Standard 1 Number and Computation:
The student uses numerical and computational concepts and procedures in a variety of situations.
Benchmark 1
Number Sense - The student demonstrates number sense for whole numbers, simple fractions, money, and decimals in a variety of situations.
Indicator 1
(K) The student knows, explains, and uses equivalent representations for:
a. whole numbers from 0 through 100,000; $
b. fractions greater than or equal to zero (halves, fourths, thirds, eighths, tenths, twelfths, sixteenths, hundredths) 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-d) $, e.g., 7¢ = $.07 = 7/100 of a dollar or a hundreds grid with 7 sections colored or .1 = 1/10
Indicator 2
(K) The students compares and orders:
a. whole numbers from 0 through 100,000 (2.4.K1b);
b. 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 (2.4.K1c);
c. decimals greater than or equal to zero through hundredths place and when used as monetary amounts (2.4.K1d). $
Indicator 1
(A) The student solves real-world problems using equivalent representations and concrete objects to: (2.4.A1a):
a. compare and order whole numbers from 0 through 100,000; (2.4.A1a) $ ; 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;
b. add and subtract whole numbers from 0 through 10,000 and decimals when used as monetary amounts, (2.4.A1a-d) $ ; 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;
c. multiply a one-digit whole number by a two-digit whole number, (2.4.A1a); e.g. ex.
Indicator 2
(A) The student determines whether or not solutions to real-world problems that involve the following are reasonable:
a. whole numbers from 0 through 10,000 (2.4.A1b), e.g., Is it reasonable for Jolene to say that there are 1000 students in grade 4 at her school?;
b. fractions (including mixed numbers) (2.4.A1c), e.g., Is it reasonable to say you ate 1/2 of your sandwich and your friend ate 3/4 of the same sandwich?;
c. decimals through hundredths place and when used as monetary amounts (2.4 A1d) $, e.g., Which of the following prices are reasonable for a pack of chewing gum? $62 , $.75 , $.09 , $75.00 , $7.50.
Benchmark 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 their properties, and extends their properties, and extends these properties to simple fractions, mixed numbers, decimals and money.
Indicator 1
(K) The student identifies, models, reads, and writes numbers using numerals, words, and expanded notation from hundredths place through one-hundred thousands place (2.4.K1b,d) $, 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.
Indicator 2
(K) The student classifies various subsets of numbers as whole numbers, fractions (including mixed numbers), or decimals (2.4.K1b-c,d).
Indicator 3
(K) The student identifies the place value of various digits from hundredths place through one hundred thousands place. (2.4.K1b) $
Indicator 4
(K) The student identifies any whole number as even or odd.
Indicator 5
(K) The student uses the concepts of these properties with the whole number system and demonstrates their meaning including the use of concrete objects (2 4.K1a): $
a. commutative properties of addition and multiplication, e.g., 12 + 18 = 18 + 12 and 8 x 9 = 9 x 8;
b. zero property of addition (additive identity) and property of one for multiplication (multiplicative identity), e.g., 24 + 0 = 24 and 75 x 1 = 75;
c. 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;
d. 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;
e. zero property of multiplication, e.g., 9 x 0 = 0 or 0 x 112 = 0;
f. distributive property, e.g., 6(7 + 3) = (6 _ 7) + (6 _ 3).
Indicator 1
(A) 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 (2.4.A1b, d-e): $
a. 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 4x5 but I know 5x4 is $20, since multiplication can be done in any order.
b. zero property of addition, e.g., a student has 6 marbles in one pocket and none in the other pocket. How many marbles altogether? 6+0=6;
c. property of one for multiplication, e.g., there are 24 students in our class, each student should have one math book; so I compute 24x1=24. Multiplying times 1 does not change the product because it is one group of 24.;
d. associative properties of addition and multiplication, e.g., a student has two dimes and a quarter; there are 2 ways to group the coins to find the total: $.10 dime) + $.10(dime) = $.20, then add the quarter, $.20 + $.25(quarter) = $.45 or $ 10(dime) = $.25(quarter) = $.35, then add the other dime to $.35 and $.35 + $.10 = $.45 or (D+D)+ Q = D +(D+Q) (coin pictures).;
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 4x0=0.
