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 rational numbers, pi, and simple algebraic expressions in one variable in a variety of situations.
Indicator 1
(K) The student knows, explains, and uses equivalent representations for:
a. whole numbers from 0 through 1,000,000 $;
b. fractions greater than or equal to zero (including mixed numbers);
c. decimals greater than or equal to zero through hundredths place and when used as monetary amounts (2.4.K1a-b,e) $.
Indicator 2
(K) The student compares and orders (2.4.K1b):
a. integers,
b. fractions greater than or equal to zero (including mixed numbers),
c. decimals greater than or equal to zero through hundredths place $.
Indicator 3
(K) The student explains the numerical relationships (relative magnitude) between whole numbers, fractions greater than or equal to zero (including mixed numbers), and decimals greater than or equal to zero through hundredths place (2.4.K1c-d).
Indicator 4
(K) (K)The student knows equivalent percents and decimals for one whole, one-half, one-fourth, three-fourths, and one tenth through nine tenths (2.4.K1c-d) e.g., 1 = 100% = 1.0, 3/4 = 75% = .75, 3/10 = 30% = .3.
Indicator 5
(K) (K)The student identifies integers and gives real-world problems where integers are used, e.g., making a T-table of the temperature each hour over a twelve hour period in which the temperature at the beginning is 10 degrees and then decreases 2 degrees per hour.
Indicator 1
(A) The student solves real-world problems using equivalent representations and concrete objects to: (2.4.A1c):
a. compare and order -
i. whole numbers from 0 through 1,000,000 $ ; e.g., using base 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 2-1/2 pizzas, Tara ate 9/4 of the pizza. Frank says he ate more. Is he correct? Show and explain.;
iii. decimals greater than or equal to zero to hundredths place $ , e.g., uses decimal squares, money (dimes as tenths, pennies as hundredths), ___ of hundred chart filled in and a number line to show that .42 is less than .59.
iv. integers, e.g., plot winter temperature for a very cold region (sub artic) 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 $ , 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 $ , 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 23x3 or 23+23=23.;
d. divide through a four-digit whole number by a two-digit whole number $ , e.g., the Boy Scout troop collected cans and held bake sales for a year and earned $492.60. The money will be divided evenly among the 12 troop members to buy new uniforms. Represent each boy's share of the money at least 2 ways - traditional division: use 4 hundreds, 9 tens, 2 ones and 6 dimes to act it out.
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 100,000 (2.4.A1c), 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 thired down? No, you have gained more than you have lost.;
b. fractions greater than or equal to zero (including mixed numbers) (2.4.A1d), e.g., Is it reasonable to say that a dog is 1/2 boxer, 1/4 bulldog, 1/4 collie and 1/4 rotweiler? Explain;
c. decimals greater than or equal to zero through hundredths place (2.4.A1e), e.g., ex.
Benchmark 2
Number Systems and Their Properties - The student demonstrates an understanding of the rational number system and pi, recognizes, applies, and explains its properties, and extends these properties to algebraic expressions in one variable.
Indicator 1
(K) The student classifies subsets of numbers as integers, whole number, fractions (including mixed numbers), or decimals (2.4.k1b,d).
Indicator 2
(K) The student identifies prime and composite numbers from 0 through 50.
Indicator 3
(K) The student uses the concepts of these properties with whole numbers, integers, fractions greater than or equal to zero (including mixed numbers), and decimals greater than or equal to zero and demonstrates their meaning including the use of concrete objects (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.
Indicator 4
(K) The student recognizes Roman Numerals that are used for dates, on clock faces, and in outlines.
Indicator 5
(K) The student recognizes the need for integers, e.g., with temperature, below zero is negative and above zero is positive; in finances, money in your pocket is positive and money owed someone is negative.
Indicator 1
(A) The student solves real-world problems with whole numbers from 0 through 100,000 and decimals through hundredths using place value models; money; and the concepts of these properties to explain reasoning (2.4.A1b-c,e-f) $:
a. commutative and associative properties of addition and multiplication, e.g., ex;
b. zero property of addition, e.g., ex;
c. property of one for multiplication, e.g., ex;
d. symmetric property of equality, e.g., ex;
e. zero property of multiplication, e.g., ex;
f. distributive property, e.g., ex;.
