GLE-Math2
COLORADO MODEL CONTENT
STANDARDS FOR MATHEMATICS
2nd Grade Level Expectations
Standard 1:
Students develop number sense and use numbers and number relationships in problem-solving situations and communicate the reasoning used in solving these problems.
1.1 Demonstrating meanings for whole numbers, commonly-used fractions and decimals (for example, 1/3, 3/4, 0.5, 0.75), and representing equivalent forms of the same number through the use of physical models, drawings, calculators, and computers.
Second grade students will:
1.1.1 using objects and pictures, represent whole numbers including odds and evens from 0 to 1,000
1.1.2 apply equalities and inequalities with whole numbers from 0 to 1,000 using the symbols=, •, <, >
1.1.3 using concrete materials, demonstrate the meanings of fractions, including halves,
thirds, fourths, eighths, and tenths of sets and wholes
1.1.4 demonstrate equivalencies of coins (for example, 5 nickels = 1 quarter)
1.1.5 combine coins up to $1.00 (for example, 20¢ = 2 dimes = 1 dime + 2 nickels = 4
nickels)
1.2 Reading and writing whole numbers and knowing place-value concepts and numeration through their relationships to counting, ordering, and grouping.
Second grade students will:
1.2.1 read and write numerals from 0 to 1,000 in meaningful contexts
1.2.2 read and write the number words for zero to one hundred
1.2.3 group objects by ones, tens, and hundreds
1.2.4 order according to place value (for example, given 9 ones, 5 tens, and 4 hundreds, the student can write the number 459; given the number 459, the student can show 4
hundreds, 5 tens, and 9 ones)
1.2.5 write three-digit numbers in expanded form (for example, 459 = 400 + 50 +
1.3 Using numbers to count, to measure, to label, and to indicate location.
Second grade students will:
1.3.1 count by 1’s, 2’s, 5’s, and 10’s
1.3.2 count from 1 to 1,000 by 100’s
1.3.3 starting with any whole number less than 1,000, count forward to 1,000
1.3.4 use ordinal positions for first through thirty-first
1.3.5 sequence selected whole numbers from 0 to 1,000
1.3.6 locate and label the halfway point between whole numbers on the number line
1.3.7 locate and label a point in the first quadrant of the coordinate plane (for example,
locates the point (4,1))
1.4 Developing, testing and explaining conjectures about properties of whole numbers, and commonly used fractions and decimals (for example, 1/3, 3/4, 0.5, 0.75).
Second grade students will:
1.4.1 verify the commutative and associative properties of addition of whole numbers
1.4.2 verify that subtraction of whole numbers is not commutative
1.5 Using number sense to estimate and justify the reasonableness of solutions to problems involving whole numbers, and commonly used fractions and decimals (for example, 1/3, 3/4, 0.5, 0.75).
Second grade students will:
1.5.1 estimate sums and differences first by rounding to the nearest ten prior to performing the operation, and then using the estimate to determine the reasonableness of the solution
Standard 2:
Students use algebraic methods to explore, model and describe patterns and functions involving numbers, shapes, data, and graphs in problem-solving situations and communicate the reasoning used in solving these problems.
2.1 Reproducing, extending, creating, and describing patterns and sequences using a variety of materials (for example, beans, toothpicks, pattern blocks, calculators, unifix cubes, colored tiles).
Second grade students will:
2.1.1 verbally describe patterns
2.1.2 create and extend patterns using symbols, such as words and numbers
2.1.3 find missing elements of a repeating pattern (for example, 1,3, __,7)
2.2 Describing patterns and other relationships using tables, graphs, and open sentences.
Second grade students will:
2.2.1 match tables and graphs of points on a coordinate plane
2.3 Recognizing when a pattern exists and using that information to solve a problem.
Second grade students will:
2.3.1 verbally describe the relationship between a graph and a table
2.4 Observing and explaining how a change in one quantity can produce a change in another (for example, the relationship between the number of bicycles and the numbers of wheels).
