Grade 4 UbD Math Unit Planning 2014 to 2015
PS 105
Unit #/Book/Topic
Unit 4b/Book 6/Fraction Operations
Approximate Days or Dates
25
Stage 1 - Identify Desired Results
Learning Outcomes
What relevant goals will this unit address?
(must come from curriculum; include specific Common Core standards)
4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
4.NF.3a Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
4.NF.3b Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an
equation. Justify decompositions, e.g., by using a visual fraction model.
4.NF.3c Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by
using properties of operations and the relationship between addition and subtraction.
4.NF.3d Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by
using visual fraction models and equations to represent the problem.
4.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
4.NF.4a Understand a fraction a/b as a multiple of 1/b.
4.NF.4b Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number.
4.NF.4c Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to
represent the problem.
Represent and interpret data
4.MD.B.4: Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction
of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and
shortest specimens in an insect collection.
**Note: Multiplying a fraction by a whole number is the same as repeated addition of fractions, so treat it that way. For example, 3 x ¾
= ¾ + ¾ + ¾ = 9/4. Do NOT use an algorithm and do NOT have students write 3 as 3/1.
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:
 The meaning of addition and subtraction are the same for fractions as
they are for whole numbers.
 Any whole number, mixed number, or fraction can be decomposed into
the sum of its unit fractions.
 Fractions can be composed or decomposed into unit fractions where the
denominators are the same.
 When fractions are composed or decomposed, the result may be a mixed
number, which is composed of whole number and a fraction.
 Mixed numbers lie between whole numbers on a number line.
 The meaning of multiplication can be extended and applied to the
multiplication of a fractions or a mixed number by a whole number.

How is adding, subtracting, and multiplying with fractions similar and
different from adding, subtracting, and multiplying with whole
numbers?
Cross-curricular connections…
Related misconceptions…
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…
o
o
o
o
o

Which forms of fractions are most useful in problem solving (e.g.,
mixed number vs. improper fraction, equivalent fraction).
That a mixed number has an equivalent improper fraction and vice
versa.
Why the denominator stays the same when combining fractions or
multiplying a fraction by a whole number.
How to justify composition and decomposition of fractions using
models when adding, subtracting, or multiplying by a whole number.
How to explain solutions to problems that includes fractions.
Academic vocabulary – unit fraction, mixed number, improper
fraction, proper fraction, equivalent fractions.






Convert mixed numbers to improper fractions and improper fractions to
mixed numbers.
Relate decomposition and composition of fractions and mixed numbers to
visual models.
Create visual models to show the addition and subtraction of fractions
and mixed numbers with like denominators.
Solve addition and subtraction problems that include fractions and
writing equations to represent them.
Create visual models to show the multiplication of a fraction or a mixed
number by a whole number.
Solve problems that include the multiplication of a fraction or a mixed
number by a whole number and writing equations to represent them.
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
#
CGI-6
Content Goal
Lesson Notes/Planned Differentiation
Multiple Groups Problems
Just as the CGI Equal Sharing problems served as the conceptual foundation
for exploring equivalent fractions, the CGI Multiple Groups problems will serve
as the foundation for adding and multiplying with fractions.
Spend five days working on these problems from the CGI book. Focus the
sharing of student work each day on the ideas in 4.NF.3 and 4.NF.4.
Since the CGI approach is new to the students, start with some “Third Grade”
problems like, “There are three children in my family and each one eats ¼ of
a pizza. What fraction of the pizza did they eat together?”
CGI-7
Multiple Groups Problems
CGI-8
CGI-9
Multiple Groups Problems
Multiple Groups Problems
CGI-10
Multiple Groups Problems
General Notes on Using
EngageNY Modules
Try problems with several groups of non-unit fractions like ¾ and 2/3 today.
Do students realize that 4 groups of ¾, for example, are 12/4 and that 12/4
is equal to 3 wholes?
When students are ready, give them multiple groups of mixed numbers too.
By the fourth day, you can introduce the division version of these problems,
but warn students to read the problems carefully. They often don’t notice the
difference.
Page 67 of the CGI book shows how to use bare equations to work on these
ideas. As you conclude the CGI multiple groups problems today, think about
using one or two bare equations as a warm up problem for the rest of this
unit.
All lessons start with Fluency Practice. This is OPTIONAL. Do any parts of the
Fluency Practice you feel would benefit your students, but be sure to stick to
the suggested times. It is meant to be fast. You can do Fluency Practice for
your ten-minute math or you can continue doing ten-minute math routines
from Investigations.
Next the lessons include Application Practice, which is like a Problem of the
Day. These should also be considered OPTIONAL.
4
sessions
4
Engage NY Module 5
Topic D
Engage NY Module 5
Next is the main lesson, which is called Concept Development. This includes
the mini-lesson and a problem set for the students. (There is also a
homework that matches the problem set closely and an optional exit ticket.)
Sometimes the mini-lesson is longer than the problem set and involves a
great deal of teacher guided practice. Feel free to adjust the lesson plan to
your needs. For example, you could split the class in half and do Concept
Development with half the class while the other half works on some center
activities to review previously taught skills, build fluency, or problem solving.
This would be a great way to differentiate instruction during this unit.
Lessons 16 through 19 only.
Lessons 22 through 25 only.
Additional Resources or Math
Centers
CGI book, chapter 3 (see pages
69-71 for advice on problem
selection)
sessions
6
sessions
3
sessions
Extra
Test
Topic E
Engage NY Module 5
Topic F
Investigations: 3A.1 to
3A.3 (Multiplying a whole
number by a fraction.)
Mixed story problems
with fractions
Unit Test
Lessons 29 through 34.
Even though students were exposed to this during the CGI week, it is a bit
tricky so take a few days to work through it.
Spend about two days on this, depending on how it is going. Students may
find that pretending the numbers in the problem are whole numbers makes it
easier to determine the operation they need to use.
http://www.k5mathteachingresources.com/supp
ort-files/fraction-word-problemslike-denominator.pdf
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?