Kansas State Standards for Mathematics: Grade 2

KS.1. Number and Computation: The student uses numerical and computational concepts and procedures in a variety of situations.

1.1. Number Sense - The student demonstrates number sense for whole numbers, fractions, and money using concrete objects in a variety of situations.

1.1.K1. Knowledge Base Indicator: The student knows, explains, and represents whole numbers from 0 through 1,000 using concrete objects.

1.1.K2a. Knowledge Base Indicator: The student compares and orders: whole numbers from 0 through 1,000 using concrete objects.

1.1.K2b. Knowledge Base Indicator: The student compares and orders: fractions greater than or equal to zero with like denominators (halves, fourths, thirds, eighths) using concrete objects.

1.1.K3. Knowledge Base Indicator: The student uses addition and subtraction to show equivalent representations for whole numbers from 0 through 100, e.g., 8 - 5 = 2 + 1 or 20 + 40 = 70 - 10.

1.1.K4. Knowledge Base Indicator: The student identifies and uses ordinal positions from first (1st) through twentieth (20th).

1.1.K5. Knowledge Base Indicator: The student identifies coins, states their values, and determines the total value to $1.00 of a mixed group of coins using pennies, nickels, dimes, quarters, and half-dollars.

1.1.K6. Knowledge Base Indicator: The student counts a like combination of currency ($1, $5, $10, $20) to $100.

1.1.A1a. Application Indicator: The student solves real-world problems using equivalent representations and concrete objects to: compare and order whole numbers from 0 through 1,000, e.g., using base ten blocks, represent the students in each class in the school; represent the numbers using digits (24) and compare and order in different ways.

1.1.A1b. Application Indicator: The student solves real-world problems using equivalent representations and concrete objects to: add and subtract whole numbers from 0 through 100, e.g., using base ten blocks, represent the number of students in each class in the school; find the total of all students in grades K, 1, and 2 and the total of all of the students in grades 3, 4, and 5 and then subtract to find the difference between the primary and intermediate grades.

1.1.A1c. Application Indicator: The student solves real-world problems using equivalent representations and concrete objects to: compare and order a mixed group of coins to $1.00, e.g., use actual coins to show 2 different amounts; students write: 47 cents is more than 31 cents

1.1.A1d. Application Indicator: The student solves real-world problems using equivalent representations and concrete objects to: find equivalent values of coins to $1.00 without mixing coins, e.g., 50 pennies = 2 quarters, 5 dimes = 2 quarters, or 10 nickels = 2 quarters.

1.1.A2. Application Indicator: The student determines whether or not numerical values that involve whole numbers from 0 through 1,000 are reasonable, e.g., if there are 26 children, plus 10 more children, is it reasonable to say there are 50 children?

1.2. Number Systems and Their Properties - The student demonstrates an understanding of whole numbers with a special emphasis on place value and recognizes, uses, and explains the concepts of properties as they relate to whole numbers in a variety of situations.

1.2.K1a. Knowledge Base Indicator: The student reads and writes whole numbers from 0 through 1,000 in numerical form, e.g., 942 is read as nine hundred forty-two and is written in numerical form as 942.

1.2.K1b. Knowledge Base Indicator: The student reads and writes whole numbers from 0 through 100 in words, e.g., 76 is read as seventy-six and is written in words as seventy-six.

1.2.K1c. Knowledge Base Indicator: The student reads and writes whole numbers from 0 through 1,000 in numerical form when presented in word form, e.g., nine hundred forty-six is read as nine hundred forty-six and is written as 946.

1.2.K2. Knowledge Base Indicator: The student represents whole numbers from 0 through 1,000 using various groupings and place value models emphasizing 1s, 10s, and 100s; explains the groups; and states the value of the digit in ones place, tens place, and hundreds place, e.g., in 385, the 3 represents 3 hundreds, 30 tens, or 300 ones; the 8 represents 8 tens or 80 ones; and the 5 represents 5 ones.

