IMPLEMENTING THE NEW MATH SOL S IN THE LIBRARY MEDIA CENTER. Adrian Stevens November 2011 VEMA Conference, Richmond, VA

Transcription

1 IMPLEMENTING THE NEW MATH SOL S IN THE LIBRARY MEDIA CENTER Adrian Stevens November 2011 VEMA Conference, Richmond, VA

2 Primary Points Math can be fun Language Arts role in mathematics Fiction and nonfiction books Lessons to reinforce what the teachers are covering in the classroom

3 Language Arts & Mathematics The language arts skills of reading, writing, and oral language are necessary when working with mathematics. In addition, it is important to understand the implied text in symbols and diagrams.

4 3 Linguistic Tools for Mathematical Language The 3 linguistic tools used for mathematical language are forms of text. They are 1. Words 2. Symbols 3. Diagrams

5 Why Language Arts Skills are Important in Mathematics 1. Words used in Mathematics have very different meanings when used in other settings (for example, big, odd, even, radical, obtuse, circle, rational). 2. Terms are defined according to specific technical uses within the realm of mathematics. 3. Language Arts skills are necessary for Communication Mathematical Reasoning Accuracy

6 Resources Superintendent s Memo Math Vocabulary K- 3 kindergarten- grade3.pdf grade4-5.pdf

7 Superintendent s Memo # COMMONWEALTH of VIRGINIA Department of Education August 26, 2011 TO: Division Superintendents FROM: Patricia I. Wright, Superintendent of Public Instruction SUBJECT: New Mathematics Tests Based on the 2009 Mathematics Standards of Learning As stated in Superintendent s Memorandum #223-10, dated September 17, 2010, implementation of the new mathematics tests based on the 2009 Mathematics Standards of Learning (SOL) will begin with the fall 2011 administration for the end-of-course (EOC) mathematics tests (Algebra I, Geometry, and Algebra II) and with the spring 2012 administration for the grades 3 through 8 mathematics tests. New Blueprints New blueprints for all mathematics tests have been developed for use with the new SOL and have been posted on the Virginia Department of Education (VDOE) Web page at The blueprints indicate the new reporting categories for each test, the number of test items in each reporting category, and the number of field test items per test. Note that the new Grade 3 Mathematics SOL test will be a grade level test rather than a cumulative test for grades K-3 and is now comprised of 40 operational items and 10 field test items. Also, the End-of-Course Geometry Test is now comprised of 50 operational items and 10 field test items. Technology-Enhanced Items Technology-enhanced items (TEI) will be included in the grades 6 through 8 and EOC mathematics tests. These item types will comprise approximately 15 percent of each test. TEI will be field tested in grades 3 through 5 in spring 2012 and will become part of the operational items that count towards a student s score for the tests in spring New Formula Sheets and Table of Standard Normal Probabilities Formula sheets for grades 6 through 8 and EOC mathematics have been developed for use with the new SOL and have been posted on the Virginia Department of Education (VDOE) Ancillary Test Materials Web page. These formula sheets will be available for the new EOC mathematics tests administered in fall 2011 and for the grades 6 through 8 mathematics tests administered in spring Teachers should incorporate these new formula sheets into instruction in and beyond. A new Algebra II SOL requires students to analyze properties of normal distributions and apply those properties to determine probabilities associated with areas under the standard normal curve. The table of Standard Normal Probabilities (z-table) is provided for use with this SOL. The z-table is posted on the VDOE Ancillary Test Materials Web page. SOL Practice Items To support student preparation for test questions that assess the 2009 mathematics SOL, a set of practice items delivered via electronic Practice Assessment Tools (epat) has been developed for each SOL mathematics test.

