Kansas State Standards for Mathematics: Grade 5

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 integers, fractions, decimals, and money in a variety of situations.

1.1.K1a. Knowledge Base Indicator: The student knows, explains, and uses equivalent representations for whole numbers from 0 through 1,000,000.

1.1.K1b. Knowledge Base Indicator: The student knows, explains, and uses equivalent representations for fractions greater than or equal to zero (including mixed numbers).

1.1.K1c. Knowledge Base Indicator: The student knows, explains, and uses equivalent representations for decimals greater than or equal to zero through hundredths place and when used as monetary amounts.

1.1.K2a. Knowledge Base Indicator: The student compares and orders integers.

1.1.K2b. Knowledge Base Indicator: The student compares and orders fractions greater than or equal to zero (including mixed numbers).

1.1.K2c. Knowledge Base Indicator: The student compares and orders decimals greater than or equal to zero through hundredths place.

1.1.K3. Knowledge Base Indicator: The student explains the numerical relationships (relative magnitude) between whole numbers, fractions greater than or equal to zero (including mixed numbers), and decimals greater than or equal to zero through hundredths place.

1.1.K4. Knowledge Base Indicator: The student knows equivalent percents and decimals for one whole, one-half, one-fourth, three-fourths, and one tenth through nine tenths, e.g., 1 = 100% = 1.0, 3/4 = 75% = .75, 3/10 = 30% = .3.

1.1.K5. Knowledge Base Indicator: The student identifies integers and gives real-world problems where integers are used), e.g., making a T-table of the temperature each hour over a twelve hour period in which the temperature at the beginning is 10 degrees and then decreases 2 degrees per hour.

1.1.A1a. Application Indicator: The student solves real-world problems using equivalent representations and concrete objects to compare and order:

1.1.A1a.i. Whole numbers from 0 through 5,000, e.g., using base ten blocks, represent the total school attendance for a week; then represent the numbers using digits and compare and order in different ways.

1.1.A1a.ii. Fractions greater than or equal to zero (including mixed numbers), e.g., Frank ate 2 1/2 pizzas, Tara ate 9/4 of the pizza. Frank says he ate more. Is he correct? Use a model to explain. With drawings and shadings, student shows amount of pizza eaten by Frank and the amount eaten by Tara.

1.1.A1a.iii. Decimals greater than or equal to zero to hundredths place, e.g., uses decimal squares, money (dimes as tenths, pennies as hundredths), the correct amount of hundred chart filled in, or a number line to show that.42 is less than.59.

1.1.A1a.iv. Integers, e.g., plot winter temperature for a very cold region for a week (use Internet data); represent on a thermometer, number line, and with integers.

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 100,000 and decimals when used as monetary amounts, e.g., use real money to show at least 2 ways to represent $846.00, then subtract the cost of a new computer setup.

1.1.A1c. Application Indicator: The student solves real-world problems using equivalent representations and concrete objects to multiply through a two-digit whole number by a two-digit whole number, e.g., George charges $23 for mowing a lawn. How much will he make after he mows 3 lawns? Represent the $23 with money models - 2 $10 bills and 3 $1 bills and repeat that 3 times or represent the $23 using base ten blocks or 23 x 3 or 23 + 23 + 23.

1.1.A1d. Application Indicator: The student solves real-world problems using equivalent representations and concrete objects to divide through a four-digit whole number by a two-digit whole number, e.g., the Boy Scout troop collected cans and held bake sales for a year and earned $492.60. The money will be divided evenly among the 12 troop members to buy new uniforms. Represent each boy's share of the money at least 2 ways - traditional division; use 4 hundreds, 9 tens, 2 ones, and 6 dimes to act out the situation; or use base ten blocks to act it out.

1.1.A2a. Application Indicator: The student determines whether or not solutions to real-world problems that involve the following are reasonable, whole numbers from 0 through 100,000, e.g., the football is placed on your own 10-yard line with 90 yards to go for a touchdown. After the first down, your team gains 7 yards. On the second down, your team loses 4 yards. Is it reasonable for the football to be placed on the 3-yard line for the beginning of the third down?

1.1.A2b. Application Indicator: The student determines whether or not solutions to real-world problems that involve the following are reasonable, fractions greater than or equal to zero (including mixed numbers), e.g., explain if it is reasonable to say that a dog is 1/2 boxer, 1/4 bulldog, 1/4 collie, and 1/4 rotweiler.

1.1.A2c. Application Indicator: The student determines whether or not solutions to real-world problems that involve the following are reasonable decimals greater than or equal to zero through hundredths place, e.g., five people ate a pizza. Is it reasonable to say that each person ate.3 of the pizza?

1.2. Number Systems and Their Properties - The student demonstrates an understanding of the whole number system; recognizes, uses, and explains the concepts of properties as they relate to the whole number system; and extends these properties to integers, fractions (including mixed numbers), and decimals.

1.2.K1. Knowledge Base Indicator: The student classifies subsets of numbers as integers, whole number, fractions (including mixed numbers), or decimals.

1.2.K2. Knowledge Base Indicator: The student identifies prime and composite numbers from 0 through 50.

1.2.K3a. Knowledge Base Indicator: The student uses the concepts of these properties with whole numbers, integers, fractions greater than or equal to zero (including mixed numbers), and decimals greater than or equal to zero and demonstrates their meaning including the use of concrete objects commutative properties of addition and multiplication, e.g., 43 + 34 = 34 + 43 and 12 x 15 = 15 x 12.

