Thinking Kids. Second Grade. NCTM Strands Covered: Number and Operations. Algebra. Geometry. Measurement. Data Analysis and Probability.


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1 Thinking Kids Second Grade NCTM Strands Covered: Number and Operations Algebra Geometry Measurement Data Analysis and Probability Posttest
2 to another N W E S How to Use This Assessment This Posttest assesses your students understanding of the concepts and objectives from the Thinking Kids TM Math Grade 2 boxed set. After your students have completed the cards from the set, use this Posttest to determine if they have mastered the concepts and to identify students that need reteaching and further practice. If students score poorly, you may want to use the Thinking Kids TM Math Grade 1 assessment to determine if the Grade 1 boxed set is better for your students. Here are the specific features of this assessment: 1 2 Name Date Count with understanding and recognize how many in sets of objects Cards: D1 and D2 Use multiple models to develop initial understandings of place value and the baseten number system Count the tally marks and write the number. 2.2 Circle the blocks needed to make the number See cards D1 and D Use multiple models to develop initial understandings of place value and the baseten number system Cards: D3 and D4 5 Circle the blocks needed to make the number. 241 See cards D3 and D Row 1: 46; 49; 50; Row 2: 119; 121; 125 See cards D5 and D Answers will vary but may include: ; = 235; two hundred thirtyfive; 2 hundreds, 3 tens, and 5 ones; ; = 184; one Write the missing numbers in each row. hundred eightyfour; 1 hundred, 8 tens, and 4 ones; 18 tens and 4 ones. See cards D7, D8, and D ; two hundred fifteen See cards D9, D10, and D See cards D12 and D , 45,, 47, 48,,, 51, 120,, 122, 123, 124, Recognize, describe, and extend patterns such as sequences of sounds and shapes or simple numeric patterns and translate from one representation Cards: D33, D34, D35, D36, D37, D38, and D Row 1: 100; 35; Row 2: 107; 37 See cards D28, D29, and D Name Date Sort, classify, and order objects by size, number, and other properties Cards: D31 and D Sort the shapes by writing their numbers in the correct spaces See cards D31 and D ; 35; 56; 70; Rule: +7; 77; 55; 22; Rule: 11 See cards D33, D34, D35, D36, D37, D38, and D Small Shapes 4 Sides Both 2.14 Write the missing numbers to complete each pattern. Then, write the rule. 7, 14, 21,,, 42, 49,, 63,, Rule: 99, 88,, 66,, 44, 33,, 11 Rule: Name Date Analyze how both repeating and growing patterns are generated Cards: D38, D40, D41, D42, D43, and D44 Illustrate general principles and properties of operations, such as commutativity, using specific numbers Card: D Draw what comes next. See cards D38, D40, D41, D42, D43, and D Write the missing numbers to complete each problem = = 12, so 5 + = Posttest Answer Key Name Date Describe attributes and parts of two and threedimensional shapes Card: D Answers will vary. Describe, name, and interpret relative positions in space and apply ideas about relative position Card: D Nadia pulled two figures out of a box. Follow the clues to find which figures she pulled out of the box. One figure has 4 angles and 4 sides that are always equal. The other figure has no corners, sides, or edges. One figure is flat and the other is not. Which figures did Nadia pull out of the box? and 2.23 Follow the directions. Draw a circle. Draw a trapezoid above the circle. Draw a triangle inside the circle. Draw a square to the left of the trapezoid. 12 Name Date See card D spaces north and 2 spaces east See card D Find and name locations with simple relationships such as near to and in coordinate systems such as maps Card: D57 Describe, name, and interpret direction and distance in navigating space and apply ideas about direction and distance 2.24 Help Becky get home from the library. Write the number of steps she needs to take and the directions she needs to travel. Zoe s Becky s Doctor Ben s Park Store Library Ty s Bank Rose s Card: D Follow the directions. Draw a square at (3,2). Draw a star at (3,5). Draw a heart at (5,5). Draw a circle at (1,1) = 9; = 9; 9 3 = 6; 9 6 = 3 See cards D14, D15, D16, D17, D18, and D ; +; +; See card D ; 7; 73; 19; 49; 50 See card D Row 1: 10; 7; Row 2: 4; 7 See cards D46 and D ; 45; 50; 40; 45; 35 Use concrete, pictorial, and verbal representations to develop an understanding of invented and conventional symbolic notations Cards: D46 and D = , so 5 + = = 99, so 99 = Write the number that is behind each shape = 30 = = = 40 = See card D Name Date Recognize and apply slides, flips, and turns Card: D a turn. 1 NCTM standard that the activity addresses 2 Corresponding Thinking Kids TM Math card(s) (Use these cards for teaching, reinforcing, or remediating the standard.) 