GLE-Math4
COLORADO MODEL CONTENT
STANDARDS FOR MATHEMATICS
4th 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.
Fourth grade students will:
1.1.1 using objects and pictures, represent whole numbers including odds and evens from 0 to 1,000,000
1.1.2 apply equalities and inequalities with whole numbers from 0 to 1,000,000 using the
symbols =, •, <, >
1.1.3 using concrete materials (for example, fraction strips), compare and order fractions
with like and unlike denominators, such as halves, thirds, fourths, eighths, and tenths
1.1.4 using concrete materials (for example, base ten blocks), represent the decimal fractions of tenths and hundredths
1.1.5 using concrete materials, equate terminating decimals to their common fraction
equivalents (for example, 0.25 = 1/4)
1.1.6 demonstrate different combinations of currency and coins for change (for example,
$2.39 = 2 dollar bills, 1 quarter, 1 dime, and 4 pennies)
1.1.7 using concrete materials, count change from the cost of the item, where the item costs no more than $10.00, up to the amount of money received
1.2 Reading and writing whole numbers and knowing place-value concepts and numeration through their relationships to counting, ordering, and grouping.
Fourth grade students will:
1.2.1 read and write numerals from 0 to 1,000,000 in meaningful contexts
1.2.2 read the number words for selected numbers from zero to one million
1.2.3 write the number words for selected numbers from zero to one hundred thousand
1.2.4 order according to place value (for example, given 9 ones, 5 tens, 4 hundreds, 7
thousands, and 8 hundred thousands, the student can write the number 807,459; given
the number 807,459, the student can show 8 hundred thousands, 7 thousands, 4
hundreds, 5 tens, and 9 ones)
1.2.5 identify place value through hundred thousands (for example, in 807,459, ‘8’ is in the hundred thousands place)
1.2.6 write six-digit numbers in expanded form (for example, 807,459 = 800,000 + 7,000 + 400 + 50 + 9)
1.2.7 relate decimals and fractions (that is, tenths and hundredths) to one another using
objects and pictures
1.2.8 demonstrate different combinations of currency and coins for change (for example,
$2.39 = 2 dollar bills, 1 quarter, 1 dime, and 4 pennies)
1.2.9 using concrete materials, count change from the cost of the item, where the item costs no more than $10.00, up to the amount of money received
1.3 Using numbers to count, to measure, to label, and to indicate location.
Fourth grade students will:
1.3.1 count forward from any number by 2’s, 3’s, 5’s, 10’s, and 100’s
1.3.2 sequence selected whole numbers from 0 to 100,000
1.3.3 locate and label 1/2’s and multiples of 1/4’s and 1/3’s between whole numbers on the number line
1.3.4 locate and label a point in the first quadrant of the coordinate plane (for example,
locates the point (27,15)) and on a city map (for example, (E23, 11))
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).
Fourth grade students will:
1.4.1 verify division of whole numbers is not commutative
1.4.2 continue to verify number properties from previous grades
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).
Fourth grade students will:
1.5.1 estimate sums and differences first by rounding to the nearest ten, hundred, and
thousand prior to performing the operation, and then using the estimate to determine the
reasonableness of the solution
1.5.2 estimate products first by rounding to the nearest ten and hundred 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).
Fourth grade students will:
2.1.1 reproduce, extend, create, and describe patterns, such as in common fractions,
geometric shapes, measurement, addition, subtraction, multiplication, and division facts
2.1.2 find missing elements of a complex repeating pattern (for example, 1,1,2,3,5,__,13,…)
2.2 Describing patterns and other relationships using tables, graphs, and open sentences.
Fourth grade students will:
2.2.1 match tables, graphs, and open sentences that represent the same numerical pattern
2.3 Recognizing when a pattern exists and using that information to solve a problem.
Fourth grade students will:
2.3.1 identify a rule using addition, subtraction, or multiplication, and solve a problem using the rule
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).
Fourth grade students will:
2.4.1 determine how the change in one variable affects the change in the other by addition, subtraction, or multiplication
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.
Fourth grade students will:
3.1.1 select the appropriate type of graph to use in various problem-solving situations
3.1.2 collect and display data using line, dot plots, circle, or bar graphs
3.1.3 use graph paper using the horizontal and vertical axes appropriately
3.1.4 explain the basic concepts of sample bias and sample size when designing a survey
3.2 Interpreting data using the concepts of largest, smallest, most often, and middle.
Fourth grade students will:
3.2.1 choose between median and mode to best describe the "middle" of a data set
3.2.2 transfer the use of median and mode to other curricular areas
3.2.3 using various displays of data, formulate questions, interpret, and draws conclusions
3.3 Generating, analyzing, and making predictions based on data obtained from surveys and chance devices.
Fourth grade students will:
3.3.1 uses survey data to make and justify a real-world decision
3.3.2 compare the outcomes of flipping a coin, spinning a spinner with four congruent
sectors, and rolling a number cube
3.3.3 analyze and predict which outcome is more likely from several events such as obtaining “heads” when flipping a coin, the spinner landing in one of the sectors, or rolling a “1” on a number cube
3.3.4 analyze the fairness of various chance devices
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).
Fourth grade students will:
3.4.1 determine the number of outcomes obtained from a variety of chance devices
3.4.2 using paper-and-pencil techniques (for example, tree diagrams), display the possible
combinations of matching two sets of 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).
