The Sequence for Learning Number Combinations and Math Facts
As we move toward the end of the year, many parents have questions about math
fact acquisition. Here is an explanation of the progression of number
combination and math facts benchmarks in the 2011 Massachusetts Frameworks for
Mathematics.
Addition and Subtraction Facts
The sequence of learning addition and subtraction facts from memory begins in
kindergarten with developing an understanding of relationships between
numbers. Students in kindergarten and first grade spend time working with
numbers in concrete ways to develop fluency with numbers to twenty. Fluency
is the ability to use numbers efficiently and to figure out number
combinations quickly. A fluent student will use counting on, numbers in
groups, making ten, known combinations, and number composition (putting
numbers together) or decomposition (breaking numbers apart) to figure out a
number problem. Fluency is about working with understanding, not from memory,
and this understanding is the base for memorization of math facts. Our goal
is for children to have a deep understanding of numbers to 20 as they enter
second grade. By the end of Grade 2 students are expected to know from memory
the sums of two one-digit numbers and the related subtraction facts.
Multiplication and Division
In Grade 2 students begin working with arrays as equal addend problems and
looking at rectangles partitioned into same size rows and columns. This is
the groundwork for the multiplication and division work students will do in
Grade 3.
By the end of Grade 3 students are expected to know from memory the products
of two one-digit numbers. In Grade 3 considerable time is spent developing an
understanding of multiplication and division as equal groups, arrays, and in
measurement quantities. Students memorize multiplication math facts but are
expected to have an understanding of the meaning of multiplication and
division as they do this. This work is the basis for use of factors and
multiples in Grades 4 and 5.
Online Activities
Okta's Rescue
Grades K and up
Rescue the oktas! Can you find groups to add up? Can you do this without
counting by 1's?
Play Okta's Rescue
Five Frames
Grades K and up
Use 5's to solve the problems. Try to count in groups.
Play 5 Frame
How Many Under the Shell?
Grades K and up
Okta is hiding some bubbles. Can you figure out how many are under his shell?
Play How Many Under the Shell
Grades K and up
Use tens to solve the problems. Do the tens help you? Do you need to count?
Play Ten Frames
Krypto
Grades 2 and up
Use your knowledge of math facts and operations to get to the target number.
Like Name That Number, the game you play in school, except you have to use all
5 cards every time. Can you meet the challenge?
Play Krypto
Deep Sea Duel
Grades 2 and up
Can you beat Okta in this game of addition wits? Give it a try.
Play Deep Sea Duel
Pan Balance
Grades 3 and up
How can your knowledge of facts help you balance the pans? Can you create
equivalent equations?
Play Pan Balance
The Factor Game
Grade 4 and 5
This is a game for practicing factors. You can play against the computer or
against another person.
Play The Factor Game
The Product Game
Grade 4 and 5.
This is a game for practicing products. You will need a partner to play.
Play The Product Game
If you have a comment on a game on this page or a question, email Julia
Hendrix, Elementary Mathematics Specialist, at jhendrix@sch.ci.lexington.ma.us