1. science
2. mathematics
3. algebra

Suggestions for Pacing
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Grade 4
The following is a suggested list of ways to adjust lessons that may support the completion of the Grade
4 modules of A Story of Units in the number of instructional days allotted by an annual schedule. Please
review these suggestions completely since some of the later recommendations impact instruction earlier
in the school year. Also, see the Appendix “Planning a Shorter Lesson” intended to empower the teacher
to more readily complete “one lesson in one day.”
Module 1
1. Omit L17. The problems from this lesson may be embedded in Topic E as extensions. Note: The
Additive comparison problem types in L17 involve subtraction, so be careful not to use them in
Topic D. (Chart excerpted from OA Progression pg. 7 http://ime.math.arizona.edu/progressions/)
2.Omit L19.
Module 2
1. Please do not omit any lessons!! Student success with M3 depends upon fluency with the
manipulation of place value units, which both M1 and M2 effectively set the foundation for.
Teachers who have taught M2 prior to M3 have reportedly moved through M3 more efficiently
than colleagues who omitted it. M2 is also setting the foundation for work with fractions and
mixed numbers in M5.
Module 3
1. It appears Topic A of Module 3 is particularly challenging to do in 3 days, especially L1.
2.L1: To reduce the time needed for this lesson, start area and perimeter fluencies in M2 L1
**
M2 L1 Replace “Convert Units” with a Perimeter fluency. – Draw varied polygons and label
the length of each side. Ask students to find the perimeters.
**
M2 L2 Replace “Convert Units” with “Find the Area” – Draw rectangles with square units.
Ask for the length and width. Ask for the number of square units. Ask for the multiplication
sentence. Erase the grids and write the measures of the dimensions and repeat the questions.
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**
M2 L3 Replace “Convert Units” with “Find the Area and Perimeter.” From M2 L4
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M2 L4 Replace “Find Area and Perimeter” with Problem 1 from M3 L1.
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M2 L5 Replace “Convert Units” with Problem 1 from M3 L1 with a more advance sequence
than used in M2 L4.
**
Therefore, Omit M3’s L1’s Problem 1 of the Concept Development (Done in M2 L4 and 5)
**
Omit Problem 4 in the M3 L1 Concept Development and use it for a center activity.
3. L8: Omit drawing the models in Problem 2. Rather, have the students think about what they
would draw, imagine, visualize. Omit drawing on Problem 2 of the Problem Set. Omit the
alternate drawing of Problem 4. Instead, use it as necessary for students to understand when
there are many re-namings.
4.Omit L10.
5. Omit L19.
6.Omit L21.
7. Omit L31. Embed analysis of division situations throughout later lessons. See the chart below
for the distinction between Measurement and Partitive Division or Number of Groups Unknown
and Group Size Unknown. (Chart excerpted from OA Progression pg. 23)
8.Omit L33. Embed this discussion into Lesson 30 rather than calling it out in one lesson.
Module 4
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1. Those from outside New York State, may want to teach Module 4 after Module 6 and truncate
the lessons using “Planning a Shorter Lesson.” (see the Appendix) This would change the order
of the Modules to the following: Module 1, 2, 3, 5, 6, 4 and 7.
2.Those from New York State might apply the following suggestions and truncate Module 4’s lessons
using “Planning a Shorter Lesson” protocol (see the Appendix).
The placement of Module 4 in A Story of Units was determined based on New York State’s “Pre and Post” document which placed
4.NF.5, 6, and 7 outside the testing window and 4.MG.5 inside the testing window. This is not in alignment with PARCC’s Content
Emphases Clusters (http://www.parcconline.org/mcf/mathematics/content-emphases-cluster) which reverses those priorities,
putting 4.NF.5-7 as a “Major Emphasis Cluster” and 4.MG.5 as an “Additional Cluster,” the status of lowest priority.
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3. Topic A might be taught simultaneously with Module 3 during an art class. Topics B and C might be
taught directly following Module 3, prior to Module 5 since they offer excellent scaffolding for the
fraction work of Module 5. Topic D might be taught simultaneously with Module 5, 6, or 7 during an
art class, when students are served well with hands-on, rigorous experiences.
4.Topics B and C are foundational to Grade 7’s missing angle problems. In Asia, missing angle problems
are used to introduced variables. When using a protractor the value of the variable, , is verifiable
and its meaning has a distinct value, eradicating the misconception that its value is “variable” when
the equation is true.
Module 5
1. Consolidate L1, L2, and L3.
2.Omit L4. Embed the contrast of the decomposition of a fraction using the tape vs. the area model
in the coming Lesson 5. “We could do it this way, too!” The area model’s cross hatches are used to
transition to multiplying to generate equivalent fractions, to add related fractions in G4 L20/L21, to
add decimals in G4 M6, to add/subtract all fractions in G5 M3, and multiply a fraction by a fraction
in G5 M4.
3. Omit L29. Embed estimation within many problems throughout the Module and curriculum.
4.Omit L40. Embed line plot problems in social studies or science. Be aware that there is a line-plot
question on the End-of-Module Assessment.
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Appendix: Planning a Shorter Lesson
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Using “Backwards Design,” , the authors of A Story of Units crafted the Problem Sets and Debriefs in Grades
1 – 5 prior to writing the Concept Developments. The Concept Developments were based upon the very
intentional sequences of the Problem Sets. This fact invites us to plan by first analyzing the Problem Set. To
use less instructional minutes, therefore, means to thoughtfully shorten the Problem Set.
Customizing a Lesson3 from a “Must Do” Problem Set
1. Analyze the Problem Set while considering the
lesson’s objective.
a. Review the “Overview of Module Topics and
Lesson Objectives” (pictured to the right)
to understand the objective’s place in the larger
sequence of the Topic and Module.
b. In the Problem Set, find the new complexities
from one problem to the next. Notice the
sequence from simple to complex, e.g. pictorial
to abstract, smaller to larger numbers.
2.Complete the Problem Set and Categorize
Problems as “Must Do,” “May Do,” or “Extension.”
a. Reflect on the lesson objective while completing
the Problem Set and answering the Debrief
questions both to have the students’ experience
and to understand the sequence of instruction
in the Concept Development.
b. Categorize the problems on the Problem Set
• “Must Do” problems are to be completed by all students to meet the objective.
-- Think, “If I were giving a more extensive assessment on this objective than the
Exit Ticket, which problems would I include?”
-- Keep a good balance, e.g. of calculations vs. word problems, a balance of word
problem types, of pictorial/abstract.
-- Refer to the Mid- and End-of-Module Assessments to be sure to include
assessed skills and concepts.
Grant Wiggins and Jay McTighe, in Understanding By Design, identify 3 stages in curriculum design: 1) identify desired results,
2) determine acceptable evidence, 3) plan learning experiences and instruction.
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The focus of this process is on the planning of the Concept Development and Debrief as they relate to the Problem Set.
At times, this will include the Application Problem if it is an integral part of the Concept Development.
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Suggestions for Pacing
• “May Do” problems enhance students’ understanding of the objective.
-- Students who complete these problems within the given Problem Set time may
need to be grouped together in order to compare answers during the Debrief.
“Extension” problems challenge students’ understanding of the objective.
• “Extension” problems challenge students’ understanding of the objective.
-- Create a challenge club or group wherein students work together to solve these
problems without instruction. Teachers can meet with this group periodically for
students to present their solutions. Invite participants to share interesting/efficient
solutions with the whole class.
c. Select Debrief questions that highlight the work from the instructional sequence and the
Problem Set. Not all Debrief questions need be used.
3. Read and modify the Concept Development.
a. Use the “Must Do” problems as a guide when modifying the sequence of instruction to hone
in on the objective.
b. Select and modify the sequence of instruction to best prepare students for independent
success on the Problem Set, specifically with the “Must Do” problems.
c. Include the Application Problem in your analysis when it is directly related to the CD lesson.
Further Considerations
Planning Exit Tickets, Homework, and Extensions
§§ Exit Tickets must be truncated to fit within a 3-minute time frame. Refer to the “Must Do”
problems to guide the edits.
§§ Homework might need to be edited to correspond to the “Must Do” Problems. (Be aware
that homework correction is not budgeted within the structure of the lesson.)
§§ Extensions can be comprised of omitted Problem Sets, Homework, word problems, Fluencies,
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Sprints, etc. and used as Remember Homework , morning work, center work, RTI, extensions,
etc. Copies of these problems in organized files might be kept accessible to students.
“Remember Homework” is that which reviews previously learned material. This phrase was coined by Karen Fuson and is used in
her Math Expressions program published by Harcourt Brace.
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Planning Fluency
After the Concept Development lesson is planned, different choices for fluency exercises may
become evident. Use professional judgment since each class’s strengths and weaknesses are best
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known by the teacher.
Alternatives:
§§ Omit a fluency or fluencies.
§§ Edit a fluency using a different sequence.
§§ Consolidate two fluencies.
§§ Use a fluency from a prior lesson that needs more practice.
We envision that Fluency might vary considerably from one classroom to the next, especially in
the first years of implementation when so much work is unfamiliar, students lack background, and
lesson delivery takes more time. The general principles of fluency are: 1) Keep the pace energetic.
2) Increase the complexity as possible. 3) Close with success.
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Keep in mind the three purposes of fluency: maintenance, preparation, and anticipation.
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