5E Lesson Plan Math
Grade Level: 2
Subject Area: Math
Lesson Title: Unit 3- Addition and
Lesson Length: 25 days
Subtraction without Algorithms
THE TEACHING PROCESS
Lesson Overview
This unit bundles student expectations that address generating, representing and solving
addition and subtraction problem situations without algorithms, recalling basic facts with
automaticity, and determining the value of a collection of coins. According to the Texas
Education Agency, mathematical process standards including application, a problem-solving
model, tools and techniques, communication, representations, relationships, and
justifications should be integrated (when applicable) with content knowledge and skills so
that students are prepared to use mathematics in everyday life, society, and the workplace.
Prior to this unit, in Grade 1, students applied basic facts, strategies, and properties of
operations to generate, represent, and solve addition and subtraction problems within 20. In
Grade 2 Unit 02, students determined the value of a collection of coins and used the dollar
symbol and decimal or the cent symbol to name the value of the coins.
During this unit, students apply strategies based on place value and properties of operations
to add up to four two-digit numbers or subtract two-digit numbers. Students explore flexible
methods and models to solve and represent addition and subtraction situations within 1,000,
including mental math, concrete models, pictorial representations, number sentences, and
open number lines. Addition and subtraction situations, where the unknown may be any one
of the terms in the problem, should include numbers that require regrouping to solve the
problem. The relationship between place value and each flexible method and/or model
should be emphasized in order to prepare students for the transition to algorithms in Unit 06.
Within this unit, students also experience generating addition and subtraction situations
when given a number sentence involving addition or subtraction of numbers within 1,000.
Continued use of basic addition and subtraction fact strategies to solve problems leads to
automatic recall and fact fluency. Students revisit determining the value of a collection of
coins up to one dollar using formal money notation, including the dollar symbol and decimal
or the cent symbol. Students also experience exchange of coins to create sets of equivalent
value and to create minimal sets of coins for a given value.
After this unit, in Unit 06, students will extend representing and solving addition and
subtraction problems within 1,000 as they connect flexible methods to the standard
algorithm.
In Grade 2, generating, representing, and solving addition and subtraction situations, and
recalling basic facts are subsumed within the Grade 2 Texas Response to Curriculum Focal
Points (TxRCFP): Using place value and properties of operations to solve problems
involving addition and subtraction of whole numbers within 1,000. Determining and
representing the value of a collection of coins are identified within the Grade 2 Texas
Response to Curriculum Focal Points (TxRCFP): Developing proficiency in the use of place
value within the base-10 numeration system. This unit is supporting the development of
the Texas College and Career Readiness Standards (TxCCRS): I. Numeric Reasoning, II.D.
Algebraic Reasoning – Representations, VIII. Problem Solving and Reasoning, IX.
Communication and Representation, and X. Connections.
Research has shown the need for educators to develop the foundation for mental math
relationships in order for students to be successful problem solvers utilizing a solid
understanding of addition and subtraction properties and strategies before computational
algorithms are introduced so students do not rely on rote procedures without
comprehension. Clements and Sarama (2009) state that “the use of written algorithms are
introduced too soon and that the use of mental computation is a more beneficial approach”
(p. 148). The authors also indicate that “there are two primary categories when addressing
mental calculation strategies: decomposition and jump are the main two strategies which
align with the two ways of interpreting two-digit numbers; the ‘collection-based’ (base-10
models) and the ‘sequence-based’ (number line and 100-chart) interpretations” (p. 149150). The direct teaching of number relationships related to operations relies on a variety of
methods and strategies so that students do not become dependent on a single approach.
The research in Adding It Up: Helping Children Learn Mathematics indicates there is not a
single preferred instructional approach and suggests the use of instructional supports
(classroom discussion, physical materials, etc.). This allows students to focus on the base10 structure of our number system and how the structure is used in the algorithms. The
authors state, “It is important for (non-algorithmic) computational procedures to be efficient,
to be used accurately, and to result in correct answers. Both accuracy and efficiency can be
improved with practice…students also need to be able to apply procedures flexibly”
((National Research Council, 2001, p. 121). Flexibility allows the student to think through
their solutions, justify their answers, and communicate their thinking.