1.2.K3b. Knowledge Base Indicator: The student uses the concepts of these properties with whole numbers, integers, fractions greater than or equal to zero (including mixed numbers), and decimals greater than or equal to zero and demonstrates their meaning including the use of concrete objects associative properties of addition and multiplication, e.g., 4 + (3 + 5) = (4 + 3) + 5.

1.2.K3c. Knowledge Base Indicator: The student uses the concepts of these properties with whole numbers, integers, fractions greater than or equal to zero (including mixed numbers), and decimals greater than or equal to zero and demonstrates their meaning including the use of concrete objects zero property of addition (additive identity) and property of one for multiplication (multiplicative identity), e.g., 342 + 0 = 342 and 576 x 1 = 576.

1.2.K3d. Knowledge Base Indicator: The student uses the concepts of these properties with whole numbers, integers, fractions greater than or equal to zero (including mixed numbers), and decimals greater than or equal to zero and demonstrates their meaning including the use of concrete objects symmetric property of equality, e.g., 35 = 11 + 24 is the same as 11 + 24 = 35.

1.2.K3e. Knowledge Base Indicator: The student uses the concepts of these properties with whole numbers, integers, fractions greater than or equal to zero (including mixed numbers), and decimals greater than or equal to zero and demonstrates their meaning including the use of concrete objects zero property of multiplication, e.g., 438,223 x 0 = 0.

1.2.K3f. Knowledge Base Indicator: The student uses the concepts of these properties with whole numbers, integers, fractions greater than or equal to zero (including mixed numbers), and decimals greater than or equal to zero and demonstrates their meaning including the use of concrete objects distributive property, e.g., 7(3 + 5) = 7(3) + 7(5).

1.2.K3g. Knowledge Base Indicator: The student uses the concepts of these properties with whole numbers, integers, fractions greater than or equal to zero (including mixed numbers), and decimals greater than or equal to zero and demonstrates their meaning including the use of concrete objects substitution property, e.g., if a = 3 and a = b, then b = 3.

1.2.K4. Knowledge Base Indicator: The student recognizes Roman Numerals that are used for dates, on clock faces, and in outlines.

1.2.K5. Knowledge Base Indicator: The student recognizes the need for integers, e.g., with temperature, below zero is negative and above zero is positive; in finances, money in your pocket is positive and money owed someone is negative.

1.2.A1a. Application Indicator: The student solves real-world problems with whole numbers from 0 through 100,000 and decimals through hundredths using place value models; money; and the concepts of these properties to explain reasoning: commutative and associative properties of addition and multiplication, e.g., lay out a $5, $10 and $20 bills. Ask for the total of the money. The student says: Because you can add in any order (commutative) I can rearrange the money and count $20, $10 and $5 for $20 + $10 + $5 or Lay out 4 $5 bills. The student is asked the amount. The student says: I don't know what 4 x 5 is, but I know 5 x 4 is $20 and since multiplication can be done in any order, then it is $20.

1.2.A1b. Application Indicator: The student solves real-world problems with whole numbers from 0 through 100,000 and decimals through hundredths using place value models; money; and the concepts of these properties to explain reasoning: zero property of addition, e.g., have students lay out 6 dimes. Tell them to add zero. How many dimes? 6 + 0 = 6.

1.2.A1c. Application Indicator: The student solves real-world problems with whole numbers from 0 through 100,000 and decimals through hundredths using place value models; money; and the concepts of these properties to explain reasoning: property of one for multiplication, e.g., there are 24 students in our class. I want one math book per student, so I compute 24 x 1= 24. Multiplying times 1 does not change the product because it is one group of 24.

1.2.A1d. Application Indicator: The student solves real-world problems with whole numbers from 0 through 100,000 and decimals through hundredths using place value models; money; and the concepts of these properties to explain reasoning: symmetric property of equality, e.g., Pat knows he has $56. He has 2 twenty-dollar bills in his wallet. How much does he have at home in his bank?

1.2.A1e. Application Indicator: The student solves real-world problems with whole numbers from 0 through 100,000 and decimals through hundredths using place value models; money; and the concepts of these properties to explain reasoning: zero property of multiplication, e.g., in science, you are observing a snail. The snail does not move over a 4-hour period. To figure its total movement, you say 4 x 0 = 0.

1.2.A1f. Application Indicator: The student solves real-world problems with whole numbers from 0 through 100,000 and decimals through hundredths using place value models; money; and the concepts of these properties to explain reasoning: distributive property, e.g., Juan has 7 quarters and 7 dimes. What is the total amount of money he has? 7($.25 + $.10) = 7($.25) + 7($.10).

1.2.A2a. Application Indicator: The student performs various computational procedures with whole numbers from 0 through 100,000 using the concepts of these properties; extends these properties to fractions greater than or equal to zero (including mixed numbers) and decimals greater than or equal to zero through hundredths place; and explains how the properties were used commutative and associative properties of addition and multiplication, e.g., given 4.2 x 10, the student says: I know that it is 42 because I know that 10 x 4.2 = 42, since you can multiply in any order and get the same answer. or The student says I don't know what 9 + 8 is, but I know my doubles of 8 + 8, so I make the 9 into 1 + 8 and after adding 8 and 8, I add 1 more.

1.2.A2b. Application Indicator: The student performs various computational procedures with whole numbers from 0 through 100,000 using the concepts of these properties; extends these properties to fractions greater than or equal to zero (including mixed numbers) and decimals greater than or equal to zero through hundredths place; and explains how the properties were used zero property of addition, e.g., given 47 + 917 + 0, the student says: I know that the answer is 964 because adding 0 does not change the answer (sum).

