Kansas State Standards for Mathematics: Grade 4

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 (including mixed numbers), decimals, and money including the use of concrete objects 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 100,000.

1.1.K1b. Knowledge Base Indicator: The student knows, explains, and uses equivalent representations for fractions greater than or equal to zero (halves, fourths, thirds, eighths, tenths, twelfths, sixteenths, hundredths) 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 whole numbers from 0 through 100,000.

1.1.K2b. Knowledge Base Indicator: The student compares and orders fractions greater than or equal to zero (halves, fourths, thirds, eighths, tenths, twelfths, sixteenths, hundredths) including mixed numbers with a special emphasis on concrete objects.

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

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 100,000, e.g., using base ten blocks, represent the attendance at the circus over a three day stay; then represent the numbers using digits 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 10,000 and decimals when used as monetary amounts, e.g., use real money to show at least 2 ways to represent $142.78, then subtract the cost of a pair of tennis shoes.

1.1.A1c. Application Indicator: The student solves real-world problems using equivalent representations and concrete objects to multiply a one-digit whole number by a two-digit whole number, e.g., use base ten blocks to represent 24 x 5 to find the total number of hours in 5 days, or use repeated addition 24 + 24 + 24 + 24 + 25 to solve, or use the algorithm.

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 10,000, e.g., a student says that there are 1,000 students in grade 4 at her school, is this reasonable?

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 (halves, fourths, thirds, eighths, tenths, sixteenths), e.g., you ate 1/2 of a sandwich and a friend ate 3/4 of the same sandwich; is this reasonable?

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 when used as monetary amounts, e.g., a pack of chewing gum costs what amount - $62 $.75 9 cents 75.00 750 cents? Is this reasonable?

1.2. Number Systems and Their Properties - The student demonstrates an understanding of whole numbers with a special emphasis on place value; recognizes, uses, and explains the concepts of properties as they relate to whole numbers; and extends these properties to fractions (including mixed numbers), decimals, and money.

1.2.K1. Knowledge Base Indicator: The student identifies, models, reads, and writes numbers using numerals, words, and expanded notation from hundredths place through one-hundred thousands place, e.g., four hundred sixty-two thousand, two hundred eighty-four and fifty hundredths = 462,284.50 or 462,284.50 = (4 x 100,000) + (6 x 10,000) + (2 x 1,000) + (2 x 100) + (8 x 10) + (4 x 1) + (5 x .1) + (0 x .01) = 400,000 + 60,000 + 2,000 + 200 + 80 + 4 + .5 + .00.

1.2.K2. Knowledge Base Indicator: The student classifies various subsets of numbers as whole numbers, fractions (including mixed numbers), or decimals.

1.2.K3. Knowledge Base Indicator: The student identifies the place value of various digits from hundredths place through one hundred thousands place.

1.2.K4. Knowledge Base Indicator: The student identifies any whole number as even or odd.

1.2.K5a. Knowledge Base Indicator: The student uses the concepts of these properties with the whole number system and demonstrates their meaning including the use of concrete objects: commutative properties of addition and multiplication, e.g., 12 + 18 = 18 + 12 and 8 x 9 = 9 x 8.

1.2.K5b. Knowledge Base Indicator: The student uses the concepts of these properties with the whole number system 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., 24 + 0 = 24 and 75 x 1 = 75.

1.2.K5c. Knowledge Base Indicator: The student uses the concepts of these properties with the whole number system and demonstrates their meaning including the use of concrete objects: associative properties of addition and multiplication. e.g., 4 + (2 + 3) = (4 + 2) + 3 and 2 x (3 x 4) = (2 x 3) x 4.

1.2.K5d. Knowledge Base Indicator: The student uses the concepts of these properties with the whole number system and demonstrates their meaning including the use of concrete objects: symmetric property of equality applied to addition and multiplication, e.g., 100 = 20 + 80 is the same as 20 + 80 = 100 and 21 = 7 x 3 is the same as 3 x 7 = 21.

1.2.K5e. Knowledge Base Indicator: The student uses the concepts of these properties with the whole number system and demonstrates their meaning including the use of concrete objects: zero property of multiplication, e.g., 9 x 0 = 0 or 0 x 112 = 0.

1.2.K5f. Knowledge Base Indicator: The student uses the concepts of these properties with the whole number system and demonstrates their meaning including the use of concrete objects: distributive property.

1.2.A1a. Application Indicator: The student solves real-world problems with whole numbers from 0 through 10,000 using place value models; money; and the concepts of these properties to explain reasoning: commutative properties of addition and multiplication, e.g., a student has a $5, a $10, and a $20 bill; a student totals the amount to see how much can be spent shopping for school supplies. The student says: Because you can add in any order, I can rearrange the money and count $20, $10, and $5 for $20 + $10 + $5. Another student has 4 $5 bills. The student is asked the amount. The student says: I don't know 4 x 5 but I know 5 x4 is $20, since multiplication can be done in any order.

1.2.A1b. Application Indicator: The student solves real-world problems with whole numbers from 0 through 10,000 using place value models; money; and the concepts of these properties to explain reasoning: zero property of addition, e.g., a student has 6 marbles in one pocket and none in the other pocket. How many marbles altogether?

1.2.A1c. Application Indicator: The student solves real-world problems with whole numbers from 0 through 10,000 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, each student should have one math book; 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 10,000 using place value models; money; and the concepts of these properties to explain reasoning: associative properties of addition and multiplication, e.g., a student has two dimes and a quarter. Using coins or money models, there are at least 2 ways to group the coins to find the total. One way is 10 cents (dime) + 10 cents (dime) = 20 cents, then add the quarter, so 20 cents + 25 cents (quarter) = 45 cents. Another way 10 cents (dime) + 25 cents (quarter) = 35 cents, then add the other dime to 35 cents so 35 cents + 10 cents = 45 cents This models that (D + D) + Q = D + (D + Q).

1.2.A1e. Application Indicator: The student solves real-world problems with whole numbers from 0 through 10,000 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.A2a. Application Indicator: The student performs various computational procedures with whole numbers from 0 through 10,000 using the concepts of the following properties; extends the properties to fractions (halves, fourths, thirds, eighths, tenths, sixteenths) including mixed numbers, and decimals through hundredths place; and explains how the properties were used: commutative property of addition and multiplication, e.g., 5 + 6 = 6 + 5, the student says: I know that 5 + 6 = 11 and adding in any order still gets the answer, so 6 + 5 is the same as 5 + 6. 4 x 6 = 6 x 4, the student says: I know that 4 x 6 = 24 and multiplying in any order still gets the answer, so 4 x 6 is the same as 6 x 4.

1.2.A2b. Application Indicator: The student performs various computational procedures with whole numbers from 0 through 10,000 using the concepts of the following properties; extends the properties to fractions (halves, fourths, thirds, eighths, tenths, sixteenths) including mixed numbers, and decimals through hundredths place; and explains how the properties were used: zero property of multiplication without computing, e.g., 158 x 0 = 0; the student says: I know the answer (product) is zero because no matter how many factors you have, when you multiply with a 0, the product is zero.

1.2.A2c. Application Indicator: The student performs various computational procedures with whole numbers from 0 through 10,000 using the concepts of the following properties; extends the properties to fractions (halves, fourths, thirds, eighths, tenths, sixteenths) including mixed numbers, and decimals through hundredths place; and explains how the properties were used: associative property of addition, e.g., 9 + 8 could be solved as 1 + (8 + 8) or (1 + 8) + 8, the student says: I don't know 9 + 8, but I know my doubles of 8 + 8, so I made the 9 into 1 + 8 and then added 1 more to make 17.

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

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

1.3.K1. Knowledge Base Indicator: The student estimates whole number quantities from 0 through 10,000; fractions (halves, fourths, thirds); and monetary amounts through $1,000 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 and explains how they are used when estimating whole numbers quantities from 0 through 10,000; fractions [(halves, fourths, thirds) including mixed numbers)]; and monetary amounts through $1,000.

1.3.K3. Knowledge Base Indicator: The student recognizes and explains the difference between an exact and an approximate answer, e.g., when asked how many desks are in the room, the student gives an estimate of about 30 and then counts the desks and indicates an exact answer is 28 desks.

1.3.K4. Knowledge Base Indicator: The student selects from an appropriate range of estimation strategies and determines if the estimate is an overestimate or underestimate.

1.3.A1. Application Indicator: The student adjusts original whole number estimates of a real-world problem using numbers from 0 through 10,000 based on additional information (a frame of reference), e.g., if given a small jar and told the number of pieces of candy it has in it, the student would adjust his/her original estimate of the number of pieces of candy in a larger jar.