Clements, D. H. & Sarama, J. (2009). Early childhood mathematics education research:
Learning trajectories for young children. New York, NY: Routledge
National Research Council. (2001). Adding it up: Helping children learn
mathematics. Kilpatrick, J., Swafford, J., and Findell, B. (Eds.) Mathematics Learning Study
Committee, Center for Education Division of Behavioral and Social Sciences and Education.
Washington, DC: National Academy Press.
Texas Education Agency & Texas Higher Education Coordinating Board. (2009). Texas
college and career readiness standards. Retrieved
fromhttp://www.thecb.state.tx.us/collegereadiness/crs.pdf
Texas Education Agency. (2013). Texas response to curriculum focal points for kindergarten
through grade 8 mathematics. Retrieved fromhttp://projectsharetexas.org/resource/txrcfptexas-response-curriculum-focal-points-k-8-mathematics-revised-2013
Unit Objectives:
Students will…
 Generate, represent, and solve addition and subtraction problem situations without
algorithms.
 Recall basic facts with automaticity.
 Determine the value of a collection of coins using the dollar symbol, decimal or cent
symbol to name the value of the coins.
 Apply strategies based on place value and properties of operations to add up to four
two-digit numbers or subtract two-digit numbers.
 Explore flexible methods and models to solve and represent addition and subtraction
situations within 1,000, including mental math, concrete models, pictorial
representations, number sentences, and open number lines.
Standards addressed:
TEKS:
2.1A- Apply mathematics to problems arising in everyday life, society, and the workplace.
2.1B- Use a problem-solving model that incorporates analyzing given information,
formulating a plan or strategy, determining a solution, justifying the solution, and evaluating
the problem-solving process and the reasonableness of the solution.
2.1C- Select tools, including real objects, manipulatives, paper and pencil, and technology
as appropriate, and techniques, including mental math, estimation, and number sense as
appropriate, to solve problems.
2.1D- Communicate mathematical ideas, reasoning, and their implications using multiple
representations, including symbols, diagrams,graphs, and language as appropriate.
2.1E- Create and use representations to organize, record, and communicate mathematical
ideas.
2.1F- Analyze mathematical relationships to connect and communicate mathematical ideas.
2.1G- Display, explain, and justify mathematical ideas and arguments using precise
mathematical language in written or oral communication.
2.4A- Recall basic facts to add and subtract within 20 with automaticity.
2.4B- Add up to four two-digit numbers and subtract two-digit numbers using mental
strategies and algorithms based on knowledge of place value and properties of operations.
2.4C- Solve one-step and multi-step word problems involving addition and subtraction within
1,000 using a variety of strategies based on place value, including algorithms.
2.4D- Generate and solve problem situations for a given mathematical number sentence
involving addition and subtraction of whole numbers within 1,000.
2.5A- Determine the value of a collection of coins up to one dollar.
2.5B- Use the cent symbol, dollar sign, and the decimal point to name the value of a
collection of coins.
2.7C- Represent and solve addition and subtraction word problems where unknowns may
be any one of the terms in the problem.
ELPS:
ELPS.c.1A use prior knowledge and experiences to understand meanings in English
ELPS.c.1C use strategic learning techniques such as concept mapping, drawing,
memorizing, comparing, contrasting, and reviewing to acquire basic and grade-level
vocabulary
ELPS.c.2A distinguish sounds and intonation patterns of English with increasing ease
ELPS.c.2C learn new language structures, expressions, and basic and academic
vocabulary heard during classroom instruction and interactions
ELPS.c.2D monitor understanding of spoken language during classroom instruction and
interactions and seek clarification as needed
ELPS.c.2E use visual, contextual, and linguistic support to enhance and confirm
understanding of increasingly complex and elaborated spoken language
ELPS.c.3B expand and internalize initial English vocabulary by learning and using highfrequency English words necessary for identifying and describing people, places, and
objects, by retelling simple stories and basic information represented or supported by
pictures, and by learning and using routine language needed for classroom communication
ELPS.c.3C speak using a variety of grammatical structures, sentence lengths, sentence
types, and connecting words with increasing accuracy and ease as more English is acquired
ELPS.c.3D speak using grade-level content area vocabulary in context to internalize new
English words and build academic language proficiency
ELPS.c.3H narrate, describe, and explain with increasing specificity and detail as more
English is acquired
ELPS.c.4C develop basic sight vocabulary, derive meaning of environmental print, and
comprehend English vocabulary and language structures used routinely in written
classroom materials
ELPS.c.5B write using newly acquired basic vocabulary and content-based grade-level
vocabulary
Misconceptions:
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Some students may think they must add or subtract in the order that the numbers are
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presented in the problem rather than performing the operation based on the meaning
and action(s) of the problem situation.