1.2.A2c. Application Indicator: The student performs various computational procedures with whole numbers from 0 through 100,000 using the concepts of these properties; extends these properties to fractions greater than or equal to zero (including mixed numbers) and decimals greater than or equal to zero through hundredths place; and explains how the properties were used property of one for multiplication, e.g., $9.62 x 1. The student says: I know the product is still $9.62 because multiplication by one never changes the product. It is like if I had $9.62 in one pile, I would just have $9.62.

1.2.A2d. Application Indicator: The student performs various computational procedures with whole numbers from 0 through 100,000 using the concepts of these properties; extends these properties to fractions greater than or equal to zero (including mixed numbers) and decimals greater than or equal to zero through hundredths place; and explains how the properties were used symmetric property of equality, e.g., given ? = 1/2 + 1/4, the student says: That is the same as 1/2 + 1/4 because I must make both sides equal.

1.2.A2e. Application Indicator: The student performs various computational procedures with whole numbers from 0 through 100,000 using the concepts of these properties; extends these properties to fractions greater than or equal to zero (including mixed numbers) and decimals greater than or equal to zero through hundredths place; and explains how the properties were used zero property of multiplication e.g., given.7 x 0, the student says: I know the answer (product) is zero because no matter how many factors you have, multiplying by 0, the product is 0.

1.2.A2f. Application Indicator: The student performs various computational procedures with whole numbers from 0 through 100,000 using the concepts of these properties; extends these properties to fractions greater than or equal to zero (including mixed numbers) and decimals greater than or equal to zero through hundredths place; and explains how the properties were used distributive property, e.g., given 4 x 614, the student can explain that you can solve it (in your head?) by computing 4(600) + 4(10) + 4(4), which is 2,400 + 40 + 4 = 2,444.

1.2.A3. Application Indicator: The student states the reason for using integers, whole numbers, fractions (including mixed numbers), or decimals when solving a given real-world problem.

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

1.3.K1. Knowledge Base Indicator: The student estimates whole numbers quantities from 0 through 100,000; fractions greater than or equal to zero (including mixed numbers); decimals greater than or equal to zero through hundredths place; and monetary amounts to $10,000 using various computational methods including mental math, paper and pencil, concrete materials, and appropriate technology.

1.3.K2. Knowledge Base Indicator: The student uses various estimation strategies to estimate whole number quantities from 0 through 100,000; fractions greater than or equal to zero (including mixed numbers); decimals greater than or equal to zero through hundredths place; and monetary amounts to $10,000 and explains how various strategies are used.

1.3.K3. Knowledge Base Indicator: The student recognizes and explains the difference between an exact and an approximate answer.

1.3.K4. Knowledge Base Indicator: The student explains the appropriateness of an estimation strategy used and whether the estimate is greater than (overestimate) or less than (underestimate) the exact answer.

1.3.A1. Application Indicator: The student adjusts original estimate using whole numbers from 0 through 100,000 of a real-world problem based on additional information (a frame of reference), e.g., given a large container of marbles, estimate the quantity of marbles. Then, using a smaller container filled with marbles, count the number of marbles in the smaller container and adjust your original estimate.

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 100,000; fractions greater than or equal to zero (including mixed numbers); decimals greater than or equal to zero to tenths place; and monetary amounts to $10,000 is reasonable and makes predictions based on the information, e.g., at your birthday party, you ate 4 1/2 pepperoni pizzas, 3 1/4 cheese pizzas, and 2 3/4 sausage pizzas. On the bill they charged you for 10 pizzas. Is that reasonable? If pizzas cost $6.99 each, about how much should you save for your next birthday party?

1.3.A3. Application Indicator: The student selects a reasonable magnitude from given quantities based on a real-world problem using whole numbers from 0 through 100,000 and explains the reasonableness of selection, e.g., about how many tulips can fit in the flower vase, 2, 10, or 25? The student chooses ten and explains that the vase at home is a jelly jar and either two or ten will fit, but ten looks prettier.

1.3.A4. Application Indicator: The student determines if a real-world problem calls for an exact or approximate answer using whole numbers from 0 through 100,000 and performs the appropriate computation using various computational methods including mental math, paper and pencil, concrete materials, and appropriate technology.

1.4. Computation - The student models, performs, and explains computation with whole numbers, fractions including mixed numbers, and decimals including the use of 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 materials, and appropriate technology.

1.4.K2a. Knowledge Base Indicator: The student performs and explains these computational procedures divides whole numbers through a 2-digit divisor and a 4-digit dividend with the remainder as a whole number or a fraction using paper and pencil.

1.4.K2b. Knowledge Base Indicator: The student performs and explains these computational procedures divides whole numbers beyond a 2-digit divisor and a 4-digit dividend using appropriate technology.

1.4.K2c. Knowledge Base Indicator: The student performs and explains these computational procedures adds and subtracts decimals from thousands place through hundredths place.

1.4.K2d. Knowledge Base Indicator: The student performs and explains these computational procedures multiplies decimals up to three digits by two digits from hundreds place through hundredths place.

1.4.K2e. Knowledge Base Indicator: The student performs and explains these computational procedures adds and subtracts fractions (like and unlike denominators) greater than or equal to zero (including mixed numbers) without regrouping and without expressing answers in simplest form with special emphasis on manipulatives, drawings, and models.

1.4.K2f. Knowledge Base Indicator: The student performs and explains these computational procedures multiplies and divides by 10; 100; 1,000; or single-digit multiples of each.

1.4.K3. Knowledge Base Indicator: The student reads and writes horizontally, vertically, and with different operational symbols the same addition, subtraction, multiplication, or division expression.

