Grade 5 UbD Math Unit Planning 2014 to 2015
PS 105
Unit #/Book(s)/Topic
Unit 7 / Book 8 / Patterns, Functions, and Change
Approximate Days or Dates
30
Stage 1 - Identify Desired Results
Learning Outcomes
What relevant goals will this unit address?
(must come from curriculum; include specific Common Core standards)
Graph points on the coordinate plane to solve real-world and mathematical problems
5.G.1: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to
coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the
first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of
the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and ycoordinate).
5.G.2: Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values
of points in the context of the situation.
Analyze patterns and relationships
5.OA.3: Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs
consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule "Add 3" and the
starting number 0, and given the rule "Add 6" and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one
sequence are twice the corresponding terms in the other sequence. Explain informally why this is so .
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 are the Essential Questions?
Are there any potential cross-curricular connections during this chapter?
Students will understand that...
Essential Question:


Graphs and tables can be used to represent change.
They can use graphs and tables to determine if change is
constant or not constant.

How can graphs and tables be used to examine the
relationships between two different things?
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…

Vocabulary for this unit including: axis, coordinate, coordinate pair,
coordinate plane, ordered pair, origin,
 Interpret the points and shape of a graph in terms of the situation the
graph represents.
 Identify points on a graph with corresponding values in a table.
 Plotting points on a coordinate plane.
 Naming points on a coordinate plane.
 Interpret points on a coordinate plane in terms of distances from the
axes.
 Compare situations by describing differences in their graphs.
 Relate the relative steepness of graphs or parts of graphs to rate of
change.
 Compare tables, graphs, and situations of constant change with those of
non-constant change.
 Use tables to represent the relationship between two quantities in a
situation of constant change.
 Interpret the numbers in a table in terms of the situation they represent.
 Find the value of one quantity in a situation with a constant rate of
change, given the value of the other.
 Write an arithmetic expression for finding the value of one quantity in
terms of the other in situations with a constant rate of change.
 Use symbolic letter notation to represent the value of one variable in
terms of another variable.
 Describe how a graph represents situations that are constant and those
that are not constant.
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
9 to 10
sessions
Graphs and Tables
Grade 4
Book 9
1.1
1.2
Temperature and
Speed Graphs
2.1
Penny Jar Growth
2.2
Penny Jar Tables
2.3
Round 20
Speed Graphs
Lesson Notes/Planned Differentiation
We are starting this unit with Grade 4--Book 9: Investigations I and II
(Note: You will need to get the SAB pages for this unit from the fourth grade class
with the corresponding number. For example, class 5-1 gets them from class 4-1.)
Do this lesson more or less as written. Expect the motion graph to be challenging
for students to understand.
Do this as written. Note that students do not need graph paper for this activity,
just plain paper, as they are meant to focus on the changing steepness and
direction of the lines, but not to specific numbers.
Do this as written. The activity is simple, but the main idea of the lesson is to
focus on the different ways that students represent the penny growth, so be
careful not to bias them toward any particular representation when you are
explaining the directions.
This lesson imposes the representation of tables. See the differentiation advice
on TG pp. 57-58. The lesson suggests ending with a lengthy whole class
discussion. If it fits with your current routines, you may prefer to have this
discussion with half of the class at a time while the other half works on some of
the Daily Practice pages in the book.
Do this lesson more or less as written, considering the differentiation advice in
the Teachers Guide. Focus today on the DIFFERENT WAYS in which students find
the totals.
Additional Resources or
Math Centers
2.4
Penny Jar Graphs
2.5
Penny Jar
Comparisons
2.6
&
2.7
Finding Cubic
Centimeters
2.8
Rules for Towers
6
sessions
Coordinate Planes
Lessons
1 to 6
Coordinate Planes
5
sessions
Height and Growth
1.1
Growth Stories
1.2
1.3
More Growth
Stories
Constant Change
1.4
Comparing Growth
1.5
Comparing Growth
This very important lesson helps students see the connection between graphs
and tables and also begins to push them to think about general rules for
describing relationships. Do NOT push them to use variables yet as that will be
addressed when we switch to the grade five book. However, be open to any
student who might suggest it.
This lesson consists of two different center activities, one of which is meant to
be used as an assessment, so be sure to have students work alone on it. Note
that there is additional time for Penny Jar Comparisons the following day.
This lesson and the next day’s lesson consist of three different center activities.
Decide if it you need the second day based on how much your students
complete.
This is a challenging lesson but a very important one. Be sure to allow students
to explain their rules using words. Not all students will be able to understand
rules expressed using variables.
This next investigation is from EngageNY, grade 5, Module 6, Topic A only.
Please read pages 21 to 25 from the file, “How to Implement a Story of Units”,
in order to familiarize yourself with this approach. You can find this file on the
wiki.
Note that you can use the new Graph Lined Desk Mats to support this
investigation.
Grade 5, Book 8, Investigation 1
(For background information on this content, see TG pp. 115 to 124.)
There are some important and tricky vocabulary words in this lesson, such as
steady and rate, that you will likely need to preview with students. See ELL
advice on page 32 of the TG. Otherwise, this lesson should not be too difficult,
since students have been using tables and graphs throughout this unit.
Do as written.
Do as written. However, consider having the discussion, “How Tall at Age 100?”
with half of the class at a time (while the other half works on Daily Practice or
other pages). Also, note the Extension advice for early finishers (see TG, p. 44).
Do as written. However, consider having the discussion, “How Do the Animals
Grow?” with half of the class at a time (while the other half works on Daily
Practice or other pages).
Do as written. However, consider having the discussion, “What is Different
About the Fastwalker?” with half of the class at a time (while the other half
works on Daily Practice or other pages).
 Windows and Towers
 Penny Jar Comparisons
 Backward Problems
 Windows and Towers
 Penny Jar Comparisons
7
sessions
Growing Patterns
Grade 5, Book 8, Investigation 2
(For background information on this content, see TG pp. 130 to 132.)
Do as written. Be sure to read the Math Notes in the margin on TG p. 70.
2.1
3 Tiles Across
2.2
Double or Not?
2.3
2.4
4, 5, and 6 Tiles
Across
10 Tiles Across
2.5
Penny Jar Patterns
Do as written. Be sure to consider the Extension advice on TG p. 100.
2.6
Growing Squares
2.7
Staircase Towers
Do as written. However, consider having the discussion, “How Do the Squares
Grow?” with half of the class at a time (while the other half works on Daily
Practice or other pages).
Do as written.
Unit
Assessment
Do as written. However, consider having the discussion, “Double or Not?” with
half of the class at a time (while the other half works on Daily Practice or other
pages).
Do as written. Be sure to read the Math Notes in the margin on TG p. 84.
Do as written.
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?