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 10,000, fractions (including mixed numbers), and monetary amounts is reasonable and makes predictions based on the information, e.g., at the movies, you bought popcorn for $2.35, a soda for $2.50, and paid $4.50 for the ticket. Is it reasonable to say you spent $10? How much will you need to save to go to the movies once a week for the next month?

1.3.A3. Application Indicator: The student selects a reasonable magnitude from three given quantities based on a familiar problem situation and explains the reasonableness of selection, e.g., about how many new pencils will fit in your pencil box? Is it about 25, about 50, or about 100? The answer will depend on the size of your pencil box.

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

1.4. Computation - The student models, performs, and explains computation with whole numbers, fractions, and money 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.K2. Knowledge Base Indicator: The student states and uses with efficiency and accuracy multiplication facts from 1 x 1 through 12 x 12 and corresponding division facts.

1.4.K3a. Knowledge Base Indicator: The student performs and explains these computational procedures: adds and subtracts whole numbers from 0 through 100,000 and when used as monetary amounts.

1.4.K3b. Knowledge Base Indicator: The student performs and explains these computational procedures: multiplies through a three-digit whole number by a two-digit whole number.

1.4.K3c. Knowledge Base Indicator: The student performs and explains these computational procedures: multiplies whole dollar monetary amounts (through three-digits) by a one- or two-digit whole number, e.g., $45 x 16.

1.4.K3d. Knowledge Base Indicator: The student performs and explains these computational procedures: multiplies monetary amounts less than $100.00 by whole numbers less than ten, e.g., $14.12 x 7.

1.4.K3e. Knowledge Base Indicator: The student performs and explains these computational procedures: divides through a two-digit whole number by a one-digit whole number with a one-digit whole number quotient with or without a remainder, e.g., 47 / 5 = 9 r

1.4.K3f. Knowledge Base Indicator: The student performs and explains these computational procedures: adds and subtracts fractions greater than or equal to zero with like denominators.

1.4.K3g. Knowledge Base Indicator: The student performs and explains these computational procedures: figures correct change through $20.00.

1.4.K4. Knowledge Base Indicator: The student identifies multiplication and division fact families.

1.4.K5. 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.K6a. Knowledge Base Indicator: The student shows the relationship between these operations with the basic fact families (addition facts with sums from 0 through 20 and corresponding subtraction facts, multiplication facts from 1 x 1 through 12 x 12 and corresponding division facts) including the use of mathematical models: addition and subtraction.

1.4.K6b. Knowledge Base Indicator: The student shows the relationship between these operations with the basic fact families (addition facts with sums from 0 through 20 and corresponding subtraction facts, multiplication facts from 1 x 1 through 12 x 12 and corresponding division facts) including the use of mathematical models: addition and multiplication.

1.4.K6c. Knowledge Base Indicator: The student shows the relationship between these operations with the basic fact families (addition facts with sums from 0 through 20 and corresponding subtraction facts, multiplication facts from 1 x 1 through 12 x 12 and corresponding division facts) including the use of mathematical models: multiplication and division.

1.4.K6d. Knowledge Base Indicator: The student shows the relationship between these operations with the basic fact families (addition facts with sums from 0 through 20 and corresponding subtraction facts, multiplication facts from 1 x 1 through 12 x 12 and corresponding division facts) including the use of mathematical models: subtraction and division.

1.4.K7. Knowledge Base Indicator: The student finds factors and multiples of whole numbers from 1 through 100.

1.4.A1a. Application Indicator: The student solves one- and two-step real-world problems with one or two operations using these computational procedures: adds and subtracts whole numbers from 0 through 10,000 and when used as monetary amounts, e.g., Lee buys a bicycle for $139, a helmet for $29, and a reflector for $6. He paid for it with a $200 check from his grandparents. How much will he have left from the $200 check?

1.4.A1b. Application Indicator: The student solves one- and two-step real-world problems with one or two operations using these computational procedures: multiplies through a two-digit whole number by a two-digit whole number, e.g., at school, there are 22 students in each classroom. If there are 24 classes, how many students are in the classrooms?

1.4.A1c. Application Indicator: The student solves one- and two-step real-world problems with one or two operations using these computational procedures: multiplies whole dollar monetary amounts (up through three-digit) by a one- or two-digit whole number, e.g., 112 third and fourth graders are planning a field trip. The cost per student is $9.00. How much will the trip cost?