1.2.K3. Knowledge Base Indicator: The student counts subsets of whole numbers from 0 through 1,000 forwards and backwards, e.g., 311, 312, ..., 320; or 210, 209, ..., 204.

1.2.K4. Knowledge Base Indicator: The student identifies the place value of the digits in whole numbers from 0 through 1,000.

1.2.K5. Knowledge Base Indicator: The student identifies any whole number from 0 through 100 as even or odd.

1.2.K6a. Knowledge Base Indicator: The student uses the concepts of these properties with whole numbers from 0 through 100 and demonstrates their meaning including the use of concrete objects: commutative property of addition, e.g., 5 + 6 = 6 + 5

1.2.K6b. Knowledge Base Indicator: The student uses the concepts of these properties with whole numbers from 0 through 100 and demonstrates their meaning including the use of concrete objects: zero property of addition (additive identity), e.g., 4 + 0 = 4

1.2.K6c. Knowledge Base Indicator: The student uses the concepts of these properties with whole numbers from 0 through 100 and demonstrates their meaning including the use of concrete objects: associative property of addition, e.g., (3 + 2) + 4 = 3 + (2 + 4)

1.2.K6d. Knowledge Base Indicator: The student uses the concepts of these properties with whole numbers from 0 through 100 and demonstrates their meaning including the use of concrete objects: symmetric property of equality applied to basic addition and subtraction facts, e.g., 10 = 2 + 8 is the same as 2 + 8 = 10 or 7 = 10 - 3 is the same as 10 - 3 = 7.

1.2.A1a. Application Indicator: The student solves real-world problems with whole numbers from 0 through 100 using place value models and the concepts of these properties to explain reasoning: commutative property of addition, e.g., group 17 students into a 9 and an 8, add to find the total, then reverse the students to show 8 + 9 still equals 17.

1.2.A1b. Application Indicator: The student solves real-world problems with whole numbers from 0 through 100 using place value models and the concepts of these properties to explain reasoning: zero property of addition, e.g., have students lay out 22 crayons, tell them to add zero (crayons). How many crayons? 22 + 0 = 22.

1.2.A2a. Application Indicator: The student performs various computational procedures with whole numbers from 0 through 100 using these properties and explains how they were used: commutative property of addition (5 + 6 = 6 + 5), e.g., given 6 + 5, the student says: I know that the answer is 11 because 5 + 6 is 11 and the order you add them in does not matter.

1.2.A2b. Application Indicator: The student performs various computational procedures with whole numbers from 0 through 100 using these properties and explains how they were used: zero property of addition (17 + 0 = 0 + 17), e.g., given 17 + 0, the student says: I know that the answer is 17 because adding 0 does not change the answer (sum).

1.3. Estimation - The student uses computational estimation with whole numbers and money in a variety of situations.

1.3.K1. Knowledge Base Indicator: The student estimates whole number quantities from 0 through 1,000 and monetary amounts through $50 using various computational methods including mental math, paper and pencil, concrete objects, and appropriate technology.

1.3.K2. Knowledge Base Indicator: The student uses various estimation strategies to estimate whole number quantities from 0 through 1,000.

1.3.A1. Application Indicator: The student adjusts original whole number estimate of a real-world problem using numbers from 0 through 1,000 based on additional information (a frame of reference), e.g., given a pint container and told the number of marbles it has in it, the student would estimate the number of marbles in a quart container.

1.3.A2. Application Indicator: The student estimates to check whether or not the result of a real-world problem using whole numbers from 0 through 1,000 and monetary amounts through $50 is reasonable and makes predictions based on the information, e.g., in the lunchroom, good behavior that day can earn the class an extra 5 minutes of recess. Is it reasonable to think you can earn an hour of extra recess in one week? After answering the first question, then ask: About how many days would it take?

1.3.A3. Application Indicator: The student selects a reasonable magnitude from three given quantities, a one-digit numeral, a two-digit numeral, and a three-digit numeral (5, 50, 500) based on a familiar problem situation and explains the reasonableness of the selection, e.g., could the basket of fruit on the kitchen table hold 7 apples, 70 apples, or 700 apples? The student chooses 7 apples because apples are about the size of baseballs and 7 will fit in a basket on the kitchen table.

