate *identify a line, a line segment, and a ray using ray labels appropriate labels *compare/contrast a line, a line segment, and a ray using appropriate labels *draw a line, a line segment, and a ray using appropriate labels 1 G.8.3.4 A. Identify intersecting and parallel lines *identify the definition of intersecting and parallel lines intersecting lines Identify and draw intersecting and parallel lines. B. Draw intersecting and parallel lines by using examples parallel lines *identify intersecting and parallel lines by using examples of real-world objects (shapes, pictures, letters) *draw intersecting and parallel lines 7. Enduring Understanding - A transformation is a specific movement of an object. 7a. Essential Question - What are translations, rotations, and reflections? 12 of 18 Northwest Arkansas Instructional Alignment WORK IN PROGRESS Third Grade Mathematics NCTM Focal # of AR Department of Education Point or Times CONTENT STANDARD/ Objective Task Analysis Essential Vocabulary Materials/Resources Connector Tested Student Learning Expectations (SLE) FP.3.3 1 of core beliefs a figure (G.9.22) Enduring Understanding - Successful problem solvers possess a set*recognize the motion of that support their G.9.3.2 Describe the motion of a two-dimensional figure as a work: problem solving is important, slide (translation) Describe the motion (transformation) of a two- flip, slide or turn *model and explain flip, slide and turn with objects flip (reflection) takes significant time and repeated efforts, and requires reflection. *describe how a figure was moved using flip, slide or dimensional figure as a flip (reflection), slide turn (rotation) (translation) or turn (rotation). turn motion 13 of 18 Northwest Arkansas Instructional Alignment WORK IN PROGRESS Third Grade Mathematics NCTM Focal # of AR Department of Education Point or Times CONTENT STANDARD/ Objective Task Analysis Essential Vocabulary Materials/Resources Connector Tested Student Learning Expectations (SLE) Enduring Understanding - Successful problem solvers possess a set of core beliefs that support their work: degree of precisionimportant, 8. Enduring Understanding - The choice of measurement tools depends on the measurable attribute and the problem solving is required. takes significant time and repeated efforts, and requires reflection. 8a. Essential Question - What determines the choice of a measurement tool? C.3.2 3 M.13.3.8 A. Use appropriate customary measurement tools for *identify which measurement tool applies to various length Use appropriate customary measurement tools for length situations (ruler, yard stick, measuring tape, capacity length, capacity and mass B. Use appropriate customary measurement tools for thermometer, scale, balance scale, teaspoons, cups, mass capacity gallons, pints, quarts) measurement tool C. Use appropriate customary measurement tools for *use the appropriate tool to measure length, capacity, ruler mass and mass yard stick measuring tape thermometer scale balance scale teaspoon cup gallon pint 1 M.12.3.3 Distinguish the temperature to contextual problems *identify that the higher you go on the Fahrenheit Fahrenheit Distinguish the temperature to contextual problems using the Fahrenheit scale on a thermometer scale the hotter it gets and the lower you go the colder vertical number line using the Fahrenheit scale on a thermometer it gets Ex. *identify that water freezes at 32 degrees Fahrenheit If I need to wear mittens and a scarf, what *apply temperatures to contextual problems temperature would it be? 35°F or 70°F? 0 M.13.3.7 A. Read temperatures on Fahrenheit scale in intervals *recognize whether it is a Fahrenheit or Celsius temperature Read temperatures on Fahrenheit and Celsius scales of two thermometer by looking at the label Fahrenheit in intervals of two and five. B. Read temperatures on Celsius scale in intervals of *count by 2's and 5's Celsius five *read temperature on Fahrenheit and Celsius degree 8b. Essential Question - What estimation strategies are used in measurement? C.3.2 2 M.13.3.9 A. Estimate length, capacity/volume and mass using *describe the order of the measurement tools (largest estimate Estimate and measure length, capacity/volume and appropriate customary units to smallest, smallest to largest) pound mass using appropriate customary units B. Measure length, capacity/volume and mass using *relate a measurement tool to a non-standard tool ounce appropriate customary units (fingertip, paper clip, arm span) in order to estimate customary units *measure length, capacity, and mass with a measurement tool 14 of 18 Northwest Arkansas Instructional Alignment WORK IN PROGRESS Third Grade Mathematics NCTM Focal # of AR Department of Education Point or Times CONTENT STANDARD/ Objective Task Analysis Essential Vocabulary Materials/Resources Connector Tested Student Learning Expectations (SLE) Enduring Understanding - Successfulpairs show an exact location onof coordinate plane. 9. Enduring Understanding - Ordered problem solvers possess a set a core beliefs that support their work: problem solving is important, takes significant time and repeated locationand requires reflection. 9a. Essential Question - How is the efforts, of a point on a grid described? 0 G.10.3.1 A. Locate and identify points on a coordinate grid *demonstrate how to locate a point on a grid by point Locate and identify points on a coordinate grid and using common language and geometric vocabulary moving horizontally on the grid then vertically on the coordinate grid name the ordered pair (quadrant one only) using B. Name the ordered pair using common language grid (which direction to move first) ordered pair common language and geometric vocabulary and geometric vocabulary *name a point on a grid horizontal (horizontal and vertical) *identify a point on a grid vertical column row 15 of 18 Northwest Arkansas Instructional Alignment WORK IN PROGRESS Third Grade Mathematics NCTM Focal # of AR Department of Education Point or Times CONTENT STANDARD/ Objective Task Analysis Essential Vocabulary Materials/Resources Connector Tested Student Learning Expectations (SLE) Enduring Understanding - Successful problem solvers possess a set of core beliefs that support their work: problem solving is important, FOURTH NINE WEEKS 1. Enduring Understanding - Both common and requires fractions can represent fractional parts. takes significant time and repeated efforts, and decimal reflection. 