1.4.A1d. Application Indicator: The student solves one- and two-step real-world problems with one or two operations using these computational procedures: multiplies monetary amounts less than $100 by whole numbers less than ten, e.g., at the book fair, a student buys 8 books on animals for $2.69 each. How much did the student pay for the books?

1.4.A1e. Application Indicator: The student solves one- and two-step real-world problems with one or two operations using these computational procedures: figures correct change through $20.00, e.g., buying a 65 cents drink, paying for it with a $1 bill, and then figuring the amount of change.

1.4.A2. Application Indicator: The student generates a family of multiplication and division facts given one equation/fact, e.g., given 8 x 9 = 72, the other facts are 9 x 8 = 72, 72 / 8 = 9, and 72 / 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 patterns, e.g., 2, 5, 11, 20, ...

2.1.K2a. Knowledge Base Indicator: The student uses these attributes to generate patterns: counting numbers related to number theory, e.g., multiples and factors through 12 or multiplying by 10, 100, or 1,000.

2.1.K2b. Knowledge Base Indicator: The student uses these attributes to generate patterns: whole numbers that increase or decrease, e.g., 20, 15, 10, ...

2.1.K2c. Knowledge Base Indicator: The student uses these attributes to generate patterns: geometric shapes including one or two attributes changes.

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

2.1.K2e. Knowledge Base Indicator: The student uses these attributes to generate patterns: money and time, e.g., $.25, $.50, $.75, ... or 1:05 p.m., 1:10 p.m., 1:15 p.m., ...

2.1.K2f. Knowledge Base Indicator: The student uses these attributes to generate patterns: things related to daily life, e.g., water cycle, food cycle, or life cycle.

2.1.K2g. Knowledge Base Indicator: The student uses these attributes to generate patterns: things related to size, shape, color, texture, or movement, e.g., rough, smooth, rough, smooth, rough, smooth, or clapping hands (kinesthetic patterns).

2.1.K3. Knowledge Base Indicator: The student identifies, states and continues a pattern presented in visual 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: counting numbers related to number theory.

2.1.A1b. Application Indicator: The student generalizes these patterns using a written description: whole number patterns.

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

2.1.A1d. Application Indicator: The student generalizes these patterns using a written description: measurement patterns.

2.1.A1e. Application Indicator: The student generalizes these patterns using a written description: money and time patterns.

2.1.A1f. 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., skip counting by 5s to 60; whole number multiples of 5 through 60; the multiplication table of 5 given the numerical pattern of 5, 10, 15, ..., 60; relating the concept of five minute time intervals to each of the numerals on a clock giving the pattern of 5, 10, 15, ..., 60; one nickel, two nickels, three nickels, ...; the number of fingers on twelve hands; recognizing that all of these representations are the same general pattern.

2.2. Variables, Equations, and Inequalities - The student uses variables, symbols, and whole numbers to solve equations including the use of concrete objects 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.

2.2.K2a. Knowledge Base Indicator: The student solves one-step equations using whole numbers with one variable and a whole number solution that find the unknown in a multiplication or division equation based on the multiplication facts from 1 x 1 through 12 x 12 and corresponding division facts, e.g., 60 = 10 x n.

2.2.K2b. Knowledge Base Indicator: The student solves one-step equations using whole numbers with one variable and a whole number solution that find the unknown in a money equation using multiplication and division based upon the facts and addition and subtraction with values through $10, e.g., 8 quarters + 10 dimes = y dollars.

2.2.K2c. Knowledge Base Indicator: The student solves one-step equations using whole numbers with one variable and a whole number solution that find the unknown in a time equation involving whole minutes, hours, days, and weeks with values through 200, e.g., 180 minutes = y hours.

2.2.K3. Knowledge Base Indicator: The student compares two whole numbers from 0 through 10,000 using the equality and inequality symbols (=, not equal to, <, >) and their corresponding meanings (is equal to, is not equal to, is less than, is greater than).

2.2.K4. Knowledge Base Indicator: The student reads and writes whole number equations and inequalities using mathematical vocabulary and notation, e.g., 15 = 3 x 5 is the same as fifteen equals three times five or 4,564 > 1,000 is the same as four thousand, five hundred sixty-four is greater than one thousand.

