Computational
Fluency
Grades 2 and 3
What is fluency?
The NCTM Principle and Standards of
School Mathematics (2000) defines
computational fluency as having efficient,
flexible and accurate
methods for computing.
The first step in achieving computational
fluency with larger numbers is an
understanding of numbers, their
relationships, and their composition.
Understanding versus Memorization
Children need to understand what it means
to add and subtract before facts can become
automatic
 They need to also understand how they are
connected
 Understanding is necessary but not sufficient
 When isolated additions and subtractions
are practiced, the emphasis is on recalling
the answers
 Teaching facts for automaticity relies on
thinking

Grade Level Expectations
By the end of second grade students are
expected to fluently:

add and subtract within 20 using mental
strategies (know from memory all sums of 2
one-digit numbers)

add and subtract within 100 using strategies
based on place value, properties of
operations, and/or relationship between
addition and subtraction
Grade Level Expectations
By the end of third grade students are
expected to fluently:

add and subtract within 1000 using strategies
based on place value, properties of
operations, and/or relationship between
addition and subtraction

multiply and divide within 100 (know single
digit products from memory)
Grade 2 Big Ideas

Addition and subtraction are used to
represent and solve many different kinds
of problems.

The properties of addition along with
place value provide the basis for our
understanding of each procedure.
Common Counting Strategies

Count all
1, 2,
3, 4, 5, 6, 7
 Count on from the first number
2,
3, 4, 5, 6, 7
 Count on from the larger number
6, 7
5
Common Addition Strategies
Counting on 1, 2, 3, and 0
 Doubling:

3+3=6

Complements of 10/ Ten Buddies
0 + 10 = 10
2 + 8 = 10
1 + 9 = 10
3 + 7 = 10
Common Addition Strategies

Near doubles:
6 + 7 = (6 + 6) + 1 or (7 + 7) – 1

Using the commutative property:
5+3=3+5
Common Addition Strategies

Using the associative property:
5 + 6 + 4 = (5 + 6) + 4
= 5 + (6 + 4)
From Single to Double Digit
Addition (with multiples of 10)

Count all (10, 20,30,…)
Counting on by tens from 50 (60, 70, 80)
*Applying the knowledge of the basic facts.
5 tens + 3 tens = 8 tens
50
+ 30
= 80

From Single to Double Digit
Subtraction
53 – 20



We start with 53, take 2 tens away and count all
that is left. (10, 20, 30, 31, 32, 33)
We might begin counting back as we take the rods
away. (43, 33)
We can apply our basic facts:
5 tens – 2 tens = 3 tens
So 53 – 20 = 33
Adding Ones with Regrouping
58 + 6

Counting on: I am going to count from the bigger
number.
64
60

62
58 59 61 63
Make Ten: I can make a ten from the 8 in 58 and the 2
from 6.
Adding Ones with Regrouping

Make Ten using Number Bonds:
58 + 6 = 60 + 4
50 8 2 4

Make Ten using the Number Line:
You try it: How would you solve?
197 + 18
Grade 3 Big Ideas

Multiplication is a fundamental operation
that is used to solve everyday problems.

Multiplication has been described as
rectangular array, repeated addition, and
area.

There are patterns and relationships in
multiplication facts and multiplication and
division are related.
Common Multiplication Strategies
I can use a multiplication fact I know, to figure out one I don’t…
Using the commutative property:
2x4=4x2
4 groups of 2
2 groups of 4

Common Multiplication Strategies

Doubling: 2 x (3 x 6) = 6 x 6
3 groups of 6 doubled
Common Multiplication Strategies

Halving and doubling: 4 x 3 = 2 x 6
4 groups of 3
2 groups of 6
Common Multiplication Strategies
Using the distributive property: 6 x 4 =
(5 x 4) + (1 x 4) = 20 + 4 = 24

Common Multiplication Strategies
Using the distributive property: 6 x 4 =
(5 x 4) + (1 x 4) = 20 + 4 = 24
Number bond

You try it: Use the distributive
property to figure out:
7x3

with an array

with a number bond
Common Multiplication Strategies
Using the distributive property with tens:
9 x 4 = (10 x 4) – 4

Part/Whole relationships
A guitar has 6 strings. How many strings are
there on 3 guitars? Write a multiplication
sentence to solve.
Great Websites for Math Practice
sheppardsoftware.com/math.htm
 topmarks.co.uk/maths-games/
 Arcademicskillbuilders.com/games
 FactMonster.com/math/flashcards.html
 Multiplication.com
 IXL.com
 k-5mathteachingresources.com/