8 These practice items will provide students an opportunity to become familiar with the types of test questions that will be administered to assess the 2009 Mathematics Standards of Learning. The sets of SOL practice items and their guides can be found at An SOL Practice Item Guide, which may be used by teachers or other adults to guide students through the practice items, has been developed for each SOL epat. The use of the guide with the epat is strongly encouraged, as it will help to ensure that students are familiar with the types of items and tools they may encounter in the new online assessments. The practice items for grades 3 through 5 do not currently include TEI. However, these epat items will be updated in fall 2011 to include examples of these item types. School divisions will be notified when these practice items have been posted. Use of Color Color will be used for some test items in the online versions of the new SOL mathematics tests. Colors used with items will be suitable for students with a color vision deficiency and will appear in gray scale should the item be presented in paper format. Emphasis Words Emphasis words such as closest, equal, and best will no longer be emphasized by italics or capital letters on any SOL mathematics tests. The only exceptions will be the words NOT and EXCEPT, which will continue to be emphasized with capital letters on all SOL mathematics tests except for grade 3. The grade 3 mathematics test will not contain test items with the words NOT and EXCEPT. If you have any questions, please contact the student assessment staff at student_assessment@doe.virginia.gov or by telephone at (804) PIW/SLR/cb

9 Superintendent s Memo # COMMONWEALTH of VIRGINIA Department of Education November 4, 2011 TO: Division Superintendents FROM: Patricia I. Wright, Superintendent of Public Instruction SUBJECT: K-12 Mathematics Standards of Learning Institutes and Professional Development Resources Over the past three years, the Virginia Department of Education held statewide K-12 Mathematics Standards of Learning (SOL) Institutes providing targeted professional development for representatives from each of Virginia s school divisions in support of the implementation of the 2009 Mathematics Standards of Learning. Each institute was designed in a train-the-trainer professional development model to facilitate the development of local expertise and increase local leadership and professional development capacity. Institute attendees are strongly encouraged to conduct analogous professional development in their local school divisions. Supporting professional development resources associated with each K-12 Mathematics SOL Institute are available online at The 2009 and 2010 K-12 Mathematics SOL Institutes: outlined the content standard changes from the 2001 Mathematics SOL to the 2009 Mathematics SOL (2009); supported district leaders and teachers in the implementation of the 2009 Mathematics SOL (2009 and 2010); provided training in the vertical progression of content and pedagogy (2010); and provided instructional guidance in content areas of greatest challenge (2010). The 2011 K-12 Mathematics SOL Institutes: provided support in the implementation of the 2009 Mathematics Standards of Learning and new assessments, framed by the five goals for students becoming mathematical problem solvers, communicating mathematically, reasoning mathematically, making mathematical connections, and using mathematical representations to model and interpret practical situations; and provided professional development to assist teachers in facilitating students mathematical understanding through problem solving, communication, reasoning. Over 570 participants from 126 school divisions and 4 state-operated programs attended one of the 2011 K-12 Mathematics SOL Institutes in Abingdon, Roanoke, Richmond, or Fredericksburg during September and October. Attendees included division-level leaders, mathematics supervisors, instructional supervisors, professional development personnel, building administrators, mathematics specialists, and classroom teachers. School divisions should consider asking their representatives to the institutes to share the information provided with other mathematics faculty in the division. Questions regarding the K-12 Mathematics SOL Institutes or associated professional development resources should be directed to Michael Bolling, mathematics coordinator, via at Michael.Bolling@doe.virginia.gov or by telephone at (804) ; or Deborah Wickham, mathematics specialist K-5, via at

10 Kindergarten through Grade 3 angle a figure formed by two rays called sides having a common endpoint called the vertex Associated terms:

11 Kindergarten through Grade 3 area the number of square units needed to cover a surface Associated terms:

12 Kindergarten through Grade 3 array a set of objects or numbers arranged in rows and columns There are 3 rows of ants. There are 4 columns of ants. There are 12 ants in this array. Associated terms:

13 Kindergarten through Grade 3 attribute a quality or characteristic, such as color, thickness, size, and shape circle blue red small square large triangle Associated terms: classify

14 Kindergarten through Grade 3 bar graph a type of graph used to display data organized by categories; each axis of a bar graph should be labeled; the bar graph should be titled and have a key Favorite After School Toy Bikes Skates Video Games Jump rope Toy Associated terms:

15 Kindergarten through Grade 3 calendar a tool for measuring time in days, weeks, months, and years; yesterday, tomorrow, next week, last week Associated terms:

16 Kindergarten through Grade 3 cardinal number numbers used for counting or answering the question "how many?" Associated terms: ordinal number

17 Kindergarten through Grade 3 certain (probability) An event is certain to occur if it has a probability of 1. Associated terms: impossible