2.2.A1. Application Indicator: The student represents real-world problems using variables and symbols with unknown whole number quantities from 0 through 1,000, e.g., How many weeks in twenty-eight days? can be represented by n x 7 = 28 or n = 28 / 7.

2.2.A2a. Application Indicator: The student generates one-step equations to solve real-world problems with one unknown (represented by a variable or symbol) and a whole number solution that add or subtract whole numbers from 0 through 1,000, e.g., Homer, Kansas has 832 nonfiction books in its library. Homer, Idaho has 652 nonfiction books in its library. How many fewer books nonfiction books are in Homer, Idaho's library? 832 - 652 = B;

2.2.A2b. Application Indicator: The student generates one-step equations to solve real-world problems with one unknown (represented by a variable or symbol) and a whole number solution that multiply or divide using the basic facts, e.g., Tom has a sticker book and each page holds 5 stickers. If the same number of stickers is placed on each page, the book will hold 30 stickers. How many pages are in his book? This is represented by 5 x S = 30 or 30 / 5 = S.

2.2.A3a. Application Indicator: The student generates real-world problems with one operation to match a given addition, subtraction, multiplication, or division equation using whole numbers through 99, e.g., given 12 x 3 = Y, the student writes: I was sick for 3 days, when I got back I had 3 pages of homework. There are 12 problems on each page. How many total problems must I work?

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 and describes whole number relationships including the use of concrete objects in a variety of situations.

2.3.K1. Knowledge Base Indicator: The student states mathematical relationships between whole numbers from 0 through 1,000 using various methods including mental math, paper and pencil, concrete materials, 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 200 using a horizontal or vertical function table (input/output machine, T-table).

2.3.K3. Knowledge Base Indicator: The student generalizes numerical patterns using whole numbers from 0 through 200 with one operation by stating the rule using words, e.g., if the pattern is 46, 68,90, 112, 134, ...; in words, the rule is add 22 to the number before.

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

2.3.A1. Application Indicator: The student represents and describes mathematical relationships between whole numbers from 0 through 1,000 using concrete objects, pictures, written descriptions, symbols, equations, tables, and graphs.

2.3.A2. Application Indicator: The student finds the rule, states the rule, and extends numerical patterns using real-world applications using whole numbers from 0 through 200.

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, mathematical relationships, and 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 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 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 and algebraic 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, or tangrams) to model perimeter, area, and properties of geometric shapes and three-dimensional geometric models (solids) and real-world objects to compare size and to model properties 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 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, pictographs, frequency tables, horizontal and vertical bar graphs, line graphs, circle graphs, Venn diagrams, line plots, charts, and tables 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 and show relationships.

2.4.K2. Knowledge Base Indicator: The student creates a mathematical model to show the relationship between two or more things.

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, coordinate planes/grids, hundred charts, measurement tools, multiplication arrays, or division sets) to model computational procedures, mathematical relationships, and 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, base ten blocks, or unfix 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 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 money models (base ten blocks or coins) to compare, order, and represent numerical quantities.

2.4.A1e. 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.A1f. 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, or tangrams) to model perimeter, area, and properties of geometric shapes and three-dimensional geometric models (solids) and real-world objects to compare size and to model properties of geometric shapes.

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 (spinners), three-dimensional geometric models (number cubes), and process models (concrete objects) to model probability.

2.4.A1h. 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, horizontal and vertical bar graphs, line graphs, Venn diagrams, line plots, charts, and tables to organize, display, explain, and interpret data.

2.4.A1i. 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 investigates their properties including the use of concrete objects in a variety of situations.

3.1.K1. Knowledge Base Indicator: The student recognizes and investigates properties of plane figures (circles, squares, rectangles, triangles, ellipses, rhombi, octagons, hexagons, pentagons) using concrete objects, drawings, and appropriate technology.

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

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

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

3.1.K5a. Knowledge Base Indicator: The student recognizes squares, rectangles, rhombi, parallelograms, trapezoids as special quadrilaterals.

3.1.K5b. Knowledge Base Indicator: The student recognizes similar and congruent figures.

3.1.K5c. Knowledge Base Indicator: The student recognizes points, lines (intersecting, parallel, perpendicular), line segments, and rays.

3.1.K6. 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.A1a. Application Indicator: The student solves real-world problems by applying the properties of plane figures (circles, squares, rectangles, triangles, ellipses, rhombi, parallelograms, hexagons) and lines of symmetry, e.g., print your name or the school's name in all capital letters. Identify the lines of symmetry in each letter.

