Grade: Third
Essential Question
How does understanding
multiplication help solve division
problems?
What is the relationship between
multiplication and division?
Lesson 5: Understand How Multiplication and
Division Are Connected
Standard: 3.OA.B.6
Understand division as an
unknown-factor problem. For
example, find 32 ÷ 8 by finding
the number that makes 32 when
multiplied by 8.
Math Practices: 2, 6
Vocabulary
array
divide
dividend
divisor
quotient
factor
product
unknown
Big Idea
Multiplication and division have an
inverse relationship, and this
relationship can be used to find the
solution to an unknown-factor
problem.
Task Arc: Multiplication and
Division within 100
Task 2: Soccer Goals
Number Talks
Books by Sherry Parrish:
Third Grade Classroom pp.316-323
Student Thinking & Number Talks in
the 3-5 Classroom pp.157-286
Find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.
This standard refers the Glossary on page 89, Table 2 (table also included at
the end of this document for your convenience) and the various problem
structures. Since multiplication and division are inverse operations, students
are expected to solve problems and explain their processes of solving
division problems that can also be represented as unknown factor
multiplication problems.
Example: A student knows that 2 x 9 = 18. How can they use that fact to
determine the answer to the following question: 18 people are divided into
pairs in P.E. class? How many pairs are there? Write a division equation
and explain your reasoning.
Multiplication and division are inverse operations and that understanding
can be used to find the unknown. Fact family triangles demonstrate the
inverse operations of multiplication and division by showing the two factors
and how those factors relate to the product and/or quotient.
https://learnzillion.com/resources/72938-understand-division-as-unknown-factorproblems-3-oa-b-6
Illustrative Math: none
Week: 8
Learning Targets
•
Students should be able to
interchangeably use various related
equations to solve for an unknown in any
position.
•
Students should be able to use,
model and/or describe various
multiplication strategies (equal groups,
arrays, skip counting, known multiplication
facts) to solve for an unknown in any
position.
Strategies:
 Draw Pictures
 Draw Arrays
 Write Equation
3-Acts: none
Activities
Name My Array
Have students work in pairs. Each
partner has one minute to draw a
simple array on a separate sheet of
paper. Partners exchange papers and
label their partners array with a
corresponding multiplication and
division equation. Have partners
share with the whole group.
Games
Card Game

http://www.k5mathteachingresources.com/supportfiles/division-as-an-unknown-factor-gamever.2.pdf


Books
Divide and Ride Stuart
Murphy
How Many Ways Can
You Cut a Pie
The Multiplying
Menace Divides
Additional Support
https://www.khanacademy.org/commo
ncore/grade-3-OA
http://www.readtennessee.org/math/te
achers/k3_common_core_math_standards/thir
d_grade/operations_algebraic_thinkin
g/3oab6.aspx
Fact Flash
Using a document camera, flash a
multiplication equation on the screen
for 5 seconds such as 3 X 4 = 12.
Have students tell the corresponding
division equation. In the example
above, 12 ÷ 3 = 4 or 12 ÷ 4 = 3Have
students explain how they got their
answer.Repeat with other examples.
Contributors: Quinena Bell, Kimberly Osburne, Christa Campbell, Misty Dobbs, Sia Phillips, Caleb Jones, Stephanie Turner
Name: ________________________________________________________
Ayne has 10 app folders on her ipad. Each app folder
has 6 apps. How many apps does she have in all?
Date: _______________________________
Round 8,409 to the nearest
6,111 – 84 = ___
ten___________
hundred ________________
3 x 5 = ____
3 x 50 = ____
4 x 5 = ____
4 x 50 = ____
4 x 500 = _____
9 in
4 in
___ inches squared
Area = length x width
Area = length + length + width + width
Billy Bob has 18 balloons. He gives 6 to Sam.
Trish gives Billy Bob 12 more balloons. How
many balloons does Billy Bob have now?
1, 672 + 845 = ____
_____ balloons
4 + 4 + 4 + 4 = ______
Write a multiplication sentence for the repeated
addition shown above.
What is the fact family of 4,7,28?
___ x ____= ___
___ x ____= ___
___ ÷____= ___
___ ÷____= ___
____ x ____ = ____
AUTHOR: HANNELORE DICKERSON
8