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Kansas Math Standards - 5th Grade
MathScore aligns to the Kansas Math Standards for 5th Grade. The standards appear below along with the MathScore topics that match. If you click on a topic name, you will see sample problems at varying degrees of difficulty that MathScore generated. When students use our program, the difficulty of the problems will automatically adapt based on individual performance, resulting in not only true differentiated instruction, but a challenging game-like experience.
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Standard 1: Number and Computation
Benchmark 1: Number Sense - The student demonstrates number sense for integers, fractions, decimals, and money in a variety of situations.AI-1 ▴N knows, explains, and uses equivalent representations for ($):
a. whole numbers from 0 through 1,000,000 (2.4.K1a-b);
b. fractions greater than or equal to zero (including mixed numbers) (2.4.K1c);
c. decimals greater than or equal to zero through hundredths place and when used as monetary amounts (2.4.K1c). (Decimal Place Value , Positive Number Line , Fraction Simplification , Fractions to Decimals , Decimals To Fractions )
AI-2 compares and orders (2.4.K1a-c) ($) :
a. integers,
b. fractions greater than or equal to zero (including mixed numbers),
c. decimals greater than or equal to zero through hundredths place. (Order Decimals , Compare Mixed Values , Compare Mixed Values 2 , Fraction Comparison , Compare Decimals , Compare Integers , Basic Fraction Comparison )
AI-3 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 (2.4.K1a-c). (Positive Number Line )
AI-4 knows equivalent percents and decimals for one whole, one-half, one-fourth, three-fourths, and one tenth through nine tenths (2.4.K1c), e.g., 1 = 100% = 1.0, 3/4 = 75% = .75, 3/10 = 30% = .3. (Percentages , Percentage Pictures )
AI-5 identifies integers and gives real-world problems where integers are used (2.4.K1a), 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.
AI-1 solves real-world problems using equivalent representations and concrete objects to ($):
a. compare and order (2.4.A1a-d) -
i. whole numbers from 0 through 1,000,000; 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; ii. fractions greater than or equal to zero (including mixed numbers), e.g., Frank ate 2 ½ 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. 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. 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;
b. add and subtract whole numbers from 0 through 100,000 and decimals when used as monetary amounts (2.4.A1a,c), e.g., use real money to show at least 2 ways to represent $846.00, then subtract the cost of a new computer setup;
c. multiply through a two-digit whole number by a two-digit whole number (2.4.A1a-b), 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.;
d. divide through a four-digit whole number by a two-digit whole number (2.4.A1a-b), e.g., the Boy Scout troop collected cans and held bake sales for a year and earned $492.60. The money will be divided evenly among the 12 troop members to buy new uniforms. Represent each boy's share of the money at least 2 ways - traditional division; use 4 hundreds, 9 tens, 2 ones, and 6 dimes to act out the situation; or use base ten blocks to act it out. (Word Problems With Remainders , Making Change , Making Change 2 )
AI-2 determines whether or not solutions to real-world problems that involve the following are reasonable ($):
a. whole numbers from 0 through 100,000 (2.4.A1a-b), 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?
b. fractions greater than or equal to zero (including mixed numbers) (2.4.A1c), e.g., explain if it is reasonable to say that a dog is ½ boxer, ¼ bulldog, ¼ collie, and ¼ rotweiler;
AI-3 decimals greater than or equal to zero through hundredths place (2.4.A1c), e.g., five people a ate pizza. Is it reasonable to say that each person ate .3 of the pizza?
Benchmark 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.
KBI-1 classifies subsets of numbers as integers, whole number, fractions (including mixed numbers), or decimals (2.4.K1a-c, 2.4.K1k).