18 Kindergarten through Grade 3 circle a circle is a closed curve with all points in one plane and the same distance (radius) from a fixed point, the center; the center is not part of the circle Associated terms:

19 Kindergarten through Grade 3 classify to sort into groups according to attribute(s) one-digit two-digit numbers numbers Associated terms:

20 Kindergarten through Grade 3 Commutative Property of Addition changing the order of the addends does not affect the sum = Associated terms:

21 Kindergarten through Grade 3 Commutative Property of Multiplication changing the order of the factors does not affect the product 8 x 6 = 6 x 8 Associated terms:

22 Kindergarten through Grade 3 cone solid figure with a usually circular base joined to a vertex by a curved surface Associated terms: geometric solids

23 Kindergarten through Grade 3 congruent figures with exactly the same size and shape Associated terms:

24 Kindergarten through Grade 3 cube solid figure with six congruent, square faces; all edges are the same length; a cube has 8 vertices, 12 edges Associated terms: geometric solids

25 Kindergarten through Grade 3 cylinder solid figure with two congruent, parallel, usually circular bases joined by a curved surface Associated terms: geometric solids

26 Kindergarten through Grade 3 data pieces of information collected to answer a question Associated terms:

27 Kindergarten through Grade 3 denominator the number of equally-sized parts that make the whole or the complete set Associated terms: fraction

28 Kindergarten through Grade 3 diagonal a line segment that joins two non-adjacent vertices in a polygon diagonal Associated terms: Kindergarten through Grade 3

29 difference the distance between 2 numbers on a number line; the answer to a subtraction problem - = The difference between 6 and 4 is 2. Associated terms: Kindergarten through Grade 3

30 digit there are 10 digits; any one of the symbols, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Associated terms: Kindergarten through Grade

31 edge in a solid figure, a line segment where two faces of the solid meet Associated terms: geometric solids Kindergarten through Grade 3

32 equal having the same amount or value Associated terms: Kindergarten through Grade 3

33 equally likely outcomes outcomes that have the same probability Associated terms: probability Kindergarten through Grade 3

34 equation number sentence; a statement that two expressions or numbers are equal = 8 Associated terms: Kindergarten through Grade 3

35 equivalent having the same value Associated terms: Kindergarten through Grade 3

36 even number any number ending in 0, 2, 4, 6, or 8 Associated terms: odd number Kindergarten through Grade 3

37 event an outcome or set of outcomes of an experiment or situation; for example, getting a 3 is one possible event produced by a rolling a fair number cube Associated terms: probability Kindergarten through Grade 3

38 experiment in probability, any activity involving chance Associated terms: probability Kindergarten through Grade 3

39 face a polygon that serves as a side of a solid Associated terms: geometric solids Kindergarten through Grade 3

40 fraction part of a group or part of a whole three out of four equal three out of four dogs parts are shaded are spotted Associated terms: Kindergarten through Grade 3

41 geometric solids three-dimensional figures such as cone, pyramid, prism, cylinder Associated terms: Kindergarten through Grade 3

42 identity properties addition: if 0 is added to any number, the sum is the same as the given number 8+0 = 8 multiplication: if a given number is multiplied by 1, the product is the same as the given number 6 x 1 =6 Associated terms: Kindergarten through Grade 3

43 impossible (probability) an event is impossible if it has a probability of 0 Associated terms: certain, probability Kindergarten through Grade 3

44 inverse operations operations that undo each other; addition and subtraction are inverse operations; multiplication and division are inverse operations Addition and subtraction are inverse operations. Multiplication and division are inverse operations. Associated terms:

45 Kindergarten through Grade 3 line Line has no definition; described as a set of points that goes on and on in both directions; has no endpoints; has 1 dimension Associated terms: plane, point

46 Kindergarten through Grade 3 line of symmetry a line dividing a figure or an arrangement of objects into two parts that are mirror images of each other Associated terms: symmetry

47 Kindergarten through Grade 3 line plot a type of graph used to display data; in a line plot, each piece of data is represented Number of Pets Owned by Students in Mrs. Willis Class X X X X X X X X X X X X X X X X X X X Associated terms: axis

48 Kindergarten through Grade 3 line segment part of a line; line segment has two endoints Associated terms:

49 Kindergarten through Grade 3 mass the amount of matter in an object; weight is determined by the pull of gravity on the mass of an object; mass of an object remains the same regardless of its location; weight of an object changes depending on the gravitational pull at its location Associated terms:

50 Kindergarten through Grade 3 mixed number a quantity expressed as a number and a proper fraction Whole number 5 1 Fraction 2 Mixed Number Associated terms:

51 Kindergarten through Grade 3 number sentence equation = = 6 Associated terms: equation

52 Kindergarten through Grade 3 numeral a symbol representing a number Associated terms:

53 Kindergarten through Grade 3 numerator how many equal parts of the whole or set we have; the number of equal parts of the whole or set being considered Associated terms: fraction

54 Kindergarten through Grade 3 odd number any number ending in 1, 3, 5, 7, or 9 Associated terms: even number

55 Kindergarten through Grade 3 ordinal number a number that names the place or position of an object in a sequence or set first second third fourth Associated terms: cardinal number

56 Kindergarten through Grade 3 outcome (probability) result of an experiment Associated terms: probability

57 Kindergarten through Grade 3 pattern numbers or objects that follow a repeating or growing rule repeating pattern growing pattern Associated terms:

58 Kindergarten through Grade 3 perimeter the distance around any two-dimensional figure Associated terms:

59 Kindergarten through Grade 3 picture graph a data display that use pictures to represent the data Associated terms:

60 Kindergarten through Grade 3 place value the value a digit represents depending on its place in the number Associated terms:

61 Kindergarten through Grade 3 plane Plane has no definition; described as a flat surface; has 2 dimensions. Associated terms: line, point

62 Kindergarten through Grade 3 plane figure a figure that lies in a plane; a two-dimensional figure Associated terms:

63 Kindergarten through Grade 3 point Point cannot be defined; is described as an exact location; has no dimension Associated terms: line, plane

64 Kindergarten through Grade 3 polygon a closed plane figure composed of line segments that do not cross Associated terms:

65 Kindergarten through Grade 3 position location of an object relative to another (above, below, next to, beside, near, far, close by, below, above, up, down) Associated terms:

66 Kindergarten through Grade 3 probability the chance of an event occurring Associated terms:

67 Kindergarten through Grade 3 product the answer in multiplication Associated terms:

68 Kindergarten through Grade 3 quadrilateral a polygon with 4 sides Associated terms: polygon

69 Kindergarten through Grade 3 quotient the answer in division dividend divisor = quotient quotient divisor = dividend dividend = quotient divisor Associated terms:

70 Kindergarten through Grade 3 ray part of a line that starts at a point (the endpoint) and continues forever in one direction Associated terms: line

71 Kindergarten through Grade 3 rectangle a quadrilateral with 4 right angles (all three shapes below are rectangles) Associated terms: quadrilateral

72 Kindergarten through Grade 3 rectangular prism a solid in which all 6 faces are rectangles Associated terms: geometric solids

73 Kindergarten through Grade 3 sample space all possible outcomes of an experiment Associated terms: probability

74 Kindergarten through Grade 3 set a collection of distinct items or elements Associated terms:

75 Kindergarten through Grade 3 sort classify Associated terms: classify, attribute

76 Kindergarten through Grade 3 sphere a three-dimensional object with all of its points the same distance from its center Associated terms: geometric solids

77 Kindergarten through Grade 3 square a rectangle with all sides congruent Associated terms: quadrilateral, rectangle

78 Kindergarten through Grade 3 square pyramid a solid with a square base with 4 sloping triangular faces that share a vertex Associated terms: geometric solids

79 Kindergarten through Grade 3 standard form of a number a method of writing numbers The standard form for the number four thousand, three hundred twenty-four is 4,324. Associated terms: number

80 Kindergarten through Grade 3 statistics the collection, organization, and analysis of data Associated terms:

81 Kindergarten through Grade 3 sum the answer in addition Example: = 5 + = addend + addend = sum Associated terms:

82 Kindergarten through Grade 3 survey the collection, organization, and analysis of data Associated terms: statistics

83 Kindergarten through Grade 3 table data organized using rows and columns Price List for Copies Size Copy Price Small $5 Medium $10 Large $20 Associated terms: array

84 Kindergarten through Grade 3 tally a method of collecting data Associated terms:

85 Kindergarten through Grade 3 thermometer an instrument used to measure temperature in degrees; temperature can be measured in degrees Fahrenheit or degrees Celsius Associated terms:

86 Kindergarten through Grade 3 triangle A polygon with 3 sides Associated terms: polygon

87 Kindergarten through Grade 3 vertex The point of intersection of the 2 rays that comprise an angle; the point of intersection of 2 adjacent line segments that comprise a polygon vertex vertex Associated terms:

88 Kindergarten through Grade 3 volume the amount a container can hold; the amount of space occupied by an object Associated terms:

89 Kindergarten through Grade 3 weight weight is determined by the pull of gravity on the mass of an object; mass of an object remains the same regardless of its location; weight of an object changes depending on the gravitational pull at its location Associated terms: mass

90 Kindergarten through Grade 3 whole numbers a number from the set {0, 1, 2, 3 } Associated terms:

91 Grade 4 and Grade 5 angle a geometric figure formed by two rays called sides having a common endpoint called the vertex Angles are classified by their measures as right angles (exactly 90 ); acute angles (less than 90 ), and obtuse angles (greater than 90 and less than 180 ). ray vertex Associated terms:

92 Grade 4 and Grade 5 Associative Property of Addition Changing the groupings of three or more addends does not change the sum. (a + b) + c = a + (b + c) (2 + 6) + 5 = 2 + (6 + 5) Associated terms: Associative Property of Multiplication

93 Grade 4 and Grade 5 Associative Property of Multiplication Changing the groupings of three or more factors does not change the product. a ( bc ) = ( ab ) c 5 x (6 x 7) = (5 x 6) x 7 Associated terms:

94 Grade 4 and Grade 5 chord a line segment whose endpoints lie on a circle a diameter is a chord that passes through the center of the circle cchhoordd r diameter Associated terms: diameter, circle

95 Grade 4 and Grade 5 circumference the distance around a circle Associated terms:

96 Grade 4 and Grade 5 coordinate plane a grid formed by two axes that intersect at the origin The axes divide the coordinate plane into four quadrants. origin--intersection of the horizontal and vertical axes in the coordinate plane described by the ordered pair (0, 0) Associated terms: quadrant

97 Grade 4 and Grade 5 denominator the number of same-size parts in a whole or set Associated terms:

98 Grade 4 and Grade 5 diameter a chord that passes through the center of a circle Associated terms:

99 Grade 4 and Grade 5 elapsed time the amount of time that passes between two points in time Associated terms:

100 Grade 4 and Grade 5 equally likely two events with the same probability of occurrence Associated terms:

101 Grade 4 and Grade 5 expression an mathematical phrase that represents a quantity; may contain variables, numbers, and/or operations Associated terms:

102 Grade 4 and Grade 5 factor a number that is multiplied by another number to find a product Associated terms:

103 Grade 4 and Grade 5 frequency the number of times an outcome occurs Associated terms: probability

104 Grade 4 and Grade 5 line plot A line plot shows the spread of data and each piece of data is represented by an x Associated terms: graphical representations, bar graphs, line graph, stem-and-leaf plot

105 Grade 4 and Grade 5 greatest common factor the largest number that divides evenly into two or more numbers Associated terms:

106 Grade 4 and Grade 5 intersecting lines lines that meet or cross in exactly one point Associated terms:

107 Grade 4 and Grade 5 kite a quadrilateral with two pairs of adjacent sides congruent but not four congruent sides Associated terms:

108 Grade 4 and Grade 5 least common denominator least common multiple of two or more denominators Associated terms: least common multiple

109 Grade 4 and Grade 5 least common multiple the smallest multiple that each of two or more numbers share Associated terms:

110 Grade 4 and Grade 5 likelihood (of an event) the chance or probability that an event occurs Associated terms: probability

111 Grade 4 and Grade 5 line graph a graph using line segments to connect the graphed data points Associated terms: graphical representations, line plot, bar graph, stem-and-leaf plot

112 Grade 4 and Grade 5 mean a measure of central tendency; the arithmetic average; a mathematical representation of the typical value of a series of numbers, computed as the sum of all the numbers in the series divided by the count of all numbers in the series. Example: Suppose you wanted to know what the arithmetic mean of a stock's closing price was over the past week. If during the five-day week the stock closed at $14.50, $14.80, $15.20, $15.50, and then $14.00, its arithmetic mean closing price would be equal to the sum of the five numbers ($74.00) divided by five, or $ Associated terms: statistics, mode. median

