Paramount Unified School District
Educational Services
Grade 1 – Unit 2
Stage One – Desired Results
Unit 2: Sums and Differences to 20
In this unit, students will……
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recognize composition and decomposition of numbers to make a ten to add and subtract larger numbers
use Commutative Property of Addition, Associative Property, and Inverse Relationship.
use different manipulatives and strategies to solve addition and subtraction problems.
add and subtract fluently within 20
model “adding and subtracting across twenty” in word problems and equations using manipulatives and/or
visual representations.
Common Misconceptions:
 Students may have difficulty when using the making 10 strategy to subtract greater numbers.
For example: 12 – 3 =
V
2 1
12 – 2 = 10
10 – 1 = 9
1
Unit 2: Sums and Differences to 20
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
OA.1 Use addition and subtraction within 20 to
solve word problems involving situations of adding
to, taking from, putting together, taking apart, and
comparing, with unknowns in all positions, e.g., by
using objects, drawings, and equations with a
symbol for the unknown number to represent the
problem.
OA.2 Solve word problems that call for addition of
three whole numbers whose sum is less than or
equal to 20, e.g., by using objects, drawings, and
equations with a symbol for the unknown number
to represent the problem.
OA.3 Apply properties of operations as strategies
to add and subtract. Examples if 8+3=11 is known,
and then 3+8 =11 is also know. (Commutative
property of addition) To add 2+6+4, the second
two numbers can be added to make a ten, so
2+6+4=2+10=12. (Associative property of addition)
OA.5 Relate counting to addition and subtraction
(e.g. by counting on 2 to add 2)
OA.6 Add and subtract within 20, demonstrating
fluency for addition and subtraction within 10. Use
strategies such as counting on; making ten,
decomposing a number leading to a ten, using the
relationship between addition and subtraction, and
creating equivalent but easier or known sums.
(e.g., adding 6+7 by creating the know equivalent
6+6+1=12+1+13)
Meaning-Making
Understandings
Students will understand that …
 Creating models helps to develop an understanding
of the meaning of operations
 There are a variety of strategies for adding and
subtracting numbers to 20
 The relationship between addition and subtraction
can be used to solve and check problems
Essential Questions
Students will consider…
• How can models help to solve addition and
subtraction problems?
 What strategies can I use to solve addition and
subtraction problems? Which strategy do you think
is best and why?
 How can the relationship between + and − help to
solve and check problems?
Acquisition
Knowledge Students will know…
Skills Students will be skilled at and able to…
 Vocabulary:
 Use drawings, objects and equations to represent a
Addition: Add to, put together, count on, number
problem
line, addends, doubles, near doubles, making a ten,  Use methods such as counting on, making tens and
in order
doubles +/- 1 or 2 to add and subtract
Subtraction: take apart, take away, count back,
 Use known or easier facts to solve problems
doubles, making a ten, related fact, fact family,
 Use properties such as Commutative and
missing addend
Associative to solve problems
 Add and subtract fluently up to 10
 Use a symbol to represent the unknown number in
 Counting forward or backward relate to addition
a problem
and subtraction
 Add three whole numbers whose sum is less than
 Properties of Addition (Commutative, Associative)
or equal to 20
 Use related facts/fact families to solve addition and
subtraction
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Paramount Unified School District
Educational Services
Grade 1 – Unit 2
Stage Two – Evidence of Learning
Unit 2: Sums and Differences to 20
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
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 2
Stage Three –Learning Experiences & Instruction
Educational Services
Unit 2: Sums and Differences to 20
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 K, students:
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Counted forward beginning from a given number within the known
sequence (instead of having to begin at 1).
Represented addition and subtraction with objects, fingers, mental
images, drawings, sounds, acting out situations, verbal explanations,
expressions or equations.
Solved addition and subtraction word problems, and added and
subtracted within 10 (e.g., by using objects or drawings to represent
the problem).
Decomposed numbers less than or equal to 10 into pairs in more
than one way by using objects or drawings, and recorded each
decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 +1).
For any number from 1 to 9, found the number that makes 10 when
added to the given number (e.g., by using objects or drawings, and
record the answer with a drawing or equation).
Fluently added and subtracted within 5.
Composed and decomposed numbers from 11 to 19 into ten ones
and some further ones.
Looking Ahead
In Grade 1, students will:
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Use addition and subtraction within 20 to solve one- and two- step
word problems involving situations of adding to, taking from,
putting together, taking apart, and comparing with unknowns in all
positions.
Fluently add and subtract within 20 using mental strategies.
Fluently add and subtract within 100 using strategies based on
place value and properties of operations.
Add up to four two-digit number using strategies based on place
value and properties of operations.
Explain why addition and subtraction strategies work using place
value and the properties of operation.
4
ST Math Objectives:
 Addition and Subtraction
Situations with Unknown
 Addition, Subtraction Equations
 Number Pairs Making 10
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.
Transfer
Goals
Unit 2: Sums and Differences to 20
Timeframe: October 24-December 16
Course Textbook: McGraw Hill, My Math
Understandings:
 Creating models helps to develop an understanding of the meaning of operations
 There are a variety of strategies for adding and subtracting numbers to 20
 The relationship between addition and subtraction can be used to solve and check
problems
Time
Skills
3 days
Use drawings,
objects and
equations to
represent a
problem
Use methods
such as
counting on to
add
Use a symbol
to represent
the unknown
number in a
problem
Learning Goal
Give Inquiry Question to see
what strategies students use
Use connecting cubes to
represent a train (e.g., 4)
Count on by a given number (e.g.,
2) without going back and
counting the objects in the
original group
Draw this representation
Relate counting on to a number
line
Draw a number line and draw the
steps you take when counting on
Apply the counting on strategy to
solve an addition equation when
the unknown is the sum
Apply the counting on strategy to
solve an addition equation when
the unknown is one of the
addends
REPEAT with various problems
Lesson/Activity/
Resource
Inquiry Question:
Kira had 5 stickers.
Her mom gave her
some more. Now
she has 8 stickers.
How many stickers
did her mom give
her?
Chapter 3
Lesson 2
Count On Using Pennies
Lesson 3
Use a Number Line to
Count On
Lesson 1
Count On 1, 2, 3
Essential Questions:
 How can models help to solve addition and subtraction problems?
 What strategies can I use to solve addition and subtraction problems?
Which strategy do you think is best and why?
 How can the relationship between + and − help to solve and check
problems?
Knowledge
Focus Questions
Teacher Notes
for Lessons
Vocabulary
How can counting Students begin by manipulating
Count On
on help me to add objects to count on, then
Sum
numbers?
progress to using a number line
Greater
to count on, represent their
Number Line
thinking on a number line, and
ultimately apply the counting on
strategy using just the numbers
in the equation (ConcreteRepresentational-Abstract)
When counting on, it is easier
for students to count on from
the largest number.
Students are expected to solve
for the unknown in different
places, not just in the sum but in
the addends.
Example:
7 + ___ = 13
5
Time
Skills
Use drawings,
objects and
equations to
represent a
problem
Learning Goal
Use connecting cubes to
add equal addends
(doubles)
Draw the representation of
adding the equal addends
(doubles)
1 day
1 day
3 days
Use methods such Write an equation using
as doubles +/- 1
equal addends (doubles)
Lesson/Activity/
Resource
Investigation: Have
students use objects to
add 1 and 1. Have them
draw this
representation. Then,
they use numbers to
represent the equation
1 + 1 = 2. Repeat for 2
and 2, 3 and 3, 4 and 4,
5 and 5—ask students,
“What patterns do you
observe?”
Knowledge
Vocabulary
Doubles
Addends
Sum
Near doubles
Doubles
plus/minus 1
Focus Questions
for Lessons
How can doubles and
near doubles be used to
find a sum?
Teacher Notes
Near doubles may
include doubles +1, +2
Students are expected
to solve for the
unknown in different
places, not just in the
sum but in the
addends
Example:
8 + ___ = 16
___ + 4 = 8
Use knowledge of doubles
to find the sum of doubles
when the unknown is the
sum (use a symbol to
Tools for Adding:
represent the unknown)
Use a symbol to
 Ten Frames
Use knowledge of doubles
represent the
Lesson
4
 Five Frames
to find the sum of doubles
unknown
Use
Doubles
to
Add
 Number Lines
when the unknown one of
number in a
 Two-Sided Counters
the addends (use a symbol
Inquiry Question: Sam has 4 red balloons
problem
 Student Work Mats
to represent the unknown)
and 5 blue balloons. How many balloons
(from My Math,
Use knowledge of doubles
does he have in all?
Workmat #2 Double
to find the sum of near
Lesson
5
Ten Frame)
doubles +1
Use Near Doubles to Add
Use knowledge of doubles
to find the sum of near
doubles +2
Cumulative Review and Error Analysis of Unit 1 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.
Use known or
easier facts to
solve problems
Independent practice with transfer goals/Questions to Ask:
 Ron has 7 books. Tim has the same number of books. How many books do they have altogether?
 On Monday, Cara made 5 cupcakes. On Tuesday, Cara made some more. She had 11 cupcakes altogether. How many cupcakes did Cara make
on Tuesday?
6
Time
Skills
3 days
Use drawings,
objects and
equations to
represent a problem
Use methods such as
making a ten to add
Learning Goal
Add by making a ten using a
ten frame
Lesson 7
Make 10 to Add
Draw a picture of how to
use a ten-frame to add
Add by making a ten
without using a ten frame
(just the equation)
REPEAT with various
problems
Use the Commutative Use two different-colored
Property to add
objects to show a sum
2 days
Use a symbol to
represent the
unknown number in
a problem
Lesson/Activity/
Resource
Draw this model using two
different-colored crayons
Use two different-colored
objects to show the same
sum but with the addends
(objects) in different order
Draw this model using two
different-colored crayons
Make observations about
the value
Solve problems using the
Commutative Property
when the unknown is the
sum
Solve problems using the
Commutative Property
when the unknown is one
of the addends
REPEAT with various
problems
Investigation: Have
students use twodifferent colored
objects to show a
sum. Then, they
draw their model to
represent the object
(addends). Now
have them
manipulate the
order of the
addends and again
draw this model.
Students compare
both the model and
their representation
while teacher asks,
“What do you
observe about the
value or the sum?”
Knowledge
Focus Questions
for Lessons
Addition facts up
to 10 fluently
How can making a ten
help to add?
Vocabulary
Addends
How can
understanding the
Commutative Property
help to add?
Commutative
Property
Teacher Notes
Lesson 8
Add in Any Order
7
Time
Skills
2 days
Use the Associative
Property to add
Learning Goal
Give Inquiry Question to see
what strategies students use
Add three whole
Use doubles to add 3 numbers
numbers whose sum
is less than or equal
to 20 using doubles Make observations
about how numbers can be
and making a 10
grouped differently yet this
Use known or easier doesn’t affect the value
(Associative Property)
facts to solve
Make a ten to add 3 numbers
problems
Make observations
about how numbers can be
grouped differently yet this
doesn’t affect the value
(Associative Property)
Lesson/Activity/
Resource
Inquiry Question:
Jasmine puts 3
daisies in a big cup,
4 daisies in a
medium cup and 3
daisies in a small
cup. How many
daisies does Jasmine
have?
Knowledge
Associative
Property
Focus Questions
for Lessons
How can I apply my
knowledge of adding
2-digit numbers to
adding 3-digit
numbers?
Teacher Notes
Students should
demonstrate
proficiency in using
properties to solve
problems, not just
identifying when they
are being used.
Lesson 9
Add 3 Numbers
1 day
1 day
Decide whether to use doubles
or make a ten to solve addition
problems
Independent practice with transfer goals: Illustrative Mathematics Task:
The Very Hungry Caterpillar https://www.illustrativemathematics.org/content-standards/tasks/1150
Independent practice with transfer goals/Questions to Ask:
 Would you get the same sum if you had two blue buttons and three red buttons as you would if you had three blue buttons and two red
buttons? Can you write the addition sentences that show that?
 Brady read for three days. At the end of the third day, Brady had read a total of 20 pages. How many pages could he have read on the first,
second and third days? What is another possibility?
8
Time
Skills
2 days
Use drawings,
objects and
equations to
represent a
problem
Use methods such
as counting on to
add
Use a symbol to
represent the
unknown number
in a problem
3 days
Use drawings,
objects and
equations to
represent a
problem
Use known or
easier facts to
solve problems
Use a symbol to
represent the
unknown number
in a problem
Learning Goal
Give Inquiry Question to see what
strategies students use
Use connecting cubes to represent a
train (e.g., 6)
Count back and remove a given
number of cubes from the train (e.g.,
2) to find the difference
Draw this representation
Count back using a number line that is
provided to students
Draw a number line and draw the
steps you take when counting back
Apply the counting on strategy to
solve an addition equation when the
unknown is the difference
Apply the counting on strategy to
solve an addition equation when the
unknown is subtrahend or minuend
REPEAT with various problems
Use connecting cubes to show
addition with doubles; connect
knowledge of addition using doubles
to subtract using doubles
Draw the representation of
subtracting with doubles
Write a subtraction equation using
doubles
Use knowledge of doubles to find the
unknown difference (use a symbol to
represent the unknown)
Lesson/Activity/
Resource
Inquiry Question:
There are 7 birds
sitting on a branch.
3 birds fly away.
How many birds are
left?
Chapter 4
Lesson 2
Use a Number Line to
Subtract
Knowledge
Vocabulary
Take apart
Take away
Subtract
Minus
Difference
Count back
Focus Questions
for Lessons
How is counting
back for
subtraction like
counting on for
addition?
Subtract
fluently up to
10
Lesson 1
Count Back 1, 2, or 3
Investigation: Have
students use
connecting cubes to
add 4 and 4 to make 8.
Ask, “How could I use
this same train to show
subtraction?”
See what students
come up with.
Lesson 3
Use Doubles to Subtract
Vocabulary
Doubles
How can doubles
and near doubles
be used to find a
difference?
How do doubles
addition facts
relate to
subtraction
facts?
Teacher Notes
Students begin by
manipulating objects
to count back, then
progress to using a
number line to count
back, represent their
thinking on a number
line, and ultimately
apply the counting
back strategy using just
the numbers in the
equation (ConcreteRepresentationalAbstract)
Near doubles may
include doubles -1, -2
Students are expected
to solve for the
unknown in different
places, not just in the
difference but in the
minuend or
subtrahend.
Example:
18 - ___ = 9
___ - 9 = 9
9
1 day
3 days (continued)
Time
Skills
Learning Goal
Use methods such
as doubles +/- 1
Use knowledge of doubles to
find the difference when the
unknown is either the
subtrahend or the minuend (use
a symbol to represent the
unknown)
Use knowledge of doubles to
find the difference of near
doubles -1
Use knowledge of doubles to
find the difference of near
doubles -2
Explain how knowledge of
doubles helps you to both add
and subtract
Use known or
easier facts to
solve problems
Use a symbol to
represent the
unknown number
in a problem
Knowledge
Focus Questions
for Lessons
Teacher Notes
Independent practice with transfer goals/Questions to Ask:
 Maria has 10 crayons. Brian has 8 less crayons than Maria. How many crayons does Brian have?
 Sara bought 12 cupcakes. Now she has 6 cupcakes. How many cupcakes did Sara give away?
Use methods such
as making a ten to
subtract
2 days
Lesson/Activity/
Resource
Observe patterns and
relationships when subtracting
tens from a larger number
using a hundreds chart
Use known or
(29 – 10)
easier facts to solve Explain why 10 is a friendly
number to work with
problems
Solve problems using the make
a ten strategy
Give problems that
require students to solve
by making a ten in which
the subtrahend is 8 or 9:
16 – 9 =
12 – 8 =
15 – 9=
17 – 8 =
Vocabulary
Making a ten
Subtract fluently
up to 10
How does the
making a ten
strategy make it
easier to subtract?
How is the making a
ten strategy in
subtraction
similar/different to
making a ten
strategy in addition?
It is easier for students
to make a ten with the
subtrahend—mentally
easier to subtract
groups of ten;
however, the textbook
doesn’t teach this.
Students should only
make a ten when
subtracting a number
that is close to 10 (like
8 or 9).
10
Time
Skills
Learning Goal
Lesson/Activity/
Resource
Use related
facts/fact
families to solve
addition and
subtraction
Use connecting cubes to
revisit related facts
(6 + 5 = 11 and 11 – 5 = 6)
Lesson 6
Use Related Facts to Add
and Subtract
Use a symbol to
represent the
unknown
number in a
problem
Draw these models
Find related facts given
just an equation
Lesson 7
Fact Families
Knowledge
Vocabulary
Related fact
Fact family
Addend (missing)
Focus Questions
for Lessons
How can understanding
addition help you to
subtract?
Subtract fluently up
to 10
2 days
3 days
Lesson 8
Use fact families to
Missing Addends
complete equations
when the unknown is the
sum or difference
Use fact families to
complete equations
when the unknown is an
addend or subtrahend/
minuend
Use knowledge of fact
families to solve addition
and subtraction word
problems
Independent practice with transfer goals/Illustrative Mathematics Tasks (select one):
 “Link –Cube Addition” https://www.illustrativemathematics.org/content-standards/tasks/1650
 “Cave Game Subtraction” https://www.illustrativemathematics.org/content-standards/tasks/1234
4 days
Dec. 13-16
Teacher Notes
Students are
expected to solve for
the unknown in
different places, not
just in the sum or
difference but in the
addends (addition) or
the minuend/
subtrahend
(subtraction).
Example:
9 + ___ = 15
15 - ___ = 9
Review and Administer Unit 2 Assessment
For Review:
 There are chickens, sheep and pigs in a barn. There are 18 animals total in the barn. How many chickens, sheep and pigs could be in the
barn?
 Gail and Bill found 12 seashells on the beach. Some of them were shaped like cones. The rest of them were shaped like half circles. How
many could have been shaped like cones? How many could have been shaped like half circles?
 Laura had 5 fish. Her mother gave her 1 more. Laura’s brother Frank had 1 fish. Their mother gave Frank 5 more. Laura cried, “That’s not
fair! He has more fish than I do!” Frank doesn’t agree. Who is correct? How you know?
 How are addition and subtraction related?
Common Core Practices
 Instruction in the Standards for Mathematical Practices
 Number Talks
 Use of Talk Moves
P
 Inquiry and Investigation
 Use of Manipulatives
 Daily Fluency Practice
11