KBI-2 identifies prime and composite numbers from 0 through 50. (Prime Numbers )
KBI-3 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 (2.4.K1a) ($):
a. commutative properties of addition and multiplication, e.g., 43 + 34 = 34 + 43 and 12 x 15 = 15 x 12;
b. associative properties of addition and multiplication, e.g., 4 + (3 + 5) = (4 + 3) + 5;
c. zero property of addition (additive identity) and property of one for multiplication (multiplicative identity), e.g., 342 + 0 = 342 and 576 x 1 = 576;
d. symmetric property of equality, e.g., 35 = 11 + 24 is the same as 11 + 24 = 35;
e. zero property of multiplication, e.g., 438,223 x 0 = 0;
f. distributive property, e.g., 7(3 + 5) = 7(3) + 7(5);
g. substitution property, e.g., if a = 3 and a = b, then b = 3. (Associative Property 1 , Associative Property 2 , Commutative Property 1 , Commutative Property 2 , Basic Distributive Property )
KBI-4 recognizes Roman Numerals that are used for dates, on clock faces, and in outlines.
KBI-5 recognizes the need for integers, e.g., with temperature, below zero is negative and above zero is positive; in finances, money in your pocket is positive and money owed someone is negative.
AI-1 solves real-world problems with whole numbers from 0 through 100,000 and decimals through hundredths using place value models; money; and the concepts of these properties to explain reasoning (2.4.A1a-c,e) ($):
a. 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.
b. zero property of addition, e.g., have students lay out 6 dimes. Tell them to add zero. How many dimes? 6 + 0 = 6
c. 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.
d. symmetric property of equality, e.g., Pat knows he has $56. He has 2 twenty-dollar bills in his wallet. How much does he have at home in his bank? This can be represented as - 56 = (2 x 20) + ▫, so ( 2 x 20) + ▫ = 56 56 = 40 + ▫, so 40 + ▫ = 56 56 = 20 + 20 + 16, so 20 + 20 + 16 = 56.
e. zero property of multiplication, e.g., in science, you are observing a snail. The snail does not move over a 4-hour period. To figure its total movement, you say 4 x 0 = 0.
f. distributive property, e.g., Juan has 7 quarters and 7 dimes. What is the total amount of money he has? 7($.25 + $.10) = 7($.25) + 7($.10). (Arithmetic Word Problems , Word Problems With Remainders , Making Change , Making Change 2 , Fraction Word Problems , Fraction Word Problems 2 )
AI-3 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 (2.4.A1a-c,e):
a. 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;
b. 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);
c. 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 $9.62;
d. symmetric property of equality, e.g., given ▫ = ½ + ¼, the student says: That is the same as ½ + ¼ because I must make both sides equal;
e. zero property of multiplication e.g., given .7 x 0, the student says: I know the answer (product) is zero because no matter how many factors you have, multiplying by 0, the product is 0;
f. distributive property, e.g., given 4 x 614, the student can explain that you can solve it (in your head?) by computing 4(600) + 4(10) + 4(4), which is 2,400 + 40 + 4 = 2,444. (Long Addition , Long Subtraction , Multiplication By One Digit , Long Multiplication , Long Division By One Digit , Long Division , Division with Remainders , Long Division with Remainders , Small Decimal Division , Multiply By Multiples Of 10 , Fraction Addition , Fraction Subtraction , Decimal Addition , Decimal Subtraction , Decimal Multiplication )
AI-4 states the reason for using integers, whole numbers, fractions (including mixed numbers), or decimals when solving a given realworld problem (2.4.A1a-c) ($).
Benchmark 3: Estimation - The student uses computational estimation with whole numbers, fractions, decimals, and money in a variety of situations.
KBI-1 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 $10,000 using various computational methods including mental math, paper and pencil, concrete materials, and appropriate technology (2.4.K1a-c) ($).
KBI-2 ▴N 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 $10,000 and explains how various strategies are used (2.4.K1a-c) ($). (Rounding Numbers , Decimal Rounding to .01 , Decimal Rounding )
KBI-3 recognizes and explains the difference between an exact and an approximate answer (2.4.K1a-c).
KBI-4 explains the appropriateness of an estimation strategy used and whether the estimate is greater than (overestimate) or less than (underestimate) the exact answer (2.4.K1a).
AI-1 adjusts original estimate using whole numbers from 0 through 100,000 of a real-world problem based on additional information (a frame of reference) (2.4.A1a) ($), 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.
