Download MATH ESSENTIALS The purpose of this list is to

MATH ESSENTIALS
The purpose of this list is to provide students, parents and teachers with some of the
most important skills needed at each grade level in order to have a good foundation for
moving on to the next. Students should be able to perform the mathematical tasks
described in each grade level prior to the one he/she is entering. For example, a 5th
grader should be able to complete all tasks listed for Preschool through 4th grade.
Preschoolers should be able to:
Count a group of at least 5 things – adult may ask the child “how many” or “get me”
Read numerals 1 to 5
Count from 1 to at least 10
Kindergarteners should be able to:
Count forward and backward starting from any number between 1-30
Name two numbers that go together to make numbers up to 5 (For example, 2 and 2, or 3 and 1 make 4)
Read and write numbers 0-20
First graders should be able to:
Count forward and backward to 120 (starting and stopping at different places)
Mentally add and subtract within 10 (Can answer questions like, “What goes with 2 to make 8?” “If I have 3 how
many more do I need to have 7?” “4 and 4 more is…” and “10 take away 3 is…” in addition to solving written
problems)
Solve addition and subtraction problems within 20 (double facts 6+6=12, adding ten 2+10=12, bridging to ten
9+4 think 10 +3, counting backward to subtract 15-2=13, counting up to subtract 10-7=3 think 7..8,9,10)
Understand tens and ones in 2 digit numbers (37 is 3 tens and 7 ones)
Read, write, and compare numbers up to 100 (Can answer questions like, “Which number is greater: 5 or 7?” and
complete phrases like, “55 is (less than, greater than or equal to) 72.” Can also give the number before and after a
given number)
Second graders should be able to:
Mentally add and subtract within 20 (Can answer questions like, “What goes with 2 to make 18?” “If I have 6 how
many more do I need to have 13?” “8 and 8 more is…” and “17 take away 3 is…” in addition to solving written
problems)
Solve addition and subtraction problems within 100
Understand hundreds, tens, and ones (132 is 1 hundred 3 tens 2 ones or 13 tens and 3 ones or 132 ones)
Read, write, and compare numbers within 1,000 (adult says 873 and the student is able to write the number, the
adult says 695 and the student is able to write the next number and tell which is greater or less; and the student can
read numbers that the adult writes within 1,000)
Third graders should be able to:
Use different strategies to solve addition and subtraction problems within 1000 (Adult presents problems
horizontally and child is able to solve using different strategies)
Knows all multiplication facts (0 to 12)
Determine the perimeter and area of a shape when all side lengths are provided
Understands that a fraction is equal parts of a whole
Understands that a fraction can represent parts of a set or parts of a whole
Fourth graders should be able to:
Multiply numbers involving three -digits by one -digit (563 X3) and two- digit by two-digit (34X12) to solve
real-world problems
Divide numbers with remainders (for example 44÷5)
Understands and applies equivalent fractions (2/4 = ½ )
Add and subtract fractions to solve real-world problems (4 ¼ + 3 2/4= 5 ¾
Compare and order decimals through the hundredths (Adult gives students 2 or 3 decimals and the student can
place the decimals in order from greatest to least or least to greatest for example: .05 is less than .5)
Fifth graders should be able to:
Perform simple calculations, such as addition, subtraction, multiplication, and division of large numbers to
solve real-world problems involving one or two steps (addition: 3.8+1.01+2.1 Subtraction: 11.507-5.1=,
multiplication 765 X 326=, division 1762÷15)
3
Use exponents and order of operations (Exponents only with powers of 10 for example: 6.7 X 10 =6.7 X (10
X10 X10) = 6,700)

Order of operations= Solve inside Parentheses first, then solve Exponents, then complete Multiplication and
Division, and finally, complete any Addition and Subtraction

For example: 2(9+9) = first solve what is inside the parentheses 9+9=18 then multiply 18 by 2=36
Identify equivalent fractions and simplify fractions to lowest terms. (For Example, 3/9 is equivalent to 9/27 and
1/3 – the lowest term is 1/3)
Complete common unit conversions, such as inches to feet or minutes to hours.
Multiply and divide fractions to solve real-world problems (For example, Jan wanted to make a batch of cookies.
The recipe calls for ¼ of a cup of sugar for one batch. How much sugar does she need for half of a batch?)
Sixth graders should be able to:
Perform calculations, such as addition, subtraction, multiplication, and division of whole numbers, decimals,
and fractions to solve real-world problems that require multiple steps
Calculate the volume of prisms (rectangular) For example:
Calculate and apply the mean, median, mode, and range of data to answer real-world problems
Understand the comparisons made with a ratio and the 3 ways a ratio can be written

Comparisons can be written as: a part to a part, a part to a whole, a whole to a part

Examples of how to write a ratio: 3:4
OR 3 to 4
OR
Solve algebraic expressions (42÷7 + 4X for x=2 so 42÷7 + 4(2) use the order of operations to solve 42÷7 + 4X First
divide =42÷7 = 6 then multiple 4(2) =8 next add 6 + 8 = 14
Seventh graders should be able to:
Compare and order decimals, fractions and integers
Use positive and negative numbers to perform calculations (addition, subtraction, division, and
multiplication)
Solve expressions and/or equations to find an unknown value
Calculate area, perimeter, and volume of three-dimensional solids (cone, sphere, prism, pyramid, cube)
Identify angle relationships in a given problem (Angle relationships: complementary, supplementary, vertical,
alternate interior, alternate exterior angles) http://www.regentsprep.org/Regents/math/geometry/GP8/Lparallel.htm
the word INTERIOR means BETWEEN the lines.
- the word EXTERIOR means OUTSIDE the lines.
- the word ALTERNATE means "alternating sides" of the transversal.
Solve percent problems (tax, tip, markdown price)
Eighth graders should be able to:
Use rules to extend and analyze patterns
Use and write numbers in Scientific Notation (Use correct format and use exponent laws correctly)
Understands what a function represents and how to represent a function using function notation

(http://www.regentsprep.org/Regents/math/algtrig/ATP5/EvaluatingFunctions.htm)

Traditionally, functions are referred to by the letter name f, but f need not be the only letter used in function
names. The following are but a few of the notations that may be used to name a function: f (x), g(x), h(a),
A(t), ...

To evaluate a function, simply replace (substitute) the function's variable with the indicated number or
expression.

A function is represented by f (x) = 2x + 5. Find f (3).

To find f (3), replace the x-value with 3. f (3) = 2(3) + 5 = 11.
The answer, 11, is called the image of 3 under f (x).
Solve systems of equations using different methods (Substitution, Elimination, and Graphing)
2
2
Identify and use the Pythagorean Theorem with right triangles Pythagorean Theorem: a + b = c
2