Indicator 2
(A) The student performs various computational procedures with whole numbers from 0 through 100,000 using the concepts of these properties; extends these properties to fractions greater than or equal to zero (including mixed numbers) and decimals greater than or equal to zero through hundredths place; and explains how the properties were used (2.4.A1b,d-e):
a. commutative and associative properties of addition and multiplication,
b. zero property of addition,
c. property of one for multiplication,
d. symmetric property of equality,
e. zero property of multiplication,
f. distributive property.
Indicator 3
(A) (A)The student states the reason for using integers, whole numbers, fractions (including mixed numbers), or decimals when solving a given real-world problem (2.4.A1c-e).
Benchmark 3
Estimation - The student uses numerical estimation with rational numbers and pi in a variety of situations.
Indicator 1
(K) The student estimates whole numbers quantities from 0 through 100,000; fractions greater than or equal to zero (including mixed numbers); decimals greater than or equal to zero through hundredths place; and monetary amounts to $10,000 using various computational methods including mental math, paper and pencil, concrete materials, and appropriate technology (2.4.K1a-c,e) $.
Indicator 2
(K) The student uses various estimation strategies to estimate whole number quantities from 0 through 100,000; fractions greater than or equal to zero including mixed numbers); decimals greater than or equal to zero through hundredths place; and monetary amounts to $10,000 and explains the process used $.
Indicator 3
(K) The student recognizes and explains the difference between an exact and an approximate answer (2.4.K1b-c,e).
Indicator 4
(K) The student explains the appropriateness of an estimation strategy used and whether the estimate is greater than (overestimate) or less than (underestimate) the exact answer (2.4.K1b).
Indicator 1
(A) The student adjusts original whole number estimate 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.
Indicator 2
(A) The student estimates to check whether or not the result of a real world problem using whole numbers from 0 through 100,000; fractions greater than or equal to zero (including mixed numbers); decimals greater than or equal to zero to tenths place; and monetary amounts to $10,000 is reasonable and makes predictions based on the information (2.4.A1b d,f) $, e.g., ex.
Indicator 3
(A) The student selects a reasonable magnitude from given quantities based on a real-world problem and explains the reasonableness of selection (2.4.A1c), e.g , About how many tulips can fit in the flower vase, 2, 10, or 2 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.
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 materials, and appropriate technology (2.4.A1a).
Benchmark 4
Computation - The student explains and performs computations with rational numbers, pi and first degree algebraic expressions in one variable 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 performs and explains these computational procedures (2.4.K1a):
a. 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, e.g., 7452 ÷ 24 = 310 r 12 or 310 ½; N
b. divides whole numbers beyond a 2-digit divisor and a 4-digit dividend using appropriate technology, e.g., 73,368 ÷ 36 = 2,038;
c. adds and subtracts decimals from thousands place through hundredths place; N
d. multiplies decimals up to three digits by two digits from hundreds place through hundredths place; N
e. adds and subtracts fractions greater than or equal to zero (including mixed numbers) without regrouping and without expressing answers in simplest form; N
f. multiplies and divides by 10; 100; 1,000; or single-digit multiples of each, e.g., 20 _ 300 or 4,400 ÷ 500. N
Indicator 3
(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 6(4) and 6x4 or 10 divided by 2 is the same as 10 ÷ 2 or 10/2.
Indicator 4
(K) (K)The student identifies, explains, and finds the greatest common factor and least common multiple of two or more whole numbers through the basic multiplication facts (2.4.K1), e.g., (factor tree example).