1.4.K4. Knowledge Base Indicator: The student identifies, explains, and finds the greatest common factor and least common multiple of two or more whole numbers through the basic multiplication facts from 1 x 1 through 12 x 12.

1.4.A1a. Application Indicator: The student solves one- and two-step real-world problems using these computational procedures (For the purpose of assessment, two-step could include any combination of a, b, c, d, e, or f.) adds and subtracts whole numbers from 0 through 100,000; e.g., Lee buys a bike for $139, a helmet for $29 and a reflector for $6. How much of his $200 check from his grandparents will he have left?

1.4.A1b. Application Indicator: The student solves one- and two-step real-world problems using these computational procedures (For the purpose of assessment, two-step could include any combination of a, b, c, d, e, or f.) multiplies through a four-digit whole number by a two-digit whole number, e.g., at the amusement park, Monday's attendance was 4,414 people. Tuesday's attendance was 3,042 people. If the cost per person is $23, how much money was collected on those days?

1.4.A1c. Application Indicator: The student solves one- and two-step real-world problems using these computational procedures (For the purpose of assessment, two-step could include any combination of a, b, c, d, e, or f.) multiplies monetary amounts up to $1,000 by a one- or two-digit whole number, e.g., what is the cost of 4 items each priced at $3.49?

1.4.A1d. Application Indicator: The student solves one- and two-step real-world problems using these computational procedures (For the purpose of assessment, two-step could include any combination of a, b, c, d, e, or f.) divides whole numbers through a 2-digit divisor and a 4-digit dividend with the remainder as a whole number or a fraction.

1.4.A1e. Application Indicator: The student solves one- and two-step real-world problems using these computational procedures (For the purpose of assessment, two-step could include any combination of a, b, c, d, e, or f.) adds and subtracts decimals from thousands place through hundredths place when used as monetary amounts (The set of decimal numbers includes whole numbers.), e.g., at the track meet, Peter ran the 100 meter dash in 12.3 seconds. Tanner ran the same race in 12.19 seconds. How much faster was Tanner?

1.4.A1f. Application Indicator: The student solves one- and two-step real-world problems using these computational procedures (For the purpose of assessment, two-step could include any combination of a, b, c, d, e, or f.) multiplies and divides by 10; 100; and 1,000 and single digit multiples of each (10, 20, 30, etc.; 100, 200, 300, etc.; 1,000; 2,000; 3,000; etc.), e.g., Matti has 1,590 stamps to place in her stamp album. 30 stamps fit on a page. What is the minimum number of pages she needs in her album?

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 in a variety of situations.

2.1.K1a. Knowledge Base Indicator: The student uses concrete objects, drawings, and other representations to work with these types of patterns repeating patterns, e.g., 9, 10, 11, 9, 10, 11, ....

2.1.K1b. Knowledge Base Indicator: The student uses concrete objects, drawings, and other representations to work with these types of patterns growing patterns, e.g., 20, 30, 28, 38, 36, ... where the rule is add 10, then subtract 2; or 2, 5, 8, ... as an example of an arithmetic sequence - each term after the first is found by adding the same number to the preceding term.

2.1.K2a. Knowledge Base Indicator: The student uses these attributes to generate patterns counting numbers related to number theory, e.g., multiples or perfect squares.

2.1.K2b. Knowledge Base Indicator: The student uses these attributes to generate patterns whole numbers, e.g., 10; 100; 1,000; 10,000; 100,000; ... (powers of ten).

2.1.K2c. Knowledge Base Indicator: The student uses these attributes to generate patterns geometric shapes through two attribute changes.

2.1.K2d. Knowledge Base Indicator: The student uses these attributes to generate patterns measurements, e.g., 3 m, 6 m, 9 m, ....

2.1.K2e. Knowledge Base Indicator: The student uses these attributes to generate patterns things related to daily life, e.g., sports scores, longitude and latitude, elections, eras, or appropriate topics across the curriculum.

2.1.K2f. Knowledge Base Indicator: The student uses these attributes to generate patterns things related to size, shape, color, texture, or movement, e.g., square dancing moves (kinesthetic patterns).

2.1.K3. Knowledge Base Indicator: The student identifies, states, 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.K4a. Knowledge Base Indicator: The student generates a pattern (repeating, growing).

2.1.K4b. Knowledge Base Indicator: The student generates a pattern using a function table (input/output machines, T-tables).

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

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

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

2.1.A1d. Application Indicator: The student generalizes these patterns using a written description patterns related to daily life.

2.1.A2. Application Indicator: The student recognizes multiple representations of the same pattern, e.g., 10; 100; 1,000; ... - represented as 10; 10 x 10; 10 x 10 x 10; ...; represented as a rod, a flat, a cube, ... using base ten blocks; or represented by a $10 bill; a $100 bill; a $1,000 bill; ....

2.2. Variables, Equations, and Inequalities - The student uses variables, symbols, whole numbers, and algebraic expressions in one variable to solve linear equations in a variety of situations.

2.2.K1. Knowledge Base Indicator: The student explains and uses variables and symbols to represent unknown whole number quantities from 0 through 1,000 and variable relationships.

2.2.K2. Knowledge Base Indicator: The student solves one-step linear equations with one variable and a whole number solution using addition and subtraction with whole numbers from 0 through 100 and multiplication with the basic facts, e.g., 3y = 12, 45 = 17 + q, or r - 42 = 36.

2.2.K3. Knowledge Base Indicator: The student explains and uses equality and inequality symbols and corresponding meanings (is equal to, is not equal to, is less than, is less than or equal to, is greater than, is greater than or equal to) with whole numbers from 0 to 100,000.