Indicator 2
(A) 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 (2.4.A1b,d-e):
a. 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 4x6 is the same as 6x4.;
b. 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;
c. 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.
Indicator 3
(A) (A)The student states the reason for using whole numbers, fractions, mixed numbers, or decimals when solving a given real-world problem (2.4.A1c-d,e).
Benchmark 3
Estimation - The student uses numerical estimation with whole numbers, simple fractions, decimals, and money in a variety of situations.
Indicator 1
(K) 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 (2.4.K1a-e). $
Indicator 2
(K) The student uses various estimation strategies to estimate whole numbers quantities from 0 through 10,000; fractions [(halves, fourths, thirds) including mixed numbers)]; and monetary amounts through $1,000 and explains the process used (2.4.K1a-e).
Indicator 3
(K) The student recognizes and explains the difference between an exact and an approximate answer (2.4.K1a), 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.
Indicator 4
(K) (K)The student selects the appropriate type of estimate (overestimate, underestimate, or range of estimates).
Indicator 1
(A) 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) (2.4.A1a), 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.
Indicator 2
(A) 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 (2.4.A1b-d,f), 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?
Indicator 3
(A) The student selects a reasonable magnitude from three given quantities based on a familiar problem situation and explains the reasonableness of selection (2.4.A1c), 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.
Indicator 4
(A) (A)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 (2.4.A1a).
Benchmark 4
Computation - The student explains and performs computation with whole numbers, addition and subtraction or proper fractions with like denominators, and money in a variety of situations.
Indicator 1
(K) The student computes with efficiency and accuracy using various computational methods including mental math, paper and pencil, concrete materials, and appropriate technology (2.4.K1a) $.
Indicator 2
(K) The student states and uses with efficiency and accuracy multiplication facts from 1 x 1 through 12 x 12 and corresponding division facts (2.4.K1a) $N.
Indicator 3
(K) The student performs and explains these computational procedures: N
a. adds and subtracts whole numbers from 0 through 100,000 and when used as monetary amounts (2.4.K1b) $;
b. multiplies through a three-digit whole number by a two-digit whole number (2.4.K1b);
c. multiplies whole dollar monetary amounts (through three-digits) by a one- or two-digit whole number (2.4.K1b,e) $, e.g., $45 x 16;
d. multiplies monetary amounts less than $100.00 by whole numbers less than ten (2.4.K1b,e) $, e.g., $14.12 x 7;
e. 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 (2.4.K1a-b), e.g., 47 ÷ 5 = 9 r 2;
f. adds and subtracts fractions greater than or equal to zero with like denominators (2.4.K1c);
g. figures correct change through $20.00 (2.4.K1e) $.
Indicator 4
(K) The student identifies multiplication and division fact families (2.4.K1a).
Indicator 5
(K) The student 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 4 x 6 and 6(4) or 10 divided by 2 is the same as 10 ÷ 2 or 10/2.
Indicator 6
(K) The student shows the relationship between these operations with the basic fact families including the use of mathematical models (2.4.K1a) $:
a. addition and subtraction,
b. addition and multiplication,
c. multiplication and division,
d. subtraction and division.
Indicator 7
(K) (K)The student finds factors and multiples of whole numbers from 1 through 100 (2.4.K1a).