Indicator 1
(A) The student solves one- and two-step real-world problems using these computational procedures (2.4.A1a-c,f) $:
a. adds and subtracts whole numbers from 0 through 100,000; e.g., ex;
b. multiplies through a four-digit whole number by a two-digit whole number, e.g., ex;
c. multiplies monetary amounts by a one- or two-digit whole number, e.g., What is the cost of 4 items each priced at $3.49? $3.49 x 4 = $13.96;
d. divides whole numbers through a 2-digit ivisor and a 4-digit dividend with the remainder as a whole number or a fraction;
e. adds and subtracts decimals from thousands place through hundredths place, e.g., ex (The set of decimal numbers includes whole numbers.);
f. multiplies and divides by 10; 100; and 1,000 and single digit multiples of each, e.g., 20; 300; or 5,000; e.g., ex.
The student uses algebraic concepts and procedures in a variety of situations.
Benchmark 1
Patterns - The student recognizes, describes, extends, develops, and explains the general rule of patterns from a variety of situations.
Indicator 1
(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. The types of patterns are:
a. repeating patterns including arithmetic sequences (2.4.K1a), e.g., 20, 30, 28, 38, 36, . where the rule repeats (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;
b. growing patterns (2.4.K1a).
Indicator 2
(K) The student 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);
Indicator 3
(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.K1f).
Indicator 1
(A) The student generalizes these patterns using a written description:
a. numerical patterns (2.4.A1b),
b. patterns using geometric shapes through two attribute changes (2.4.A1a,g),
c. measurement patterns (2.4.A1b),
d. patterns related to daily life (2.4.A1b),
Indicator 2
(A) The student 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, rational numbers, and simple algebraic expressions in one variable to solve linear 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 and variable relationships.
Indicator 2
(K) The student solves one-step linear equations with one variable and a whole number solution using addition and subtraction with whole numbers from 0 through 100 and multiplication with the basic facts (2.4.A1a), e.g., 3y = 12, 45 = 17 + q, or r - 42 = 36.
Indicator 3
(K) The student explains and uses equality and inequality symbols (=, , <, ≤, >, ≥) and corresponding meanings (is equal to, is not equal to is less than, is less than or equal to, is greater than, is greater than or equal to) with whole numbers from 0 to 100,000 $.
Indicator 4
(K) The student recognizes ratio as a comparison of part-to-part and part-to-whole relationships, e.g., the relationship between the number of boys and the number of girls (part-to-part) or the relationship between the number of girls to the total number of students in the classroom (part to-whole).
Indicator 1
(A) The student represents real-world problems using variables, symbols, and one-step equations with unknown whole number quantities from 0 through 1,000 $; e.g., ex.
Indicator 2
(A) The student generates one-step linear equations to solve real-world problems with whole numbers from 0 through 1,000 with one unknown and a whole number solution using addition, subtraction, multiplication, and division (2 4.A1a), e.g., Ninety-six items are being shared with four people. How much does each receive? becomes 96 ÷ 4 = n. The solution is 24 items.
Indicator 3
(A) (A)The student generates:
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, ex;
b. number comparison statements using equality and inequality symbols (=, <, >) with whole numbers, measurement, and money (2.4.A1b,f), e.g., 1 ft < 15 in or 10 quarters > $2.
Benchmark 3
Functions - The student recognizes, describes, and examines constant and linear relationships in a variety of situations.
Indicator 1
(K) The student states mathematical relationships between whole numbers from 0 through 10,000 using various methods including mental math, paper and pencil, concrete objects, and appropriate technology (2.4.K1a) $.
Indicator 2
(K) (K)The student finds the values, determines the rule, and states the rule using symbolic notation with one operation of whole numbers from 0 through 10,000 using a vertical or horizontal function table (input/output machine, T-table), 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
Indicator 3
(K) (K)The student generalizes numerical patterns using whole numbers from 0 through 5,000 up to two operations by stating the rule using words (2.4.K1f), 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 number before 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 multiple the number by 2 and add 3.
Indicator 4
(K) (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.K1f).
Indicator 5
(K) (K)The student plots and locates points for integers (positive and negative whole numbers) on a horizontal number line and vertical number line.
Indicator 6
(K) (K)The student describes whole number relationships using letters and symbols.