AI-2 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 $10,000 is reasonable and makes predictions based on the information (2.4.A1a-c) ($), e.g., at your birthday party, you ate 4 ½ pepperoni pizzas, 3 ¼ cheese pizzas, and 2 ¾ sausage pizzas. On the bill they charged you for 10 pizzas. Is that reasonable? If pizzas cost $6.99 each, about how much should you save for your next birthday party? (Estimated Addition , Estimated Subtraction , Money Addition , Money Subtraction , Estimated Multiplication , Estimated Division , Estimated Multiply Divide Word Problems )
AI-3 selects a reasonable magnitude from given quantities based on a real-world problem using whole numbers from 0 through 100,000 and explains the reasonableness of selection (2.4.A1a), e.g., about how many tulips can fit in the flower vase, 2, 10, or 25? The student chooses ten and explains that the vase at home is a jelly jar and either two or ten will fit, but ten looks prettier.
AI-4 ▴ ■ determines if a real-world problem calls for an exact or approximate answer using whole numbers from 0 through 100,000 and performs the appropriate computation using various computational methods including mental math, paper and pencil, concrete materials, and appropriate technology (2.4.A1a) ($). (Estimated Multiply Divide Word Problems )
Benchmark 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.
KBI-1 computes with efficiency and accuracy using various computational methods including mental math, paper and pencil, concrete materials, and appropriate technology (2.4.K1a).
KBI-2 performs and explains these computational procedures:
a. N 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 (2.4.K1a-b), e.g., 7452 ÷ 24 = 310 r 12 or 310 ½;
b. divides whole numbers beyond a 2-digit divisor and a 4-digit dividend using appropriate technology (2.4.K1a-b), e.g., 73,368 ÷ 36 = 2,038;
c. N adds and subtracts decimals from thousands place through hundredths place (2.4.K1c);
d. N multiplies decimals up to three digits by two digits from hundreds place through hundredths place (2.4.K1c);
e. N 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; (2.4.K1c);
f. N multiplies and divides by 10; 100; 1,000; or single-digit multiples of each (2.4.K1a-b), e.g., 20 • 300 or 4,400 ÷ 500. (Long Division By One Digit , Long Division , Division with Remainders , Long Division with Remainders , Small Decimal Division , Multiply By Multiples Of 10 , Basic Fraction Addition , Fraction Addition , Basic Fraction Subtraction , Fraction Subtraction , Decimal Addition , Decimal Subtraction , Decimal Multiplication )
KBI-3 reads and writes horizontally, vertically, and with different operational symbols the same addition, subtraction, multiplication, or division expression, e.g., 6 • 4 is the same as 6 x 4 is the same as 6(4) and 6 x 4 or 10 divided by 2 is the same as 10 ÷ 2 or 10/2.
KBI-4 ▴N 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 (2.4.K1d). (Greatest Common Factor , Least Common Multiple )
AI-1 ▴N solves one- and two-step real-world problems using these computational procedures ($) (For the purpose of assessment, twostep could include any combination of a, b, c, d, e, or f.):
a. adds and subtracts whole numbers from 0 through 100,000 (2.4.A1a-b); 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?
b. multiplies through a four-digit whole number by a two-digit whole number (2.4.A1a-b), 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?
c. multiplies monetary amounts up to $1,000 by a one- or two-digit whole number (2.4.A1c), e.g., what is the cost of 4 items each priced at $3.49?
d. divides whole numbers through a 2-digit divisor and a 4-digit dividend with the remainder as a whole number or a fraction (2.4.A1a-c);
e. adds and subtracts decimals from thousands place through hundredths place when used as monetary amounts (2.4.A1a-c) (The set of decimal numbers includes whole numbers.), e.g., at the track meet, Peter ran the 100 meter dash in 12.3 seconds. Tanner ran the same race in 12.19 seconds. How much faster was Tanner?