2.2.K4. Knowledge Base Indicator: The student recognizes ratio as a comparison of part-to-part and part-to-whole relationships, e.g., the relationship between the number of boys and the number of girls (part-to-part) or the relationship between the number of girls to the total number of students in the classroom (part-to-whole).

2.2.A1. Application Indicator: The student represents real-world problems using variables, symbols, and one-step equations with unknown whole number quantities from 0 through 1,000; e.g., Your parents say you must read 5 minutes each and every day of the next year. How many minutes will you read? This is represented by 365 x 5 = M.

2.2.A2. Application Indicator: The student generates one-step linear equations to solve real-world problems with whole numbers from 0 through 1,000 with one unknown and a whole number solution using addition, subtraction, multiplication, and division, e.g., Ninety-six items are being shared with four people. How much does each person receive? becomes 96/4 = n.

2.2.A3a. Application Indicator: The student generates a real-world problem with one operation to match a given addition, subtraction, multiplication, or division equation using whole numbers from 0 through 1,000, e.g., given 95/5 = x students write: There are 95 kids at camp who need to be divided into teams of 5. How many teams will there be?

2.2.A3b. Application Indicator: The student generates number comparison statements using equality and inequality symbols (=, <, >) with whole numbers, measurement, and money e.g., 1 ft < 15 in or 10 quarters > $2.

2.3. Functions - The student recognizes, describes, and examines whole number relationships in a variety of situations.

2.3.K1. Knowledge Base Indicator: The student states mathematical relationships between whole numbers from 0 through 10,000 using various methods including mental math, paper and pencil, concrete objects, and appropriate technology.

2.3.K2. Knowledge Base Indicator: The student finds the values, determines the rule, and states the rule using symbolic notation with one operation of whole numbers from 0 through 10,000 using a vertical or horizontal function table (input/output machine, T-table).

2.3.K3. Knowledge Base Indicator: The student generalizes numerical patterns using whole numbers from 0 through 5,000 up to two operations by stating the rule using words, e.g., If the sequence is 2400, 1200, 600, 300, 150, ...; in words, the rule could be split the number in half or divide the previous number by 2 or if the sequence is 4, 11, 25, 53, 109, ...; in words, the rule could be double the number and add 3 to get the next number or multiply the number by 2 and add 3.

2.3.K4. Knowledge Base Indicator: The student uses a function table (input/output machine, T-table) to identify, plot, and label whole number ordered pairs in the first quadrant of a coordinate plane.

2.3.K5. Knowledge Base Indicator: The student plots and locates points for integers (positive and negative whole numbers) on a horizontal number line and vertical number line.

2.3.K6. Knowledge Base Indicator: The student describes whole number relationships using letters and symbols.

2.3.A1. Application Indicator: The student represents and describes mathematical relationships between whole numbers from 0 through 5,000 using written and oral descriptions, tables, graphs, and symbolic notation.

2.3.A2. Application Indicator: The student finds the rule, states the rule, and extends numerical patterns using real-world problems with whole numbers from 0 through 5,000. e.g., the class sells cookies at lunch recess to raise money for a field trip. The goal is to sell 3,000 cookies at 25 cents each. A student notices that every 4th day, a new case of cookies has to be opened. Each case holds 450 cookies. If the class keeps selling cookies at the same rate, how many days will it take to sell 3,000 cookies? A student's answer might be: 28 days because that will be 150 over the goal or on day 27 until 3,000 cookies are sold.

2.3.A3. Application Indicator: The student translates between verbal, numerical, and graphical representations including the use of concrete objects to describe mathematical relationships, e.g., when the temperature is 20 degrees and then it drops 2 degrees an hour for 12 hours, the result is a negative number; the student could model this using a vertical number line.

2.4. Models - The student develops and uses mathematical models including the use of concrete objects to represent and explain 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, hundred charts, measurement tools, multiplication arrays, division sets, or coordinate planes/grids) to model computational procedures and mathematical relationships and to solve equations.

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, base ten blocks, or unifix cubes) 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 and mixed number models (fraction strips or pattern blocks) and decimal and money models (base ten blocks or coins) 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 factor trees to find least common multiple and greatest common factor.

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

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 (geoboards or dot paper) to model perimeter, area, and properties of geometric shapes and three-dimensional models (nets or solids) and real-world objects to compare size and to model volume and properties of geometric shapes.

2.4.K1h. Knowledge Base Indicator: The student knows, explains, and uses mathematical models to represent mathematical concepts, procedures, and relationships. Mathematical models include tree diagrams to organize attributes through three different sets and determine the number of possible combinations.

2.4.K1i. Knowledge Base Indicator: The student knows, explains, and uses mathematical models to represent mathematical concepts, procedures, and relationships. Mathematical models include two- and three-dimensional geometric models (spinners or number cubes) and process models (concrete objects, pictures, diagrams, or coins) to model probability.

2.4.K1j. 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, pictographs, frequency tables, bar graphs, line graphs, circle graphs, Venn diagrams, line plots, charts, tables, and single stem-and-leaf plots to organize and display data.

2.4.K1k. 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 and show relationships.

2.4.K2. Knowledge Base Indicator: The student creates mathematical models to show the relationship between two or more things, e.g., using trapezoids to represent numerical quantities.

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, hundred charts, measurement tools, multiplication arrays, division sets, or coordinate planes/grids) to model computational procedures, mathematical relationships, and problem situations and to solve equations.

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, base ten blocks, or unifix cubes) to model problem situations.