1.4. Computation - The student models, performs, and explains computation with whole numbers and money using concrete objects in a variety of situations.

1.4.K1. Knowledge Base Indicator: The student computes with efficiency and accuracy using various computational methods including mental math, paper and pencil, concrete objects, and appropriate technology.

1.4.K2. Knowledge Base Indicator: The student states and uses with efficiency and accuracy basic addition facts with sums from 0 through 20 and corresponding subtraction facts.

1.4.K3. Knowledge Base Indicator: The student skip counts by 2s, 5s, and 10s through 100 and skip counts by 3s through 36.

1.4.K4. Knowledge Base Indicator: The student uses repeated addition (multiplication) with whole numbers to find the sum when given the number of groups (ten or less) and given the same number of concrete objects in each group (twenty or less), e.g., five classes of 15 students visit the zoo; 15 + 15 + 15 + 15 + 15 = 75.

1.4.K5. Knowledge Base Indicator: The student uses repeated subtraction (division) with whole numbers when given the total number of concrete objects in each group to find the number of groups, e.g., there are 25 cookies. If each student gets 3 cookies, how many students get cookies? 25 - 3 - 3 - 3 - 3 - 3 - 3 - 3 - 3 or 25 minus 3 eight times means eight students get 3 cookies each and there is 1 cookie left over.

1.4.K6. Knowledge Base Indicator: The student fair shares/measures out (divides) a total amount through 100 concrete objects into equal groups, e.g., fair sharing 48 eggs into four groups resulting in four groups of 12 eggs or measuring out 48 eggs with 12 eggs in each group resulting in four groups of 12 eggs.

1.4.K7a. Knowledge Base Indicator: The student performs and explains these computational procedures: adds and subtracts three-digit whole numbers with and without regrouping including the use of concrete objects.

1.4.K7b. Knowledge Base Indicator: The student performs and explains these computational procedures: adds and subtracts monetary amounts through 99 cents using cent notation (25 cents + 52 cents) and money models.

1.4.K8. Knowledge Base Indicator: The student identifies basic addition and subtraction fact families (facts with sums from 0 through 20 and corresponding subtraction facts).

1.4.K9. Knowledge Base Indicator: The student reads and writes horizontally and vertically the same addition or subtraction expression.

1.4.A1a. Application Indicator: The student solves one-step real-world addition or subtraction problems with various groupings of: two-digit whole numbers with regrouping, e.g., for the food drive, the class collected 64 cans (cylinders) and 28 boxes (rectangular prisms). How many did they collect in all? This problem could be solved with base 10 models, or by saying 64 + 20 = 84 and 84 + 8 = 92 or 60 + 20 = 80 and 4 + 8 = 12 and 80 + 12 = 92 or with the traditional algorithm.

1.4.A1b. Application Indicator: The student solves one-step real-world addition or subtraction problems with various groupings of: monetary amounts to 99 cents with regrouping), e.g., an extra carton of milk costs 25 cents. If three students want an extra carton, how much money should the teacher collect? The student could solve by using coins (q + q + q or d + d + n + d + d + n + d + d + n) or by counting by 25s or by drawing or using base 10 models or with the traditional algorithm.

1.4.A2. Application Indicator: The student generates a family of basic addition and subtraction facts given one fact/equation, e.g., given 9 + 8 = 17; the other facts are 8 + 9 = 17, 17 - 8 = 9, and 17 - 9 = 8.

KS.2. Algebra: The student uses algebraic concepts and procedures in a variety of situations.

2.1. Patterns - The student recognizes, describes, extends, develops, and explains relationships in patterns using concrete objects in a variety of situations.

2.1.K1a. Knowledge Base Indicator: The student uses concrete objects, drawings, and other representations to work with types of patterns: repeating patterns.