3 Grade level and problem number 2.9 Drawings will vary, but three equal groups of six should be drawn = 6 sheep See cards D21, D22, D23, D24, and D Row 1: = 14; = 15; Row 2: = 10; = 12; Row 3: = 9; = 10; Row 4: = 18; = 20 See cards D26 and D Row 1: 13; 12; Row 2: 11; 17; Row 3: 7; 9 See cards D28, D29, and D30. See cards D48 and D From top to bottom: 45; 48; 47; 50 See card D A triangle and a square should be drawn. triangle; square See cards D51 and D The large triangle, = 63 7 = 49 = 9 4 Symbol for the NCTM strand covered in the activities (See page 1 for a key depicting each strand.) 5 Test item that relates to the standard and assesses students readiness levels 6 Activity answers and corresponding cards to use to assess the standard parallelogram, small triangle, and rhombus should be circled. See cards D51 and D square and sphere See card D53. See card D Recognize and create shapes that have symmetry Cards: D59 and D60 Recognize and create shapes that have symmetry Cards: D59 and D60 Draw how each shape would look after a slide, a flip, and Shape Slide Flip Turn Name Date Recognize and apply slides, flips, and turns Card: D Draw how each shape would look after a slide, a flip, and a turn. Shape Slide Flip Turn 2.27 Complete each picture by drawing the missing symmetrical half Complete each picture by drawing the missing symmetrical half. 14 See cards D59 and D Row 1: cube, square; Row 2: rectangular prism, rectangle See card D inches 14 See card D62. Reprinted with permission from Principles and Standards for School Mathematics, copyright 2000 by the National Council of Teachers of Mathematics (NCTM). All rights reserved. NCTM does not endorse the content or validity of these alignments. 2
3 Count with understanding and recognize how many in sets of objects 2.1 Count the tally marks and write the number. Cards: D1 and D2 Use multiple models to develop initial understandings of place value and the baseten number system 2.2 Circle the blocks needed to make the number. 241 Cards: D3 and D4 Develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections Cards: D5 and D Write the missing numbers in each row. 44, 45,, 47, 48,,, 51, 120,, 122, 123, 124, 3
4 Develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers Cards: D7, D8, and D Use number words or number sentences to show each number a different way Connect number words and numerals to the quantities they represent, using various physical models and representations 2.5 Count the blocks. Then, answer the questions. Cards: D9, D10, and D11 Write the number. Write the number using number words. 4
5 Understand and represent commonly used fractions, such 1 as 4, 1 3, and Answer the question. Cards: D12 and D13 What fraction of the shirts are striped? Understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations Cards: D14, D15, D16, D17, D18, and D Write four related number sentences using the numbers below. 3, 6, 9 + = + = = = 5
6 Understand the effects of adding and subtracting whole numbers Card: D Write + or to make each number sentence true = = = = 1 Understand situations that entail multiplication and division, such as equal groupings of objects and sharing equally Cards: D21, D22, D23, D24, and D Draw a picture and write the number sentence to solve the problem. Eighteen sheep are in a field. The farmer moves an equal number of sheep into 3 barns. How many sheep are in each barn? = sheep 6
7 Develop and use strategies for wholenumber computations, with a focus on addition and subtraction Cards: D26 and D Write the missing number sentences to complete the table. Doubles Doubles Plus 1 Doubles Plus = = = = 19 Develop fluency with basic number combinations for addition and subtraction Cards: D28, D29, and D Solve each problem = 18 7 = = = 16 9 = 17 8 = Use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators Cards: D28, D29, and D Solve each problem = = = = 7
8 Sort, classify, and order objects by size, number, and other properties Cards: D31 and D Sort the shapes by writing their numbers in the correct spaces Small Shapes Both 4 Sides Recognize, describe, and extend patterns such as sequences of sounds and shapes or simple numeric patterns and translate from one representation to another 2.14 Write the missing numbers to complete each pattern. Then, write the rule. 7, 14, 21,,, 42, 49,, 63, Cards: D33, D34, D35, D36, D37, D38, and D39 Rule: 99, 88,, 66,, 44, 33,, 11 Rule: 8