Indicator 1
(A) The student solves one- and two-step real-world problems with one or two operations using these computational procedures (2.4.A1a-c,f):
a. adds and subtracts whole numbers from 0 through 10,000 and when used as monetary amounts,(2.4.A1a-e) $, e.g., Lee buys a bicycle for $139.29, a helmet for $29.99, and a reflector for $6.50. How much of his $200 check from his grandparents will he have left?;
b. multiplies through a two-digit whole number by a two-digit whole number, (2.4 A1a), e.g., at school, there are 22 students in each classroom. If there are 24 classes, how many students are at the school?;
c. multiplies whole dollar monetary amounts (up through three-digit) by a one- or two-digit whole number,(2.4.A1a-e) $, e.g., 112 third and forth graders are planning a field trip. The cost per student is $9.00. How much will the trip cost?;
d. multiplies monetary amounts less than $100 by whole numbers less than ten, (2.4.A1a-e) $, 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?;
e. figures correct change through $20.00,(2.4.A1-e), e.g., buying a 65¢ drink, paying for it with a $1 bill, and then figuring the amount of change.
Indicator 2
(A) The student generates a family of multiplication and division facts given one equation/fact (2.4.A1b), e.g., 8 x 9 = 72, the remaining facts generated are 9 x 8 = 72, 72 ÷ 8 = 9, and 72 ÷ 9 = 8.
The student uses algebraic concepts and procedures in a variety of situations.
Benchmark 1
Patterns - The student recognizes, describes, extends, develops, and explains relationships in patterns from a variety of situations.
Indicator 1
(K) The student uses concrete objects, drawings, and other representations to work with types of patterns(2.4.K1a):
a. repeating patterns, e.g., an AB pattern is like 1-2, 1-2, .; an ABC pattern is like dog-horse-pig, dog-horse-pig, .; an AAB pattern; or a repeating pattern where the rule repeats (add 5, then multiply by 2)such as 3,8,16,21,42,...;
b. growing patterns e.g., 2, 5, 11, ...;
Indicator 2
(K) The student uses these attributes to generate patterns:
a. counting numbers related to number theory (2.4.K1a), e.g., multiples and factors through 12 or multiplying by 10, 100, or 1,000;
b. whole numbers that increase or decrease (2.4.K1a), e.g., 20, 15, 10, .;
c. geometric shapes including one or two attributes changes (2.4.K1h), e.g., Such as when the next shape has one more side; or when both color and shape change at the same time.
d. measurements (2.4.K1a), e.g., 3 ft., 6 ft., 9 ft., ...;
e. money and time (2.4.K1e) $, e.g., $.25, $.50, $.75, ... or 1:05 p.m., 1:10 p.m., 1:15 p.m., ...;
f. things related to daily life (2.4.K1a), e.g., water cycle, food cycle, or life cycle;
g. things related to size, shape, color, texture, or movement (2.4.K1a), e.g., rough, smooth, rough, smooth, rough, smooth, ...; or clapping hands (kinesthetic patterns);
Indicator 3
(K) (K)The student identifies, states, and continues a pattern presented in various formats including numeric (list or table), visual (picture, table, or graph), verbal (oral description), kinesthetic (action), and written (2.4.K1a) $.
Indicator 4
(K) (K)The student generates a pattern (2.4.K1a).
Indicator 5
(K) (K)The student generates a pattern using a function table (input/output machines, T-tables) to (2.4.K1e).
Indicator 1
(A) The students generalizes these patterns using a written description:
a. counting numbers related to number theory (2.4.A1a),
b. whole number patterns (2.4.A1a),
c. patterns using geometric shapes (2.4.A1h),
d. measurement patterns (2.4.A1a),
e. money and time patterns (2.4.A1a,e) $,
f. patterns using size, shape, color, texture, or movement (2.4.A1a).
Indicator 2
(A) The student recognizes multiple representations of the same pattern (2.4 A1a), 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.
Benchmark 2
Variables, Equations, and Inequalities - The student uses symbols and whole numbers to solve simple equations and inequalities in a variety of situations.
Indicator 1
(K) The student explains and uses variables and symbols to represent unknown whole number quantities from 0 through 1,000.