2.1.K1b. Knowledge Base Indicator: The student uses concrete objects, drawings, and other representations to work with types of patterns: growing (extending) patterns, e.g., 7, 9, 11, ... where the rule could be add 2 or the odd numbers beginning with 7.

2.1.K2a. Knowledge Base Indicator: The student uses the following attributes to generate patterns: counting numbers related to number theory, e.g., evens, odds, or skip counting by 3s, or 4s.

2.1.K2b. Knowledge Base Indicator: The student uses the following attributes to generate patterns: whole numbers that increase or decrease, e.g., 11, 22, 33, ... or 98, 88, 78, ...

2.1.K2c. Knowledge Base Indicator: The student uses the following attributes to generate patterns: geometric shapes.

2.1.K2d. Knowledge Base Indicator: The student uses the following attributes to generate patterns: measurements, e.g., 1'', 3'', 5'', ... or 5 lbs, 10 lbs, 15 lbs, ...

2.1.K2e. Knowledge Base Indicator: The student uses the following attributes to generate patterns: the calendar, e.g., Sunday, Monday, Tuesday, ...

2.1.K2f. Knowledge Base Indicator: The student uses the following attributes to generate patterns: money and time, e.g., $5, $10, $15, ... or 1:15, 1:30, 1:45, ...

2.1.K2g. Knowledge Base Indicator: The student uses the following attributes to generate patterns: things related to daily life, e.g., seasons, temperature, or weather.

2.1.K2h. Knowledge Base Indicator: The student uses the following attributes to generate patterns: things related to size, shape, color, texture, or movement.

2.1.K3. Knowledge Base Indicator: The student identifies and continues a pattern presented in various formats including numeric (list or table), visual (picture, table, or graph), verbal (oral description), kinesthetic (action), and written.

2.1.K4. Knowledge Base Indicator: The student generates repeating patterns, e.g., 1-2, 1-2, 1-2, ... where the elements repeat; growing (extending) patterns, e.g., 1, 4, 7, ...where the rule is add 3.

2.1.A1a. Application Indicator: The student generalizes these patterns using a written description: whole number patterns.

2.1.A1b. Application Indicator: The student generalizes these patterns using a written description: patterns using geometric shapes.

2.1.A1c. Application Indicator: The student generalizes these patterns using a written description: calendar patterns.

2.1.A1d. Application Indicator: The student generalizes these patterns using a written description: money and time patterns.

2.1.A1e. Application Indicator: The student generalizes these patterns using a written description: patterns using size, shape, color, texture, or movement.

2.1.A2. Application Indicator: The student recognizes multiple representations of the same pattern, e.g., the ABB pattern could be represented by clap, snap, snap, ... or red, blue, blue, ... or square, circle, circle, ...

2.1.A3. Application Indicator: The student uses concrete objects to model a whole number patterns.

2.2. Variables, Equations, and Inequalities - The student uses symbols and whole numbers to solve addition and subtraction equations using concrete objects in a variety of situations.

2.2.K1. Knowledge Base Indicator: The student explains and uses symbols to represent unknown whole number quantities from 0 through 100.

2.2.K2a. Knowledge Base Indicator: The student finds the sum or difference in one-step equations with: whole numbers from 0 through 99.

2.2.K2b. Knowledge Base Indicator: The student finds the sum or difference in one-step equations with: up to two different coins.

2.2.K3. Knowledge Base Indicator: The student finds unknown addend or subtrahend using basic addition and subtraction facts (fact family).

2.2.K4. Knowledge Base Indicator: The student describes and compares two whole numbers from 0 through 1,000 using the terms: is equal to, is less than, is greater than.

2.2.A1. Application Indicator: The student represents real-world problems using symbols and whole numbers from 0 through 30 with one operation (addition, subtraction) and one unknown, e.g., when asked to give the total number of students in class today, the students write: 14 boys and 9 girls = __ students.

2.2.A2a. Application Indicator: The student generates addition or subtraction equations to match a given real-world problem with one operation and one unknown using whole numbers from 0 through 99, e.g., a boy has 45 stickers. How many more stickers does he need to have 80 stickers? This is represented by 45 + n = 80 or 80 - 45 = n.

