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, fractions, and money using concrete objects in a variety of situations.
Indicator 1
(K) The student knows, explains, and represents whole numbers from 0 through 100 using concrete objects (2.4.K1a). $
Indicator 2
(K) The student compares and orders:
a. whole numbers from 0 through 100 using concrete objects (2.4.K1a), $
b. fractions with like denominators (halves and fourths) using concrete objects (2 4.K1a,c).
Indicator 3
(K) The student recognizes a whole, a half, and a fourth and represents equal parts of a whole (halves, fourths) using concrete objects, pictures, diagrams, fraction strips, or pattern blocks (2.4.K1a,c,f). $
Indicator 4
(K) The student identifies and uses ordinal numbers first (1st) through tenth 10th) (2.4.K1a).
Indicator 5
(K) The student identifies coins (pennies, nickels, dimes, quarters) and currency $1, $5, $10) and states the value of each coin and each type of currency using money models (2.4.K1d). $
Indicator 6
(K) The student recognizes and counts a like group of coins (pennies, nickels, dimes) (2.4.K1d). $
Indicator 1
(A) The student solves real-world problems using equivalent representations and concrete objects to compare and order whole numbers from 0 through 50 (2.4 A1a). $
Indicator 2
(A) The student determines whether or not numerical values using whole numbers from 0 through 50 are reasonable (2.4.A1a), $ e.g., when asked if 40 books will fit inside the student's desk, the student answers no and explains why.
Indicator 3
(A) The student demonstrates that smaller whole numbers are within larger whole numbers using whole numbers from 0 to 30 (2.4.A1a), $ e.g., if there are five pigs in a pen, there are also three pigs in the pen.
Benchmark 2
Number Systems and Their Properties - The student demonstrates an understanding whole numbers with a special emphasis on place value and recognizes, applies, and explains whole number properties.
Indicator 1
(K) The student reads and writes whole numbers from 0 through 100 in numerical form. $
Indicator 2
(K) The students represents whole numbers from 0 through 100 using various groupings and place value models (place value mats, hundred charts, or base ten blocks) emphasizing ones, tens, and hundreds (2.4.K1b), $ e.g., How many groups of tens are there in 32? or How many groups of tens and ones in 62?
Indicator 3
(K) The student counts subsets of whole numbers from 0 through 100 both forwards and backwards (2.4.K1a). $
Indicator 4
(K) The student writes in words whole numbers from zero through ten. $
Indicator 5
(K) The student identifies the place value of the digits in whole numbers from 0 through 100 (2.4.K1b). $
Indicator 6
(K) The student identifies any whole number from 0 through 30 as even or odd 2.4.K1a).
Indicator 7
(K) (K)The student uses the concepts of these properties with whole numbers from 0 through 100 and demonstrates their meaning using concrete objects (2.4 K1a): $
a. commutative property of addition, e.g., 3 + 2 = 2 + 3,
b. zero property of addition (additive identity), e.g., 4 + 0 = 4.
Indicator 1
(A) The student solves real-world problems with whole numbers from 0 through 50 using place value models (place value mats, hundred charts, or base ten blocks) and the concepts of these properties to explain reasoning (2.4.A1a-b): $
a. commutative property of addition, e.g., group 5 students into a group of 3 and a group of 2, add to find the total; then reverse the order of the students to show that 2+3 sill equals 5.
b. zero property of addition, e.g., have students lay out 11 crayons, tell them to add zero (crayons); then ask: How many crayons are there?
Benchmark 3
Estimation - The student uses numerical estimation with whole numbers in a variety of situations.
Indicator 1
(K) The student estimates whole number quantities from 0 through 100 using various computational methods including mental math, paper and pencil, concrete objects, and appropriate technology (2.4.K1a). $
Indicator 2
(K) The student estimates to check whether or not results of whole number quantities from 0 through 100 are reasonable (2.4.K1a).
Indicator 1
(A) The student adjusts original whole number estimate of a real-world problem using whole numbers from 0 through 50 based on additional information (a frame of reference) (2.4.A1a), e.g., An estimate is made about the number of tennis balls in a shoebox; about half of the tennis balls are removed from the box and counted. With this additional information, an adjustment of the original estimate is made.