Some students may think subtraction is commutative rather than recognizing the
minuend as the total amount and the subtrahend as the amount being subtracted
(e.g., 5 – 3 is not the same as 3 – 5, etc.).
Some students may think you record the dollar symbol after the numerals when
recording one dollar because you orally say “dollar” after “one” rather than recording
the dollar symbol, numeral, decimal, and 00.
Some students may think you can use the dollar symbol, decimal, and cent symbol in
the same representation when describing the value of coins rather than either using
the dollar symbol with a decimal or using the cent symbol.
Some students may think a given amount of money can be represented only one way
rather than recognizing that the value of coins and bills may be represented with
different combinations of coins as long as the total value remains the same.
Underdeveloped Concepts:
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Some students may not recognize the difference between an addition situation and a
subtraction situation based on the context of the problem.
Some students may interpret the equal sign to mean that an operation must be
performed on the numbers on one side and the result of this operation is recorded on
the other side of the equal sign, rather than understanding the equal sign as
representing equivalent values (e.g., 10 + 8 = 13 + 5).
Some students may confuse the –, +, and = symbols due to not fully understanding
the meaning of each symbol.
Some students may correctly determine related addition number sentences but have
difficulty determining the subtraction number sentences within a fact family.
Some students may view addition and subtraction as discrete and separate
operations due to not recognizing the inverse relationship between the operations.
Some students may recognize the traditional views of coins and bills but not recognize new
or commemorative views (e.g., state quarters, buffalo nickels, new paper money, etc.).
Vocabulary:
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Addend – a number being added or joined together with another number(s)
Automaticity – executing a basic fact with little or no conscious effort
Compose numbers – to combine parts or smaller values to form a number
Counting (natural) numbers – the set of positive numbers that begins at one and
increases by increments of one each time {1, 2, 3, ..., n}
Decompose numbers – to break a number into parts or smaller values
Difference – the remaining amount after the subtrahend has been subtracted from
the minuend
Digit – any numeral from 0 – 9
Expression – a mathematical phrase, with no equal sign, that may contain a
number(s), an unknown(s), and/or an operator(s)
Fact families – related number sentences using the same set of numbers
Minuend – a number from which another number will be subtracted
Number sentence – a mathematical statement composed of numbers, and/or an
unknown(s), and/or an operator(s), and an equality or inequality symbol
Open number line – an empty number line where tick marks are added to represent
landmarks of numbers, often indicated with arcs above the number line (referred to
as jumps) demonstrating approximate proportional distances
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Place value – the value of a digit as determined by its location in a number such as
ones, tens, hundreds, one thousands, etc.
Subtrahend – a number to be subtracted from a minuend
Sum – the total when two or more addends are joined
Term – a number and/or an unknown in an expression separated by an operation
symbol(s)
Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}
Related Vocabulary
 Addition
 Cent symbol (¢)
 Change unknown
 Comparison problem
 Decimal
 Dime
 Dollar sign ($)
 Half-dollar
 Nickel
 Operation
 Part-part-whole
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Penny
Properties of operations
Quarter
Regrouping
Result unknown
Skip counting
Solution
Start unknown
Strategy
Subtraction
Value
INSTRUCTIONAL SEQUENCE
Phase One: Engage
Materials:
Handouts:
 paper strips (different lengths cut
from construction paper)
Day 1 Activity:
Teacher information, if not familiar with bar modeling, it can be found in the “Bar Modeling
for Parents and Teachers” packet. Teachers can also use this link to model the process of
bar modeling, projected for the whole class discussions- http://www.thinkingblocks.com/
Activity:
Discuss and review place value with students. Stress the importance of place value when
representing a number, adding numbers and subtracting numbers. Tell students that today
they will be adding and subtracting one-digit numbers and will be practicing using the
vocabulary words: sum, addend, difference, minuend and subtrahend.