2.4.A1c. Application Indicator: The student recognizes that various mathematical models can be used to represent the same problem situation. Mathematical models include fraction and mixed number models (fraction strips or pattern blocks) and decimal and 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 factor trees to find least common multiple and greatest common factor.

2.4.A1e. Application Indicator: The student recognizes that various mathematical models can be used to represent the same problem situation. Mathematical models include equations and inequalities to model numerical relationships.

2.4.A1f. Application Indicator: The student recognizes that various mathematical models can be used to represent the same problem situation. Mathematical models include function tables (input/output machines, T-tables) to model numerical and algebraic relationships.

2.4.A1g. 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 or dot paper) to model perimeter, area, and properties of geometric shapes and three-dimensional models (nets or solids) and real-world objects to compare size and to model volume and properties of geometric shapes.

2.4.A1h. Application Indicator: The student recognizes that various mathematical models can be used to represent the same problem situation. Mathematical models include scale drawings to model large and small real-world objects.

2.4.A1i. Application Indicator: The student recognizes that various mathematical models can be used to represent the same problem situation. Mathematical models include tree diagrams to organize attributes through three different sets and determine the number of possible combinations.

2.4.A1j. Application Indicator: The student recognizes that various mathematical models can be used to represent the same problem situation. Mathematical models include two- and three-dimensional geometric models (spinners or number cubes) and process models (concrete objects, pictures, diagrams, or coins) to model probability.

2.4.A1k. 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, pictographs, frequency tables, bar graphs, line graphs, circle graphs, Venn diagrams, line plots, charts, and tables to organize, display, explain, and interpret data.

2.4.A1l. Application Indicator: The student recognizes that various mathematical models can be used to represent the same problem situation. Mathematical models include Venn diagrams to sort data and show relationships.

2.4.A2. Application Indicator: The student selects a mathematical model and explains why some mathematical models are more useful than other mathematical models in certain situations.

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 compares their properties in a variety of situations.

3.1.K1. Knowledge Base Indicator: The student recognizes and investigates properties of plane figures and solids using concrete objects, drawings, and appropriate technology.

3.1.K2a. Knowledge Base Indicator: The student recognizes and describes regular polygons having up to and including ten sides.

3.1.K2b. Knowledge Base Indicator: The student recognizes and describes similar and congruent figures.

3.1.K3. Knowledge Base Indicator: The student recognizes and describes the solids (cubes, rectangular prisms, cylinders, cones, spheres, triangular prisms, rectangular pyramids, triangular pyramids) using the terms faces, edges, and vertices (corners).

3.1.K4. Knowledge Base Indicator: The student determines if geometric shapes and real-world objects contain line(s) of symmetry and draws the line(s) of symmetry if the line(s) exist(s).

3.1.K5a. Knowledge Base Indicator: The student recognizes, draws, and describes points, lines, line segments, and rays.

3.1.K5b. Knowledge Base Indicator: The student recognizes, draws, and describes angles as right, obtuse, or acute.

3.1.K6. Knowledge Base Indicator: The student recognizes and describes the difference between intersecting, parallel, and perpendicular lines.

3.1.K7. Knowledge Base Indicator: The student identifies circumference, radius, and diameter of a circle.

3.1.A1a. Application Indicator: The student solves real-world problems by applying the properties of plane figures (circles, squares, rectangles, triangles, ellipses, rhombi, parallelograms, hexagons, pentagons) and the line(s) of symmetry; e.g., twins are having a birthday party. The rectangular birthday cake is to be cut into two pieces of equal size and with the same shape. How would the cake be cut? Would the cut be a line of symmetry? How would you know?

3.1.A1b. Application Indicator: The student solves real-world problems by applying the properties of solids (cubes, rectangular prisms, cylinders, cones, spheres, triangular prisms) emphasizing faces, edges, vertices, and bases; e.g., ribbon is to be glued on all of the edges of a cube. If one edge measures 5 inches, how much ribbon is needed? If a letter was placed on each face, how many letters would be needed?

3.1.A1c. Application Indicator: The student solves real-world problems by applying the properties of intersecting, parallel, and perpendicular lines; e.g., relate these terms to maps of city streets, bus routes, or walking paths. Which street is parallel to the street where the school is located?

3.1.A2. Application Indicator: The student identifies the plane figures (circles, squares, rectangles, triangles, ellipses, rhombi, octagons, pentagons, hexagons, trapezoids, parallelograms) used to form a composite figure.

3.2. Measurement and Estimation - The student estimates, measures, and uses measurement formulas in a variety of situations.

3.2.K1. Knowledge Base Indicator: The student determines and uses whole number approximations (estimations) for length, width, weight, volume, temperature, time, perimeter, and area using standard and nonstandard units of measure.

3.2.K2a. Knowledge Base Indicator: The student selects, explains the selection of, and uses measurement tools, units of measure, and degree of accuracy appropriate for a given situation to measure length, width, weight, volume, temperature, time, perimeter, and area using customary units of measure to the nearest fourth and eighth inch.

3.2.K2b. Knowledge Base Indicator: The student selects, explains the selection of, and uses measurement tools, units of measure, and degree of accuracy appropriate for a given situation to measure length, width, weight, volume, temperature, time, perimeter, and area using metric units of measure to the nearest centimeter.

3.2.K2c. Knowledge Base Indicator: The student selects, explains the selection of, and uses measurement tools, units of measure, and degree of accuracy appropriate for a given situation to measure length, width, weight, volume, temperature, time, perimeter, and area using nonstandard units of measure to the nearest whole unit.

3.2.K2d. Knowledge Base Indicator: The student selects, explains the selection of, and uses measurement tools, units of measure, and degree of accuracy appropriate for a given situation to measure length, width, weight, volume, temperature, time, perimeter, and area using time including elapsed time.