f. ■ multiplies and divides by 10; 100; and 1,000 and single digit multiples of each (10, 20, 30, ...; 100, 200, 300, ...; 1,000; 2,000; 3,000; ...) (2.4.A1a-b), e.g., Matti has 1,590 stamps to place in her stamp album. 30 stamps fit on a page. What is the minimum number of pages she needs in her album? (Arithmetic Word Problems , Word Problems With Remainders , Making Change )
Standard 2: Algebra
Benchmark 1: Patterns - The student recognizes, describes, extends, develops, and explains relationships in patterns in a variety of situations.KBI-6 uses concrete objects, drawings, and other representations to work with these types of patterns(2.4.K1a):
a. repeating patterns, e.g., 9, 10, 11, 9, 10, 11, ...;
b. growing patterns, e.g., 20, 30, 28, 38, 36, ... where the rule is add 10, then subtract 2; or 2, 5, 8, ... as an example of an arithmetic sequence - each term after the first is found by adding the same number to the preceding term. (Patterns: Numbers , Function Tables , Function Tables 2 )
KBI-7 uses these attributes to generate patterns:
a. counting numbers related to number theory (2.4.K1a), e.g., multiples or perfect squares;
b. whole numbers (2.4.K1a) ($), e.g., 10; 100; 1,000; 10,000; 100,000; ... (powers of ten);
c. geometric shapes through two attribute changes (2.4.K1g), e.g., ... when the next shape has one more side; or when both the color and the shape change at the same time;
d. measurements (2.4.K1a), e.g., 3 m, 6 m, 9 m, ...;
e. things related to daily life (2.4.K1a), e.g., sports scores, longitude and latitude, elections, eras, or appropriate topics across the curriculum;
f. things related to size, shape, color, texture, or movement (2.4.K1a), e.g., square dancing moves (kinesthetic patterns)
KBI-3 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 (2.4.K1a) ($). (Function Tables , Function Tables 2 )
KBI-4 generates:
a. a pattern (repeating, growing) (2.4.K1a).
b. a pattern using a function table (input/output machines, T-tables) (2.4.K1g).
AI-1 generalizes these patterns using a written description:
a. numerical patterns (2.4.K1a) ($),
b. patterns using geometric shapes through two attribute changes (2.4.A1a,g),
c. measurement patterns (2.4.A1a),
d. patterns related to daily life (2.4.A1a)
AI-2 recognizes multiple representations of the same pattern (2.4.A1a) ($), 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 $1,000 bill; ....
Benchmark 2: Variables, Equations, and Inequalities - The student uses variables, symbols, whole numbers, and algebraic expressions in one variable to solve linear equations in a variety of situations.
KBI-1 ▴ explains and uses variables and symbols to represent unknown whole number quantities from 0 through 1,000 and variable relationships (2.4.K1a)
KBI-2 ▴N solves one-step linear equations with one variable and a whole number solution using addition and subtraction with whole numbers from 0 through 100 and multiplication with the basic facts (2.4.K1a,e) ($), e.g., 3y = 12, 45 = 17 + q, or r - 42 = 36. (Missing Factor , Missing Term , Single Variable Equations )
KBI-3 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 (2.4.K1a-b) ($). (Number Comparison , Order Numbers )
KBI-4 recognizes ratio as a comparison of part-to-part and part-to-whole relationships (2.4.K1a), e.g., the relationship between the number of boys and the number of girls (part-to-part) or the relationship between the number of girls to the total number of students in the classroom (part-to-whole). (Ratios )
AI-1 represents real-world problems using variables, symbols, and onestep equations with unknown whole number quantities from 0 through 1,000 (2.4.A1a,e) ($); 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. (Arithmetic Word Problems , Algebraic Word Problems , Algebraic Sentences )
AI-2 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 (2.4.A1a,e) ($), e.g., Ninety-six items are being shared with four people. How much does each person receive? becomes 96 ÷ 4 = n. (Arithmetic Word Problems , Algebraic Word Problems )
AI-3 generates (2.4.A1a,e) ($):
a. 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 (2.4.A1a), 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?
b. number comparison statements using equality and inequality symbols (=, <, >) with whole numbers, measurement, and money e.g., 1 ft < 15 in or 10 quarters > $2.
Benchmark 3: Functions - The student recognizes, describes, and examines whole number relationships in a variety of situations.
KBI-1 states mathematical relationships between whole numbers from 0 through 10,000 using various methods including mental math, paper and pencil, concrete objects, and appropriate technology (2.4.K1a) ($).
KBI-2 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) (2.4.K1f), e.g., using the function table, fill in the values and find the rule, the rule is N • 80. N 4 9 11 ? 2 7 ? ? 320 720 880 640 ? ? 800 (Function Tables , Function Tables 2 )
KBI-3 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.