TW line up 6 students and then ask another student to split the group of students to make
two groups. The student could do 2 and 4, 3 and 3, 5 and 1, etc. Once the two groups are
made, the TW ask the class to identify the two addends that made the overall, whole group
of 6. SW build this model on their desks using the paper strips to represent two bars with
each one representing one of the addends. TW observe if students start to make the smaller
number values as shorter bars, on their own. Next SW need to create a bar for the whole
(sum) as well. TW have several students come up and move the whole group of 6 students
into different possible combinations as students build the bar models on their desk, using
the paper strips to show the addends and the sum.
Repeat the process of students lining up, but this time with 10 students. The students that
are still at their desks will build the models as they are created but this time they will also
write down the addends and a box where the unknown number will go, which in this case is
the sum.
(addend + addend = sum)
**This same activity will be done for subtraction. Incorporate subtraction practice problems
into your math lesson for the day. For example:
TW line up 6 students and then ask another student to split the group of students to make
two groups. The student could do 2 and 4, 3 and 3, 5 and 1, etc. Once the two groups are
made, the TW ask the class to identify the minuend, subtrahend and the difference. SW
build this model on their desks using the paper strips to represent two bars with one
representing the minuend and one representing the subtrahend. TW observe if students
start to make the smaller number values as shorter bars (subtrahend), on their own. Next
SW need to create a bar for the larger number values as the longer bars (minuend) as well.
TW have several students come up and move the whole group of 6 students into different
possible combinations as students build the bar models on their desk, using the paper strips
to show the difference.
(minuend – subtrahend = difference)
**TW = Teacher will…
**SW = Student will…
What’s the teacher doing?
 Choosing students to participate in
the front of the room and observing
the other students as they build
models
 Expose vocabulary words: sum,
addend, minuend, subtrahend,
difference.
 Review place value
What are the students doing?
 Participating in the front of the room
and/or choosing the groups of two to
split the whole into
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Building models with paper strips to
show the addends and sum
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Writing the addition problem with the
addends and a box for the unknown
which is the sum
Phase Two: Explore
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Materials:
smaller Ziploc bags (enough for each
student to have 2)
larger Ziploc bags (enough for each
student to have 1)
various items such as buttons, lids,
paper clips etc (enough for each
student to have 30-40 of the same
item)
dry erase markers
Handouts:
Day 2 Activity:
Activity:
Review place value, discussing the ones, tens, hundreds and thousands place. Also, review
vocabulary words from the day before: sum, addend, difference, minuend and subtrahend.
Each student will get two small Ziploc bags and one large Ziploc bag along with, at least,
30-40 buttons, lids, paper clips or other small items.
SW be asked to place 12 items in the big Ziploc bag, which will represent the sum (whole) of
the group they are going to work with. They still need to show 10 items in one of the small
Ziploc bags. This represents one of the addends. The student now has a small Ziploc bag
that is empty and this represents the unknown addend. Students can write the sum (whole)
number on the big bag with a dry erase marker and the addend number on the small bag.
TW have the students lay the bags on their desk with the small addends lined up next to
each other and the sum to the far right. SW use the dry erase marker to write the number on
their desk, under the addend bag and the number under the sum bag. They will represent
the unknown with an empty box drawn on the desk, under the empty bag.
TW tell the students to continue this same process with their items and bags but they must
always start with a larger number in the large bag and make sure that they have enough
items to equal that and split them into the small bags then write out the problems on the
desk with their dry erase marker.
SW do this process several times until the student can explain what they are doing and how
to find the unknown.
SW then verbalize to the teacher as he/she is circulating and then to the class as a whole,
how they figured out the unknown. Chances are that they will have counted on from the
known addend or subtracted the known from the sum to get the unknown. Discuss these
different methods.
**This same activity will be done for subtraction, as you are working through the addition
problems.
What’s the teacher doing?
What are the student’s doing?
