Paramount Unified School District
Educational Services
Grade 2 – Unit 5
Stage One – Desired Results
Unit 5: Money and Data
In this unit, students will:
 Apply addition and subtraction strategies within 100 and problem-solving when working with money and data
 Identify coins and their values, find the total value of a group of coins or bills, and compare sets of coins
 Use coins in multiple ways to represent the same quantity, sometimes using the fewest number of coins
 Make change from one dollar using counting on, simplifying strategies (e.g., number bonds), and the relationship
between addition and subtraction
 Solve one- and two-step word problems using tape diagrams and number bonds to find the total value of a group of
bills including $1, $5, and $10
 Organize and represent data with up to four categories using tally charts, picture graphs and bar graphs; make
comparisons using all graphs; analyze graphs and answer questions about the data
 Relate graphs to a line plot (e.g., tally chart); generate measurement data and represent it with a line plot
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Unit 5: Money and Data
Transfer Goals
1) Demonstrate perseverance by making sense of a never-before-seen problem, developing a plan, and evaluating a strategy and solution.
2) Effectively communicate orally, in writing, and using models (e.g., concrete, representational, abstract) for a given purpose and audience.
3) Construct viable arguments and critique the reasoning of others using precise mathematical language.
Standards
MD.8 Solve word problems
involving dollar bills, quarter, dimes,
nickels, and pennies, using $ and ¢
symbols appropriately. Example: If
you have 2 dimes and 3 pennies,
how many cents do you have?
MD.9 Generate measurement data
by measuring lengths of several
objects to the nearest whole unit, or
by making repeated measurements
of the same object. Show the
measurement by making a line plot,
where the horizontal scale is marked
off in whole-number units.
MD.10 Draw a picture graph and a
bar graph (with single-unit scale) to
represent a data set with up to four
categories. Solve simple puttogether, take-apart, and compare
problems using information
presented in a bar graph.
Meaning-Making
Understandings
Students will understand that…
 Understanding money can be useful in real-life
situations
 Similar to numbers, the same amount of
money can be represented using a variety of
different coin combinations
 A variety of different graphs and charts can be
used to represent the same information
Essential Questions
Students will keep considering…
 How important is understanding money in real-life?
 How can the same amount of money be represented using
different coins?
 What is the value of recording and analyzing data using graphs and
charts?
Acquisition
Knowledge
Students will know…
 Vocabulary:
Money
Penny, nickel, dime, quarter, cent, value, skip
count, bill, dollar, change, equivalent ,
value/worth
Data
Data, survey, tally chart, analyze/interpret,
picture graph, symbol, bar graph, line plot
Skip count by 5s, 10s and 25s
Skills
Students will be skilled at and able to do the following…
Money
 Identify coins and know the value of each
 Count to find the value of a set of coins using skip counting and
counting on
 Compare 2 sets of coins
 Recognize and make equivalent collections of coins
 Select coins for a given amount
 Make change up to $1.00
 Solve word problems with whole dollar amounts (including bills of
$1, $5 and $10) and cents (no decimals)
Data
 Take a survey and record the data on a tally chart
 Use data from tally charts to create picture graphs, bar graphs and
line plots
 Identify similarities and differences of different data displays
 Analyze graphs to solve simple put-together, take-apart, and
compare problems
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Paramount Unified School District
Educational Services
Grade 2 – Unit 5
Stage Two – Evidence of Learning
Unit 5: Money and Data
Transfer is a student’s ability to independently apply understanding in a novel or unfamiliar situation. In mathematics, this requires that students use reasoning
and strategy, not merely plug in numbers in a familiar-looking exercise, via a memorized algorithm.
Transfer goals highlight the effective uses of understanding, knowledge, and skills we seek in the long run – that is, what we want students to be able to do when
they confront new challenges, both in and outside school, beyond the current lessons and unit. These goals were developed so all students can apply their
learning to mathematical or real-world problems while simultaneously engaging in the Standards for Mathematical Practices. In the mathematics classroom,
assessment opportunities should reflect student progress towards meeting the transfer goals.
With this in mind, the revised PUSD transfer goals are:
1) Demonstrate perseverance by making sense of a never-before-seen problem, developing a plan, and evaluating a strategy and solution.
2) Effectively communicate orally, in writing, and by using models (e.g., concrete, representational, abstract) for a given purpose and audience.
3) Construct viable arguments and critique the reasoning of others using precise mathematical language.
Multiple measures will be used to evaluate student acquisition, meaning-making and transfer. Formative and summative assessments play an important role in
determining the extent to which students achieve the desired results in stage one.
Formative Assessment
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Summative Assessment
Aligning Assessment to Stage One
What constitutes evidence of understanding for this lesson?
 What evidence must be collected and assessed, given the desired results
defined in stage one?
Through what other evidence during the lesson (e.g. response to
questions, observations, journals, etc.) will students demonstrate
 What is evidence of understanding (as opposed to recall)?
achievement of the desired results?
 Through what task(s) will students demonstrate the desired
How will students reflect upon, self-assess, and set goals for their future
understandings?
learning?
Opportunities
Discussions and student presentations
 Unit assessments
Checking for understanding (using response boards)
 Teacher-created chapter tests or mid-unit assessments
Ticket out the door, Cornell note summary, and error analysis
 Challenge lessons
Learn Zillion end-of-lesson assessments
 Illustrative Mathematics tasks (https://www.illustrativemathematics.org/)
“Check My Progress”, teacher-created assessments/quizzes
 Performance tasks
ST Math (curriculum progress, data reports, etc.)
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Paramount Unified School District
Grade 2 – Unit 5
Stage Two – Evidence of Learning
Educational Services
Unit 5: Money and Data
Prior to planning for instruction, it is important for teachers to understand the progression of learning and how the current unit of instruction connects to previous
and future courses. Teachers should consider: What prior learning do the standards and skills build upon? How does this unit connect to essential understandings
of later content? How can assessing prior knowledge help in planning effective instruction? What is the role of activating prior knowledge in inquiry?
Looking Back
In Grade 1, students:

Looking Ahead
In Grade 3, students will:
Used addition and subtraction within 20 to solve word problems
involving situations of adding to, taking from, putting together, taking
apart, and comparing, without unknowns in all positions, (e.g., by using
objects, drawings, and equations with a symbol for the unknown
number to represent the problem).

Draw a scale 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.

Organize, represent, and interpret data with up to three categories


Generate measurement data by measuring lengths using rulers marked
with halves and fourths of an inch.
Ask and answer questions about the total number of data points, how
many in each category, and how many more or less in one category
than in another.

Show the data by making a line plot, where the horizontal scale is marked
off in appropriate units-whole numbers, halves, or quarters
4
Transfer
Goals
Unit 5: Money and Data
Timeframe: Feb. 16-March 24
Course Textbook: McGraw Hill, My Math
ST Math Objectives:
 Skip Counting
 Money
 Measurement
 Creating Graphs
 Line Plots
1) Demonstrate perseverance by making sense of a never-before-seen problem, developing a plan, and evaluating a strategy and solution.
2) Effectively communicate orally, in writing, and using models (e.g., concrete, representational, abstract) for a given purpose and audience.
3) Construct viable arguments and critique the reasoning of others using precise mathematical language.
4 days
Understandings:
Essential Questions:
 Understanding money can be useful in real-life situations
 How important is understanding money in real-life?
 Similar to numbers, the same amount of money can be represented using a
 How can the same amount of money be represented using different
variety of different coin combinations
coins?
 A variety of different graphs and charts can be used to represent the same
 What is the value of recording and analyzing data using graphs and
information
charts?
Time
Skills
Learning Goal
Lesson/Activity/Resource
Knowledge
Focus Questions
Teacher
for Lessons
Notes
Inquiry Question:
Identify coins
Identify a penny, a nickel and a
Vocabulary
How are the
Patrick has $0.25 in his pocket.
and know the
dime and know the value of each
Penny
strategies for
What coins could he have?
value of each
Nickel
counting coins
See what students come up since
Count by ones (pennies); count by
Dime
similar to strategies
they have likely had some real-life
fives (nickels); count by tens
Count to find the
Cent
for counting
experiences with money. This is
(dimes)
value of a set of
Value
numbers?
almost like a pre-assessment.
Count to find the value of a set of
coins using skip
Quarter
coins (pennies, nickels and dimes
counting and
Chapter 8
Skip count
What is the
only) using skip counting and
counting on
Lesson 1
relationship
counting on; start with the coin
Pennies, Nickels and Dimes
Skip count by 5s, between a dollar
that has the largest value
10s and 25s
and cents?
Identify a quarter and a dollar and
Lesson 2
know the value of each
Quarters (see Model the Math, pg. 489B)
Count by 25 (use a hundreds
chart, if needed)
Lesson 3
Count to find the value of a set of
Count Coins (see Model the Math,
coins (including quarters) using
pg. 495B)
Inquiry Question:
skip counting and counting on;
Evan has $1.00 in his pocket. What different
start with the coin that has the
coin combinations could he have?
largest value
Lesson 5
Dollars (See Model the Math, pg. 509B)
5
Time
Skills
2 days
Compare 2 sets of
coins
Recognize and make
equivalent collections
of coins
Solve word problems
with cents up to $1.00
Make change up to
$1.00
4 days
Solve problems
involving bills of $1,
$5 and $10
Learning Goal
Lesson/Activity/Resource
Compare two sets of
coins to determine which
is less/more
Inquiry Question:
Mary put 2 quarters, 3
dimes, 2 nickels, and 4
pennies in her piggy bank.
How much money did
Mary place in her piggy
bank? Is there another way
to show this same amount
using different coins?
Given a set of coins,
create an equivalent set
of coins
Given a set of coins,
create an equivalent set
of coins using the fewest
number of coins
Apply understanding of
coins to solve word
problems up to $1.00
Solve one-step problems
using tape diagrams and
number bonds to find
change up to $1.00
Knowledge
Vocabulary
Equivalent
Value/worth
Focus Questions
for Lessons
How can the same
amount of money
be represented
using different coin
combinations?
Lesson 4
Problem Solving (include
problems that total $1.00)
Engage NY Lesson 12—Solve
word problems involving
different ways to make change
from $1.00
Solve multi-step word
Engage NY Lesson 8—Solve
problems to find change
word problems involving the
up to $1.00
total value of a group of bills
Solve one-step word
problems using tape
The textbook does not
diagrams and number
address this part of the
bonds to find the total
standard. Students should
value of a group of bills
understand how to use
including $1, $5, and $10
models such as number
Solve multi-step word
bonds, tape diagrams and
problems to find the total drawings to show word
value of a group of bills
problems involving bills.
including $1, $5, and $10
Vocabulary
Change
Teacher
Notes
Just as students learn
that a number (38)
can be represented
different ways (3
tens and 8 ones; 2
tens and 18 ones),
they can apply this
understanding to
money. For example,
25 cents can be
represented with a
quarter, two dimes
and a nickel or 25
pennies.
How can
understanding
change be useful in
real life?
Sample Question:
How many different
ways can you make
37¢ using pennies,
What combinations nickels, dimes and
of different bills are quarters?
possible in $10?
$20? $100?
6
2 days
1 day
1 day
Time
Skills
Learning Goal
Lesson/Activity/
Resource
Knowledge
Focus Questions
for Lessons
Teacher
Notes
Independent practice with transfer goals---Questions to Ask:
 A pencil costs 75¢, an eraser costs 45¢, and a piece of paper costs 59¢. Which one of these items can you purchase with exactly 6 coins?
 Carla’s brother says he’ll trade her 2 quarters, 4 dimes, and 2 nickels for a one-dollar bill. Is this a fair trade? How do you know?
 Sam gets 92¢ change back from the cashier. What combination of coins might he have received? Is there another possibility?
Cumulative Review and Error Analysis of Unit 4 Extended Constructed Responses
Introduce students to the 4-point Extended-Constructed Response rubric. Use this opportunity to get students familiar with rubric.
Possible activities include evaluating their own work, peer feedback, whole-class discussion about displayed exemplars, reflecting on next steps, etc.
Take a survey and
record data on a tally
chart
Take a survey and record
data using a tally chart
Analyze graphs to
solve simple puttogether, take-apart
and compare
problems
Answer questions by
analyzing the data in the
tally chart
Inquiry Question:
Ms. Lee’s class took a survey
of students’ favorite
afterschool activities. 7
students like playing soccer,
6 students like going to the
library, and 9 students like
playing video games. Using
what you know about
graphs and charts from 1st
grade, how can you
represent this data?
Chapter 9
Lesson 1
Take a Survey (see Explore and
Explain)—students take a survey
and record data using tally charts.
Then students can write questions
from the graph and have a friend
answer the questions.
Vocabulary
Survey
Data
Tally chart
Analyze
Interpret
How can I organize
and interpret
survey data using a
tally chart?
Tally charts,
picture graphs
and bar graphs
are all review
from grade 1.
However, in
grade 1, students
organize,
represent and
interpret data
with up to 3
categories. In
grade 2, this is
extended up to 4
categories.
7
Time
Skills
Use data from a
tally chart to
create a picture
graph
4 days
Identify
similarities and
differences of
different data
displays
Analyze graphs to
solve simple puttogether, takeapart and
compare
problems
Learning Goal
Identify how a tally chart
and a picture graph are
similar/different
Use the data to create a
picture graph
Answer questions by
analyzing the data in the
picture graph
Identify how a picture graph
and a bar graph are
similar/different
Use the data to create a bar
graph
Answer questions by
analyzing the data in the bar
graph
Identify how all 3 types of
graphs are similar/different
Lesson/Activity/
Resource
Investigation #1:
Show students an example of a
tally chart and then of a picture
graph that represents the same
data.
Guiding Questions:
 What do you notice about the
displays?
 How are the displays similar?
Different?
Use students’ tally chart from the
survey. Ask students how they
could represent their data from
the tally chart in a picture graph.
Students create a picture graph
representing the same data.
Lesson 2
Make Picture Graphs
Lesson 3
Analyze Picture Graphs
Investigation #2
Lesson 4
Make Bar Graphs
Lesson 4
Analyze Bar Graphs
Knowledge
Focus Questions
for Lessons
Vocabulary
Picture graph
Symbol
Analyze
Interpret
Bar graph
How is a picture
graph similar
to/different from a
tally chart?
How is a bar graph
similar to/different
from a tally chart? A
picture graph?
Teacher
Notes
Note: A picture
graph uses
different
pictures or
symbols to
represent the
data (not a
single picture).
Be sure to
include
examples of
bar graphs that
are horizontal
and vertical.
Investigation #2:
Show students the same examples
of a tally chart and a picture graph.
Then, show a bar graph that
represents the same data.
Guiding Questions:
 What do you notice about the
displays?
 How are the displays similar?
Different?
Use students’ picture graph. Ask
students how they could represent
their data from the picture graph in
a bar graph. Students create a bar
graph representing the same data.
8
Time
Skills
2 days
2 days
Use data from a
tally chart to
create a line
plot
Mar.
21-24
4 days
Analyze graphs
to solve simple
put-together,
take-apart and
compare
problems
Learning Goal
Lesson/Activity/
Resource
Knowledge
Use data from a tally
Lesson 7
Vocabulary
chart to create a line
Make Line Plots (see
Line Plot
plot
Model the Math, pg.
Analyze
567B)
Interpret
Answer questions by
analyzing the data in
Lesson 8
the line plot
Analyze Line Plots
Take measurements
and record data on a
line plot
Investigation:
With a partner, measure each other’s arm span to the
nearest inch. Plot whole class data on a line plot.
Guiding Questions:
 What was the most common arm span
measurement in our class?
 If we collected data from the entire grade level, do
you think the most common arm span will change?
Why or why not?
 If we collect arm span data from your parents,
would the most common arm span change? Why or
why not?
Focus Questions
for Lessons
Teacher
Notes
How is a line plot
similar to/different
from a tally chart? A
picture graph? A bar
graph?
Line plots are diagrams that
show frequency of data on a
number line. The numbers on a
line plot must be consecutive,
even if that piece of data is not
evident in the data set. The
numbers do not need to start at
0, but must show consecutive
values (just like a regular
number line). The purpose of a
line plot is to see the frequency
of the numbers for one
category (e.g., number of
siblings, height, years teaching,
numbers spun).
When you look at a
line plot, how is it
similar and
different from a
number line?
The standard requires that
students measure the lengths
of several objects to the nearest
whole unit and then show the
measurement by making a line
plot.
Class Project
Students work collaboratively in small groups to take a survey of their class. Then, they create a tally chart, picture graph, bar graph and line plot of
their data. Students present their work to the class and pose questions to the class about their graphs. The students in the audience analyze the data
and answer their questions. At the end of the presentation, the teachers asks students, “What is the value of recording and analyzing data using
graphs and charts?
Unit 5 Assessment Review and Administration
Questions for Review:
 Denise has three dollars and seven dimes. Dave has three dollars and eight dimes. A smoothie costs $3.74. Can either Denise or Dave buy a
smoothie? How do you know?
 Sean buys a baseball card. He gives the cashier $1.00. He received 2 dimes, 1 quarter, and 1 penny as change. How much did Sean’s baseball
card cost?
 How does a line plot differ from picture and bar graphs? Can you use all three to represent the same data?
9
Inquiry and