2.2.A2b. Application Indicator: The student generates a real-world problem to match a given addition or subtraction equation with one operation using the basic facts.

2.3. Functions - The student recognizes and describes whole number relationships using concrete objects in a variety of situations.

2.3.K1. Knowledge Base Indicator: The student states mathematical relationships between whole numbers from 0 through 100 using various methods including mental math, paper and pencil, and concrete objects, e.g., every time a dog is added to the pack, 2 more ears are added to the total.

2.3.K2. Knowledge Base Indicator: The student finds the values and determines the rule that involve addition or subtraction of whole numbers from 0 through 100 using a horizontal or vertical function table (input/output machine, T-table), e.g., after looking at the function table, different students might respond that the rule is In + 2 equals Out, the rule is N + 2, or the rule is plus 2.

2.3.K3. Knowledge Base Indicator: The student generalizes numerical patterns using whole numbers from 0 through 100 with one operation (addition, subtraction) by stating the rule using words, e.g., if a set of numbers is 2, 4, 6, 8,10, ...; the rule is add two.

2.3.A1. Application Indicator: The student represents and describes mathematical relationships between whole numbers from 0 through 100 using concrete objects, pictures, oral descriptions, and symbols.

2.3.A2. Application Indicator: The student finds the rule, states the rule, and extends numerical patterns with whole numbers from 0 through 100, e.g., given 1, 3, 5, 7, 9 and continues with 11, 13, 15, 17, ... recognizing that the pattern could be the odd numbers.

2.4. Models - The student uses mathematical models including concrete objects to represent, show, and communicate mathematical relationships in a variety of situations.

2.4.K1a. Knowledge Base Indicator: The student knows, explains, and uses mathematical models to represent mathematical concepts, procedures, and relationships. Mathematical models include process models (concrete objects, pictures, diagrams, number lines, unifix cubes, hundred charts, or measurement tools) to model computational procedures and mathematical relationships, to compare and order numerical quantities, and to represent fractional parts.

2.4.K1b. Knowledge Base Indicator: The student knows, explains, and uses mathematical models to represent mathematical concepts, procedures, and relationships. Mathematical models include place value models (place value mats, hundred charts, or base ten blocks) to compare, order, and represent numerical quantities and to model computational procedures.

2.4.K1c. Knowledge Base Indicator: The student knows, explains, and uses mathematical models to represent mathematical concepts, procedures, and relationships. Mathematical models include fraction models (fraction strips or pattern blocks) to compare, order, and represent numerical quantities.

2.4.K1d. Knowledge Base Indicator: The student knows, explains, and uses mathematical models to represent mathematical concepts, procedures, and relationships. Mathematical models include money models (base ten blocks or coins) to compare, order, and represent numerical quantities.

2.4.K1e. Knowledge Base Indicator: The student knows, explains, and uses mathematical models to represent mathematical concepts, procedures, and relationships. Mathematical models include function tables (input/output machines, T-tables) to model numerical relationships.

2.4.K1f. Knowledge Base Indicator: The student knows, explains, and uses mathematical models to represent mathematical concepts, procedures, and relationships. Mathematical models include two-dimensional geometric models (geoboards, dot paper, pattern blocks, tangrams, or attribute blocks) to model perimeter and properties of geometric shapes and three-dimensional geometric models (solids) and real-world objects to compare size and to model attributes of geometric shapes.

2.4.K1g. Knowledge Base Indicator: The student knows, explains, and uses mathematical models to represent mathematical concepts, procedures, and relationships. Mathematical models include two-dimensional geometric models (spinners), three-dimensional geometric models (number cubes), and process models (concrete objects) to model probability.

2.4.K1h. Knowledge Base Indicator: The student knows, explains, and uses mathematical models to represent mathematical concepts, procedures, and relationships. Mathematical models include graphs using concrete objects, representational objects, or abstract representations, pictographs, frequency tables, horizontal and vertical bar graphs, Venn diagrams or other pictorial displays, and line plots to organize and display data.