113 Grade 4 and Grade 5 median a measure of central tendency; in a set of ordered data, the middle value If the data are shown with a histogram the "mode" is simply the value which corresponds to the highest point(s) on the curve. Associated terms: mean, mode, statistics, range

114 Grade 4 and Grade 5 metric measurement system a system of measurement based on multiples of 10; basic units are meter (length), gram (mass), and liter (volume or capacity) Associated terms:

115 Grade 4 and Grade 5 mode a measure of central tendency; the value(s) that occurs most often Associated terms: statistics, mean, median, range

116 Grade 4 and Grade 5 numerator a representation of the number of same-size parts being considered in terms of the whole Associated terms: denominator

117 Grade 4 and Grade 5 ordered pair Identifies a location in a coordinate plane (i. e., (3, 5)) The first number in the ordered pair indicates the distance of the point from the vertical axis. The second number in the ordered pair indicates the distance of the point from the horizontal axis. Associated terms:

118 Grade 4 and Grade 5 parallel lines coplanar lines that do not intersect Associated terms:

119 Grade 4 and Grade 5 parallelogram a quadrilateral with both pairs of opposite sides parallel Associated terms: quadrilateral

120 Grade 4 and Grade 5 perpendicular lines lines that intersect to form right angles Associated terms:

121 Grade 4 and Grade 5 place value the value a digit represents depending on its place in the number (tenth, hundredth, thousandth) Hundrredss Tenss Oness Decciimalll Tentthss h Hundrredtth Thousandtth s Associated terms:

122 Grade 4 and Grade 5 plane described as a flat surface that extends infinitely in all directions; has two dimensions Associated terms: point, line

123 Grade 4 and Grade 5 polygon a two-dimensional, simple, closed geometric figure that has line segments as sides Associated terms:

124 Grade 4 and Grade 5 quadrant one of four portions into which a plane is divided by the horizontal and vertical axes Quadrrantt IIII Quadrrantt II Quadrrantt IIIII I Quadrrantt IV I Associated terms: coordinate plane

125 Grade 4 and Grade 5 radius a line segment from the center of a circle to any point on the circle radius Associated terms:

126 Grade 4 and Grade 5 range (of a set of data) a measure of variation; the difference between the greatest and least values in a data set Associated terms:

127 Grade 4 and Grade 5 rational number any number that can be written as a ratio (fraction, decimal) Associated terms:

128 Grade 4 and Grade 5 rhombus a parallelogram with all sides congruent Associated terms: parallelogram

129 Grade 4 and Grade 5 trapezoid a quadrilateral with exactly one pair of parallel sides Associated terms: quadrilateral

130 Grade 4 and Grade 5 tree diagram a organized list of all possible outcomes for an event Associated terms: probability

131 Grade 4 and Grade 5 triangle a polygon with three sides Triangles can be classified by their angle types. An acute triangle has 3 acute angles. A right triangle has exactly one right angle. An obtuse triangle has exactly one obtuse angle. acute triangle right triangle obtuse triangle Associated terms: polygon, quadrilateral

132 Grade 4 and Grade 5 U. S. Customary measurement system the system of measurement commonly used in the United States; common units are inches, feet, yards, and miles-length; ounces, pounds, and tons-weight; ounces, cups, pints, quarts, and gallons-capacity Associated terms:

133 Grade 4 and Grade 5 variable a symbol that represents an unknown quantity Associated terms:

134

135 How to Make an Abacus Materials needed per abacus: 6 popsicle sticks 6 thin round sticks 12 white beads 30 blue beads Hot glue gun Glue for hot glue gun Instructions: To do before class: Glue the 6 thin round sticks to one Popsicle stick. Glue one Popsicle stick to the above sticks so that they are secured. Let dry. During first class: Explain an abacus its purpose and function. Read the book, The Warlord s Beads, by Virginia W. Pilegard. For the activity: Allow students to put blue beads on structure. Glue next two Popsicle sticks in place. Let dry. During second class: Allow students to put white beads on structure. Glue last two Popsicle sticks in place. Let dry. During third class: Try out the abacus!