KBI-4 ▴ ■ 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 (2.4.K1a,f).
KBI-5 plots and locates points for integers (positive and negative whole numbers) on a horizontal number line and vertical number line (2.4.K1a). (Compare Integers , Ordered Pairs )
KBI-6 describes whole number relationships using letters and symbols.
AI-1 represents and describes mathematical relationships between whole numbers from 0 through 5,000 using written and oral descriptions, tables, graphs, and symbolic notation (2.4.A1a) ($).
AI-2 finds the rule, states the rule, and extends numerical patterns using real-world problems with whole numbers from 0 through 5,000 (2.4.A1a,f) ($), 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¢ 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.
AI-3 translates between verbal, numerical, and graphical representations including the use of concrete objects to describe mathematical relationships (2.4.A1a,k), e.g., when the temperature is 20° and then it drops 2° an hour for 12 hours, the result is a negative number; the student could model this using a vertical number line. Day # of Cookies Sold 4 450 8 900 12 1350 16 1800 20 2250 24 2700 28 3150 (Function Tables , Function Tables 2 )
Benchmark 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.
KBI-1 knows, explains, and uses mathematical models to represent mathematical concepts, procedures, and relationships. Mathematical models include:
a. 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 (1.1.K1a, 1.1K1c, 1.1.K2, 1.1.K3, 1.1.K5, 1.2.K1, 1.2.K3, 1.3.K1-4, 1.4.K1, 1.4.K2a-b, 1.4.K.2f, 2.1.K1, 2.1.K2a-b, 2.1.K2d-h, 2.1.K2, 2.2.K1-4, 2.3.K1, 2.3.K4-5, 3.1.K1-6, 3.2.K1- 4, 3.3.K1-2, 3.4.K1-4, 4.2.K3) ($);
b. place value models (place value mats, hundred charts, base ten blocks, or unifix cubes) to compare, order, and represent numerical quantities and to model computational procedures (1.1.K1a, 1.1.K2, 1.1.K4, 1.2.K1, 1.3.K1-3, 1.4.K2a-b, 1.4.K2f, 2.2.K3) ($);
c. 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 (1.1.K1b, 1.1.K2-4, 1.2.K1, 1.3.K1-3, 1.4.K2c-e, 4.1.K4) ($);
d. factor trees to find least common multiple and greatest common factor (1.2.K2, 1.4.K4);
e. equations and inequalities to model numerical relationships (2.2.K2) ($);
f. function tables (input/output machines, T-tables) to model numerical and algebraic relationships (2.1.K1c, 2.1.K1j, 3.1.K1- 8, 3.2.K7-8, 3.3.K1-3) ($);
g. two-dimensional geometric models (geoboards or dot paper) to model perimeter, area, and properties of geometric shapes and three-dimensional models (nets or solids) and real-world objects to compare size and to model volume and properties of geometric shapes (2.1.K2c, 2.1.K4b, 3.2.K5, 3.3.K3, 4.1.K2);
h. tree diagrams to organize attributes through three different sets and determine the number of possible combinations (4.1.K2, 4.2.K1a-d, 4.2.K1f-I; 4.2.K2, 4.2);
i. two- and three-dimensional geometric models (spinners or number cubes) and process models (concrete objects, pictures, diagrams, or coins) to model probability (4.1.K1-3, 4.2.K1e, 4.2.K2) ($) ;
j. 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 (4.1.K2, 4.2.K1-2) ($) ;
k. Venn diagrams to sort data and show relationships. (Decimal Place Value , Number Comparison , Order Numbers , Order Decimals , Compare Mixed Values , Positive Number Line , Compare Decimals , Compare Integers , Basic Fraction Comparison , Fraction Comparison , Percentage Pictures , Stem And Leaf Plots , Tally and Pictographs , Bar Graphs , Line Graphs , Function Tables , Function Tables 2 )
KBI-2 creates mathematical models to show the relationship between two or more things, e.g., using trapezoids to represent numerical quantities - .5 or 1/2 1 or 1.0 1.5 or 1 1/2 2 or 2.0
AI-1 recognizes that various mathematical models can be used to represent the same problem situation. Mathematical models include:
a. process models (concrete objects, pictures, diagrams, number lines, hundred charts, measurement tools, multiplication arrays, division sets, or coordinate planes/grids) to model computational procedures, mathematical relationships, and problem situations and to solve equations (1.1.A1, 1.1.A2a, 1.2.A1-3, 1.3.A1-4, 1.4.A1a-b, 1.4.A1d-f, 2.1.A1a, 2.1.A1c-d, 2.1.A2, 2.2.A1-3, 2.3.A1-3, 3.2.A1a-f, 3.2.A2-4, 3.3.A1, 3.4.A1-2. 4.2.A2) ($);
b. place value models (place value mats, hundred charts, base ten blocks, or unifix cubes) to model problem situations (1.1.A1, 1.1.A2a, 1.2.A1-3, 1.3.A2, 1.4.A1a-b, 1.4.A1f, 1.4.A3a-e, 2.2.K3) ($);
c. fraction and mixed number models (fraction strips or pattern blocks) and decimal and money models (base ten blocks or coins) to compare, order, and represent numerical quantities (1.1.A1a-b, 1.1.A2b-c, 1.2.A1-3, 1.3.A2, 1.4.A1c-e) ($);
d. factor trees to find least common multiple and greatest common factor;
e. equations and inequalities to model numerical relationships (2.1.A1-2, 2.2.A1-3) ($);
f. function tables (input/output machines, T-tables) to model numerical and algebraic relationships (2.3.A2, 3.2.A1g-h, 3.3.A3) ($);
g. 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 (2.1.A1b, 3.1.A1-2, 3.2.A4, 4.1.A1-3);
h. scale drawings to model large and small real-world objects (3.3.A2);
i. tree diagrams to organize attributes through three different sets and determine the number of possible combinations;
j. two- and three-dimensional geometric models (spinners or number cubes) and process models (concrete objects, pictures, diagrams, or coins) to model probability (4.1.A1- 3, 4.2.A1) ($);
k. graphs using concrete objects, pictographs, frequency tables, bar graphs, line graphs, circle graphs, Venn diagrams, line plots, charts, and tables to organize, display, explain, and interpret data (2.3.A3; 4.1.A1-2, 4.2.A1, 4.2.A3-4) ($);
l. Venn diagrams to sort data and show relationships. (Decimal Place Value , Number Comparison , Order Numbers , Order Decimals , Compare Mixed Values , Positive Number Line , Compare Decimals , Compare Integers , Basic Fraction Comparison , Fraction Comparison , Percentage Pictures , Stem And Leaf Plots , Tally and Pictographs , Bar Graphs , Line Graphs , Function Tables , Function Tables 2 )
AI-2 selects a mathematical model and explains why some mathematical models are more useful than other mathematical models in certain situations.
Standard 3: Geometry
Benchmark 1: Geometric Figures and Their Properties - The student recognizes geometric shapes and compares their properties in a variety of situations.KBI-1 recognizes and investigates properties of plane figures and solids using concrete objects, drawings, and appropriate technology (2.4.K1g).
KBI-2 recognizes and describes (2.4.K1g):
a. regular polygons having up to and including ten sides;
b. similar and congruent figures. (Polygon Names , Congruent And Similar Triangles )
KBI-3 ▴ 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) (2.4.K1g).
KBI-4 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) (2.4.K1g).
KBI-5 recognizes, draws, and describes (2.4.K1g):
a. points, lines, line segments, and rays;
b. angles as right, obtuse, or acute.
KBI-6 recognizes and describes the difference between intersecting, parallel, and perpendicular lines (2.4.K1g). (Parallel and Perpendicular Lines )
KBI-7 identifies circumference, radius, and diameter of a circle (2.4.K1g). (Circle Measurements , Circle Circumference )
AI-1 solves real-world problems by applying the properties of (2.4.A1g):
a. ▴ 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?
b. 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?
c. 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?
AI-2 identifies the plane figures (circles, squares, rectangles, triangles, ellipses, rhombi, octagons, pentagons, hexagons, trapezoids, parallelograms) used to form a composite figure (2.4.A1g).
Benchmark 2: Measurement and Estimation - The student estimates, measures, and uses measurement formulas in a variety of situations.