Second grade students will:
2.4.1 using concrete or pictorial patterns, determine how the change in one variable affects
the change in another (for example, how changing the number of hands changes the
number of fingers)
Standard 3:
Students use data collection and analysis, statistics, and probability in
problem-solving situations and communicate the reasoning and processes used in solving these problems.
3.1 Constructing, reading, and interpreting displays of data including tables, charts,
pictographs, and bar graphs.
Second grade students will:
3.1.1 design a survey and collect data
3.1.2 display data using tallies, bar graphs, pictographs, or tables
3.1.3 transfer the same set of data to different displays (for example, from a table to a bar
graph)
3.2 Interpreting data using the concepts of largest, smallest, most often, and middle.
Second grade students will:
3.2.1 interpret and compare data from displays, using the terms "least often," "most often", and "how much more" or "how much less"
3.3 Generating, analyzing, and making predictions based on data obtained from surveys and chance devices.
Second grade students will:
3.3.1 use survey data to make predictions about a larger similar population (for example,
from a class survey make a prediction about all second graders in the school)
3.3.2 roll a number cube to generate and record results
3.3.3 analyze the results (including likely, more likely, less likely, and unlikely outcomes) of spinning a spinner
3.3.4 recognize if different spinners are fair or unfair
3.4 Solving problems using various strategies for making combinations (for example,
determining the number of different outfits that can be made using two blouses and three skirts).
Second grade students will:
3.4.1 determine the number of outcomes when spinning a spinner
3.4.2 using manipulatives or pictures, determine the possible combinations of matching a set containing two elements with a different set containing two elements
Standard 4:
Students use geometric concepts, properties, and relationships in problemsolving situations and communicate the reasoning used in solving these problems.
4.1 Recognizing shapes and their relationships (for example, symmetry and congruence) using a variety of materials (for example, pasta, boxes, pattern blocks).
Second grade students will:
4.1.1 identify congruent figures from a selection of similar figures
4.1.2 slide, flip, and turn concrete materials such as tangrams and pattern blocks to create and reproduce simple designs
4.1.3 describe symmetry
4.1.4 identify lines of symmetry of squares and rectangles
4.2 Identifying, describing, drawing, comparing, classifying, and building physical models of geometric figures.
Second grade students will:
4.2.1 describe the attributes of circles, triangles, and quadrilaterals such as squares and
rectangles
4.2.2 identifies right angles and not-right angles
4.2.3 recognize the three-dimensional figures: cubes, spheres, cylinders, cones, and pyramids
4.2.4 draw right angles and not-right angles
4.3 Relating geometric ideas to measurement and number sense.
Second grade students will:
4.3.1 measure the lengths of the sides of triangles, squares, and rectangles to the nearest half inch and centimeter
4.3.2 measures the perimeter of triangles, squares, and rectangles using non-standard and
standard units
4.4 Solving problems using geometric relationships and spatial reasoning (for example, using rectangular coordinates to locate objects, constructing models of three-dimensional objects).
4.4.1 draw a picture or diagram to solve a problem (for example, draw a map of the room to show how to get from a desk to the reading area; draw a map of the neighborhood)
4.4.2 investigate and predict which pattern block shapes can be formed from the pattern
block triangles
4.4.3 investigate and predict the geometric shapes that result from cutting along a line of
symmetry
Standard 5:
Students use a variety of tools and techniques to measure, apply the results in problem-solving situations, and communicate the reasoning used in solving these problems.
5.1 Knowing, using, describing, and estimating measures of length, perimeter, capacity, weight, time, and temperature; and 5.3 Demonstrating the process of measuring and explaining the concepts related to units of measurement.