3.2.K3. Knowledge Base Indicator: The student states the number of feet and yards in a mile.

3.2.K4a. Knowledge Base Indicator: The student converts within the customary system: inches and feet, feet and yards, inches and yards, cups and pints, pints and quarts, quarts and gallons, pounds and ounces.

3.2.K4b. Knowledge Base Indicator: The student converts within the metric system: centimeters and meters, meters and kilometers, milliliters and liters, grams and kilograms.

3.2.K5. Knowledge Base Indicator: The student knows and uses perimeter and area formulas for squares and rectangles.

3.2.A1a. Application Indicator: The student solves real-world problems by applying appropriate measurements and measurement formulas length to the nearest eighth of an inch or to the nearest centimeter, e.g., in science, we are studying butterflies. What is the wingspan of each of the butterflies studied to the nearest eighth of an inch?

3.2.A1b. Application Indicator: The student solves real-world problems by applying appropriate measurements and measurement formulas temperature to the nearest degree, e.g., what would the temperature be if it was a good day for swimming?

3.2.A1c. Application Indicator: The student solves real-world problems by applying appropriate measurements and measurement formulas weight to the nearest whole unit (pounds, grams, nonstandard units), e.g., if you bought 200 bricks (each one weighed 5 pounds), how much would the whole load of bricks weigh?

3.2.A1d. Application Indicator: The student solves real-world problems by applying appropriate measurements and measurement formulas time including elapsed time, e.g., Bob left Wichita at 10:45 a.m. He arrived in Kansas city at 1:30. How long did it take Bob to travel to Kansas City?

3.2.A1e. Application Indicator: The student solves real-world problems by applying appropriate measurements and measurement formulas hours in a day, days in a week, and days and weeks in a year, e.g., John spent 59 days in New York City. How many weeks did he stay in New York City?

3.2.A1f. Application Indicator: The student solves real-world problems by applying appropriate measurements and measurement formulas months in a year and minutes in an hour, e.g., it took Susan 180 minutes to complete her homework assignment. How many hours did she spend doing homework?

3.2.A1g. Application Indicator: The student solves real-world problems by applying appropriate measurements and measurement formulas perimeter of squares, rectangles, and triangles, e.g., Mark wants to put up a fence up in his rectangle-shaped back yard. If his yard measures 18 feet by 36 feet, how many feet of fence will he need to go around his yard?

3.2.A1h. Application Indicator: The student solves real-world problems by applying appropriate measurements and measurement formulas area of squares and rectangles, e.g., a farmer's square-shaped field is 35 feet on each side. How many square feet does he have to plow?

3.2.A2. Application Indicator: The student solves real-world problems that involve conversions within the same measurement system: inches and feet, feet and yards, inches and yards, cups and pints, pints and quarts, quarts and gallons, centimeters and meters, e.g., you estimate that each person will chew 6 inches of bubblegum tape. If each package has 9 feet of bubblegum tape, how many people will get gum from that package?

3.2.A3. Application Indicator: The student estimates to check whether or not measurements or calculations for length, weight, temperature, time, perimeter, and area in real-world problems are reasonable, e.g. is it reasonable to say you need 30 mL of water to fill a fish tank or would you need 30 L of water to fill the fish tank?

3.2.A4. Application Indicator: The student adjusts original measurement or estimation for length, width, weight, volume, temperature, time, and perimeter in real-world problems based on additional information (a frame of reference), e.g., after estimating the outside temperature to be 75 degrees F, you find out that yesterday's high temperature at 3 p.m. was 62 degrees. Should you adjust your estimate? Why or why not?

3.3. Transformational Geometry - The student recognizes and performs transformations on geometric shapes including the use of concrete objects in a variety of situations.

3.3.K1. Knowledge Base Indicator: The student recognizes and performs through two transformations (reflection, rotation, translation) on a two-dimensional figure.

3.3.K2. Knowledge Base Indicator: The student recognizes when an object is reduced or enlarged.

3.3.K3. Knowledge Base Indicator: The student recognizes three-dimensional figures (rectangular prisms, cylinders, cones, spheres, triangular prisms, rectangular pyramids) from various perspectives (top, bottom, side, corners).

3.3.A1. Application Indicator: The student describes and draws a two-dimensional figure after performing one transformation (reflection, rotation, translation).

3.3.A2. Application Indicator: The student makes scale drawings of two-dimensional figures using a simple scale and grid paper, e.g., using the scale 1 cm = 3 m, the student makes a scale drawing of the classroom.

3.4. Geometry From An Algebraic Perspective - The student relates geometric concepts to a number line and the first quadrant of a coordinate plane in a variety of situations.

3.4.K1. Knowledge Base Indicator: The student locates and plots points on a number line (vertical/horizontal) using integers (positive and negative whole numbers).

3.4.K2. Knowledge Base Indicator: The student explains mathematical relationships between whole numbers, fractions, and decimals and where they appear on a number line.

3.4.K3. Knowledge Base Indicator: The student identifies and plots points as ordered pairs in the first quadrant of a coordinate plane (coordinate grid).

3.4.K4. Knowledge Base Indicator: The student organizes whole number data using a T-table and plots the ordered pairs in the first quadrant of a coordinate plane (coordinate grid).

3.4.A1. Application Indicator: The student solves real-world problems that involve distance and location using coordinate planes (coordinate grids) and map grids with positive whole number and letter coordinates, e.g., identifying locations and giving and following directions to move from one location to another.