 Building the models with the bags and
 Modeling the bag activity on the
items
board
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Observing students as they build and
work with the models
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Meeting with small groups and/or one
on one as needed with struggling
students
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Recording the corresponding
problems on the desks with dry erase
markers
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Discussing with groups of students
and the teacher
Phase Three: Explain
Materials:
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Handouts:
Unit 3, “Word Problems for Addition”
Day 3 Explain handout (possibly only
for teacher use)
Day 3 Activity:
TW now work through some word problems with the students as they analyze and decide
what the known addends and/or sum would be. They will find the unknown with their
counters that can be combined with other groups to have enough, and the baggies. Use the
“Bar Model Word Problems for Addition” page from Math in Focus.
After groups of students have attempted the word problems, the class will go through each
problem and discuss what is known and unknown and how they should look with the bag
models and what the actual math expression/equation would look like.
**This same activity will be done for subtraction. For the subtraction, use these problems:
Subtraction Problems - Result Unknown
1. Finn has 9 goldfish. 4 of the goldfish die. How many goldfish are left? (Separate - Result
Unknown)
2. You have 28 M&M candies. You eat 6 of them. How many M&M candies are left?
(Separate - Result Unknown)
3. There are 58 kids on the school bus. 22 get off. How many kids are left on the school
bus? (Separate - Result Unknown without Regrouping)
4. 31 birds are looking for worms in the grass. 18 of the birds fly away. How many birds are
left looking for worms on the grass? (Separate - Result Unknown with Regrouping)
Have students solve the problems as well as reflect on how he/she solved the problem.
What’s the teacher doing?
What are the students doing?
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Observing how students work
through the models and word
problems along with listening to the
students justification of their
processes
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Justifying the knowns and unknowns of
their models and working through the
word problems
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Building the models
Meeting with smaller groups of
students who are struggling
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Writing the corresponding equations on
their desks, under the bags
Phase Four: Elaborate
Materials:
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Handouts:
http://www.k5learning.com/free-mathworksheets/second-grade-2/wordproblems use questions from this link
Day 4 Activity:
Activity:
Continue to review and discuss place value. SW now be given questions from this
link http://www.k5learning.com/free-math-worksheets/second-grade-2/word-problems.
They can use the baggies and items if needed but should also attempt the problems with
just counters and drawing out the scenarios.
SW highlight the bar that represents the unknown from the problem so the teacher can see
that they do truly understand the unknown from the word problem.
This is also a time that the teacher can meet with smaller groups or one on one with
students that are still struggling.
**This same activity will be done for subtraction, as you are teaching the addition
problems.http://www.k5learning.com/free-math-worksheets/second-grade-2/word-problems
using this link, you will also find subtraction problems.
What’s the teacher doing?
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Working with small groups or one
on one with students that are still
struggling
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Observing the students as they
work and watching for patterns in
how they figure out the unknowns
from the problems
What are the students doing?
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Working through the task card with have
different unknowns
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Highlighting the unknowns from the
story problems to show that they do
understand
Phase Five: Evaluate
Materials:

Handouts:
Performance Assessment #1 (1 per
student)
Day 5 Activity:
Provide a variety of concrete tools based on place value. Present the following situation and
tasks:
1) Mrs. Koske’s class is participating in a Butterfly Project to release more butterflies into the
environment. They started with a collection of larvae in a butterfly tent. Each day as the
butterflies hatch, the students will count and record the number of butterflies they release.
Their goal is to release 95 butterflies in a week. On Monday, the class counted and released
11 butterflies. On Tuesday, the class counted and released 24 butterflies. On Wednesday,
the class counted and released 26 butterflies. On Thursday, the class counted and released
17 butterflies.
For each question:
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Model and solve each of the real-life addition and subtraction problem situations
above using concrete and/or pictorial models.
Create a written record of the models and strategies used to solve each problem.
Use mathematical language to describe how place value was used in the solution
process.
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Justify the reasonableness of each solution by explaining the relationship between
the operation used and the solution.
a) How many total butterflies did the class count and release during the first four days of the
project?
b) How many more butterflies will need to be released to reach the class goal?
c) How many fewer butterflies were released on Monday and Tuesday than on Wednesday
and Thursday?
d) On Friday, the class counted and released some more butterflies. Now, the total number
of butterflies released for the week was 87. How many butterflies did the class count and
release on Friday?
e) At the end of the week, Mrs. Koske noticed that 13 of the original butterfly larvae had not
hatched into butterflies. How many butterfly larvae did Mrs. Koske’s class begin with?