Indicator 1
(A) The student represents and describes mathematical relationships between whole numbers from 0 through 5,000 using written and oral descriptions, tables, graphs, and symbolic notation (2.4.A1b) $.
Indicator 2
(A) (A)The student finds the rule, states the rule, and extends numerical patterns using real-world problems with whole numbers from 0 through 5,000 (2.4.A1g) $, e.g., The class sells cookies at lunch recess to raise money for a field trip. The goal is to sell 3000 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 they need to sell the 3000 cookies?
Day / # of Cookies Sold
4th / 450
8th / 900
12th / 1350
16th / 1800
20th / 2250
24th / 2700
28th / 3150The student's answer might be: 28 days, since that will be 150 over the goal, or the answer could be: on the 27th day, until 3000 are sold.
Indicator 3
(A) (A)The student translates between verbal, numerical, and graphical representations including the use of concrete objects to describe mathematical relationships, e.g., when the temperature is 20 degrees and then it drops 2 degrees an hour for 12 hours, the result is a negative number; the student could model this on a vertical number line.
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 and mathematical relationships and to solve equations (1.1.K1, 1.2.K1 2, 1.2.K5-6, 1.3.K1-5, 1.4 K1-4, 1.4.K6-7, 2.1.K1a-b, 2.1.K1d-h, 2.1.K1l, 2.1.K2-3, 2.2.K2-3, 2.3.K1, 2.3.K4, 3.2.K1-2, 3.2.K4, 3.3.K3, 3.4.K1-2, 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) and decimal and money models (base ten blocks or coins) to compare, order, and represent numerical quantities(1.1.K1b, 1.1.K2b, 1.2.K1-2, 1.3.K1-2) $;
d. factor trees to find least common multiple and greatest common factor (1.1 K3-4, 1.1.K6, 1.2.K1-2);
e. equations to model numerical relationships (2.1.K4, 2.3.K2-4, 3.4.K4,);
f. function tables (input/output machines, tables) to find numerical and algebraic relationships (2.1.K1c, 2.1.K1j, 3.1.K1-8, 3.2.K7-8, 3.3.Kk1-3, );
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 model volume and properties of geometric shapes and to compare size of geometric shapes (4.1.K1-3);
h. tree diagrams to organize attributes 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 (4.2.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;
k. Venn diagrams to sort data and show relationships
Indicator 2
(K) The student creates mathematical models to show the relationship between two or more things, e.g., using trapezoids to represent numerical quantities,
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, or division sets) to model computational procedures, mathematical relationships, and problem situations and to solve equations (1.1.A1, 1.1.A2a-b, 1.2.A1-3, 1.3.A1-3, 1.4.A1-2, 2.1.A1a-b, 2.1.A1d-g, 2.1.A2, 2.2.A2, 2.2.A31-b, 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 unifix cubes) to model problem situations (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) and decimal and money models (base ten blocks or coins to compare, order, and represent numerical quantities (1.1.K1b, 1.1.K2b, 1.2.K1-2, 1.3.K1-2,);
d. factor trees to find least common multiple and greatest common factor (1.1 A2e, 1.2.A1-3,);
e. equations to model numerical relationships (2.1.A1c, 2.3.A2);
f. function tables (input/output machines, T-tables) to find numerical and algebraic relationships (3.1.A1-3, 3.2.A1h, 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 model volume and properties of geometric shapes and to compare size of geometric shapes (4.1.A1-3);
h. tree diagrams to organize attributes through three different sets and determine the number of possible combinations (4.1.A1e, 4.2.A1a-d, f h, 4.2.A3-4);
i. two- and three-dimensional geometric models (spinners or number cubes) and process models (concrete objects, pictures, diagrams, or coins) to model probability (4.2.A1e, 4.2.A3);
j. graphs using concrete objects, pictographs, frequency tables, bar graphs, line graphs, circle graphs, Venn diagrams, line plots, charts, and tables to organize, describe, display, and interpret data;
k. Venn diagrams to sort data and show relationships.