Indicator 2
(K) The student solves one-step equations using whole numbers with one variable and a whole number solution that:
a. 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 (2.4.K1a), e.g., 60 = 10 x n;
b. find the unknown in a money equation using multiplication and division based upon the facts and addition and subtraction with values through $10 (2.4.A1e) $, e.g., 8 quarters + 10 dimes = y dollars;
c. find the unknown in a time equation involving whole minutes, hours, days, and weeks with values through 200 (2.4.A1a), e.g., 180 minutes = y hours.
Indicator 3
(K) (K)The student compares two whole numbers from 0 through 10,000 using the equality and inequality symbols (=, ?,, <, >) and their corresponding meanings (is equal to, is not equal to, is less than, is greater than) (2.4.K1b) $.
Indicator 4
(K) (K)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.
Indicator 1
(A) The student represents real-world problems using variables and symbols with unknown whole number quantities from 0 through 1,000, (2.4.A1a) $; e.g., How many weeks in twenty-eight days? can be represented by n x 7 = 28 or n = 28 ÷ 7.
Indicator 2
(A) 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 (2.4.A1a) $:
a. add or subtract whole numbers from 0 through 1,000; e.g., Homer, Kansas has a population of 4,743 people. Homer, Idaho has a population of 17,027 people. How much larger is the Idaho, Homer? 17,027-4,743=P;
b. 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 5xS=30 or 30/5=S.
Indicator 3
(A) (A)The student generates (2.4.A1a) $:
a. real-world problems with one operation to match a given addition, subtraction, multiplication, or division equation using whole numbers through 99 (2.4.A1a), e
g., given 12x3=Y, the student writes: I was sick for 3 days, when I get back I had 3 pages of homework. There are 12 problems on each page. How many total problems must I work?;
b. number comparison statements using equality and inequality symbols (=, <, >) with whole numbers, measurement, and money (2.4.A1a,e), e.g., 1 ft < 15 in or 10 quarters > $2.
Benchmark 3
Functions - The student recognizes and describes relationships between whole numbers in a variety of situations.
Indicator 1
(K) 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 (2.4.K1a) $.
Indicator 2
(K) The student find 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) (2.4.K1e), e g., using the function table, find the rule, the rule is N _ 4.
N ?
1 4
5 20
2 8
3 ?
4 ?
? 24
Indicator 3
(K) The student generalizes numerical patterns using whole numbers from 0 through 200 with one operation by stating the rule using words (2.4.K1f), e.g., if the pattern is 46, 68,90, 112, 134, .; in words, the rule is add 22 to the number before.
Indicator 4
(K) 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 (2.4 K1a,f).
Indicator 1
(A) 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 (2.4.A1a) $.
Indicator 2
(A) The student finds the rule, states the rule, and extends numerical patterns using real-world applications using whole numbers from 0 through 200, e.g., The teacher must order supplies for field day. For every 12 students, one red rubber ball is needed. If 6 balls are ordered, how many students will be able to play? A solution using a function table might be:
Number of Students 12, 24, 36, 48, 60, 72, N
Number of Balls 1, 2, 3, 4, 5, 6,(N/12)The rule is divide the number of students by 12 or for each group of 12 students, another ball is added. Other solutions might be using a pattern to count by 12 six times - 12, 24, 36, 48, 60, 72 or to skip count by 12 for each group of 6 students.
Benchmark 4
Models - The student develops and uses models to represent and justify mathematical relationships found in a variety of situations.