9 Analyze how both repeating and growing patterns are generated 2.15 Draw what comes next. Cards: D38, D40, D41, D42, D43, and D44 Illustrate general principles and properties of operations, such as commutativity, using specific numbers Card: D Write the missing numbers to complete each problem. 7 + = 12, so 5 + = = 24 = , so 5 + = = 99, so 99 = Use concrete, pictorial, and verbal representations to develop an understanding of invented and conventional symbolic notations 2.17 Write the number that is behind each shape = = 40 Cards: D46 and D47 = = = = 49 = = 9
10 Model situations that involve the addition and subtraction of whole numbers, using objects, pictures, and symbols 2.18 Follow the rules. Write the missing number on each fruit. Cards: D48 and D49 = +5 = Describe qualitative change, such as a student s growing taller Card: D Write the missing heights to complete the table. Child Old Height Height Now Growth Brandy 32 inches inches 13 inches Holly 36 inches inches 12 inches Diane 33 inches inches 14 inches Dawn 35 inches inches 15 inches 10
11 Recognize, name, build, draw, compare, and sort two and threedimensional shapes Cards: D51 and D Follow the clues to draw the shapes. Then, name the shapes. This shape has 3 corners and 3 sides. It is a face on a pyramid. This shape has an even number of sides and corners. It is a face on a cube. What shape is this? What shape is this? Investigate and predict the results of putting together and taking apart two and threedimensional shapes 2.21 Circle the shapes used to make the picture. Cards: D51 and D54 11
12 Describe attributes and parts of two and threedimensional shapes Card: D Nadia picked two figures out of a box. Follow the clues to find and name the figures. One figure has 4 angles and 4 sides that are always equal. The other figure has no corners, sides, or edges. One figure is flat and the other is not. Which figures did Nadia pick out of the box? and Describe, name, and interpret relative positions in space and apply ideas about relative position Card: D Follow the directions. Draw a circle. Draw a trapezoid above the circle. Draw a triangle inside of the circle. Draw a square to the left of the trapezoid. 12
13 Describe, name, and interpret direction and distance in navigating space and apply ideas about direction and distance Card: D Help Becky get home from the library. Write the number of spaces that she needs to move and the directions she needs to travel. N Zoe s Becky s W S E Doctor Ben s Park Store Library Bank Ty s Rose s Find and name locations with simple relationships such as near to and in coordinate systems such as maps Card: D Follow the directions. Draw a square at (3,2). Draw a star at (3,5). 6 5 Draw a heart at (5,5). Draw a circle at (1,1)
14 Recognize and apply slides, flips, and turns Card: D Draw how each shape would look after a slide, a flip, and a turn. Shape Slide Flip Turn Recognize and create shapes that have symmetry Cards: D59 and D Complete each picture by drawing the missing symmetrical half. 14
15 Recognize and represent shapes from different perspectives Card: D Name the solid figure that describes each object. Then, name each solid figure s face. Object Solid Figure Face Relate ideas in geometry to ideas in number and measurement Card: D Find the missing length. 15 in. 15 in. 15 in. in. P = 60 inches Missing Side = inches 15
16 Recognize geometric shapes and structures in the environment and specify their location Card: D Draw a line to connect each picture to the correct name. cube cone pyramid 16
17 Recognize the attributes of length, volume, weight, area, and time Cards: D64, D65, D66, D67, D68, D69, and D José walks with his father to school every day. They leave home at 7:35. They arrive at school at 7:55. Draw hands on the clocks to show the time that José left home and the time that he arrived at school. Then, write how long it takes José to walk to school. minutes Compare and order objects according to these attributes Cards: D64, D65, D66, D67, D68, and D Number the pictures from 1 to 4 to order them from lightest to heaviest. 17
18 Understand how to measure using nonstandard and standard units 2.33 Review how each child measured the crayon. Explain why she measured it correctly or incorrectly. Cards: D70, D71, D72, D73, and D Did Paige measure the crayon correctly? Explain your answer Did Nora measure the crayon correctly? Explain your answer. 18