3.4.A2. Application Indicator: The student solves real-world problems by plotting ordered pairs in the first quadrant of a coordinate plane (coordinate grid) , e.g., graph daily the cumulative number of recess minutes in a 5-day school week.

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 to draw conclusions and to make predictions and decisions including the use of concrete objects in a variety of situations.

4.1.K1. Knowledge Base Indicator: The student recognizes that all probabilities range from zero (impossible) through one (certain).

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

4.1.K3. Knowledge Base Indicator: The student recognizes a simple event in an experiment or simulation where the probabilities of all outcomes are equal.

4.1.K4. Knowledge Base Indicator: The student represents the probability of a simple event in an experiment or simulation using fractions.

4.1.A1. Application Indicator: The student conducts an experiment or simulation with a simple event including the use of concrete materials; records the results in a chart, table, or graph; uses the results to draw conclusions about the event; and makes predictions about future events.

4.1.A2. Application Indicator: The student uses the results from a completed experiment or simulation of a simple event to make predictions in a variety of real-world situations, e.g., the manufacturer of Crunchy Flakes puts a prize in 20 out of every 100 boxes. What is the probability that a shopper will find a prize in a box of Crunchy Flakes, if they purchase 10 boxes?

4.1.A3. Application Indicator: The student compares what should happen (theoretical probability/expected results) with what did happen (empirical probability/experimental results) in an experiment or simulation with a simple event.

4.2. Statistics - The student collects, organizes, displays, explains, and interprets numerical (rational numbers) and non-numerical data sets in a variety of situations with a special emphasis on measures of central tendency.

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 and decimal 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 and decimal intervals using these data displays: pictographs.

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 and decimal intervals using these data displays: frequency tables.

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 and decimal intervals using these data displays: bar and line 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 and decimal intervals using these data displays: Venn diagrams and other pictorial displays.

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 and decimal intervals using these data displays: line plots.

4.2.K1g. 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 and decimal intervals using these data displays: charts and tables.

4.2.K1h. 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 and decimal intervals using these data displays: circle graphs.

4.2.K1i. 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 and decimal intervals using these data displays: single stem-and-leaf plots.

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

4.2.K3a. Knowledge Base Indicator: The student identifies, explains, and calculates or finds these statistical measures of a whole number data set of up to twenty whole number data points from 0 through 1,000 minimum and maximum values.

4.2.K3b. Knowledge Base Indicator: The student identifies, explains, and calculates or finds these statistical measures of a whole number data set of up to twenty whole number data points from 0 through 1,001 range.

4.2.K3c. Knowledge Base Indicator: The student identifies, explains, and calculates or finds these statistical measures of a whole number data set of up to twenty whole number data points from 0 through 1,002mode (no-, uni-, bi-).

4.2.K3d. Knowledge Base Indicator: The student identifies, explains, and calculates or finds these statistical measures of a whole number data set of up to twenty whole number data points from 0 through 1,003median (including answers expressed as a decimal or a fraction without reducing to simplest form).

4.2.K3e. Knowledge Base Indicator: The student identifies, explains, and calculates or finds these statistical measures of a whole number data set of up to twenty whole number data points from 0 through 1,004mean (including answers expressed as a decimal or a fraction without reducing to simplest form).

4.2.A1a. Application Indicator: The student interprets and uses data to make reasonable inferences, predictions, and decisions, and to develop convincing arguments from these data displays: graphs using concrete materials.

4.2.A1b. Application Indicator: The student interprets and uses data to make reasonable inferences, predictions, and decisions, and to develop convincing arguments from these data displays: pictographs.

4.2.A1c. Application Indicator: The student interprets and uses data to make reasonable inferences, predictions, and decisions, and to develop convincing arguments from these data displays: frequency tables.

4.2.A1d. Application Indicator: The student interprets and uses data to make reasonable inferences, predictions, and decisions, and to develop convincing arguments from these data displays: bar and line graphs.

4.2.A1e. Application Indicator: The student interprets and uses data to make reasonable inferences, predictions, and decisions, and to develop convincing arguments from these data displays: Venn diagrams and other pictorial displays.

4.2.A1f. Application Indicator: The student interprets and uses data to make reasonable inferences, predictions, and decisions, and to develop convincing arguments from these data displays: line plots.

4.2.A1g. Application Indicator: The student interprets and uses data to make reasonable inferences, predictions, and decisions, and to develop convincing arguments from these data displays: charts and tables.

4.2.A1h. Application Indicator: The student interprets and uses data to make reasonable inferences, predictions, and decisions, and to develop convincing arguments from these data displays: circle graphs.

4.2.A2a. Application Indicator: The student uses these statistical measures of a whole number data set to make reasonable inferences and predictions, answer questions, and make decisions minimum and maximum values.

4.2.A2b. Application Indicator: The student uses these statistical measures of a whole number data set to make reasonable inferences and predictions, answer questions, and make decisions range.

4.2.A2c. Application Indicator: The student uses these statistical measures of a whole number data set to make reasonable inferences and predictions, answer questions, and make decisions mode.

4.2.A2d. Application Indicator: The student uses these statistical measures of a whole number data set to make reasonable inferences and predictions, answer questions, and make decisions median.

4.2.A2e. Application Indicator: The student uses these statistical measures of a whole number data set to make reasonable inferences and predictions, answer questions, and make decisions mean when the data set has a whole number mean.

4.2.A3. Application Indicator: The student recognizes that the same data set can be displayed in various formats and discusses why a particular format may be more appropriate than another.

4.2.A4. Application Indicator: The student recognizes and explains the effects of scale and interval changes on graphs of whole number data sets.