Indicator 1
(K) The student 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, coordinate planes/grids, hundred charts, measurement tools, multiplication arrays, or division sets) to model computational procedures, mathematical relationships, and equations (1.1.K1a, 1.2.K1a, 1.2.K5-6, 1.3.K1-3, 1.4.K4, 1.4 K6-7, 2.1.K1, 2.1.K2d, 2.1.K2f-g, 2.1.K3-4, 2.2.K1a-b, 2.2.K2a, 2.2.K2c, 2.3.K1, 2.3.K4, 3.2.K1-2, 3.2.K4, 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.K2a, 1.2.K1-2, 1.3.K1-2, 1.4.K3a-e, 2.2 K3) $;
c. fraction and mixed number models (fraction strips or pattern blocks) to compare, order, and represent numerical quantities (1.1.K1b, 1.1.K2b, 1.2.K2, 1 3.K1-2) $;
d. decimal models (base ten blocks or coins) to compare, order, and represent numerical quantities (1.2.K1-2) $;
e. money models (base ten blocks or coins) to compare, order, and represent numerical quantities (1.1.K1a, 1.3.K1-2, 1.4.K3g, 2.1.K2e, 2.2.K2b) $;
f. function tables (input/output machines, T-tables) to find numerical and algebraic relationships (2.1.K5);
g. 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 model properties of geometric shapes (2.1.K2c, 2.1.K1j, 3.1.K1-6, 3.2 K4-6, 3.3.K1-3);
h. two-dimensional geometric models (spinners), three-dimensional models number cubes), and process models (concrete objects) to model probability (4.1 K1-3) $;
i. 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 (4.1.K2, 4.2.K1a d, 4.2.K2, 4.2.K1f-i, 4.2 K2) $;
j. Venn diagrams to sort data and to show relationships (4.2K1e, 4.2.K2).
Indicator 2
(K) The student creates a mathematical model to show the relationship between two or more things, e.g., Using pattern blocks, a whole (1) can be represented using a (1/1) or two (2/2) or three (3/3) or six (6/6).
Indicator 1
(A) The student 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, coordinate planes/grids, hundred charts, measurement tools, multiplication arrays, division sets, or measurement tools) to model computational procedures, mathematical relationships, and problem situations (1.1.A1, 1.2.A1-2, 1.3.A1-3, 2.1.A1a-b, 2.1.A1d-f, 2.1.A2, 2.2.A2, 2.2.A3a, 2.3.A1, 3.2.A1a-g, 3.2.A2-3, 3.3 A1-2, 3.4.A1-2, 4.2.A2) $;
b. place value models (place value mats, hundred charts, base ten blocks, or unfix cubes) to model problem situations (1.1.A2a, 1.2.A1-2, 1.3.A2, 1.4.A1) $;
c. fraction and mixed number models (fraction strips or pattern blocks) to compare, order, and represent numerical quantities (1.1.A2b, 1.2.A3, 1.3.A2) $;
d. money models (base ten blocks or coins) to compare, order, and represent numerical quantities (1.2.A1-3, 2.1.A1e, 2.2.A3b) $;
e. function tables (input/output machines, T-tables) to find numerical and algebraic relationships (2.1.A1c, 2.3.A2);
f. two-dimensional geometric models (geoboards, dot paper, pattern blocks, or tangrams) to model perimeter, area, and attributes of geometric shapes and three-dimensional geometric models (solids) and real-world objects to compare size and model properties of geometric shapes (2.1.A1c, 3.1.A1-2, 3.2.A1h, 3.3 A3) $;
g. two-dimensional geometric models (spinners), three-dimensional geometric models (number cubes), and process models (concrete objects) to model probability (3.1.A1-3, 3.2.A1h, 3.3.A3, 4.1.A1-3) $;
h. 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 (4.1.A1-3, 4.2.A1a-d, 4.2.A1f-h, 4.2 A3-4) $;
i. Venn diagrams to sort data and to show relationships (4.2.A1e, 4.2.A3).
Indicator 2
(A) (A)The student selects a mathematical model and explains why some mathematical models are more useful than other mathematical models in certain situations.
The student uses geometric concepts and procedures in a variety of situations.
Benchmark 1
Geometric Figures and Their Properties - The student recognizes or investigates properties of simple geometric figures in a variety of situations.
Indicator 1
(K) 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 (2.4.K1h).
Indicator 2
(K) The student recognizes, draws, and describes plane figures (circles, squares, rectangles, triangles, ellipses, rhombi, octagons, hexagons, pentagons) 2.4.K1h).