19 Measure with multiple copies of units of the same size, such as paper clips laid end to end 2.34 Use small paper clips to measure each picture. Cards: D71 The snake is about paper clips long. The gecko is about paper clips long. Use repetition of a single unit to measure something larger than the unit, for instance, measuring the length of a room with a single meterstick Cards: D72 and D Circle the answer to each question. Dawn measured her desk with a connecting cube. Which measurement would be closest to her measurement? 5 cubes 25 cubes 50 cubes 75 cubes Brad measured the width of his hand with a ruler. Which measurement would be closest to his measurement? 20 inches 11 inches 3 inches 1 inch 19
20 Develop common referents for measures to make comparisons and estimates 2.36 Use connecting cubes to measure the marker. Then, answer the questions. Cards: D72 and D73 The marker is about cubes long. About how many markers tall is this paper? About how many cubes tall is this paper? markers cubes Use tools to measure Card: D Draw a line to connect each tool to the item that it would most likely measure. Teaspoon
21 Sort and classify objects according to their attributes and organize data about the objects 2.38 Sort the leaves into groups. Label the groups. Cards: D75 and D Both 21
22 Represent data using concrete objects, pictures, and graphs Cards: D77 and D Heath collected data on the number of hours that he and his friends exercised last month. Create a pictograph using the information provided. Heath Amy Cindy Pedro 10 hours 20 hours 15 hours 25 hours Hours Exercised Last Month Name Number of Hours Heath Amy Cindy Pedro = 5 hours 22
23 Describe parts of the data and the set of data as a whole to determine what the data show Cards: D79, D80, and D A class took a survey about their favorite foods on the lunch menu. Use the graph to answer the questions. Number of Students Favorite Foods pizza fruit tacos salad Foods Which food is the favorite? Which food is the least favorite? How many students took the survey? students Discuss events related to students experiences as likely or unlikely 2.41 Answer the questions. Cards: D82, D83, and D84 Is it likely or unlikely that the spinner will land on white? Is it likely or unlikely that the spinner will land on white? 23
24 Name Date See cards D1 and D Use multiple models to develop initial understandings of place value and the baseten number system Cards: D3 and D Circle the blocks needed to make the number. 241 Describe attributes and parts of two and threedimensional shapes Posttest Answer Key Card: D Row 1: 100; 35; Row 2: 107; 37 See cards D28, D29, and D Sort, classify, and order objects by size, number, and other properties Cards: D31 and D Sort the shapes by writing their numbers in the correct spaces Answers will vary. Describe, name, and interpret relative positions in space and apply ideas about relative position Card: D Nadia pulled two figures out of a box. Follow the clues to find which figures she pulled out of the box. One figure has 4 angles and 4 sides that are always equal. The other figure has no corners, sides, or edges. One figure is flat and the other is not. Which figures did Nadia pull out of the box? and 2.23 Follow the directions. Draw a circle. Draw a trapezoid above the circle. Draw a triangle inside the circle. Draw a square to the left of the trapezoid. See cards D3 and D Row 1: 46; 49; 50; Row 2: 119; 121; 125 See cards D5 and D Answers will vary but may include: ; = 235; two hundred thirtyfive; ; = 184; one hundred eightyfour. See cards D7, D8, and D ; two hundred fifteen See cards D9, D10, and D See cards D12 and D = 9; = 9; 9 3 = 6; 9 6 = 3 See cards D14, D15, D16, D17, D18, and D ; +; +; See card D Drawings will vary, but three equal groups of six should be drawn = 6 sheep See cards D21, D22, D23, D24, and D Row 1: = 14; = 15; Row 2: = 10; = 12; Row 3: = 9; = 10; Row 4: = 18; = 20 See cards D26 and D Row 1: 13; 12; Row 2: 11; 17; Row 3: 7; 9 See cards D28, D29, and D30. Recognize, describe, and extend patterns such as sequences of sounds and shapes or simple numeric patterns and translate from one representation to another Cards: D33, D34, D35, D36, D37, D38, and D39 Small Shapes 3 Both Sides Write the missing numbers to complete each pattern. Then, write the rule. See cards D31 and D32. 