By the end of grade four, students understand large
numbers and addition, subtraction,
multiplication, and division of whole numbers. They describe and compare simple
fractions
and decimals. They understand the properties of, and the relationships between,
plane geometric figures. They collect, represent, and analyze data to answer
questions.
Number Sense
1.0 Students understand the place value of whole numbers and decimals to
two Read and write whole numbers in the millions. Order and compare whole numbers and decimals to two decimal places.
Round whole
numbers through the millions to the nearest ten, hundred, Decide when a
rounded solution is called for and explain why such a Solve each of the following problems and
observe the different roles played 1.5 Explain different interpretations of
fractions, for example, parts of a whole, True or false? 1.6 Write tenths and hundredths in decimal and
fraction notations and know the 1.7 Write the fraction represented by a drawing of
parts of a figure; represent a Which number represents the shaded part of the
figure? (Adapted from Use concepts
of negative numbers (e.g., on a number line, in counting, in True or false? Identify on a
number line the relative position of positive fractions, positive 2.0 Students extend their use and understanding
of whole numbers to the 2.1 Estimate and compute the sum or difference of
whole numbers and positive Solve 55.73  48.25 = ? 2.2 Round twoplace decimals to one decimal or the
nearest whole number and Solve 17.91 + 2.18 = ?
Students
solve problems involving addition, subtraction, multiplication,
Demonstrate
an understanding of, and the ability to use, standard algorithms Solve 619,581  23,183 = ?
Demonstrate
an understanding of, and the ability to use, standard algorithms Solve:
Solve
problems involving multiplication of multidigit numbers by twodigit Solve problems
involving division of multidigit numbers by onedigit 4.0 Students know how to factor small whole
numbers:
Know that
numbers such as 2, 3, 5, 7, and 11 do not have any factors except List all the distinct prime factors of 210. 
Note: The sample problems illustrate the standards and are written to help clarify them. Some problems are written in a form that can be used directly with students; others will need to be modified, particularly in the primary grades, before they are used with students. The symbol


Algebra and Functions 1.0 Students
use and interpret variables, mathematical symbols, and properties to 1.1 Use letters, boxes, or other symbols to stand
for any number in simple Tanya has read the first 78 pages of a 130page
book. Give the number of 1. 130 + 78 = ___ Interpret and evaluate mathematical expressions that now use parentheses. Evaluate the two expressions: (28  10)  8 = ___ and 28  (10  8) = ___.
Use
parentheses to indicate which operation to perform first when writing Solve Solve 1.4 Use and interpret formulas (e.g., area =
length × width or A = lw) to answer
Understand
that an equation such as y = 3x + 5 is a prescription for determining Students know how to manipulate equations: Know and understand that equals added to equals are equal.
Know and
understand that equals multiplied by equals are equal. 

Measurement and Geometry 1.0
Students understand perimeter and area:
Students use
twodimensional coordinate grids to represent points and graph
Draw the
points corresponding to linear relationships on graph paper
Understand
that the length of a horizontal line segment equals the difference
Understand
that the length of a vertical line segment equals the difference What is the length of the line segment joining
the points (121, 3) to 3.0 Students demonstrate an understanding of
plane and solid geometric objects 3.5 Know the definitions of a right angle, an
acute angle, and an obtuse angle. 3.8 Know the definition of different
quadrilaterals (e.g., rhombus, square, 

Statistics, Data Analysis, and Probability
1.0 Students organize, represent, and interpret
numerical and categorical data and The following table shows the ages of the girls
and boys in a club. Use the
Ages of students 1.1 Formulate survey questions; systematically
collect and represent data on a 2.0 Students make predictions for simple
probability situations: 

Mathematical Reasoning 1.0 Students make decisions about how to approach problems: 1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns. 1.2 Determine when and how to break a problem into simpler parts. 2.0 Students use strategies, skills, and concepts in finding solutions: 2.1 Use estimation to verify the reasonableness of calculated results. 2.2 Apply strategies and results from simpler problems to more complex problems. 2.3 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning. 2.4 Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work.
2.5 Indicate the relative advantages of exact and approximate solutions
to 