Grade Four
The fourth-grade standards place
emphasis on multiplication and division with whole numbers and solving problems
involving addition and subtraction of fractions and decimals. Students will
continue to learn and use the basic multiplication facts as they become
proficient in multiplying larger numbers. Students also will refine their
estimation skills for computations and measurements and investigate
relationships between and among simple two-dimensional (plane) figures and
three-dimensional (solid) figures. Students will identify and draw
representations of points, lines, line segments, and rays. Students will graph
points in the first quadrant in the coordinate plane and extend and duplicate
patterns. Concrete materials and two-dimensional representations will be used
to solve problems involving perimeter, patterns, probability, and equivalence
of fractions and decimals. Students will recognize a geometric transformation,
such as reflection (flip), translation (slide), and rotation (turn).
While learning mathematics,
students will be actively engaged, using concrete materials and appropriate
technologies such as calculators and computers. However, facility in the use of
technology shall not be regarded as a substitute for a student’s understanding
of quantitative concepts and relationships or for proficiency in basic
computations.
Mathematics
has its own language, and the acquisition of specialized vocabulary and
language patterns is crucial to a student’s understanding and appreciation of
the subject. Students should be encouraged to use correctly the concepts,
skills, symbols, and vocabulary identified in the following set of standards.
Problem
solving has been integrated throughout the six content strands. The development
of problem-solving skills should be a major goal of the mathematics program at
every grade level. Instruction in the process of problem solving will need to
be integrated early and continuously into each student’s mathematics education.
Students must be helped to develop a wide range of skills and strategies for
solving a variety of problem types.
4.1 The student will
a) identify (orally and in writing) the place value for each digit in a whole number expressed through millions;
b) compare two whole numbers expressed through millions, using symbols ( >, <,
or = ); and
c) round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand.
4.2 The student will
a) identify, model, and compare rational numbers (fractions and mixed numbers), using concrete objects and pictures;
b) represent equivalent fractions; and
c) relate fractions to decimals, using concrete objects.
4.3 The student will compare the numerical value of fractions (with like and unlike denominators) having denominators of 12 or less, using concrete materials.
4.4 The student will
a) read, write, represent, and identify decimals expressed through thousandths;
b) round to the nearest whole number, tenth, and hundredth; and
c) compare the value of two decimals, using symbols (<, >, or =), concrete materials, drawings, and calculators.
4.5 The student will estimate whole-number sums and differences and describe the method of estimation. Students will refine estimates, using terms such as closer to, between, and a little more than.
4.6 The student will add and subtract whole numbers written in vertical and horizontal form, choosing appropriately between paper and pencil methods and calculators.
4.7 The
student will find the product of two whole numbers when one factor has two
digits or fewer and the other factor has three digits or fewer, using
estimation and paper and pencil. For larger products (a two-digit numeral times
a three-digit numeral), estimation and calculators will
be used.
4.8 The student will estimate and find the quotient of two whole numbers, given a one-digit divisor.
4.9 The student will
a) add and subtract with fractions having like and unlike denominators of 12 or less, using concrete materials, pictorial representations, and paper and pencil;
b) add and subtract with decimals through thousandths, using concrete materials, pictorial representations, and paper and pencil; and
c) solve problems
involving addition and subtraction with fractions having like and unlike
denominators of 12 or less and with decimals expressed through thousandths,
using various computational methods, including calculators, paper and pencil, mental computation, and estimation.
4.10 The student will
a) estimate and measure weight/mass, using actual measuring devices, and describe the results in U.S. Customary/metric units as appropriate, including ounces, pounds, grams, and kilograms;
b) identify equivalent measurements between units within the U.S. Customary system (ounces and pounds) and between units within the metric system (grams and kilograms); and
c) estimate the
conversion of ounces and grams and pounds and kilograms, using approximate
comparisons (1 ounce is about 28 grams, or 1 gram is about the weight of a paper clip; 1 kilogram is a little more
than 2 pounds). *
* The intent of this standard is for
students to make ballpark comparisons and not to
memorize conversion factors between U.S. Customary and metric units.
4.11 The student will
a) estimate and measure length, using actual measuring devices, and describe the results in both metric and U.S. Customary units, including part of an inch (1/2, 1/4, and 1/8), inches, feet, yards, millimeters, centimeters, and meters;
b) identify equivalent measurements between units within the U.S. Customary system (inches and feet; feet and yards; inches and yards) and between units within the metric system (millimeters and centimeters; centimeters and meters; and millimeters and meters); and
c) estimate the conversion of inches and centimeters, yards and meters, and miles and kilometers, using approximate comparisons (1 inch is about 2.5 centimeters, 1 meter is a little longer than 1 yard, 1 mile is slightly farther than 1.5 kilometers, or 1 kilometer is slightly farther than half a mile). *
* The intent of this standard is for students
to make ballpark comparisons and not to memorize conversion factors between
U.S. Customary and metric units.
4.12 The student will
a) estimate and measure liquid volume, using actual measuring devices and using metric and U.S. Customary units, including cups, pints, quarts, gallons, milliliters, and liters;
b) identify equivalent measurements between units within the U.S. Customary system (cups, pints, quarts, and gallons) and between units within the metric system (milliliters and liters); and
c) estimate the conversion of quarts and liters, using approximate comparisons (1 quart is a little less than 1 liter, 1 liter is a little more than 1 quart).*
* The intent of this standard is for students
to make ballpark comparisons and not to memorize
conversion factors between U. S. Customary and metric units.
4.13 The student will
a) identify and describe situations representing the use of perimeter and area; and
b) use measuring
devices to find perimeter in both standard and nonstandard units of measure.
4.14 The
student will investigate and describe the relationships between and among
points, lines, line segments, and rays.
4.15 The student will
a) identify and draw representations of points, lines, line segments, rays, and angles, using a straightedge or ruler; and
b) describe the path of shortest distance between two points on a flat surface.
4.16 The
student will identify and draw representations of lines that illustrate
intersection, parallelism, and perpendicularity.
4.17 The student will
a) analyze and compare the properties of two-dimensional (plane) geometric figures (circle, square, rectangle, triangle, parallelogram, and rhombus) and three-dimensional (solid) geometric figures (sphere, cube, and rectangular solid [prism]);
b) identify congruent and noncongruent shapes; and
c) investigate congruence of plane figures after geometric transformations such as reflection (flip), translation (slide) and rotation (turn), using mirrors, paper folding, and tracing.
4.18 The
student will identify the ordered pair for a point and locate the point for an
ordered pair in the first quadrant of a coordinate
plane.
4.19 The student will
a) predict the
likelihood of outcomes of a simple event, using the terms certain, likely, unlikely, impossible; and
b) determine the probability of a given simple event, using concrete materials.
4.20 The student will collect, organize, and display data in line and bar graphs with scale increments of one or greater than one and use the display to interpret the results, draw conclusions, and make predictions.
4.21 The
student will recognize, create, and extend numerical and geometric patterns,
using concrete materials, number lines, symbols,
tables, and words.
4.22 The student will recognize and demonstrate the meaning of equality, using symbols representing numbers, operations, and relations [e.g., 3 + 5 = 5 + 3 and
15 + (35 + 16) = (15 + 35) + 16].