KBI-1 determines and uses whole number approximations (estimations) for length, width, weight, volume, temperature, time, perimeter, and area using standard and nonstandard units of measure (2.4.K1a) ($).
KBI-2 selects, explains the selection of, and uses measurement tools, units of measure, and degree of accuracy appropriate for a given situation to measure length, width, weight, volume, temperature, time, perimeter, and area using (2.4.K1a) ($):
a. customary units of measure to the nearest fourth and eighth inch,
b. metric units of measure to the nearest centimeter,
c. nonstandard units of measure to the nearest whole unit,
d. time including elapsed time.
KBI-3 states the number of feet and yards in a mile (2.4.K1a).
KBI-4 converts (2.4.K1a):
a. ▴ ■ 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;
b. within the metric system: centimeters and meters, meters and kilometers, milliliters and liters, grams and kilograms. (Distance Conversion , Volume Conversion , Weight Conversion )
KBI-5 knows and uses perimeter and area formulas for squares and rectangles (2.4.K1g). (Compare Rectangle Area and Perimeter )
AI-1 solves real-world problems by applying appropriate measurements and measurement formulas ($):
a. ▴ length to the nearest eighth of an inch or to the nearest centimeter (2.4.A1a), 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?
b. temperature to the nearest degree (2.4.A1a), e.g., what would the temperature be if it was a good day for swimming?
c. ▴ weight to the nearest whole unit (pounds, grams, nonstandard units) (2.4.A1a), e.g., if you bought 200 bricks (each one weighed 5 pounds), how much would the whole load of bricks weigh?
d. time including elapsed time (2.4.A1a), 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?
e. hours in a day, days in a week, and days and weeks in a year (2.4.A1a), e.g., John spent 59 days in New York City. How many weeks did he stay in New York City?
f. ▴ months in a year and minutes in an hour (2.4.A1a), e.g., it took Susan 180 minutes to complete her homework assignment. How many hours did she spend doing homework?
g. ▴ perimeter of squares, rectangles, and triangles (2.4.A1g), 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?
h. ▴ area of squares and rectangles (2.4.A1g), e.g., a farmer's square-shaped field is 35 feet on each side. How many square feet does he have to plow? (Time Intervals , Perimeter and Area Word Problems )
AI-2 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 (2.4.A1a), 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?
AI-3 estimates to check whether or not measurements or calculations for length, weight, temperature, time, perimeter, and area in real-world problems are reasonable (2.4.A1a) ($), 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?
AI-4 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) (2.4.A1a,g) ($), e.g., after estimating the outside temperature to be 75° F, you find out that yesterday's high temperature at 3 p.m. was 62°. Should you adjust your estimate? Why or why not?
Benchmark 3: Transformational Geometry - The student recognizes and performs transformations on geometric shapes including the use of concrete objects in a variety of situations.
KBI-1 recognizes and performs through two transformations (reflection, rotation, translation) on a two-dimensional figure (2.4.K1a).
KBI-2 recognizes when an object is reduced or enlarged (2.4.K1a).
KBI-3 ▴ recognizes three-dimensional figures (rectangular prisms, cylinders, cones, spheres, triangular prisms, rectangular pyramids) from various perspectives (top, bottom, side, corners) (2.4.K1g).
AI-1 describes and draws a two-dimensional figure after performing one transformation (reflection, rotation, translation) (2.4.A1a).
AI-2 makes scale drawings of two-dimensional figures using a simple scale and grid paper (2.4.A1h), e.g., using the scale 1 cm = 3 m, the student makes a scale drawing of the classroom.
Benchmark 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.
KBI-1 locates and plots points on a number line (vertical/horizontal) using integers (positive and negative whole numbers) (2.4.K1a). (Compare Integers , Ordered Pairs )
KBI-2 explains mathematical relationships between whole numbers, fractions, and decimals and where they appear on a number line (2.4.K1a). (Positive Number Line , Number Line )
KBI-3 identifies and plots points as ordered pairs in the first quadrant of a coordinate plane (coordinate grid) (2.4.K1a).
KBI-4 organizes whole number data using a T-table and plots the ordered pairs in the first quadrant of a coordinate plane (coordinate grid) (2.4.K1a,f).