3.1.A1b. Application Indicator: The student solves real-world problems by applying the properties of solids (cubes, rectangular prisms, cylinders, cones, spheres), e.g., you want to design something to store school supplies. Which of the solids could you use for storage? Why did you select that solid?

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

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

3.2.K1. Knowledge Base Indicator: The student 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, and height to the nearest fourth of an inch or to the nearest centimeter.

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 volume to the nearest cup, pint, quart, or gallon; to the nearest liter; or to the nearest whole unit of a nonstandard unit.

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 weight to the nearest ounce or pound or to the nearest whole unit of a nonstandard unit of measure.

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 temperature to the nearest degree.

3.2.K2e. 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 time including elapsed time.

3.2.K3a. Knowledge Base Indicator: The student states the number of weeks in a year.

3.2.K3b. Knowledge Base Indicator: The student states the number of ounces in a pound.

3.2.K3c. Knowledge Base Indicator: The student states the number of milliliters in a liter, grams in a kilogram, and meters in a kilometer.

3.2.K3d. Knowledge Base Indicator: The student states the number of items in a dozen.

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.

3.2.K4b. Knowledge Base Indicator: The student converts within the metric system: centimeters and meters.

3.2.K5a. Knowledge Base Indicator: The student finds the perimeter of two-dimensional figures given the measures of all the sides.

3.2.K5b. Knowledge Base Indicator: The student finds the area of squares and rectangles using concrete objects.

3.2.A1a. Application Indicator: The student solves real-world problems by applying appropriate measurements: length to the nearest fourth of an inch, e.g., how much longer is the math textbook than the science textbook?

3.2.A1b. Application Indicator: The student solves real-world problems by applying appropriate measurements: length to the nearest centimeter, e.g., a new pencil is about how many centimeters long?

3.2.A1c. Application Indicator: The student solves real-world problems by applying appropriate measurements: temperature to the nearest degree, e.g., what would the temperature outside be if it was a good day for sledding?

3.2.A1d. Application Indicator: The student solves real-world problems by applying appropriate measurements: weight to the nearest whole unit (pounds, grams, nonstandard unit), e.g., Brendan went to the store and bought 2 packages of hamburger for a meatloaf. One of the hamburger packages weighed 1 lb. and 8 ozs. The other packages weighed 1 lb. and 7 ozs. What is the combined weight (to the nearest pound) of the two packages of hamburger?

3.2.A1e. Application Indicator: The student solves real-world problems by applying appropriate measurements: time including elapsed time, e.g., Joy went to the mall at 10:00 a.m. She shopped until 4:15 p.m. How long did she shop at the mall?

3.2.A1f. Application Indicator: The student solves real-world problems by applying appropriate measurements: months in a year, e.g., if it takes 208 weeks to get a college degree, and Susan has completed one year, how many more weeks does she have to complete to get her degree?

3.2.A1g. Application Indicator: The student solves real-world problems by applying appropriate measurements: minutes in an hour, e.g., Bob has spent 240 minutes working on a project for Science. How many hours has he worked on the project?

3.2.A1h. Application Indicator: The student solves real-world problems by applying appropriate measurements: perimeter of squares, rectangles, and triangles, e.g., a triangle has 3 equal sides of 32 inches. What is the perimeter of the triangle?

3.2.A2. Application Indicator: The student estimates to check whether or not measurements and calculations for length, width, weight, volume, temperature, time, and perimeter in real-world problems are reasonable, e.g., which is the most reasonable weight for your scissors - 2 ounces, 2 pounds, 20 ounces, or 20 pounds? A teacher measures one side of a square desktop at 2 feet. Which of the following perimeters is reasonable for the desktop - 2 feet, 4 square feet, 6 square feet, or 8 feet?

3.2.A3. 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., your class has a large jar and a small jar. You estimate it will take 5 small jars of liquid to fill the large jar. After you pour the contents of 2 small jars in, the large jar is more that half full. Should you need to adjust your estimate?

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

3.3.K1. Knowledge Base Indicator: The student describes a transformation using cardinal points or positional directions, e.g., go north three blocks and then west four blocks or move the triangle three units to the right and two units up.