136 Bodach, V. K. (2007). Bar graphs. (p. 32). Mankato, MN: Capstone Press. Bodach, V. K. (2008). Pictographs. (p. 32). Mankato, MN: Capstone Press. Bodach, V. K. (2008). Pie Graphs. (p. 32). Mankato, MN: Capstone Press. Bodach, V. K. (2008). Tally charts. (p. 32). Mankato, MN: Capstone Press. Bussell, L. (2008). Working with numbers in the news (math in our world). (p. 24). Pleasantville, NY: Weekly Reader Books. Cleary, B. P. (2005). The mission of addition. (p. 31). Minneapolis, MN: Millbrook Press. Cleary, B. P. (2006). The action of subtraction. (p. 31). Minneapolis, MN: Millbrook Press. Cleary, B. P. (2008). On the scale, a weighty tale. (p. 32). Minneapolis, MN: Millbrook Press. Clemson, W. (2004). Using math to conquer extreme sports. (p. 32). Milwaukee, WI: Gareth Stevens Publishing. Clemson, W. (2004). Using math to solve a crime. (p. 32). Milwaukee, WI: Gareth Stevens Publishing. Clemson, W. (2004). Using math to win a grand prix. (p. 32). Milwaukee, WI: Gareth Stevens Publishing. Dowdy, P. J. (2008). Graphing (my pathway to math). (p. 24). New York: Crabtree Publishing. Dowdy, P. J. (2008). Measurement (my pathway to math). (p. 24). New York: Crabtree Publishing. Freese, J. (2008). Tables and graphs of healthy things (math in our world). (p. 24). Pleasantville, NY: Weekly Reader Books. Gisler, D. (2001). Addition Annie. (p. 32). New York: Children s' Press. Green, D. (2010). Math: A book you can count on! (p. 64). New York: Kingfisher. Leedy, L. (1997). Mission: Addition. (p. 32). New York: Holiday House. Marrewa, J. (2008). Graphing favorite things. (p. 24). Pleasantville, NY: Weekly Reader Books.

137 Murphy, P. J. (2008). Measuring puppies and kittens. (p. 32). Berkeley Heights, NJ: Enslow Elementary. Murphy, S. J. (2000). Beep beep, vroom vroom! (p. 33). New York: HarperCollins Publishers. Murphy, S. J. (2001). Shark swimathon. (p. 33). New York: HarperCollins Children's Books. Nagda, A. W. (2000). Tiger math: Learning to graph from a baby tiger. (p. 29). New York: Henry Holt & Company. Piddock, C. (2010). Line, bar, and circle graphs (my path to math). (p. 24). New York: Crabtree Publishing. Pilegard, V. W. (2001). The warlord's beads. (p. 29). Gretna, LA: Pelican Publishing Company. Pilegard, V. W. (2002). The warlord's fish. (p. 29). Gretna, LA: Pelican Publishing Company Pilegard, V. W. (2003). The warlord's puppeteers. (p. 29). Gretna, LA: Pelican Publishing Company. Pilegard, V. W. (2005). The warlord's messengers. (p. 29). Gretna, LA: Pelican Publishing Company. Pilegard, V. W. (2007). The warlord's puzzle. (p. 29). Gretna, LA: Pelican Publishing Company. Rauen, A. W. (2008). Finding shortest and longest. (p. 16). Pleasantville, NY: Weekly Reader Books. Salzmann, M. E. (2009). What in the world is a cup? (p. 24). Edina, MN: ABDO Publishing Company. Salzmann, M. E. (2009). What in the world is a foot? (p. 24). Edina, MN: ABDO Publishing Company. Salzmann, M. E. (2009). What in the world is a pound? (p. 24). Edina, MN: ABDO Publishing Company. Salzmann, M. E. (2009). What in the world is an inch? (p. 24). Edina, MN: ABDO Publishing Company.

138 Salzmann, M. E. (2009). What in the world is an ounce? (p. 24). Edina, MN: ABDO Publishing Company. Scieszka, J. (1995). Math curse. (p. 30). New York: Penguin Group. Tang, G. (2004). Math fables: Lessons that count. (p. 38). New York: Scholastic, Inc. Tang, G. (2007). Math fables too: Making science count. (p. 38). New York: Scholastic Press.