NVACS: Operations and Algebraic Thinking
Addition, Subtraction, Multiplication, and Division
Concept Overview for 4th Graders
4.OA.1
Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 X 7 as a statement that 35 is 5
times as many as 7 as 7 times as many as 5. Represent verbal statements of multiplicative comparisons
as multiplication equations.
4.OA.2
Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings
and equations with symbols for the unknown number to represent the problem, distinguish
multiplicative comparison from additive comparison.
4.OA.3
Solve multistep word problems posed with whole numbers and having while-numbers answers using the
four operations, including problems in which remainders must be interpreted. Represent these
problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of
answers using mental computation and estimation strategies.
4.OA.4
Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple
of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or
composite.
4.OA.4
Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern
that were not explicit in the rule itself.
In grade 3-5 students need to develop a stronger understanding of the various meanings of different
types of multiplication and division problems. These are called Problem Situations. Using algebraic
reasoning in grades 3-5 prepares students for algebra in middle school.
Different Problem Situations for Multiplication and Division
❏ Multiplication Equal Grouping Problems: One factor tells the number of things in a group and
the other factor tells the number of equal sized groups.
RPDP.net
Some of the examples in the concept overview were modified and used from the North Carolina Unpacking Document.
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NVACS: Operations and Algebraic Thinking
Addition, Subtraction, Multiplication, and Division
Concept Overview for 4th Graders
❏ Array Problems: This type of problem is often known as an area problem. In an array problem
the role of the factors is interchangeable.
❏ Multiplicative Comparison: One number identifies the quantity in one group or set while the
other number is the comparison factor.
❏ Division Equal Group Problems:
❏ Quotative Division: Sometimes referred to as repeated subtraction, the number of
objects in each group is known, but the number of groups is unknown.
❏ Partitive Division: Dividing a set into a predetermined number of groups
Examples of Different Problem Situations for Multiplication and Division
❏ Multiplication Equal Grouping Problems:
I have 5 friends that need 4 cookies each.
How many cookies to I need to bake? 5 x 4 = 20
❏ Array Problems:
How many desks would there be in the classroom if I had 6 rows of 7 desks. 6 x 7 = 35
❏ Multiplicative Comparison:
Jill wrote ten pages for the group assignment. Sara wrote 5 times as many. How many
pages did Sara write?
RPDP.net
Some of the examples in the concept overview were modified and used from the North Carolina Unpacking Document.
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NVACS: Operations and Algebraic Thinking
Addition, Subtraction, Multiplication, and Division
Concept Overview for 4th Graders
❏ Division Equal Group Problems:
Quotative Division:
I have 30 popsicles and I want to give 5 to each person. How many people will get
popsicles?
Partitive Division:
Mark has 24 apples. He wants to share equally among his 4 friends. How many apples
will each friend receive?
Letter representing an unknown quantity
In earlier grades students solved open sentences with boxes for the unknown or missing
value. In the upper grades of elementary students need to transition to variables from
the use of boxes. 5 + n = 12. In elementary school students should use relational
thinking to find the value of the variable. Context (story problems) can help students
develop the meaning of variables.
David ate 23 grapes and Sue ate some, too. The container of grapes had 51 and they
were all gone! How many did Sue eat? 23 + g = 51 or 51 - 21 = g
Estimation
Students need to determine when estimation is appropriate, what the level of accuracy
is needed, selecting the appropriate method of estimation, and verifying solutions or
determining the reasonableness of situations using various estimation strategies.
RPDP.net
Some of the examples in the concept overview were modified and used from the North Carolina Unpacking Document.
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NVACS: Operations and Algebraic Thinking
Addition, Subtraction, Multiplication, and Division
Concept Overview for 4th Graders
Interpreting Remainders
Students need to understand that a remainder in a division problem can have different meaning based
on the context of the problem.
Examples of word problems to show interpreting remainders for 44 ÷6 = p
❏ Remain as a left over
Maria had 44 pencils. Six pencils fit into each of her pencil pouches. How many pouches
could she fill and how many pencils would she have left? 44 ÷6 = p; p = 7 r. 2, Maria can
fill 7 pouches with 2 left over.
Answer: 7 R. 2
❏ Partitioned into fractions or decimals
Maria had 44 pencils and put 6 pencils in each pouch. What fraction represents the
2
number of pouches that Mary filled? 44 ÷6 = p = 7 6
Answer: 7
2
6
❏ Discard leaving only the whole number answer
Maria had 44 pencils. Six pencils fit into each of her pencil pouches. How many pouches
did she fill? 44 ÷6 = p; p = 7 R. 2, Maria can fill 7 pouches completely.
Answer: 7
❏ Increase the whole number answer up one
Maria has 44 pencils. Six pencils fit into each of her pencil pouches. What would be
the fewest number of pouches she would need in order to hold all of her pencils? 44 ÷6
= p; p = 7 R. 2; Maria needs 8 pouches to hold all the pencils.
Answer: 8
❏ Round to the nearest whole number for an approximate result
Maria had 44 pencils. She divided them equally among her friends before giving one of
the leftovers to each of her friends. How many pencils could her friends have received?
44 ÷6 = p; p = 7 R. 2; some of her friends received 7 pencils and some of her friends
received 8.
Answer: 7 or 8
Prime
RPDP.net
Some of the examples in the concept overview were modified and used from the North Carolina Unpacking Document.
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NVACS: Operations and Algebraic Thinking
Addition, Subtraction, Multiplication, and Division
Concept Overview for 4th Graders
Prime numbers have exactly 2 factors, the number one and their own number.
Example: 17, Factors of 17 are 1 and 17.
Composite
Composite numbers have more than 2 factors.
Example: 24, Factors of 24 are 1,2,3,4,6,8,12,24.
Factor
Are numbers you multiply together to find the product.
Example: 2 x 3 = 6, two and three are factors of 6.
Factor Pairs
The factor pairs are the two numbers you multiply together to find the product.
Example: Factor pairs for 96 are, 1 and 96, 2 and 48, 3 and 32, 4 and 24, 6 and 16, 8 and
12
Generate a number or shape pattern that follows a given rule. Identify apparent features of the
pattern that were not explicit.
Number Pattern
1, 4,9,16,25
Shape Pattern
Rule
Each number in the pattern can be described by
multiplying the number of the pattern sequence
by itself. For the 5th shape in the pattern you
multiply 5 by 5 and the answer is 25.
n x n = 25. n= the number in the sequence.
Features
The numbers in this pattern can be used to build
arrays that are squares. The dimensions in the
pattern match the number of the pattern in the
RPDP.net
Some of the examples in the concept overview were modified and used from the North Carolina Unpacking Document.
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NVACS: Operations and Algebraic Thinking
Addition, Subtraction, Multiplication, and Division
Concept Overview for 4th Graders
sequence. The 3rd shape in the pattern has 3 as
the dimension.
RPDP.net
Some of the examples in the concept overview were modified and used from the North Carolina Unpacking Document.
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