2.4.K1i. Knowledge Base Indicator: The student knows, explains, and uses mathematical models to represent mathematical concepts, procedures, and relationships. Mathematical models include Venn diagrams to sort data.

2.4.K2. Knowledge Base Indicator: The student creates a mathematical model to show the relationship between two or more things, e.g., using pattern blocks, a whole (1) can be represented using

2.4.A1a. Application Indicator: The student recognizes that various mathematical models can be used to represent the same problem situation. Mathematical models include process models (concrete objects, pictures, diagrams, number lines, unifix cubes, hundred charts, or measurement tools) to model computational procedures and mathematical relationships, to compare and order numerical quantities, and to model problem situations.

2.4.A1b. Application Indicator: The student recognizes that various mathematical models can be used to represent the same problem situation. Mathematical models include place value models (place value mats, hundred charts, or base ten blocks) to compare, order, and represent numerical quantities and to model computational procedures.

2.4.A1c. Application Indicator: The student recognizes that various mathematical models can be used to represent the same problem situation. Mathematical models include money models (base ten blocks or coins) to compare, order, and represent numerical quantities.

2.4.A1d. Application Indicator: The student recognizes that various mathematical models can be used to represent the same problem situation. Mathematical models include two-dimensional geometric models (geoboards, dot paper, pattern blocks, tangrams, or attribute blocks) to model perimeter and properties of geometric shapes and three-dimensional geometric models (solids) and real-world objects to compare size and to model attributes of geometric shapes.

2.4.A1e. Application Indicator: The student recognizes that various mathematical models can be used to represent the same problem situation. Mathematical models include two-dimensional geometric models (spinners), three- dimensional geometric models (number cubes), and process models (concrete objects) to model probability.

2.4.A1f. Application Indicator: The student recognizes that various mathematical models can be used to represent the same problem situation. Mathematical models include graphs using concrete objects, representational objects, or abstract representations, pictographs, horizontal and vertical bar graphs.

2.4.A2. Application Indicator: The student selects a mathematical model that is more useful than other mathematical models in a given situation.

KS.3. Geometry: The student uses geometric concepts and procedures in a variety of situations.

3.1. Geometric Figures and Their Properties - The student recognizes geometric shapes and describes their properties using concrete objects in a variety of situations.

3.1.K1. Knowledge Base Indicator: The student recognizes and investigates properties of circles, squares, rectangles, triangles, and ellipses (ovals) (plane figures/two-dimensional shapes) using concrete objects, drawings, and appropriate technology.

3.1.K2. Knowledge Base Indicator: The student recognizes, draws, and describes circles, squares, rectangles, triangles, ellipses (ovals) (plane figures).

3.1.K3. Knowledge Base Indicator: The student recognizes cubes, rectangular prisms, cylinders, cones, and spheres (solids/three-dimensional figures).

3.1.K4. Knowledge Base Indicator: The student recognizes the square, triangle, rhombus, hexagon, parallelogram, and trapezoid from a pattern block set.

3.1.K5. Knowledge Base Indicator: The student compares geometric shapes (circles, squares, rectangles, triangles, ellipses) to one another.

3.1.K6. Knowledge Base Indicator: The student recognizes whether a shape has a line of symmetry.

3.1.A1. Application Indicator: The student solves real-world problems by applying the properties of plane figures (circles, squares, rectangles, triangles, ellipses), e.g., which shape could be used to completely cover the lid of a pencil box with no overlapping?

3.1.A2a. Application Indicator: The student demonstrates how plane figures (circles, squares, rectangles, triangles, ellipses) can be combined or separated to make a new shape.

3.1.A2b. Application Indicator: The student demonstrates how solids (cubes, rectangular solids, cylinders, cones, spheres) can be combined or separated to make a new shape.

3.1.A3. Application Indicator: The student identifies the plane figures (circles, squares, rectangles, triangles, ellipses) used to form a composite figure.