What’s the teacher doing?
 Setting clear testing expectations
 Walking and monitoring student
activity
What are the students doing?
 Working independently and quietly on
completing performance assessment.
Phase One: Explore/Explain
MATERIALS
Bag of coins (14 pennies, 40 nickels,
20 dimes, 8 quarters, 4 half-dollars) –
1 bag per 2 students
 Chart paper – For Teacher
Day 6 Activity:
Identification of Coins and Values
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HANDOUTS
Coin Value Recording Sheet (1 per student)
Teacher Money Symbols (1 per student for
Journal)
Topics:
 Identification of coins and their value
 Counting like coins
 Number lines
Explore/Explain
Students identify pennies, nickels, and dimes in a set and determine the value of each set of
“like” coins by skip counting.
Instructional Procedure:
1. Place students in pairs and distribute a Bag of Coins to each pair.
2. Instruct student pairs to select 4 pennies from their Bag of Coins and place them in front
of them.
3. Display 1 penny from a Bag of Coins for the class to see.
Ask:
 What is the name of this coin? (a penny)
 What is the value of this coin? (one cent)
 What is the symbol used to represent cents? (¢)
Explain that the symbol can be used instead of writing the word cents.
 How would you represent one penny using numbers and symbols? (1¢)
4. Trace a penny on a sheet of chart paper, write the name of the coin (penny), record the
value of the coin in words (one cent), and inside the coin, write the value of the coin
using 1 and the cent symbol ¢ (1¢).
1¢
1¢
penny
one cent
5. Display 3 additional pennies from a Bag of Coins for the class to see.
Ask:
 How would you count this collection of coins? (by ones)
6. Instruct students to replicate the model and count the coins in front of them. Chorally
count the coins aloud “1, 2, 3, 4” using the displayed coins. Explain to students that they
are counting by ones because a penny has a value of one cent.
Ask:
 What is the value of your four coins? (four cents)
 How would you represent the total value of this collection using numbers and
symbols? (4¢)
7. Instruct students to take a total of 7 pennies from their Bag of Coins and place them in
front of them. Display 3 additional pennies from a Bag of Coins for the class to see.
Chorally count aloud “1, 2, 3, 4, 5, 6, 7” using the displayed coins. Remind students that
they are counting by ones because the value of the coin they are counting is one cent.
Ask:
 What is the value of this collection of coins? (seven cents)
 How would you represent the total value of this collection using numbers and
symbols? (7¢)
8. Instruct students to return the pennies to their Bag of Coins and place 4 nickels in front
of them.
9. Display a nickel from a Bag of Coins for the class to see.
Ask:
 What is the name of this coin? (a nickel)
 What is the value of this coin? (five cents)
 How would you represent one nickel using numbers and symbols? (5¢)
10. Trace a nickel on the sheet of chart paper, write the name of the coin (nickel), record the
value of the coin in words (five cents), and inside the coin, write the value of the coin
using 5 and the cent symbol ¢ (5¢).
5¢
5¢
nickel
five cents
11. Display 3 additional nickels from a Bag of Coins for the class to see.
Ask:
 How do you count this collection of coins? (by fives)
12. Instruct students to replicate the model and count the coins in front of them. Chorally
count the coins aloud “5, 10, 15, 20” using the displayed coins. Explain to students that
they are counting by fives because the value of the coin is five cents.
Ask:
 What is the value of the four coins? (twenty cents)
 How would you represent the total value of this collection using numbers and
symbols? (20¢)
13. Instruct students to take a total of 8 nickels from their Bag of Coins and place them in
front of them. Display 4 additional nickels from a Bag of Coins for the class to see.
Chorally count aloud “5, 10, 15, 20, 25, 30, 35, 40.” Explain to students that when
counting “like” coins, the value of the coin determines what number to use for skip
counting.
Ask:
 What is the value of this collection of coins? (forty cents)
 How would you represent the total value of this collection using numbers and
symbols? (40¢)
14. Instruct students to return the nickels to their Bag of Coins and place 5 dimes in front of
them.