Second grade students will:
5.1.1 time to the nearest fifteen minutes, using an analog and digital clock
5.1.2 use AM and PM
5.1.3 estimate and measure the length of objects to the nearest half inch, foot, yard,
centimeter, and meter
5.1.4 estimate and measure the perimeter of a figure using non-standard and standard units
5.1.5 estimate and measure the capacity of a container in cups, pints, quarts and gallons
5.1.6 estimate and weigh an object on a balance with a non-standard unit and use a scale to measure an object to the nearest pound
5.1.7 measures temperature to the nearest 2o and 10oF
5.1.8 describe the units for measuring time, length, capacity, weight, and temperature
5.1.9 know the number of hours in a day, months in a year, inches in a foot, feet in a yard,
and cups in a pint
5.2 Comparing and ordering objects according to measurable attributes (for example, longest to shortest, lightest to heaviest).
Second grade students will:
5.2.1 compare objects according to the measurable attributes of length, capacity, weight, and temperature
5.2.2 order objects according to the measurable attributes of length, capacity, weight and
temperature
5.2.3 compare and order various times
5.4 Using the approximate measures of familiar objects (for example, the width of your finger, the temperature of a room, the weight of a gallon of milk) to develop a sense of measurement.
Second grade students will:
5.4.1 use familiar objects as referents for measurement (for example, a second grader is a
little taller than a meter)
5.5 Selecting and using appropriate standard and non-standard units of measurement in problem-solving situations.
Second grade students will:
5.5.1 select the appropriate units of measurement of time, length, capacity, weight, and
temperature
Standard 6:
Students link concepts and procedures as they develop and use computational techniques, including estimation, mental arithmetic, paper-and-pencil, calculators, and computers, in problem-solving situations and communicate the reasoning used in solving these problems.
6.1 Demonstrating conceptual meanings for the four basic arithmetic operations of addition, subtraction, multiplication, and division.
6.1.1 using concrete materials, demonstrate and verbally explain addition of whole numbers with regrouping for two-digit numbers
6.1.2 using concrete materials, demonstrate and verbally explain subtraction of whole
numbers without regrouping for two-digit numbers
6.1.3 using concrete materials or pictures, demonstrate multiplication without regrouping of whole numbers (for example, using arrays or grouping sets of objects)
6.1.4 using concrete materials or pictures, demonstrate division of whole numbers without remainders as partitioning of sets
6.1.5 using concrete materials or pictures, demonstrate the inverse relationship of addition and subtraction of whole numbers
6.1.6 using concrete materials or pictures, demonstrate multiplication of whole numbers as repeated addition
6.2 Adding and subtracting commonly used fractions and decimals using physical models (for example, 1/3, 3/4, 0.5, 0.75).
Second grade students will:
6.2.1 using concrete materials or pictures, add and subtract halves, thirds, and fourths
6.2.2 find the total value of coins not to exceed $1.00
6.3 Demonstrating understanding of and proficiency with basic addition, subtraction,
multiplication, and division facts without the use of a calculator.
Second grade students will:
6.3.1 demonstrate understanding of basic addition and subtraction facts
6.3.2 demonstrate automatic recall of basic addition and subtraction facts
6.3.3 use sums on an addition facts table to locate all addends for a particular sum (for
example, 7 = 0 + 7, 7 = 1 + 6, . . . )
6.4 Constructing, using, and explaining procedures to compute and estimate with whole numbers.
Second grade students will:
6.4.1 use estimation techniques such as rounding and compatible numbers (numbers whose sum is 10) before performing operations
6.4.2 using paper-and-pencil, demonstrate addition of two-digit whole numbers with and
without regrouping
6.4.3 using paper-and-pencil, demonstrate subtraction of two-digit whole numbers without regrouping
6.5 Selecting and using appropriate methods for computing with whole numbers in problemsolving situations from among mental arithmetic, estimation, paper-and-pencil, calculator and computer methods.
Second grade students will:
6.5.1 given a real-world problem-solving situation, use the correct operation (addition or
subtraction) and appropriate method (mental arithmetic, estimation, paper-and-pencil,
calculator, or computer) to solve the problem
6.5.2 determine from real-world problems whether an estimated or exact sum or difference is acceptable