3.2. Measurement and Estimation - The student estimates and measures using standard and nonstandard units of measure with concrete objects in a variety of situations.

3.2.K1. Knowledge Base Indicator: The student uses whole number approximations (estimations) for length, weight, and volume using standard and nonstandard units of measure, e.g., the height of the classroom door is 14 chalkboard erasers laid end to end or 7 feet high or an apple weighs about 42 unifix cubes.

3.2.K2. Knowledge Base Indicator: The student reads and tells time by five-minute intervals using analog and digital clocks.

3.2.K3. Knowledge Base Indicator: The student selects and uses appropriate measurement tools and units of measure for length, weight, volume, and temperature for a given situation.

3.2.K4a. Knowledge Base Indicator: The student measures length to the nearest inch or foot and to the nearest whole unit of a nonstandard unit.

3.2.K4b. Knowledge Base Indicator: The student measures weight to the nearest nonstandard unit.

3.2.K4c. Knowledge Base Indicator: The student measures volume to the nearest cup, pint, quart, or gallon.

3.2.K4d. Knowledge Base Indicator: The student measures temperature to the nearest degree.

3.2.K5a. Knowledge Base Indicator: The student states the number of minutes in an hour.

3.2.K5b. Knowledge Base Indicator: The student states the number of days in each month.

3.2.A1. Application Indicator: The student compares the weights of more than two concrete objects using a balance.

3.2.A2a. Application Indicator: The student solves real-world problems by applying appropriate measurements: length to the nearest inch or foot, e.g., a cookie is almost how many inches wide?

3.2.A2b. Application Indicator: The student solves real-world problems by applying appropriate measurements: length to the nearest whole unit of a nonstandard unit, e.g., how many paper clips long is a candy bar?

3.2.A3. Application Indicator: The student estimates to check whether or not measurements or calculations for length in real-world problems are reasonable, e.g., is it reasonable to say that you measured your thumb and it is 2 feet long?

3.2.A4. Application Indicator: The student adjusts original measurement or estimation for length and weight in real-world problems based on additional information (a frame of reference), e.g., I estimated that the stapler is 20 paperclips long. Then I lay out 4 paper clips next to the stapler. I realize that since I am half done, my estimate is too high; so I adjust my estimate to 8 paper clips.

3.3. Transformational Geometry - The student recognizes and shows one transformation on simple shapes and concrete objects in a variety of situations.

3.3.K1. Knowledge Base Indicator: The student knows and uses the cardinal points (north, south, east, west).

3.3.K2. Knowledge Base Indicator: The student recognizes that changing an object's position or orientation including whether the object is nearer or farther away does not change the name, size, or shape of the object.

3.3.K3. Knowledge Base Indicator: The student recognizes when a shape has undergone one transformation (flip/reflection, turn/rotation, slide/translation).

3.3.A1. Application Indicator: The student shows two concrete objects or shapes are congruent by physically fitting one shape or object on top of the other.

3.3.A2. Application Indicator: The student follows directions to move objects from one location to another using appropriate vocabulary and the cardinal points (north, south, east, west).

3.4. Geometry From An Algebraic Perspective - The student identifies one or more points on a number line in a variety of situations.

3.4.K1. Knowledge Base Indicator: The student locates and plots whole numbers from 0 through 1,000 on a segment of a number line (horizontal/vertical), e.g., using a segment of a number line from 800 to 820 to locate the whole number 805.

3.4.K2. Knowledge Base Indicator: The student represents the distance between two whole numbers from 0 through 1,000 on a segment of a number line.

3.4.K3. Knowledge Base Indicator: The student uses a segment of a number line to model addition and subtraction using whole numbers from 0 through 1,000, e.g., 333 + n = 349 or 333 + 16 = n or 400 - n = 352 or 400 - 48 = n.

3.4.A1. Application Indicator: The student solves real-world problems involving counting, adding, and subtracting whole numbers from 0 through 1,000 using a segment of a number line, e.g., Adam had collected 894 marbles. He lost nine marbles. How many does he have now? Using the number line, Adam shows how he solved the problem.