Indicator 3
(K) The student describes the solids (cubes, rectangular prisms, cylinders, cones spheres, triangular prisms) using the terms faces, edges, and vertices (corners) 2.4.K1h).
Indicator 4
(K) The student recognizes and describes the square, triangle, rhombus, hexagon, parallelogram, and trapezoid from a pattern block set (2.4.K1h).
Indicator 5
(K) The student recognizes (2.4.k1h):
a. squares, rectangles, rhombi, parallelograms, trapezoids as special quadrilaterals;
b. similar and congruent figures;
c. points, lines (intersecting, parallel, perpendicular), line segments, and rays (2 4.K1g).
Indicator 6
(K) 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) (2.4 K1h).
Indicator 1
(A) The student solves real-world problems by applying the properties of (2.4 A1h):
a. plane figures (circles, squares, rectangles, triangles, ellipses, rhombi, parallelograms, hexagons) and lines of symmetry, e.g., ex;
b. solids (cubes, rectangular prisms, cylinders, cones, spheres), e.g., ex
Indicator 2
(A) The student identifies the plane figures (circles, squares, rectangles, triangles, ellipses, rhombi, octagons, hexagons, pentagons, trapezoids) used to form a composite figure (2.4.A1h).
Benchmark 2
Measurement and Estimation - The student estimates and measures using standard and nonstandard units in a variety of situations.
Indicator 1
(K) The student 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) $.
Indicator 2
(K) 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 (2.4.K1a) $:
a. length, width, and height to the nearest fourth of an inch or to the nearest centimeter;
b. volume to the nearest cup, pint, quart, or gallon; to the nearest liter; or to the nearest whole unit of a nonstandard unit;
c. weight to the nearest ounce or pound or to the nearest whole unit of a nonstandard unit of measure;
d. temperature to the nearest degree;
e. time including elapsed time.
Indicator 3
(K) The student states:
a. the number of weeks in a year;
b. the number of ounces in a pound;
c. the number of milliliters in a liter, grams in a kilogram, and meters in a kilometer.
Indicator 4
(K) The student 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;
b. within the metric system: centimeters and meters
Indicator 5
(K) The student finds(2.4.K1h):
a. the perimeter of two-dimensional figures given the measures of all the sides.
b. the area of squares and rectangles using concrete objects.
Indicator 1
(A) The student solves real-world problems by applying appropriate measurements:
a. length to the nearest fourth of an inch (2.4.A1b), e.g., ex;
b. length to the nearest centimeter (2.4.A1b), e.g., ex;
c. temperature to the nearest degree (2.4.A1b), e.g., ex;
d. weight to the nearest whole unit (pounds, grams, nonstandard unit) (2.4.A1b), e.g., ex;
e. time including elapsed time (2.4.A1b), e.g., ex;
f. months in a year (2.4.A1b), e.g., ex;
g. minutes in an hour (2.4.A1b), e.g., ex;
h. perimeter of squares, rectangles, and triangles (2.4.A1h), e.g., ex.
Indicator 2
(A) 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 (2.4.A1a) $, e.g., ex.
Indicator 3
(A) 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) (2.4.A1a), e.g., ex.
Benchmark 3
Transformational Geometry - The student recognizes up to two transformations of basic geometric figures in a variety of situations.
Indicator 1
(K) The student describes a transformation using cardinal points or positional directions (2.4.K1h), e.g., go north three blocks and then west four blocks or move the triangle three units to the right and two units up.
Indicator 2
(K) (K)The student recognizes, performs, and describes one transformation reflection/flip, rotation/turn, translation/slide) on a two dimensional figure or concrete object (2.4.K1h).
Indicator 3
(K) (K)The student recognizes three-dimensional figures (rectangular prisms, cylinders) and concrete objects from various perspectives (top, bottom, sides, corners) (2.4.K1a,h).
Indicator 1
(A) The student recognizes real-world transformations (reflection/flip, rotation/turn, translation/slide) (2.4.A1a).
