3rd Grade Unit LUES Clues
Dear Parents/Guardians:
Third grade has started a new unit. We hope you find this information
useful when helping your student at home. 
Subject
Unit
SOL
Objective
Math
Fact Families (addition and subtraction)
Identity and Commutative Property
3.2, 3.20
3.2
 Use the inverse relationships between
addition/subtraction to solve related basic fact
sentences. For example, 5 + 3 = 8 and 8 – 3 = __.
 Write three related basic fact sentences when given
one basic fact sentence for addition/subtraction. For
example, given 3 + 2 = 5, solve the related facts __+ 3 =
5.
3.20
 Recognize that the commutative property for addition
is an order property. Changing the order of the addends
does not change the sum (5 + 4 = 9 and 4 + 5 = 9).
 Investigate the identity property for addition and
determine that when the number zero is added to
another number or another number is added to the
number zero, that number remains unchanged.
Examples of the identity property for addition are 0 + 2
= 2; 5 + 0 = 5.
 Identify examples of the identity property for addition.
Important
Vocabulary
Inverse relationship
Number sentence
Related facts
Addend
Sum
Property
Identity property
Commutative property
Equal
Strategies
and
Examples
Opposite operations
A group of numbers that includes a mathematical
operation (addition, subtraction, multiplication, or
division), along with either an inequality (< or >) or
an equal sign. And just like a written sentence, it
tells a fact. For example, 1 + 1 = 2.
Facts that are related in some way.
A number that is added to another number
Answer to an addition problem
Relationships that are always true in mathematical
operations.
The sum of 0 and any number is the same number.
8+0=8
You can add numbers in any order and the answer
will always be the same.
Same in number or amount, having the same
mathematical value
For a given set of numbers, there are relationships that are always true called
properties. In third grade we focus on two properties of addition: Identity and
commutative.
Identity Property of addition: The sum of zero and any number is that same
number. Example: 2+0=2
Commutative Property of Addition (order property): You can add numbers in any
order and the sum will be the same.
Example: 6+4=10, 4+6=10
6 + 4 = 10
4 + 6 = 10
To reinforce this concept, have students have students use house hold item such
as macaroni. They can show a group of 6 macaroni and a group of 4 macaroni
then add the groups to get 10. Then have your child write the fact (4+6=10). Have
them switch the groups and write the new fact (6+4=10).
Inverse relationship: There is an inverse relationship between addition and
subtraction. If a math fact is considered, for example 3 + 7 = 10. Then the
following are also true:
10 - 3 = 7
10 - 7 = 3
Similar relationships exist for subtraction, for example if 10 - 3 = 7. Then the
following are also true:
3 + 7 = 10
7 + 3 = 10
Addition and subtraction facts are inverse operations because they are opposite.
Generally, subtraction facts are harder for children to learn than addition facts. If
a child knows that 6 + 9 = 15, and he or she sees the subtraction sentence 15 – 9 =
__, the child can think, 9 added to __?__ equals 15? This use of thinking of the
related addition fact when children encounter a subtraction fact they don't know
should be encouraged. Children often find themselves either counting up or
counting back to solve subtraction. If children learn the important inverse
relationship between addition and subtraction, subtraction facts will become
much easier.
Related Facts
For every addition fact, there is a related subtraction fact. Related facts are
addition and/or subtraction number sentences that are alike in some way.
For Example: 3+2=5 and 5-2=3
These number sentences are related because they both have
3, 2, and 5 in them. Knowing the answer to a number sentence will help you
quickly figure out the answer to all related facts.
Fact Family
A Fact Family is a collection of related addition and subtraction facts, or
multiplication and division facts, made from the same numbers.
There can only be three numbers in every family, and the operations that are
performed on them are related to each other.
Example: The fact family for 3, 6, 9
3+6=9
6+3=9
9-3=6
9-6=3
Have students use a fact family house to show their facts. They
can draw a triangle roof with the 3 numbers. Then draw a square
to show the rest of the house a write the facts in the square.
Sincerely,
The Third Grade Team