KS.4. Data: The student uses concepts and procedures of data analysis in a variety of situations.

4.1. Probability - The student applies the concepts of probability using concrete objects in a variety of situations.

4.1.K1. Knowledge Base Indicator: The student recognizes any outcome of a simple event in an experiment or simulation as impossible, possible, certain, likely, or unlikely.

4.1.K2. Knowledge Base Indicator: The student lists some of the possible outcomes of a simple event in an experiment or simulation including the use of concrete objects.

4.1.A1. Application Indicator: The student makes a prediction about a simple event in an experiment or simulation; conducts the experiment or simulation including the use of concrete objects; records the results in a chart, table, or graph; and makes an accurate statement about the results.

4.2. Statistics - The student collects, organizes, displays, and explains numerical (whole numbers) and non-numerical data sets including the use of concrete objects in a variety of situations.

4.2.K1a. Knowledge Base Indicator: The student organizes, displays, and reads numerical (quantitative) and non-numerical (qualitative) data in a clear, organized, and accurate manner including a title, labels, categories, and whole number intervals using these data displays: graphs using concrete objects.

4.2.K1b. Knowledge Base Indicator: The student organizes, displays, and reads numerical (quantitative) and non-numerical (qualitative) data in a clear, organized, and accurate manner including a title, labels, categories, and whole number intervals using these data displays: pictographs with a whole symbol or picture representing one, two, or ten (no partial symbols or pictures).

4.2.K1c. Knowledge Base Indicator: The student organizes, displays, and reads numerical (quantitative) and non-numerical (qualitative) data in a clear, organized, and accurate manner including a title, labels, categories, and whole number intervals using these data displays: frequency tables (tally marks).

4.2.K1d. Knowledge Base Indicator: The student organizes, displays, and reads numerical (quantitative) and non-numerical (qualitative) data in a clear, organized, and accurate manner including a title, labels, categories, and whole number intervals using these data displays: horizontal and vertical bar graphs.

4.2.K1e. Knowledge Base Indicator: The student organizes, displays, and reads numerical (quantitative) and non-numerical (qualitative) data in a clear, organized, and accurate manner including a title, labels, categories, and whole number intervals using these data displays: Venn diagrams or other pictorial displays, e.g., glyphs.

4.2.K1f. Knowledge Base Indicator: The student organizes, displays, and reads numerical (quantitative) and non-numerical (qualitative) data in a clear, organized, and accurate manner including a title, labels, categories, and whole number intervals using these data displays: line plots.

4.2.K2. Knowledge Base Indicator: The student collects data using different techniques (observations, interviews, or surveys) and explains the results.

4.2.K3. Knowledge Base Indicator: The student identifies the minimum (lowest) and maximum (highest) values in a whole number data set.

4.2.K4. Knowledge Base Indicator: The student finds the range for a data set using two-digit whole numbers.

4.2.K5a. Knowledge Base Indicator: The student finds the mode (most) for a data set using concrete objects that include quantitative/numerical data (whole numbers through 100).

4.2.K5b. Knowledge Base Indicator: The student finds the mode (most) for a data set using concrete objects that include qualitative/non-numerical data (category that occurs most often).

4.2.A1a. Application Indicator: The student communicates the results of data collection and answers questions based on information from graphs using concrete objects.

4.2.A1b. Application Indicator: The student communicates the results of data collection and answers questions based on information from pictographs with a whole symbol or picture representing one (no partial symbols or pictures).

4.2.A1c. Application Indicator: The student communicates the results of data collection and answers questions based on information from horizontal and vertical bar graphs.

4.2.A2. Application Indicator: The student determines categories from which data could be gathered, e.g., categories could include shoe size, height, favorite candy bar, or number of pockets in clothing.

4.2.A3. Application Indicator: The student recognizes that the same data set can be displayed in various formats including the use of concrete objects.

4.2.A4. Application Indicator: The student recognizes appropriate conclusions from data collected.