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Standard: MACC.3.OA.4.9
Depth of Knowledge
Identify arithmetic patterns (including patterns in the addition
Level 3: Strategic Thinking
table or multiplication table), and explain them using properties of & Complex Reasoning
operations. For example, observe that 4 times a number is always
even, and explain why 4 times a number can be decomposed into
two equal addends.
Content Limits/Clarifications:
Sample Test Item
This standard calls for students to examine arithmetic
Ralph loves to look for patterns in numbers.
patterns involving both addition and multiplication.
One day, he was looking at a multiplication
Arithmetic patterns are patterns that change by the same
chart and noticed that the product of 5 times
rate, such as adding the same number. For example, the
series 2, 4, 6, 8, 10 is an arithmetic pattern that increases an odd number always has 5 ones (5, 15, 25,
35, etc.) and the product of 5 times an even
by 2 between each term. This standard also mentions
identifying patterns related to the properties of
number always has zero ones (10, 20, 30, 40,
operations. Using a multiplication table, highlight a row
etc.). He made some arrays to help him figure
of numbers and ask students what they notice about the
out the pattern.
highlighted numbers.
Explain a pattern using properties of operations.
When (commutative property) one changes the order of
the factors they will still gets the same product, example
6 x 5 = 30 and 5 x 6 = 30.
Teacher: What pattern do you notice when 2, 4, 6, 8, or
10 are multiplied by any number (even or odd)?
Student: The product will always be an even number.
Teacher: Why?
In an addition table ask what patterns they notice? Explain
why the pattern works this way?
Students need ample opportunities to observe and identify
important numerical patterns related to operations. They
should build on their previous experiences with properties
related to addition and subtraction. Students investigate
addition and multiplication tables in search of patterns
and explain why these patterns make sense
mathematically. Students also investigate a hundreds
chart in search of addition and subtraction patterns. They
record and organize all the different possible sums of a
number and explain why the pattern makes sense.
Ideas to Support MACC.3.OA.4.9
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The use of manipulatives is useful for practice with
this skill. Such activities allow students to create their
own patterns and then express their creations with a
numeric sentence. For example, students can
highlight all of the even numbers on a 100s chart.
They can then express the pattern as "plus 2" to go
from one highlighted number to the next. 2 + 2 = 4,
and 4 + 2 = 6, etc. Similarly, students can highlight all
of the multiples of 10, and express these as a "plus 10"
rule. They could show that 10 + 10 = 20, and 20 + 10 =
30, and all extensions of these equations will
correspond with the highlighted numbers on the 100s
chart.
Using a multiplication table, students can look for all
of the occurrences of a given number, say 24, and
then express 24 as multiplication expressions that are
all equivalent. 24 = 6 x 4 = 4 x 6 = 8 x 3 = 3 x 8.
Teachers need to guide students’ interpretation of
patterns they encounter into numeric sentences.
Explain the pattern that Ralph found.
On Monday morning the baker baked 4 full trays
of cookies to sell in his shop. Each tray had the
same number of cookies on it. Here is what the
trays looked like on Monday evening.
a. How many cookies did the baker sell on
Monday? Show how to use multiplication
equations and other operations, if needed,
to show how you solved the problem. Refer
to the trays of cookies in your explanation.
b. Use words or equations to explain how you
know your total is correct.
Connections:
SMPs to be Emphasized
MP1- Make sense of problems and persevere in
solving them.
MP2- Reason abstractly and quantitatively.
MP3- Construct viable arguments and critique the
reasoning of others.
MP6- Attend to precision.
MP7- Look for and make use of structure.
Critical Area
 Critical Area #1: Developing understanding of
multiplication and division and strategies for
multiplication and division within 100.
3rd Grade Related Standards:
 MACC.3.OA.4.8
Foundational Skills for 4th Grade:
 Use the four operations with whole numbers to
solve problems.
FCAT 2.0 Connections:
Related NGSSS Standard(s)
MA.3.A.4.1- Create, analyze, and represent
patterns and relationships using words,
variables, tables, and graphs.
FCAT 2.0 Test Item Specification
Benchmark Clarification:
 Students may extend numeric or graphic patterns
beyond the next step, or find one or more
missing elements in a numeric or graphic pattern.
 Students will identify the rule for a pattern or the
relationship between numbers.
Content Limits:
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Common Misconceptions:
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None listed.
Items may use numeric patterns, graphic patterns,
function tables, or graphs (bar graphs, pictographs, or
line plots only).
Numeric patterns should be shown with three or more
elements.
Graphic patterns should be shown with three or more
examples of the pattern repeated.
Students should not be asked to extend the pattern
more than three steps beyond what is given or to
provide more than three missing elements.
Items will not include extending the pattern on a bar
graph or pictograph.
Rules for numeric patterns and relationships shown in
function tables must include only one operation limited
to addition, subtraction, or multiplication. Patterns or
relationships involving multiplication are limited to the
multiplication facts of 0 X 0 through 9 X 9.
Function rules or relationships may be described
using words, tables, graphs, or expressions using
variables or geometric shapes (e.g., n, , ∆ );
however, the intent of the benchmark is not to assess
solving equations.