15. Display a dime from a Bag of Coins for the class to see.
Ask:
 What is the name of this coin? (a dime)
 What is the value of this coin? (ten cents)
 How would you represent one dime using numbers and symbols? (10¢)
16. Trace a dime on the sheet of chart paper, write the name of the coin (dime), record the
value of the coin in words (ten cents), and inside the coin, write the value of the coin
using 10 and the cent symbol ¢ (10¢).
10¢
10¢
dime
ten cents
17. Display 4 additional dimes from a Bag of Coins for the class to see.
Ask:
 How do you count this collection of coins? (by tens)
18. Instruct students to replicate the model and count the coins in front of them. Chorally
count the coins aloud “10, 20, 30, 40, 50” using the displayed coins. Explain to students
that they are counting by tens because the value of the coin is 10 cents.
Ask:
 What is the value of your five coins? (fifty cents)
 How would you represent the total value of this collection using numbers and
symbols? (50¢)
19. Instruct students to add an additional 2 dimes from their Bag of Coins to the collection of
dimes in front of them.
Ask:
 What is the value of this collection of coins? Explain your thinking. (Seventy
cents because I skip counted by tens seven times; seventy cents because I skip
counted by ten two more times from fifty.)
 How would you represent your collection using numbers and symbols? (70¢)
20. Display the chart paper with the coin tracings for the class to see and reference for the
duration of the lesson. Facilitate a class discussion comparing the size of each coin and
the value of the coin. Explain to students that the size of a coin does not reflect the value
of the coin.
21. Distribute handout: Coin Value Recording Sheet to each student to each student.
22. Display teacher resource: Coin Value Recording Sheet. Explain to students that they
will select 10 nickels from their Bag of Coins. Students will trace and label the coins
above the number line. Below the number line, students will label the number line as
they skip count by 5s. Students will then record the value of the collection of 10 nickels in
the last column of the handout. Model for students how to complete the nickel portion of
the handout
Coin Value Recording Sheet KEY
5¢
5¢
5¢
5¢
5¢
5¢
5¢
5¢
5¢
5¢
50¢
5
10
15
20
25
30
35
40
45
50
Ask:
 What do you notice about the value of the collection of nickels and the number
line? (The last number on the number line is the same as the value of the collection
of nickels.)
23. Instruct students to repeat the complete the handout be counting and recording a
collection of 10 pennies and then 10 dimes. Allow students time to complete the activity.
Monitor and assess students to check for understanding.
24. Facilitate a class discussion about the values of coins and the connection between the
number line.
Ask:
 How is counting a collection of coins like counting numbers on a number line?
Answers may vary. The value of each coin is like the intervals on a number line; skip
counting can be used to count a collection of like coins and also for counting
numbers on a number line; etc.
 All three collections contained 10 coins. What do you notice about the total
value of each collection? Answers may vary. All of the collections had the same
number of coins, but different total values; 10 pennies is less than 10 nickels or 10
dimes; 10 nickels is more than 10 pennies but less than 10 dimes; 10 dimes is more
than 10 pennies or 10 nickels; etc.
****JOURNAL****
TEACHER MONEY SYMBOLS. This should be a journal activity. Let students cut out
the money symbols and write examples next to each symbol in their journal.
What’s the teacher doing?
 Asking students questions about
coins and their value.
 Modeling how to count coins using
a number line.
What are the students doing?
 Answering questions and participating in
class discussion.
 Complete Coin Value Recording Sheet
and journal entry.
 Practice skip counting by 1s, 5s, and
10s.
Phase One: Explore/Explain
MATERIALS
Bag of coins (previously created) (1
per 2 students)
Day 7 Activity:
Topics:
 Counting like coins
 Number lines
 Skip Counting


HANDOUTS
Quarter/Half-Dollar Recording Sheet (1 per
student)
Explore/Explain
Students identify quarters and half-dollars and determine the value of each set of “like” coins
by skip counting.
Instructional Procedures:
1. Using the displayed chart paper with the coin tracings, review the names and values of
the coins already listed.
2. Place students in pairs and distribute a Bag of Coins to each pair.
3. Instruct student pairs to select a quarter from their Bag of Coins and place them in front
of them.