AI-1 solves real-world problems that involve distance and location using coordinate planes (coordinate grids) and map grids with positive whole number and letter coordinates (2.4.A1a), e.g., identifying locations and giving and following directions to move from one location to another.
AI-2 solves real-world problems by plotting ordered pairs in the first quadrant of a coordinate plane (coordinate grid) (2.4.A1a) ($) , e.g., graph daily the cumulative number of recess minutes in a 5-day school week.
Standard 4: Data
Benchmark 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.KBI-1 recognizes that all probabilities range from zero (impossible) through one (certain) (2.4.K1i) ($).
KBI-2 lists all possible outcomes of a simple event in an experiment or simulation in an organized manner including the use of concrete objects (2.4.K1g-j).
KBI-3 recognizes a simple event in an experiment or simulation where the probabilities of all outcomes are equal (2.4.K1i).
KBI-4 represents the probability of a simple event in an experiment or simulation using fractions (2.4.K1c). (Probability )
AI-1 ■ conducts an experiment or simulation with a simple event including the use of concrete materials; records the results in a chart, table, or graph; uses the results to draw conclusions about the event; and makes predictions about future events (2.4.A1j-k). (Requires outside materials )
AI-2 uses the results from a completed experiment or simulation of a simple event to make predictions in a variety of real-world situations (2.4.A1j-k), e.g., the manufacturer of Crunchy Flakes puts a prize in 20 out of every 100 boxes. What is the probability that a shopper will find a prize in a box of Crunchy Flakes, if they purchase 10 boxes? (Batting Averages )
AI-3 compares what should happen (theoretical probability/expected results) with what did happen (empirical probability/experimental results) in an experiment or simulation with a simple event (2.4.A1j).
Benchmark 2: Statistics - The student collects, organizes, displays, explains, and interprets numerical (rational numbers) and non-numerical data sets in a variety of situations with a special emphasis on measures of central tendency.
KBI-1 organizes, displays, and reads numerical (quantitative) and nonnumerical (qualitative) data in a clear, organized, and accurate manner including a title, labels, categories, and whole number and decimal intervals using these data displays (2.4.K1j) ($):
a. graphs using concrete objects,
b. pictographs,
c. frequency tables,
d. bar and line graphs,
e. Venn diagrams and other pictorial displays, e.g., glyphs,
f. line plots,
g. charts and tables,
h. circle graphs,
i. single stem-and-leaf plots. (Stem And Leaf Plots , Tally and Pictographs , Bar Graphs , Line Graphs )
KBI-2 collects data using different techniques (observations, polls, tallying, interviews, surveys, or random sampling) and explains the results (2.4.K1j) ($). (Requires outside materials )
KBI-3 ▴ identifies, explains, and calculates or finds these statistical measures of a whole number data set of up to twenty whole number data points from 0 through 1,000 (2.4.K1a) ($):
a. minimum and maximum values,
b. range,
c. mode (no-, uni-, bi-),
d. median (including answers expressed as a decimal or a fraction without reducing to simplest form),
e. mean (including answers expressed as a decimal or a fraction without reducing to simplest form). (Mean, Median, Mode )
AI-1 ▴ interprets and uses data to make reasonable inferences, predictions, and decisions, and to develop convincing arguments from these data displays (2.4.A1k) ($):
a. graphs using concrete materials,
b. pictographs,
c. frequency tables,
d. bar and line graphs,
e. Venn diagrams and other pictorial displays,
f. line plots,
g. charts and tables,
h. circle graphs. (Stem And Leaf Plots , Tally and Pictographs , Bar Graphs , Line Graphs )
AI-2 uses these statistical measures of a whole number data set to make reasonable inferences and predictions, answer questions, and make decisions (2.4.A1a) ($):
a. minimum and maximum values,
b. range,
c. mode,
d. median,
e. mean when the data set has a whole number mean. (Mean, Median, Mode )
AI-3 recognizes that the same data set can be displayed in various formats and discusses why a particular format may be more appropriate than another (2.4.A1k) ($).
AI-4 recognizes and explains the effects of scale and interval changes on graphs of whole number data sets (2.4.A1k).
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