Indicator 2
(A) The student gives and uses cardinal points or positional directions to move from one location to another on a map or grid (2.4.A1a).
Indicator 3
(A) 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 (2.4.A1h).
Benchmark 4
Geometry From an Algebraic Perspective - The student relates geometric concepts to the number line and the first quadrant of the coordinate plane in a variety of situations.
Indicator 1
(K) 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 (2.4.K1a).
Indicator 2
(K) The student uses points in the first quadrant of a coordinate plane coordinate grid) to identify locations (2.4.K1a).
Indicator 3
(K) The student identifies and plots points as ordered pairs in the first quadrant of a coordinate plane (coordinate grid) (2.4.K1a).
Indicator 4
(K) (K)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) (2.4 K1a,j).
Indicator 1
(A) 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 (2.4.A1a), e.g., identifying locations and giving and following directions to move from one location to another.
Indicator 2
(A) (A)The student solves real-world problems by plotting ordered pairs in the first quadrant of a coordinate plane (coordinate grid) (2.4.A1a), e.g., graphing the number of people and the total cost of tickets for all to attend a movie.
The student uses concepts and procedures of data analysis in a variety of situations.
Benchmark 1
Probability - The student uses probability to make predictions and decisions in a variety of situations.
Indicator 1
(K) The student recognizes that the probability of an impossible event is zero and that the probability of a certain event is one (2.4.K1i) $.
Indicator 2
(K) The student lists all possible outcomes of a simple event in an experiment or simulation including the use of concrete objects (2.4.K1i j).
Indicator 3
(K) (K)The student recognizes and states the probability of a simple event in an experiment or simulation (2.4.K1i), e.g., when a coin is flipped, the probability of landing heads up is ½ and the probability of landing tails up is ½ that can be read as one out of two or one half.
Indicator 1
(A) 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 (2.4.A1i-j).
Indicator 2
(A) 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 (2.4.A1i-j). e g., ex.
Indicator 3
(A) (A)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(2.4.A1i-j).
Benchmark 2
Statistics - The student generates, organizes, and interprets whole number and other data in a variety of situations.
Indicator 1
(K) 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: $
a. graphs using concrete objects (2.4.K1i);
b. 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 (2.4.K1i);
c. frequency tables (tally marks) (2.4.K1i);
d. horizontal and vertical bar graphs (2.4.K1i);
e. Venn diagrams or other pictorial displays (2.4.K1j), e.g., glyphs;
f. line plots (2.4.K1i);
g. charts and tables (2.4.K1i);
h. line graphs (2.4.K1i);
i. circle graphs (2.4.K1i).
Indicator 2
(K) The student collects data using different techniques (observations, polls, surveys, interviews, or random sampling) and explains the results (2.4.k1) $.
Indicator 3
(K) 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 (2.4.K1a) $:
a. minimum and maximum values,
b. range,
c. mode,
d. median when data set has an odd number of data points,
e. mean when data set has a whole number mean.
Indicator 1
(A) The student interprets and uses data to make reasonable inferences and predictions, answer questions, and make decisions from these data displays $:
a. graphs using concrete objects (2.4.A1j)
b. 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 (2.4.A1j);
c. frequency tables (tally marks) (2.4.A1j);
d. horizontal and vertical bar graphs (2.4.A1j);
e. Venn diagrams or other pictorial displays (2.4.A1k);
f. line plots (2.4.A1j);
g. charts and tables (2.4.A1j);
h. line graphs (2.4.A1j).
Indicator 2
(A) 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 (2.4.A1b) $:
a. minimum and maximum values,
b. range,
c. mode,
d. median when the data set has an odd number of data points,
e. mean when the data set has a whole number mean.
Indicator 3
(A) The student recognizes that the same data set can be displayed in various formats including the use of concrete objects (2.4.A1j-k).
Indicator 4
(A) (A)The student recognizes and explains the effects of scale and interval changes on graphs of whole number data sets (2.4.A1j).
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