Fourth grade students will:
4.1.1 define similarity and congruence
4.1.2 identify the transformation that occurs when a figure is translated, reflected, or rotated
4.1.3 identify the lines of symmetry of an equilateral triangle, parallelogram, and rhombus
4.2 Identifying, describing, drawing, comparing, classifying, and building physical models of geometric figures.
Fourth grade students will:
4.2.1 identify parallel, perpendicular, and intersecting lines
4.2.2 identify attributes of closed curves
4.2.3 recognize and identify polygons including quadrilaterals such as trapezoids,
parallelograms, and rhombuses
4.2.4 draw geometric polygons including quadrilaterals such as trapezoids, parallelograms,
and rhombuses
4.2.5 describe squares as rectangles
4.2.6 describe a right angle as having a measure of 90o
4.2.7 classify triangles by their angles (obtuse, acute, right)
4.2.8 draw obtuse, acute, and right triangles on a coordinate plane and identify the vertices with coordinates
4.2.9 compare what is the same and what is different between two-dimensional figures and three-dimensional figures
4.2.10 identify rectangular prisms
4.2.11 recognize and identify in three-dimensional figures the vertices, edges, and faces
4.2.12 build cubes, prisms, and pyramids (for example, using straws and string)
4.3 Relating geometric ideas to measurement and number sense.
Fourth grade students will:
4.3.1 measure the sides and perimeters of geometric shapes to the nearest fourth inch and
centimeter
4.3.2 measure the area of geometric figures using 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).
Fourth grade students will:
4.4.1 draw a picture or diagram to solve a problem (for example, uses triangular pattern
blocks to create a star; uses pattern blocks to tile a plane)
4.4.2 investigate and predict the changing of angles (for example, those made from the hands of a clock over time)
4.4.3 investigate and predict what must occur for similar figures to become congruent figures
4.4.4 investigate and predict the geometric figures 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.
Fourth grade students will:
5.1.1 tell time to the nearest minute, using an analog and digital clock
5.1.2 tell the number of minutes in a day, days in a year and when a leap year occurs
5.1.3 describes the units for measuring time
5.1.4 estimate the perimeters of similarly-sized figures (for example, trapezoids,
parallelograms and rectangles), measure the sides, and determine the perimeters
5.1.5 measure the lengths of the sides of squares and rectangles and determine the areas
5.1.6 measure the lengths of the sides of cubes and determine the volumes
5.1.7 estimate and measure the capacity of containers
5.1.8 estimate and weigh objects on a balance to the nearest ounce and gram
5.1.9 compare the relationship between the temperature in Fahrenheit and Celsius
5.1.10 determine the distance between points on vertical and horizontal line segments on a coordinate plane
5.1.11 given a distance, find pairs of points on the coordinate plane separated by that distance
5.1.12 describe the units for measuring length, area, volume, capacity, and temperature in U.S. customary and metric units
5.1.13 know the number of years in a decade and a century, feet in a mile, millimeters and centimeters in a meter, ounces in a pound, and pounds in a ton
5.2 Comparing and ordering objects according to measurable attributes (for example, longest to shortest, lightest to heaviest).
Fourth grade students will:
5.2.1 compare objects according to the measurable attributes of length, area, volume,
capacity, weight, and temperature in U.S. customary and metric units
5.2.2 order objects according to the measurable attributes of length, area, volume, capacity, weight and temperature in U.S. customary and metric units
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.
Fourth grade students will:
5.4.1 use familiar objects as referents for measurement (for example, one paper clip equals one gram; the length of the arm span equals approximately one meter)
5.5 Selecting and using appropriate standard and non-standard units of measurement in problem-solving situations.
Fourth grade students will:
5.5.1 select the appropriate units of measurement of time
5.5.2 select the appropriate units of measurement of length, area, volume, capacity, weight, and temperature in U.S. customary and metric units
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.
Fourth grade students will:
6.1.1 explain in writing what addition, subtraction, multiplication, and division of whole
numbers means
6.1.2 demonstrate the inverse relationship of multiplication and division of whole numbers
6.1.3 demonstrate division of whole numbers as repeated subtraction
6.2 Adding and subtracting commonly used fractions and decimals using physical models (for example, 1/3, 3/4, 0.5, 0.75).
6.2.1 using concrete materials, demonstrate addition and subtraction of proper fractions with common denominators of twelve or less without regrouping
6.2.2 using concrete materials, demonstrate addition and subtraction of mixed numerals with common denominators of twelve or less
6.2.3 add and subtract decimals to the one-hundredths
6.2.4 compute the total cost of items to $10.00
6.2.5 determine change received for $10.00 or less
6.3 Demonstrating understanding of and proficiency with basic addition, subtraction,
multiplication, and division facts without the use of a calculator.
Fourth grade students will:
6.3.1 demonstrate understanding of basic multiplication and division facts through 100
6.3.2 demonstrate automatic recall of basic multiplication and division facts through 100
6.3.3 continue automatic recall of basic addition and subtraction facts
6.4 Constructing, using, and explaining procedures to compute and estimate with whole numbers.
Fourth grade students will:
6.4.1 use estimation techniques such as front-end rounding, rounding, compatible numbers (numbers whose sum is 10, 100, 1,000...) and clustering (for example, 27 + 28 + 30 + 31 equals approximately 4 x 30 = 120) before performing operations
6.4.2 using paper-and-pencil, demonstrate the four basic operations of whole numbers
including
a) multiplication of two digits by two digits and three digits by one digit with
regrouping
6.4.3 division of two digits by a one-digit divisor
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.
Fourth grade students will:
6.5.1 given a real-world problem-solving situation, use the correct operation (addition,
subtraction, multiplication, or division) 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, difference,
product, or quotient is acceptable