Indicator 2
(A) The student selects a mathematical model and explains why some mathematical models are more useful than other mathematical models in certain situations, e.g., (need example).
The student uses geometric concepts and procedures in a variety of situations.
Benchmark 1 Geometric Figures and Their Properties - The student recognizes, applies, and compares properties of geometric figures in a variety of situations.
Indicator 1
(K) The student recognizes and investigates properties of plane figures and solids using concrete objects, drawings, and appropriate technology (2.4.K1g).
Indicator 2
(K) The student recognizes and describes (2.4.K1g):
a. regular polygons having up to and including ten sides;
b. similar and congruent figures.
Indicator 3
(K) The student recognizes and describes the solids (cubes, rectangular prisms, cylinders, cones, spheres, triangular prisms, rectangular pyramids, triangular pyramids) using the terms faces, edges, and vertices (corners) (2.4.K1g).
Indicator 4
(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 K1g).
Indicator 5
(K) The student recognizes, draws, and describes (2.4.K1g):
a. points, lines, line segments, and rays;
b. angles as right, obtuse, or acute.
Indicator 6
(K) The student recognizes and describes the difference between intersecting, parallel, and perpendicular lines (2.4.K1g).
Indicator 7
(K) The student identifies circumference, radius, and diameter of a circle (2.4 K1g).
Indicator 1
(A) The student solves real-world problems by applying the properties of:
a. plane figures (circles, squares, rectangles, triangles, ellipses, rhombi, parallelograms, hexagons, pentagons) and the line(s) of symmetry (2.4.A1h); e.g , ex;
b. solids (cubes, rectangular prisms, cylinders, cones, spheres, triangular prisms emphasizing faces, edges, vertices, and bases (2.4.A1h); e.g., ex;
c. intersecting, parallel, and perpendicular lines (2.4.A1h); e.g., ex.
Indicator 2
(A) (A)The student identifies the plane figures (circles, squares, rectangles, triangles, ellipses, rhombi, octagons, pentagons, hexagons, trapezoids, parallelograms) used to form a composite figure (2.4.A1h).
Benchmark 2
Measurement and Estimation - The student estimates, measures, and uses measurement formulas in a variety of situations.
Indicator 1
(K) The student determines and uses whole number approximations (estimations for length, width, weight, volume, temperature, time, perimeter, and area using standard and nonstandard units of measure (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 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.
Indicator 3
(K) The student states the number of feet and yards in a mile.
Indicator 4
(K) The student converts:
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 (2.4.K1a).
b. within the metric system: centimeters and meters, meters and kilometers, milliliters and liters, grams and kilograms (2.4.K1a).
Indicator 5
(K) (K)The student knows and uses perimeter and area formulas for squares and rectangles (2.4.K1g).
Indicator 1
(A) The student 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.A1b), e.g., ex;
b. temperature to the nearest degree (2.4.A1b), e.g., ex;
c. weight to the nearest whole unit (pounds, grams, nonstandard units) (2.4.A1b) e.g., ex;
d. time including elapsed time (2.4.A1b), e.g., ex;
e. hours in a day, days in a week, and days and weeks in a year (2.4.A1b), e.g., ex;
f. months in a year and minutes in an hour (2.4.A1b), e.g., ex;
g. perimeter of squares, rectangles, and triangles (2.4.A1h), e.g., ex;
h. area of squares and rectangles (2.4.A1h), e.g., ex.
Indicator 2
(A) The student solves real-world problems that involve conversions within the same measurement system: inches and feet, feet and yards, inches and yards, cups and pints, pints and quarts, quarts and gallons, centimeters and meters (2.4.A1b), e.g., ex.
Indicator 3
(A) The student estimates to check whether or not measurements or calculations for length, weight, temperature, time, perimeter, and area in a real-world problems are reasonable (2.4.A1b), e.g., ex.
Indicator 4
(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.A1b), e.g., ex.
Benchmark 3
Transformational Geometry - The student recognizes and performs transformations of two-dimensional figures in a variety situations.