7, 14, 21,,, 42, ; 35; 56; 49, 70;, 63, Rule:, +7; 77; 55; 22; Rule: 11 99, 88,, 66, See cards D33, D34, D35, D36,, 44, 33,, 11 D37, D38, Rule: and D Name Date 2.15 Analyze how both repeating and growing Draw what comes next. patterns are generated Cards: D38, D40, D41, D42, D43, and D44 See cards D38, D40, D41, D42, D43, and D Illustrate general principles and Write the missing numbers to complete each problem. properties of operations, such as commutativity, using specific numbers 7 + = 12, so 5 + = 12. Card: D = 24 = , so 5 + = = 99, so 99 = ; 7; 73; 19; 49; 50 See card D Use concrete, pictorial, and verbal Write the number that is behind each shape. representations to develop an understanding of invented and 2.17 Row conventional 1: + 10; 20 = 30 7; Row 47 2: = 4; 40 7 symbolic notations Cards: D46 and D47 = = See cards D46 and D ; 45; ; + 40; = 20 45; = 49 = See cards D48 and D49. = From top to bottom: 45; 48; 47; 50 See card D A triangle and a square should be drawn. triangle; square See cards D51 and D The large triangle, parallelogram, small triangle, and rhombus should be circled. See cards D51 and D square and sphere See card D Name Date 2.24 Describe, name, and interpret direction Help Becky get home from the library. Write the number and distance in of steps she needs to take and the directions she needs navigating space and apply ideas about to travel. N direction and distance Card: D56 W E S Zoe s Becky s See card D spaces north and 2 spaces east Doctor Ben s Park See card D56. Store Library Ty s 2.25 Find and name locations with simple relationships such as near to and in coordinate systems such as maps Card: D57 Bank 2.25 Follow the directions. Draw a square at (3,2). Draw a star at (3,5) Rose s Draw a heart at (5,5). Draw a circle at (1,1) See card D Name Date Recognize and apply slides, flips, and turns Card: D58 Recognize and create shapes that have symmetry See card D Cards: D59 and D Draw how each shape would look after a slide, a flip, and a turn. Shape Slide Flip Turn Name Date 2.26 Recognize and apply slides, flips, and turns Draw how each shape would look after a slide, a flip, and a turn. Card: D58 Shape Slide Flip Turn Recognize and create shapes that have symmetry Cards: D59 and D Complete each picture by drawing the missing symmetrical half Complete each picture by drawing the missing symmetrical half. 14 See cards D59 and D Row 1: cube, square; Row 2: rectangular prism, rectangle See card D inches See card D
25 2.30 Lines should be drawn to connect the pyramid and pyramid; the die and cube; and the party hat and cone. See card D Recognize the attributes of length, volume, weight, area, and time Cards: D64, D65, D66, D67, D68, D69, and D Draw hands on the clocks to show the time that José left home and the time that he arrived at school. Then, write how long it takes José to walk to school. José walks with his father to school every day. They leave home at 7:35. They arrive at school at 7:55. Posttest Answer Key 2.38 Sort and classify objects according to their attributes and organize data about the objects Cards: D75 and D Sort the leaves into groups smooth 1 Both 2 3 pointed minutes See card D64, D65, D66, D67, D68, D69, and D , 3, 1, 2 See cards D64, D65, D66, D67, D68, and D Paige s measurement is incorrect because she didn t have the end of the ruler lined up with the edge of the crayon. Nora s measurement is correct because she has the end of the ruler even with the edge of the crayon. See cards D70, D71, D72, D73, and D Answers will vary depending on the paper clips used. See card D cubes; 3 inches See cards D72 and D Answers will vary depending on the size of the cubes used. Estimates will vary. Answers will vary but students should use their measurements and their estimates to estimate how tall the paper is in cubes. See cards D72 and D Lines should be drawn to connect the teaspoon and the sugar; the ruler and the book; and the measuring cup and the gallon jug. See cards D74. Answers will vary. See cards D75 and D Represent data using 2.39 concrete objects, Heath collected data on the number of hours that he and pictures, and graphs his friends exercised last month. Create a pictograph using Cards: D77 and D78 the information provided. Heath 10 hours Amy 20 hours Cindy 15 hours Pedro 25 hours Hours Exercised Last Month Name Number of Hours Heath Amy Cindy Pedro = 5 hours See cards D77 and D tacos; pizza; 32 students See cards D79, D80, and D likely; unlikely See cards D82, D83, and D
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