1a. Essential Question - How are numbers that represent fractional parts compared? FP.3.2 0 NO.1.3.4 Express fractions (halves, thirds, fourths, sixths and *use objects to model halves, thirds, fourths, sixths, fraction Represent fractions (halves, thirds, fourths, sixths and eighths) using words, numerals and physical models and eighths as they relate to parts of a set and parts halves eighths) using words, numerals and physical models of a whole *understand the thirds Ex. meaning of the numbers in a fraction fourths Identify and illustrate parts of a whole and parts of *write the fraction in words sixths sets of objects *recognize that a fractional part of a model does not eighths Recognize that a fractional part of a rectangle does have to be shaded in contiguous (touching) parts numerator not have to be shaded with contiguous parts denominator contiguous (touching) parts whole set FP.3.2 0 NO.1.3.7 Write a fraction that is equivalent to a given fraction *use models (to ensure conceptual understanding) to equivalent Write a fraction that is equivalent to a given fraction with the use of models show equivalent fractions (fraction circles, fraction fraction with the use of models. Ex. 1/2 = 4/8 = 8/16 kits, fraction towers, fraction steps, fraction bars, student-created fraction strips, etc.) *recognize and write equivalent fractions using various models FP.3.2 0 NO.1.3.5 Recognize that the size of the whole determines the *use different size models to represent a whole to quantity Utilize models to recognize that the size of the whole size of the fraction depending on the original quantity show, for example, half of a larger shape is different whole determines the size of the fraction depending on the using models than half of a smaller shape (large pizza vs. small fractions original quantity pizza) FP.4.2 0 NO.1.3.6 A. Represent (using the place value structure of the *recognize that $1 is a whole decimal point Use the place value structure of the base ten number base ten number system) decimals to hundredths in *recognize that the coins are parts of a whole dollar sign system and be able to represent and compare money *recognize that the decimal point means "and" base ten decimals to hundredths in money (using models, B. Compare (using the place value structure of the (separating the whole from the parts) place value illustrations, symbols, expanded notation and problem base ten number system) decimals to hundredths in *recognize that the numbers after the decimal tens solving) money represent the parts of a whole ("change") tenths Ex: *compare two money amounts using <, >, = hundreds $193.76 _____$139.67 *write a money amount in expanded notation hundredths ones expanded notation numeral value 16 of 18 Northwest Arkansas Instructional Alignment WORK IN PROGRESS Third Grade Mathematics NCTM Focal # of AR Department of Education Point or Times CONTENT STANDARD/ Objective Task Analysis Essential Vocabulary Materials/Resources Connector Tested Student Learning Expectations (SLE) Enduring Understanding - Successful problem solvers possess a set of core graphically. support their work: problem solving is important, 2. Enduring Understanding - Probability can be represented numerically and beliefs that takes significant time and repeated efforts, represented numerically? 2a. Essential Question - How is probability and requires reflection. C.7.4 0 DAP.17.3.1 Use fractions to predict probability of an event *identify what probability is probability Use fractions to predict probability of an event *relate fractions to probability as parts of a set fraction *express probability in fraction form and word form event *relate part to whole outcome numerator denominator 2b. Essential Question - How is the likelihood of an event determined and communicated? 0 DAP.17.3.3 Use physical models, pictures and organized lists to *manipulate objects to find combinations of two sets of physical model Use physical models, pictures and organized lists to find combinations of two sets of objects objects organized list find combinations of two sets of objects *develop a strategy for organizing and finding combinations (organized list, pictures, web, table, objects) 5 DAP.17.3.2 A. Conduct simple probability experiments and record *conduct many various simple probability experiments probability OR -1 Conduct simple probability experiments, record the the data (spinners, tiles, number cubes) and record the data fair data and draw conclusions about the likelihood of B. Draw conclusions about the likelihood of possible *use strategy to choose how to record data unfair possible outcomes (roll number cubes, pull tiles from outcomes *determine the fairness of a game by playing fair and tally marks a bag, spin a spinner, or determine the fairness of unfair games experiment games) *use tally marks to record data during experiment data *use data to conclude the likelihood of a possible conclusion outcome outcome possible outcome chance most likely less likely equally likely 17 of 18 Northwest Arkansas Instructional Alignment WORK IN PROGRESS Third Grade Mathematics NCTM Focal # of AR Department of Education Point or Times CONTENT STANDARD/ Objective Task Analysis Essential Vocabulary Materials/Resources Connector Tested Student Learning Expectations (SLE) Enduring Understanding - Successful problem solvers possess a set of core beliefsplacesupport their work: problem solving is important, 3. Enduring Understanding - Strategies for multiplication and division are based on that value concepts. takes significant time and repeated efforts, and place value help with multiplication and division of large numbers? 3a. Essential Question - How can knowledge of requires reflection. FP.4.1;C.4.5 3 NO.3.3.3 A. Discover efficient and accurate methods of *develop and use strategies for multiplying and product OR-1 Develop with and without appropriate technology, computing in two-digit by one-digit multiplication, dividing numbers factor computational fluency in multiplication and division up using contextual problems: strategies for multiplying, *perform operations in more than one way divisor to two-digit by one-digit numbers using two-digit by estimation of products, in order to develop *estimate products and quotients in appropriate dividend one-digit contextual problems computational fluency situations quotient B. Discover efficient and accurate methods of *show the relationship between multiplication and doubles computing in two-digit by one-digit division, using division multiple contextual problems: strategies for division, *solve contextual problems involving multiplication estimation of quotients in appropriate situations, in and division of two-digit numbers by one-digit order to develop computational fluency numbers with and without appropriate technology C. Show relationships between two-digit by one-digit multiplication and division 18 of 18

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posted: | 11/27/2010 |

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