Benchmark 4
Computation - The student models, performs and explains computation with whole numbers using concrete objects 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 objects, and appropriate technology (2.4.K1a). $
Indicator 2
(K) The student states and uses with efficiency and accuracy basic addition facts with sums from 0 through 10 and corresponding subtraction facts. $ N
Indicator 3
(K) The student skip counts by 2s, 5s, and 10s through 50 (2.4.K1a).
Indicator 4
(K) The student uses repeated addition (multiplication) with whole numbers to find the sum when given the number of groups (ten or less) and given the same number of concrete objects in each group (ten or less) (2.4.K1a), e.g., three plates of cookies with 10 cookies on each plate means 10 + 10 +10 = 30 cookies
Indicator 5
(K) The student uses repeated subtraction (division) with whole numbers when given the total number of concrete objects in each group to find the number of groups (2.4.K1a), e.g., There are 9 pencils. If each student gets 2 pencils, how many students get pencils? 9 - 2 - 2 - 2 - 2 or 9 minus 2 four times means four students get 2 pencils each and there is 1 pencil left over. or There are 30 pieces of candy to put equally into five bowls, how many pieces of candy will be in each bowl? 30 - 5 - 5 - 5 - 5 - 5 - 5 means there are six in each bowl.
Indicator 6
(K) The student performs and explains these computational procedures (2.4 K1a-b):
a. adds whole numbers with sums through 99 without regrouping using concrete objects, e.g., 42 straws (bundled in 10s) + 21 straws (bundled in 10s) = 63 straws (bundled in 10s);
b. subtracts two-digit whole numbers without regrouping using concrete objects, e.g., 63 cubes - 21 cubes = 42 cubes.
Indicator 7
(K) The student shows that addition and subtraction are inverse operations using concrete objects (2.4.K1a). $
Indicator 8
(K) The student reads and writes horizontally and vertically the same addition expression, e.g., 5 + 4 is the same as 4 + 5.
Indicator 1
(A) The student solves one-step real-world addition or subtraction problems with various groupings of two-digit whole numbers without regrouping (2.4.A1a-b), $ e.g., Jo has 48 crayons and 16 markers in her desk. How many more crayons does she have then markers? This problem could be solved using base 10 models or a number line or by saying 48-10=38 and 38-6=32.
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 a pattern using concrete objects in a variety of situations.
Indicator 1
(K) The student uses concrete objects, drawings, and other representations to work with types of patterns:
a. repeating patterns (2.4.K1a), e.g., an AB pattern is like 1-2, 1-2, .; an ABC pattern is like dog-horse-pig, dog-horse-pig, .;
b. growing (extending) patterns (2.4.K1a), e.g., 1, 2, 3, .
Indicator 2
(K) The student uses the following attributes to generate patterns:
a. counting numbers related to number theory, e.g., evens, odds, or skip counting by 2s, 5s, or 10s;
b. whole numbers that increase (2.4.K1a), e.g., 11, 21, 31, ... or like 2, 4, 6, .;
c. geometric shapes (2.4.K1e),
d. measurements (2.4.K1a), e.g., counting by inches or feet;
e. the calendar (2.4.K1a), e.g., January, February, March, .;
f. money and time (2.4.K1d), $ e.g., 10¢, 20¢, 30¢, . or 1:00, 1:30, 2:00, ...;
g. things related to daily life (2.4.K1a), e.g., seasons, temperature, or weather;
h. things related to size, shape, color, texture, or movement (2.4.K1a); tall-short, tall-short, tall-short, .; or snapping fingers, clapping hands, or stomping feet kinesthetic patterns).
Indicator 3
(K) The student identifies 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 (2.4.K1a):
a. repeating patterns for the AB pattern, the ABC pattern, and the AAB pattern;
b. growing patterns that add 1, 2, 5, or 10.
Indicator 1
(A) The student generalizes the following patterns using pictorial, oral, and/or written descriptions including the use of concrete objects:
a. whole number patterns (2.4.A1b); $
b. patterns using geometric shapes (2.4.A1d);
c. calendar patterns (2.4.A1b);
d. patterns using size, shape, color, texture, or movement (2.4.A1b).
Indicator 2
(A) The student recognizes multiple representations of the same pattern (2.4 A1a) e.g., the AB pattern could be represented by clap, snap, clap, snap, . or red green, red, green, . or square, circle, square, circle,.
Indicator 3
(A) (A)The student uses concrete objects to model a whole number pattern (2.4 A1b):
a. counting by ones:
b. counting by twos:
c. counting by fives:
g. counting by tens:
Benchmark 2
Variables, Equations, and Inequalities - The student solves addition and subtraction equations using concrete objects in a variety of situations.
Indicator 1
(K) The student explains and uses symbols to represent unknown whole number quantities from 0 through 20.
Indicator 2
(K) The student finds the unknown sum or difference of the basic facts using concrete objects (2.4.K1a), $ e.g., 12 dominoes - 5 dominoes = Ä dominoes or Ä cubes = 2 cubes + 4 cubes.
Indicator 3
(K) The student describes and compares two whole numbers from 0 through 100 using the terms: is equal to, is less than, is greater than (2.4.K1a-b).
Indicator 1
(A) The student represents real-world problems using concrete objects, pictures, oral descriptions, and symbols and the basic addition and subtraction facts with one operation and one unknown (2.4. A1a), $ e.g., given some marbles, Sue says: 3 red marbles and 3 blue marbles equal 6 marbles. Sue also shows and writs the problem and solution; 3+3=__ or RRR+BBB=___, 3+3=6.
Indicator 2
(A) The student generates and solves problem situations using the basic facts to find the unknown sum or difference with concrete objects (2.4.A1a), e.g., A student generates a problem: I have 6 marbles. My sister has 4. How many do we have altogether? The student shows 6+4=__, and 6+4=10.
Notes: Using symbols to represent an unknown in an equation is a precursor to variables.
Benchmark 3
Functions - The student recognizes and describes whole number relationships using concrete objects in a variety of situations.
Indicator 1 (K) The student plots whole numbers from 0 through 100 on segments of a number line (2.4.K1a).
Indicator 2
(K) The student states mathematical relationships between whole numbers from 0 through 50 using various methods including mental math, paper and pencil, and concrete objects (2.4.K1a), e.g., every time a hand is added to the set, five more fingers are added to the total.
Indicator 3
(K) The student states numerical relationships for whole numbers from 0 through 50 in a horizontal or vertical function table (input/output machine, T-table) (2.4 K1e), e.g., $
Number of bicycles 1 2 3 4 5 .
Number of wheels 2 4 6 8 10 .
on each bicycle _ _ _ _ _The student states: For every bicycle added, you add two more wheels.
Indicator 1
(A) The student represents and describes mathematical relationships for whole numbers from 0 through 50 using concrete objects, pictures, oral descriptions, and symbols (2.4.A1a). $
Indicator 2
(A) The student recognizes numerical patterns (counting by 2s, 5s, and 10s) through 50 using a hundred chart (2.4.A1b).
Benchmark 4
Models - The student uses mathematical models including concrete objects to represent and show mathematical relationships 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, unifix cubes, hundred charts, measurement tools, or calendars) to model computational procedures and mathematical relationships, to compare and order numerical quantities, and to represent fractional parts (1.1.K1 4, 1.2.K3, 1.2.K6-7 1.3.K1-2, 1.4.K1-8, 2.1.K1a-b, 2.1.K1d, 2.2.K2-3, 2.3.K1-2, 3.2.K1-6, 3.3.K1-3, 3 4.K1-3, 4.1.K2, 4.2.K1a, 4.2.K1e, 4.2.K3-4); $
b. place value models (place value mats, hundred charts, or base ten blocks) to compare, order, and represent numerical quantities and to model computational procedures (1.2.K2, 1.2.K5, 1.4.K7, 2.2.K3); $
c. fraction models (fraction strips or pattern blocks) to compare, order, and represent numerical quantities (1.1.K2-3); $
d. money models (base ten blocks or coins) to compare, order, and represent numerical quantities (1.1.K5-6); $
e. function tables (input/output machines, T-tables) to model numerical relationships (2.3.K3). $
f. two-dimensional geometric models (geoboards, dot paper, pattern blocks, tangrams, or attribute blocks), three-dimensional geometric models (solids), and real-world objects to compare size and to model attributes of geometric shapes 1.1.K3, 2.1.K1c, 3.1.K1-3);
g. two-dimensional geometric models (spinners), three-dimensional geometric models (number cubes), and concrete objects to model probability (4.1.K1-2); $
h. graphs and tables using concrete objects, representationa objects, or abstract representation to display data (2.3.K3); $
i. uses Venn diagrams to sort data (4.2.K1e, 4.2.K5).
Indicator 2
(K) The student concrete objects, pictures, diagrams, drawings, or dramatizations to show the relationship between two or more things (2.1.K1).4.2 K1a-d, 4.2.K2); $
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, unifix cubes, measurement tools, or calendars) to model computational procedures and mathematical relationships, to compare and order numerical quantities, and to model problem situations (1.1.A1-3, 1.2.A1, 1.3.A1, 1.4.A1, 2.2.A1-2, 2.3.A1, 3.2.A1-3, 3.3.A1-2, 3.4.A1, 4.1.A1, 4.2.A2); $
b. place value models (place value mats, hundred charts, or base ten blocks) to compare, order, and represent numerical quantities and to model computational procedures (1.2.A1, 1.4.A1, 2.3.A2); $
c. two-dimensional geometric models (geoboards, dot paper, pattern blocks, tangrams, or attribute blocks), three-dimensional geometric models (solids), and real-world objects to compare size and to model attributes of geometric shapes 3.1.A1-2);
d. two-dimensional geometric models (spinners), three-dimensional geometric models (number cubes), and concrete objects to model probability (4.1.A1);
e. graphs and tables including the use of concrete objects to organize, display, and explain data (4.1.A1, 4.2.A1-2). $
The student uses geometric concepts and procedures in a variety of situations.
Benchmark 1
Geometric figures and Their Properties : The student recognizes geometric shapes and describes their attributes using concrete objects in a variety of situations.
Indicator 1
(K) The student recognizes and draws circles, squares, rectangles, triangles, and ellipses (ovals) (plane figures/two-dimensional figures) (2.4.K1f).
Indicator 2
(K) The student recognizes and investigates attributes of circles, squares, rectangles, triangles, and ellipses (plane figures) using concrete objects, drawings, and appropriate technology (2.4.K1f).
Indicator 3
(K) The student recognizes cubes, rectangular prisms, cylinders, cones, and spheres (solids/three-dimensional figures) (2.4.K1f).
Indicator 1
(A) The student demonstrates how:
a. a geometric shape made of several plane figures (circles, squares, rectangles, triangles, ellipses) can be separated to make two or more different plane figures 2.4.A1c);
b. several plane figures (circles, squares, rectangles, triangles, ellipses) can be combined to make a new geometric shape (2.4.A1c);
c. several solids (cubes, rectangular prisms, cylinders, cones, spheres) can be combined to make a new geometric shape (2.4.A1c).
Indicator 2
(A) The student sorts plane figures and solids (circles, squares, rectangles, triangles, ellipses, cubes, rectangular prisms, cylinders, cones, spheres) by a given attribute (2.4.A1c).
Benchmark 2
Measurement and Estimation - The student estimates and measures using nonstandard units with concrete objects in a variety of situations. SD
Indicator 1
(K) The student uses whole number approximations (estimations) for length and weight using nonstandard units of measure (2.4.K1a), $ e.g., the width of the chalkboard is about 10 erasers long or the weight of one encyclopedia is about five picture books.
Indicator 2
(K) The student compares two measurements using these attributes (2.4.K1a): $
a. longer, shorter (length);
b. taller, shorter (height);
c. heavier, lighter (weight);
d. hotter, colder (temperature).
Indicator 3
(K) The student reads and tells time at the hour and half-hour using analog and digital clocks.(2.4.K1a)
Indicator 4
(K) The student selects appropriate measuring tools for length, weight, volume, and temperature for a given situation (2.4.K1a). $
Indicator 5
(K) The student measures length and weight to the nearest whole unit using nonstandard units (2.4.K1a). $
Indicator 6
(K) The student states number of days in a week and months in a year.(2.4.K1a)
Indicator 1
(A) The student compares and orders concrete objects by length or weight.(2.4 A1a) $
Indicator 2
(A) The student compares the weight of two concrete objects using a balance (2 4.A1a).
Indicator 3
(A) The student locates and names concrete objects that are about the same length, weight, or volume as a given concrete object (2.4.A1a). $
Benchmark 3
Transformational Geometry - The student develops the foundation for spatial sense using concrete objects.
Indicator 1
(K) The student describes the spatial relationship between two concrete objects using appropriate vocabulary (2.4.K1a), e.g., (behind, above, below, on, under, beside, or in front of).
Indicator 2
(K) The student recognizes that changing an object's position or orientation does not change the name, size, or shape of the object (2.4.K1a).
Indicator 3
(K) The student describes movement of concrete objects using appropriate vocabulary (2.4.K1a), e.g., right, left, up, or down.
Indicator 1
(A) The student shows two concrete objects or shapes are congruent by physically fitting one on top of the other.(2.4.A1a).
Indicator 2
(A) (A)The student gives and follows directions to move concrete objects from one location to another using appropriate vocabulary(2.4.A1a), e.g., right, left, up down, behind, or above.
Benchmark 4
Geometry From an Algebraic Perspective - The student identifies one or more points on a number line in a variety of situations.
Indicator 1
(K) The student locates and plots whole numbers from 0 through 100 on a segment of a number line (horizontal/vertical) (2.4.K1a), e.g., using a segment of a number line from 45 to 60 to locate the whole number 50.
Indicator 2
(K) The student describes a given whole number from 0 to 100 as coming before or after another number on a number line (2.4.K1a).
Indicator 3
(K) The student uses a number line to model addition and counting using whole numbers from 0 to 100 (2.4.K1a).
Indicator 1
(A) The student solves real-world problems involving counting and adding whole numbers from 0 to 50 using a number line (2.4.A1a), e.g., ex
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. SD
Indicator 1
(K) The student recognizes whether an outcome of a simple event in an experiment or simulation is impossible, possible, or certain (2.4.K1g). $
Indicator 2
(K) The student recognizes and states whether a simple event in an experiment or simulation including the use of concrete objects can have more than one outcome (2.4.K1a,g).
Indicator 1
(A) The student makes a prediction about a simple event in an experiment or simulation, conducts the experiment or simulation, and records the results in a graph using concrete objects, a pictograph with a symbol or picture representing only one, or a bar graph (2.4.A1a,d-e).
Notes: Probability experiences should be addressed through the use of concrete objects, e.g., spinners or number cubes (geometric models). These informal activities reinforce concepts in the other Standards, primarily Number and Computation.
Benchmark 2
Statistics - The student collects, displays, and explains data sets including the use of concrete objects in a variety of situations.
Indicator 1
(K) The student displays and reads numerical(quantitative) and non numerical qualitative) data in a clear, organized, and accurate manner including a title, labels, and whole number intervals using these data displays: $
a. graphs using concrete objects (2.4.K1h),
b. pictographs with a whole symbol or picture representing one (no partial symbols or pictures) (2.4.K1h),
c. frequency tables (tally marks) (2.4.K1h),
d. horizontal and vertical bar graphs (2.4.K1h),
e. Venn diagrams or other pictorial displays (2.4.K1h), e.g., glyphs.
a. graphs using concrete objects,
b. pictographs with a symbol or picture representing only one,
c. frequency tables (tally marks),
d. bar graphs,
e. Venn diagrams or other pictorial displays, e.g., glyphs.
Indicator 2
(K) The students collects data using different techniques (observations or interviews) and explains the results (2.4.K1g). $
Indicator 3
(K) The student identifies the minimum (lowest) and maximum (highest) values in a data set (2.4.K1a). $
Indicator 4
(K) The student determines the mode (most) after sorting by one attribute (2.4 K1a).
Indicator 5
(K) The student sorts and records qualitative (non-numerical, categorical) data sets using one attribute (2.4.K1i), $ e.g., color, shape, or size.
Indicator 1
(A) The student communicates the results of data collection and answers questions (identifying more, less, fewer, greater than, or less than) based on information (2.4.A1e) $ from:
a. graphs using concrete objects
b. a pictograph with a whole symbol or picture representing only one (no partial symbols or pictures),
c. a horizontal or vertical bar graph.
Indicator 2
(A) The student determines categories from which data could be gathered (2.4 A1a,e), $ e.g., categories could include shoe size, height, favorite candy bar, or number of pockets in clothing.
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