Download 3.OA_.B.61

3.OA.B.6
*This standard is part of a major cluster
Standard
Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by
finding the number that makes 32 when multiplied by 8.
Standard Unpacked
This standard refers to various problem structures (table included at the end of this
document) 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.
Example:
Sarah did not know the answer to 63 divided by 7. Are each of the following was an
appropriate way for Sarah to think about the problem? Explain why or why not with a
picture or words for each one.
Multiplication and division are inverse operations. They both involve a number of
groups, a number in each group and a total number. In multiplication, both the number
in each group are usually known, but the total number needs to be found. With division,
either the number of groups or the number in each group and the total number are
usually known. The unknown number needs to be found. A table of multiplication facts
can be used to find division facts. One of the major strategies for division facts is Think
Multiplication.
The language in the array examples shows the easiest form of array problems. A harder
form is to use the terms rows and columns: The apples in the grocery window are in 3
rows and 6 columns. How many apples are in there? Both forms are valuable.
3rd Grade Mathematics ● Unpacked Content Page 48
Area involves arrays of squares that have been pushed together so that there are no
gaps or overlaps, so array problems include these especially important measurement
situations.
Domain: Speaking
Questions/ Activities to check for understanding and increase rigor:
 Jahyden was sharing his candy with his friends. He shared 32 pieces of candy.
How many friends could he have shared the candy with? Explain your
thinking.
 Danielle has 48 lollipops to share with her friends. If she has 6 friends, how
many lollipops would each friend get? If she has 8 friends, how many
lollipops would each friend get? Why does the number of lollipops change
based on the number of her friends?
 Explain how you can use multiplication to solve a division problem. Use
models, drawings and/or examples to support your answer.
 Rachel says that if you know 4 x 6 = 24, then you know what n equals in 24 ÷
n = 6. Why is she correct?
 Use the numbers 5, 6, and 30 to write a multiplication story. Write a related
division story.
Level 1
Entering
Explain
division as an
unknownfactor
problem
using key
words to
teacher.
Level 2
Emerging
Explain
division as an
unknownfactor
problem
using key
phrases to a
partner.
Level 3
Developing
Explain
division as an
unknownfactor
problem using
simple
sentences
with sentence
frames in a
cooperative
group.
Level 4
Expanding
Explain
division as an
unknown
factor
problem
using complex
sentences in a
cooperative
group.
Level 5
Bridging
Explain
division as an
unknown
factor problem
using a variety
of simple &
complex
sentences that
justify their
thinking
independently.
ELD Standard #3: English Language Learners communicate information, ideas,
and concepts necessary for academic success in the content area of
Mathematics.