3.3.K2. Knowledge Base Indicator: The student recognizes, performs, and describes one transformation (reflection/flip, rotation/turn, translation/slide) on a two-dimensional figure or concrete object.

3.3.K3. Knowledge Base Indicator: The student recognizes three-dimensional figures (rectangular prisms, cylinders) and concrete objects from various perspectives (top, bottom, sides, corners).

3.3.A1. Application Indicator: The student recognizes real-world transformations (reflection/flip, rotation/turn, translation/slide).

3.3.A2. Application Indicator: The student gives and uses cardinal points or positional directions to move from one location to another on a map or grid.

3.3.A3. Application Indicator: The student describes the properties of geometric shapes or concrete objects that stay the same and the properties that change when a transformation is performed.

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 uses a number line (horizontal/vertical) to model whole number multiplication facts from 1 x 1 through 12 x 12 and corresponding division facts.

3.4.K2. Knowledge Base Indicator: The student uses points in the first quadrant of a coordinate plane (coordinate grid) to identify locations.

3.4.K3. Knowledge Base Indicator: The student identifies and plots points as whole number 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 whole number ordered pairs in the first quadrant of a coordinate plane (coordinate grid), e.g., given that each movie ticket cost $5, the student graphs the number of tickets bought and the total cost of tickets to attend a movie.

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 the probability of an impossible event is zero and that the probability of a certain event is one.

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

4.1.K3. Knowledge Base Indicator: The student recognizes and states the probability of a simple event in an experiment or simulation, e.g., when a coin is flipped, the probability of landing heads up is 1/2 and the probability of landing tails up is 1/2. This can be read as one out of two or one half.

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

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 problems, 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 (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, (for testing, does not have to use concrete objects in items).

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 symbol or picture representing one, two, five, ten, twenty-five, or one-hundred including partial symbols when the symbol represents an even amount.

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.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 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 intervals using these data displays: line 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 intervals using these data displays: circle graphs.

4.2.K2. Knowledge Base Indicator: The student collects data using different techniques (observations, polls, surveys, interviews, 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 data set with less than ten whole number data points using whole numbers 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 data set with less than ten whole number data points using whole numbers from 0 through 1,000: range.

4.2.K3c. Knowledge Base Indicator: The student identifies, explains, and calculates or finds these statistical measures of a data set with less than ten whole number data points using whole numbers from 0 through 1,000: mode.

4.2.K3d. Knowledge Base Indicator: The student identifies, explains, and calculates or finds these statistical measures of a data set with less than ten whole number data points using whole numbers from 0 through 1,000: median when data set has an odd number of data points.

4.2.K3e. Knowledge Base Indicator: The student identifies, explains, and calculates or finds these statistical measures of a data set with less than ten whole number data points using whole numbers from 0 through 1,000: mean when data set has a whole number mean.

4.2.A1a. Application Indicator: The student interprets and uses data to make reasonable inferences and predictions, answer questions, and make decisions from these data displays: graphs using concrete objects.

4.2.A1b. Application Indicator: The student interprets and uses data to make reasonable inferences and predictions, answer questions, and make decisions from these data displays: pictographs with a symbol or picture representing one, two, five, ten, twenty-five, or one-hundred including partial symbols when the symbol represents an even amount.

4.2.A1c. Application Indicator: The student interprets and uses data to make reasonable inferences and predictions, answer questions, and make decisions from these data displays: frequency tables (tally marks).

4.2.A1d. Application Indicator: The student interprets and uses data to make reasonable inferences and predictions, answer questions, and make decisions from these data displays: horizontal and vertical bar graphs.

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

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

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

4.2.A1h. Application Indicator: The student interprets and uses data to make reasonable inferences and predictions, answer questions, and make decisions from these data displays: line graphs.

4.2.A2a. Application Indicator: The student uses these statistical measures of a data set using whole numbers from 0 through 1,000 with less than ten whole number data points 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 data set using whole numbers from 0 through 1,000 with less than ten whole number data points 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 data set using whole numbers from 0 through 1,000 with less than ten whole number data points 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 data set using whole numbers from 0 through 1,000 with less than ten whole number data points to make reasonable inferences and predictions, answer questions, and make decisions: median when the data set has an odd number of data points.

4.2.A2e. Application Indicator: The student uses these statistical measures of a data set using whole numbers from 0 through 1,000 with less than ten whole number data points 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 including the use of concrete objects.

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