18.104.22.168 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.
22.214.171.124 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.
5.1.2 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.
126.96.36.199 classifies subsets of numbers as integers, whole number, fractions (including mixed numbers), or decimals.
188.8.131.52 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:
184.108.40.206.a commutative properties of addition and multiplication, e.g., 43 + 34 = 34 + 43 and 12 x 15 = 15 x 12;
5.1.3 The student uses computational estimation with whole numbers, fractions, decimals, and money in a variety of situations.
220.127.116.11 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.
18.104.22.168 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.
22.214.171.124 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
126.96.36.199 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
188.8.131.52.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.
184.108.40.206.c geometric shapes through two attribute changes, e.g., when the next shape has one more side; or when both the color and the shape change at the same time;
220.127.116.11.d measurements, e.g., 3 m, 6 m, 9 m, ;
18.104.22.168.e things related to daily life, e.g., sports scores, longitude and latitude, elections, eras, or appropriate topics across the curriculum;
22.214.171.124.f things related to size, shape, color, texture, or movement, e.g., square dancing moves (kinesthetic patterns);
126.96.36.199 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.
188.8.131.52 solves one-step linear equations with one variable and a whole number solution using addition and subtraction with whole numbers from 0 through 100 and multiplication with the basic facts, e.g., 3y = 12, 45 = 17 + q, or r - 42 = 36.
184.108.40.206 explains and uses equality and inequality symbols (=, not equal to, <, less than or equal to, >, greater than or equal to) 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.
220.127.116.11 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).
18.104.22.168 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),
22.214.171.124 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 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 multiply the number by 2 and add 3.
5.2.4 The student develops and uses mathematical models including the use of concrete objects to represent and explain mathematical relationships in a variety of situations.
126.96.36.199 knows, explains, and uses mathematical models to represent mathematical concepts, procedures, and relationships. Mathematical models include:
188.8.131.52.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;
184.108.40.206.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;
220.127.116.11.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;
18.104.22.168 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:
22.214.171.124.a customary units of measure to the nearest fourth and eighth inch,
5.4.2 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.
126.96.36.199 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: