Standard 1: Number and Computation

The student uses numerical and computational concepts and procedures in a variety of situations.

First Grade

Benchmark 1
The student demonstrates number sense for whole numbers, fractions, and money using concrete objects in a variety of situations. Knowledge Base Indicators
  1. The student knows, explains, and represents whole number from 0 through 100 using concrete objects.
  2. The student compares and orders.
    1. whole numbers from 0 through 100 using concrete objects.
    2. fractions with like denominators (halves and fourths) using concrete objects.
  3. 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.
  4. The student identifies and uses ordinal numbers first (1st) through tenth (10th).
  5. The student identifies coins (pennies, nickels, dimes, quarters) and currency ($1, $5, $10) and states the values of each coin and each type of currency using money models.
  6. The student recognizes and counts a like group of coins (pennies, nickels, dimes).
Application Indicators
  1. The student solves real-world problems using equivalent representations and concrete objects to compare and order whole numbers from 0 through 50.
  2. The student determines whether or not numerical values using whole numbers from 0 through 50 are reasonable.
  3. The student demonstrates that smaller whole numbers are within larger whole numbers using whole numbers from 0 to 30.
 Benchmark 2
The student demonstrates an understanding of whole numbers with a special emphasis on place value and recognizes, applies, and explains the of properties as they relate to whole numbers in a variety of situations. Knowledge Base Indicators
  1. The student reads and writes whole numbers from 0 through 100 in numerical form.
  2. The student 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.
  3. The student counts subsets of whole numbers from 0 through 100 both backwards and forwards.
  4. The student writes in words whole numbers from 0 through 10.
  5. The student identifies the place value of the digits in whole numbers from 0 through 100.
  6. The student identifies any whole number from 0 through 30 as even or odd.
  7. The student uses the concepts of these properties with whole numbers from 0 through 100 and demonstrates their meaning using concrete objects.
    1. commutative property of addition.
    2. zero property of addition (additive identity).
Application Indicators
  1. The student solves real-world problems with whole numbers from 0 through 50 using place value modes (place value mats, hundred charts, or base ten blocks) and the concepts of these properties to explain reasoning.
    1. communicative property of addition.
    2. zero property of addition.
 Benchmark 3
The student uses computational estimation with whole numbers in a variety of situations. Knowledge Base Indicators
  1. 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. The student estimates to check whether or not results of whole number quantities from 0 through 100 are reasonable.
Application Indicator
  1. 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).
 Benchmark 4
The student models, performs, and explains computation with whole numbers using concrete objects in a variety of situations. Knowledge Base Indicators
  1. The student computes with efficiency and accuracy using various computational methods including mental math, paper and pencil, concrete objects, and appropriate technology.
  2. The student states and uses with efficiency and accuracy basic addition facts with sums from 0 through 10 and corresponding subtraction facts.
  3. The student skip counts by 2s, 5s, and 10s through 50.
  4. 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).
  5. 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.
  6. The student performs and explains these computational procedures:
    1. adds whole numbers with sums through 99 without regrouping using concrete objects.
    2. subtracts two-digit whole numbers without regrouping using concrete objects.
  7. The student shows that addition and subtraction are inverse operations using concrete objects.
  8. The student reads and writes horizontally and vertically the same addition expression.
Application Indicators
  1. The student solves one-step real-world addition or subtraction problems with various groupings of two-digit whole numbers without regrouping.

Standard 2: Algebra

The student uses algebraic concepts and procedures in a variety of situations.

First Grade

Benchmark 1
The student recognizes, describes, extends, develops, and explains relationships in patterns using concrete objects in a variety of situations. Knowledge Base Indicators
  1. The student uses concrete objects, drawings, and other representations to work with types of patterns.
    1. repeating patterns,
    2. growing (extending) patterns,
  2. The student uses the following attributes to generate patterns:
    1. counting numbers related to number theory,
    2. whole numbers that increase,
    3. geometric shapes,
    4. measurements,
    5. the calendar,
    6. money and time,
    7. things related to daily life,
    8. things related to size, shape, color, texture, or movement;
  3. 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.
  4. The student generates:
    1. repeating patterns for the AB pattern, the ABC pattern, and the AAB pattern;
    2. growing patterns that add 1, 2, 5, or 10.
Application Indicators
  1. The student generalizes the following patterns using pictorial, oral, and/or written descriptions including the use of concrete objects:
    1. whole number patterns;
    2. patterns using geometric shapes;
    3. calendar patterns;
    4. patterns using size, shape, color, texture, or movement.
  2. recognizes multiple representations of the same pattern.
  3. uses concrete objects to model a whole number pattern
    1. counting by ones;
    2. counting by twos;
    3. counting by fives;
    4. counting by tens;
 Benchmark 2
The student solves addition and subtraction equations using concrete objects in a variety of situations. Knowledge Base Indicators
  1. The student explains and uses symbols to represent unknown whole number quantities from 0 through 20.
  2. The student finds the unknown sum or difference of the basic facts using _dominoes or _cubes = 2 cubes + 4 cubes.
  3. The student describes and compares two who numbers from 0 through 100 using the terms: is equal to, is less than, is greater than.
 Application Indicators
  1. The student represents real-world problems using concrete objects, pictures, oral descriptions, and symbols and the basic addition and subtraction facts.
  2. The student generates and solves problem situations using the basic facts to find the unknown sum or difference with concrete objects.
Benchmark 3
The student recognizes and describes whole number relationships using concrete objects in a variety of situations. Knowledge Base Indicators
  1. The student plots whole numbers from 0 through 100 on segments of a number line.
  2. The student states mathematical relationships between whole numbers from 0 through 50 using various methods including mental math, paper and pencil, and concrete objects.
  3. The student states numerical relationships for whole numbers from 0 through 50 in a horizontal or vertical function table (input/output machine, T-table).

Application Indicators
  1. The student represents and describes mathematical relationships for whole numbers from 0 through 50 using concrete objects, pictures, oral descriptions, and symbols.
  2. The student recognizes numerical patterns (counting 2s, 5s, and 10s) through 50 using a hundred chart.
 Benchmark 4
The student uses mathematical models including concrete objects to represent, show, and communicate mathematical relationships in a variety of situations. Knowledge Base Indicators
  1. The student knows, explains, and uses mathematical models to represent mathematical concepts, procedures, and relationships.
    Mathematical models include:
    1. 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.
    2. place value models (place value mats, hundred charts, or base ten blocks) to compare, order, and represent numerical quantities.
    3. fraction models (fraction strips or pattern blocks) to compare, order, and represent numerical quantities.
    4. money models (base ten blocks or coins) to compare order, and represent numerical quantities.
    5. function tables (input/output machines, T-tables) to model numerical relationships.
    6. 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
    7. two-dimensional geometric models (spinners), three-dimensional geometric models (number cubes), and concrete objects to model probability
    8. graphs using concrete objects, pictographs, frequency tables, horizontal and vertical bar graphs, and Venn diagrams or other pictorial displays to organize, display, and explain data
    9. Venn diagrams to sort data
  2. The student uses concrete objects, pictures, diagrams, drawings, or dramatizations to show the relationship between two or more things.
Application Indicators
  1. The student recognizes that various mathematical models can be used to represent the same problem situation.
    Mathematical models include:
    1. 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;
    2. place value models (place value mats, hundred charts, or base ten blocks) to compare, order, and represent numerical quantities and to model computational procedures;
    3. two-dimensional geometric models (geoboards, dot paper, pattern blocks, tangrams, or attribute blocks), three-dimentional geometric models (solids), and real-world objects to compare size and to model attributes of geometric shapes;
    4. two-dimensional geometric models (spinners), three-dimensional geometric models (number cubes), and concrete objects to model probability;
    5. graphs using concrete objects, pictographs, frequency tables, and horizontal and vertical bar graphs to organize, display, and explain data.

Standard 3: Geometry

The student uses geometric concepts and procedures in a variety of situations.

First Grade

Benchmark 1
The student recognizes geometric shapes and their attributes using concrete objects in a variety of situations. Knowledge Base Indicators
  1. The student recognizes and draws circles, squares, rectangles, triangles, and ellipses (ovals) (plane figures/two-dimensional figures).
  2. The student recognizes and investigates attributes of circles, squares, rectangles, triangles, and ellipses (plane figures) using concrete objects, drawings, and appropriate technology.
  3. The student recognizes cubes, rectangular prisms, cylinders, cones, and spheres (solids/tree-dimensional figures).
Application Indicators
  1. The student demonstrates how:
    1. 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. several plane figures (circles, squares, rectangles, triangles, ellipses) can be combined to make a new geometric shape;
    3. several solids (cubes, rectangular prisms, cylinders, cones, spheres) can be combined to make a new geometric shape.
  2. The student sorts plane figures and solids (circles, squares, rectangles, triangles, ellipses, cubes, rectangular prisms, cylinders, cones, spheres) by a given attribute.
 Benchmark 2
The student estimates and measures using standard and units of measure with concrete objects in a variety of situations. Knowledge Base Indicators
  1. The student uses whole number approximations (estimations) for length and weight using nonstandard units of measure.
  2. The student compares two measurements using these attributes:
    1. longer, shorter (length);
    2. taller, shorter (height);
    3. heavier, lighter (weight);
    4. hotter, colder (temperature).
  3. The student reads and tells time at the hour and half-hour using analog and digital clocks.
  4. The student selects appropriate measuring tools for length, weight, volume, and temperature for a given situation.
  5. The student measures length and weight to the nearest whole unit using nonstandard units.
  6. The student states the number of days in a week and months in a year.
Application Indicators
  1. The student compares and orders concrete objects by length or weight.
  2. The student compares the weight of two concrete objects using a balance.
  3. The student locates and names concrete objects that are about the same length, weight, or volume as a given concrete object.
 Benchmark 3
The student develops the foundation for spatial sense using objects in a variety of situations. Knowledge Base Indicators
  1. The student describes the spatial relationship between two concrete objects using appropriate vocabulary.
  2. The student recognizes that changing an object's position or orientation does not change the name, size, or shape of the object.
  3. The student describes movement of concrete objects using appropriate vocabulary.
Application Indicators
  1. The student shows two concrete objects or shapes are congruent by physically fitting one object or shape on top of the other.
  2. The student gives and follows directions to move concrete objects from one location to another using appropriate vocabulary.
 Benchmark 4
The student identifies one or more points on a line in a variety of situations. Knowledge Base Indicators
  1. The student locates and plots whole numbers from 0 through 100 on a segment of a number line (horizontal/vertical).
  2. The student describes a given whole number from 0 to 100 as coming before or after another number on a number line.
  3. The student uses a number line to model addition and counting using whole numbers from 0 to 100.
Application Indicators
  1. The student solves real-world problems involving counting and adding whole numbers from 0 to 50 using a number line.

Standard 4: Data

The student uses concepts and procedures of data analysis in a variety of situations.

First Grade

Benchmark 1
The student applies the concepts of probability using concrete objects in a variety of situations. Knowledge Base Indicators
  1. The student recognizes whether an outcome of a simple event in an experiment or simulation is impossible, possible, or certain.
  2. 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.
Application Indicators
  1. 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.
 Benchmark 2
Statistics - The student collects, displays, and explains numerical (whole numbers) and non-data sets including the use of concrete objects in a variety of situations. Knowledge Base Indicators
  1. 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:
    1. graphs using concrete objects,
    2. pictographs with a whole symbol or picture representing one (no partial symbols or pictures),
    3. frequency tables (tally marks),
    4. horizontal and vertical bar graphs,
    5. Venn diagrams or other pictorial displays.
  2. The student collects data using different techniques (observations or interviews) and explains the results.
  3. The student identifies the minimum (lowest) and maximum (highest) values in a data set.
  4. The student determines the mode (most) after sorting by one attribute.
  5. The student sorts and records qualitative (non-numerical, categorical) data sets using one attribute.
Application Indicators
  1. The student communicates the results of data collection and answers questions (identifying more, less, fewer, greater than, or less than) based on information from:
    1. graphs using concrete objects,
    2. a pictograph with a whole symbol or picture representing only one (no partial symbols or pictures),
    3. a horizontal or vertical bar graph
  2. The student determines categories from which data could be gathered.