Date: Wed, 27 Jan 2021 15:12:00 -0500 (EST) Message-ID: <1902406007.6371.1611778320673@wikis-prod-01.uit.tufts.edu> Subject: Exported From Confluence MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_Part_6370_433051033.1611778320673" ------=_Part_6370_433051033.1611778320673 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Content-Location: file:///C:/exported.html Third Grade Lessons

Each of our activities is designed to be flexible and self-conta= ined. Please feel free to use any of the activities as the basis of your te= aching or as supplementary materials.

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You do not need to do more than one of the activities in order for them = to be useful. However, we have listed them here in the approximate order th= at we have used them with students. This may be helpful for teachers lookin= g for a series of activities.

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Please explore our categorizations by activity type, process, and math c= oncept if you are looking for something specific!

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1. S= ymbols - Discussion about what symbols are; writing messages o= r "stories" with symbols; interpreting symbols.
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3. Comparisons - Comparisons and comparison operators: =3D, = =E2=89=A0, <, >.
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5. Comparisons and Attributes - Work with compa= risons and comparison operators (=3D, =E2=89=A0, <, >).
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7. Comparing Heights I - Students compare the heights = of two children, measure, compare, and represent one's own height in relati= on to a peer's height, and focus on the differences between heights.
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9. Comparing Discrete Quantities - Students = compare amounts of tokens and unknown amounts of discrete quantities. In bo= th cases they are guided to adopt line segments to represent discrete amoun= ts and the differences between them. They are also asked to discuss composi= tion of measures: "the difference plus the smaller amount is equal to the l= arger amount" and, "the larger amount minus the difference is equal to the = smaller amount".
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11. Heights as Functions - In this class children will= work on the functional representation of two unknown heights and on the co= mposition of the shorter height plus the difference between the heights as = equal to the second height.
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13. Candy Boxes - This class centers on the possible amounts of= candies two children, John and Maria, have. They each have the same, unspe= cified number of candies inside their own candy box. John has, in addition,= one extra candy and Maria has three extra candies. What are the possible t= otal candies they might have?
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15. Part-Whole Relations - This class follows the disc= ussion from the Candy Boxes I class. The challenge is to work with a visual= representation of the relationships among the various quantities in the ca= ndy box problem and to relate the visual and numerical information containe= d in visual diagram(s) to verbal descriptions and to algorithms for finding= unknown values.
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17. Number Line - Locations - Students place themse= lves at points on the number line. Main contexts: stairs, age, money, tempe= rature, and pure number.
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19. Number Line Shortcuts - The students will use a n= umber line to see how two addends or subtrahends are equivalent to one sing= le change once combined.
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21. Partial and Total Changes - Students learn th= at two partial changes are equivalent to a single total change. On the numb= er line, this corresponds to the idea of a shortcut. Three notations are em= phasized: words, number lines with hopping arrows, and numerical expression= s.
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23. Multiple Number Lines - Students continue to lear= n that two partial changes that start at different points on the number lin= e are equivalent. At the end, they will work with notation for variables (N= + 5 - 3 or N + 2).
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25. N-Number Line I - Students work with the table they bui= lt in the previous class for multiple number lines, focusing on the notatio= n for variables (N + 5 - 3 or N + 2).
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27. N-Number Line II - Students use the N-Number line to m= ake generalizations about an unknown amount of money in a piggy bank.
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29. Piggy Banks - The whole lesson revolves around a multipart = story problem involving changes in two quantities over several days of a we= ek. The initial quantities are equal yet unknown. Then transformations are = applied to the quantities. Students are asked to compare the quantities thr= oughout the week even though only their relative relationship can be determ= ined.
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31. Guess my Rule - Tables - Two children create sec= ret rules for transforming input numbers. The teacher uses a doubling rule.=
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33. Guess my Rule - Multiplicative Tables - Two children create secret rules for transforming input numbers. The= teacher uses a doubling or tripling rule.
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35. Three Heights - In this class we will explore: (a) How th= e children deal with comparisons, (b) How they draw inferences from compari= sons, and (c) How they represent comparisons between three unknown amounts.=
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37. Comparison Problems & Tables - This class will be used to= review concepts and representations as applied to the solution of verbal c= omparison problems and to work on function tables.
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39. All Things Being Equal II - The equals sign s= ignifies that amounts on each side are the same. The students will use Unif= ix blocks and the corresponding equations to represent equalities between a= dditive amounts.
