Grade 3 UbD Math Unit Planning 2014 to 2015
PS 105
Grade/ Unit #/ Book(s)/Topic
Grade 3 / Unit 2 / Book 5 / Multiplication and Division
Approximate Days or Dates
35
Stage 1 - Identify Desired Results
Learning Outcomes
What relevant goals will this unit address?
(must come from curriculum; include specific Common Core standards)
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3.OA.1: Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example,
describe a context in which a total number of objects can be expressed as 5 × 7.
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3.OA.2: Interpret whole-number quotients of whole numbers, e.g., interpret 56 ✄ 8 as the number of objects in each share when 56 objects are
partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each.
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3.OA.3: Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement
quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
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3.OA.4: Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the
unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = � ÷ 3, 6 × 6 = ?.
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3.OA.5: Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known.
(Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30.
(Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 +
16 = 56. (Distributive property.)
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3.OA.6: Understand division as an unknown-factor problem.
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3.OA.7: Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8
× 5 = 40, one knows 40 × 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
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3.OA.9: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of
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.
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3.NBT.3: Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and
properties of operations.
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3.MBT.3: Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one-and two-step “how many
more” and “how many less” problems using information presented in scaled bar graphs.
Enduring Understandings
What understandings about the big ideas are desired? (what you want
students to understand & be able to use several years from now)
What misunderstandings are predictable?
Essential Questions
What is the Go Math Chapter Essential Questions?
Are there any potential cross-curricular connections during this chapter?
Students will understand that...
Essential Question:
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What are the best ways to learn our multiplication and division facts?
There are no general strategies for multiplying all single-digit
numbers (like there is for addition). Instead there are many patterns
and strategies that are dependent on the specific numbers.
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Some basic multiplication facts can be found by breaking apart the
unknown fact into known facts. Then the answers to the known facts
are combined to give the final value.
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Relationships can be described and generalizations made for
mathematical situations that have numbers that repeat in predictable
ways (for example, there are patterns in the products for
multiplication facts with factors of 0, 1, 2, 5, and 9). Another
example: since 40 is equal to 4 tens, 6 x 40 equals 6 groups of 4
tens, which equals 24 tens, which equals 240.
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Multiplication and division are inverse operations.
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Some real world problems involving joining equal groups or
separating equal groups can be solved using multiplication or division.
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There are a variety of ways to model division.
How can you use multiplication facts, place value, and properties to solve
multiplication problems?
What kind of real world problems can we solve with multiplication and
division?
Related misconceptions…
 Students may fail to interpret objects as a group.(Ex. shelves ,teams,
people etc.)
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Students sometimes only conceive of division as equal sharing.
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Students sometimes struggle to properly identify the total when given
a word problem.
Cross-curricular connections…
Knowledge:
What knowledge will student acquire as a result of this unit? This content
knowledge may come from the chapter’s goals, or might also address
pre-requisite knowledge that students will need for this unit.
Skills:
What skills will students acquire as a result of this unit? List the skills and/or
behaviors that students will be able to exhibit as a result of their work in this
unit.
Students will know...
Students will be able to…
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In Equal Group problems, one factor indicates the number of objects
per group and the other factor indicates the number of groups. In
the United States it is customary for the first number to indicate the
number of groups, e.g., 3 x 4 is used to mean 3 groups of 4.
In Array situations, the roles of the two factors do not differ. One
factor indicates the rows and the other the columns. But if the array
is rotated 90 degrees, the rows and columns are reversed.
Multiplication is commutative.
Multiplication is associative.
The identity property of multiplication.
Zero property of multiplication.
Division is represented by problem contexts in which the total is
known and either the number of groups or the number of objects in
each group is unknown.
That division facts can be found by thinking about multiplication
(i.e., fact families).
When 0 is divided by any non-zero number, the quotient is zero, and
0 cannot be a divisor.
Multiplication can be used to check the answer to a division problem.
When you divide whole numbers sometimes there is a remainder.
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Interpret multiplication situations of equal groups and arrays
(multiplicative comparison situations are introduced in grade four).
Use a variety of strategies to multiply basic facts (single digit by single
digit), beginning with skip counting, moving to more complex methods,
and culminating by the end of third grade with memorization.
Use the distributive property to multiply basic facts (e.g., 3 x 4 + 3 x 4 =
6 x 4).
Use number sense to solve missing factor problems (e.g., 7 x __ = 49).
Multiply single digit numbers by multiples of tens using place value
knowledge and other non-algorithmic strategies.
Construct simple pictograph. Read and interpret data in a pictograph.
Recognize both types of division situations in story problems (partitive
and measurement).
Use a variety of strategies to solve basic division facts.
Fluently solve division facts by the end of third grade.
Stage 2 – Assessment Evidence
Evidence
Through what evidence (work samples, observations, quizzes, tests,
journals or other means) will students demonstrate achievement of the
desired results? Formative and summative assessments used throughout
the unit to arrive at the outcomes.
Student Self-Assessment
How will students reflect upon or self-assess their learning?
Stage 3 – Learning Plan
#
Content Goal
Lesson Notes/Planned Differentiation
Book 5 Notes:
The first 3 investigations in this book (with the Common Core add ons)
serve as a fine introduction to multiplication, but in order to meet the
standard for multiplication fact fluency, intensive practice through math
centers (and/or at-home practice) will need to happen throughout the
year, especially after the test when there is less time pressure.
4
sessions
Investigation 1:
Things That Come in Groups
Works fine as written.
6
sessions
15
sessions
Investigations 2:
Skip Counting and 100 Charts
Investigation 3:
Arrays
10
sessions
Investigation 4:
Division
Works fine as written. Be sure to read the Math Note for session 2.6 on
page CC29 of the Common Core supplemental book.
Skip session 3.1a (do during the area unit instead). Skip session 3.5.
Add sessions 3.5a, 3.5b, and 3.7a (from Common Core add on lessons).
Most teachers find that having students make their own set of paper
array cards is too cumbersome, so this is optional (unless laminated
array cards are not available in your classroom). However, students
should each receive a set of paper multiplication cards.
Works fine as written. Be sure to read the Teaching Notes for sessions
4.2 and 4.4 on page CC29 of the Common Core supplemental book.
Additional Resources or Math
Centers
Supplement with EngageNY
Modules 1 and 3.
5 sessions have been added to
this investigation for
supplemental practice. Consider
using EngageNY Module 3.
3 sessions have been added for
supplemental practice. Consider
using EngageNY Module 3.
Post-Unit Reflection
Considerations
Comments
Required Areas of Study:
Was there alignment between outcomes, performance
assessment and learning experiences?
Adaptive Dimension:
Did I make purposeful adjustments to the curriculum
content (not outcomes), instructional practices, and/or
the learning environment to meet the learning needs and
diversities of all my students?
For struggling students:
For students who need a challenge:
Suggested Changes:
How would I do the unit differently next time?