Indicator 1
(K) The student recognizes and performs through two transformations (reflection rotation, translation) on a two-dimensional figure (2.4.K1g).
Indicator 2
(K) The student recognizes when an object is reduced or enlarged (2.4.K1a,g).
Indicator 3
(K) (K)The student recognizes three-dimensional figures (rectangular prisms, cylinders, cones, spheres, triangular prisms, rectangular pyramids) from various perspectives (top, bottom, side, corners) (2.4.K1g).
Indicator 1
(A) The student describes and draws a two-dimensional figure after performing one transformation (reflection, rotation, translation) (2.4.A1a).
Indicator 2
(A) (A)The student makes scale drawings of two-dimensional figures using a simple scale and grid paper (2.4.A1b), e.g., using the scale 1 cm = 3 m, the student makes a scale drawing of the classroom.
Benchmark 4
Geometry From and Algebraic Perspective - The student will analyze two-dimensional geometry using a coordinate system in a variety of situations.
Indicator 1
(K) The student locates and plots points on a number line (vertical/horizontal) using integers (positive and negative whole numbers) (2.4.K1a).
Indicator 2
(K) The student explains mathematical relationships between whole numbers, fractions, and decimals and where they appear on a number line (2.4.K1a).
Indicator 3
(K) (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.K1f.
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 by day the cumulative number of recess minutes in a week.
The student uses concepts and procedures of data analysis in a variety of situations.
Benchmark 1
Probability - The student uses probability to generate convincing arguments, draw conclusions, and make decisions in a variety of situations.
Indicator 1
(K) The student recognizes that all probabilities range from zero (impossible) through one (certain) (2.4.K1h) $.
Indicator 2
(K) The student lists all possible outcomes of a simple event in an experiment or simulation in an organized manner including the use of concrete objects (2.4 K1g-i).
Indicator 3
(K) (K)The student recognizes a simple event in an experiment or simulation where the probabilities of all outcomes are equal (2.4.K1h).
Indicator 4
(K) (K)The student uses fractions to represent the probability of a simple event.
Indicator 1
(A) The student conducts an experiment or simulation with a simple event including the use of concrete materials; records the results in a chart, table, or graph; uses the results to draw conclusions about the event; and makes predictions about future events (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 situations (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 (experimental probability/empirical results) in an experiment or simulation with a simple event 2.4.A1i-j).
Benchmark 2 Statistics
The student generates, organizes, and interprets rational number and other data in a variety of situations. The student applies measures of central tendency when drawing conclusions from the data.
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 and decimal intervals using these data displays:
a. graphs using concrete objects (2.4.K1i),
b. pictographs (2.4.K1i),
c. frequency tables (2.4.K1i),
d. bar and line graphs (2.4.K1i),
e. Venn diagrams and other pictorial displays (2.4.K1j), e.g., glyphs,
f. line plots (2.4.K1i),
g. charts and tables (2.4.K1i),
h. circle graphs (2.4.K1I),
i. single stem-and-leaf plots (2.4.K1i).
Indicator 2
(K) The student collects data using different techniques (observations, polls, tallying, interviews, surveys, or random sampling) and explains the results (2.4 K1i-j).
Indicator 3
(K) The student identifies, explains, and calculates or finds these statistical measures of a whole number data set of up to twenty whole number data points from 0 through 1,000 (2.4.K1a):
a. minimum and maximum values,
b. range,
c. mode,
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).
Indicator 1
(A) The student interprets and uses data to make reasonable inferences, predictions, and decisions, and to develop convincing arguments from these data displays:
a. graphs using concrete materials (2.4.A1j),
b. pictographs (2.4.A1j),
c. frequency tables (2.4.A1j),
d. bar and line graphs (2.4.A1j),
e. Venn diagrams and other pictorial displays (2.4.A1k),
f. line plots (2.4.A1j),
g. charts and tables (2.4.A1j),
h. circle graphs (2.4.A1j).
Indicator 2
(A) The student uses these statistical measures of a whole number data set 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,
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 and discusses why a particular format may be more appropriate than another (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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