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41. All Things Being Equal III - The students wi= ll write equations to represent verbal statements and successive transforma= tions that maintain or do not maintain the equality.
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43. Dots Problem - We present to the students a problem dealin= g with a growing pattern over time. To begin, there is one dot. With each p= assing minute four more dots are drawn around the previous dot(s).
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45. Functions - Earning Money - The students will= create tables and equations from given stories. The functions are additive= and multiplicative.
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47. Functions II - The students will use three functions that = are represented as a sequence of patterns and create a sequence of hops on = the number line, a data table, and an algebraic expression to express the f= unctions.
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49. Linear vs Quadratic Functions - The stude= nts will use two functions (a linear and a quadratic) that are represented = as a sequence of patterns and create a sequence of hops on the number line = and an algebraic expression to express the functions.
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51. Comparing Different Functions - The stude= nts will discuss, represent, and solve a verbal problem involving the choic= e between two functions.
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53. Functions from Tables - Students work with a func= tion, beginning with a table and then a formula, to generate ordered pairs = that follow the rule of the function.
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55. Starting With A Rule - Students focus on whether g= iven outputs are consistent with a given rule.
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57. Rules and Formulas - Students are given a rule and a= data table supposedly generated according to the rule. Students evaluate w= hether: (1) the proper rule has been applied and (2) the result is correct.=
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59. Formulas and Stories - The students will be requir= ed to work with the relation between different mathematical expressions (fo= rmulas) and stories.
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61. Dinner Tables I - Students work with a function relatin= g number of tables to the number of available seats. One table seats 4, two= tables seat 8, three tables seat 12....
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63. Dinner Tables II - Students work with a function relat= ing the number of tables (in a straight line) to the number of available se= ats. One table seats 4, two tables seat 6, three tables seat 8....
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65. Functioning Together - Students work together to d= evelop multiple representations of a function. The students split up into g= roups of three with each student having a separate responsibility. When all= the input values have been used up, the students are asked to, together, m= ake up a story that describes their function.
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67. Times Two - The lesson focuses on a function that multiplies = the input by two. New notations are introduced.
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69. Recipes that Exchange - The lesson focuses on a f= unction that multiplies input by two but also changes the ingredient to ano= ther type of ingredient.
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71. Human Graph I - Students plot themselves on a Cartesian p= lane. Each student will get a large card with a place for an ordered pair: = (x, y), where x refers to hours worked, and y refers to amount earned. The = students must name the coordinate pair for the point they themselves are st= anding on.
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73. Human Graph II - Students graph the functions k x 2 \$/h = and k x 3 \$/h. The idea is to show that for each linear function the points= fall onto a straight line.
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75. Rates vs Totals - Students compare points on an hours/p= ay Cartesian space. The main challenge lies in recognizing that, although o= ne student earned more, the other student was paid better, that is, at a hi= gher rate of pay. They must indicate the difference in pay and the differen= ces in amount worked.
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77. Comparing Graphs - Students are given an hourly rate o= f pay and infer coordinates for (h, \$) over a range of hours. They produce = a table and a graph of work-pay. Then they produce another graph for anothe= r rate of pay and discuss differences in time and pay.
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79. How Many Points? - Students work with: (a) a context =E2=80= =94 distance as a function of time; (b) generating coordinates.
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81. Interpreting Maps - Students construct a narrative of= a trip, given a simplified map and a table of arrival and departure times.= They also determine how much time was spent along each segment of the trip= (and how much time was spent at each place along the way.) If time permits= , they construct a table ordered by time, showing the duration of each segm= ent and the accumulated times.
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83. Maps to Graphs - Students will be given two linear dista= nce-time graphs and asked to tell a story about each graph and to compare t= hem. They will later explore comparisons between points in each line.
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85. Time and Time Lines - Students will discuss and lea= rn about points and intervals on time lines of various sorts.
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87. Interpreting Graphs - Students will be given two li= near distance-time graphs and asked to tell a story about each graph and to= compare them. They will later explore comparisons between points in each l= ine.
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