4. Display a quarter from a Bag of Coins for the class to see.
Ask:
 What is the name of this coin? (a quarter)
 What is the value of this coin using words? (twenty-five cents)
 How would you represent one quarter using numbers and symbols? (25¢)
5. Facilitate a class discussion about the cent symbol. Explain to students that the cent
symbol is written as the letter "c" with a vertical line through the center. Emphasize to
students that the cent symbol is always written after the number representing the value
of the money.
6. Trace a quarter on a new sheet of chart paper, write the name of the coin (quarter),
record the value of the coin in words (twenty-five cents), and inside the coin, write the
value of the coin using 25 and the cent symbol ¢ (25¢).
25¢
one quarter
twenty-five cents
25¢
Ask:
 How would you count a collection of this type of coin? (by 25s)
7. Display an additional quarter from a Bag of Coins for the class to see.
Ask:
 What is the name of each coin? (a quarter)
8. Trace two quarters on the sheet of chart paper, write the quantity and name of the coins
(two quarters), record the value of the coins in words (fifty cents) and with the cent
symbol ¢ (50¢), and inside each coin, write the value of the coin using 25 and the cent
symbol ¢ (25¢).
25¢
25¢
25
,
50
two quarters
fifty cents
50¢
Ask:
 What is the value of each coin? (25¢)
 How many quarters do you have? (two quarters)
 How would you count this collection of coins? (by 25s)
9. Instruct students to replicate the model and count the coins in front of them. Chorally
count the coins aloud “25, 50” using the displayed coins. Remind students that they are
counting by 25 because the value of each quarter is twenty-five cents.
Ask:
 What is the value of the collection of coins? (fifty cents)
 How do you represent the total value of this collection using numbers and
symbols? (50¢)
10. Display an additional quarter from a Bag of Coins for the class to see.
Ask:
 What is the name of each coin? (quarter)
11. Trace three quarters on the sheet of chart paper, write the quantity and name of the
coins (three quarters), record the value of the coins in words (seventy-five cents) and
with the cent symbol ¢ (75¢), and inside each coin, write the value of the coin using 25
and the cent symbol ¢ (25¢).
25
25¢
25¢
25¢
,
50
,
75
three quarters
seventy-five cents
75¢
Ask:
 What is the value of each coin? (25¢)
 How many quarters do you have? (three quarters)
 How would you count the total coins in this collection? (by 25s)
12. Instruct students to replicate the model and count the coins in front of them. Chorally
count the coins aloud “25, 50, 75” using the displayed coins. Remind students that they
are counting by 25 because the value of each quarter is twenty-five cents.
Ask:
 What is the value of the collection of coins? (seventy-five cents)
 How do you record the total value of this collection using numbers and
symbols? (75¢)
13. Instruct students to place 4 quarters in front of them. Display four quarters.
Ask:
 What is the name of each coin? (a quarter)
14. Display an additional quarter from a Bag of Coins for the class to see.
Ask:
 What is the name of each coin? (quarter)
15. Trace four quarters on the sheet of chart paper, write the quantity and name of the coins
(four quarters), record the value of the coins in words (one dollar), with the cent symbol ¢
(100¢), and with the dollar symbol $ ($1.00), and inside each coin, write the value of the
coin using 25 and the cent symbol ¢ (25¢).
25
,
50
25¢
25¢
25¢
25¢
,
75
,
100
four quarters
one dollar
100¢
$1.00
Ask:
 What is the value of each coin? (25¢)
 How many quarters do you have? (four quarters)
 How would you count the total coins in this collection? (by 25s)
16. Instruct students to replicate the model and count the coins in front of them. Chorally
count the coins aloud “25, 50, 75, 100” using the displayed coins. Remind students that
they are counting by 25 because the value of each quarter is twenty-five cents.
Ask:
 When you counted by 25, you ended on 100. What does the 100 represent? (100
cents)
 What amount of money is equivalent to 100 cents? (one dollar)
Record both representations for the class to see.
 How do you record the total value of the coin using numbers and symbols?
(100¢)
Facilitate a class discussion about the dollar symbol and decimal. Explain to students
that the dollar symbol is written as an "S" with a vertical line through the center.
Explain to students that the decimal is used to separate the whole dollar amount from
the cent amount. Emphasize to students that the dollar symbol will always be written
in before the numbers representing the value of the money even though when
reading the amount, the word "dollars" is said after the number. Also emphasize that
the dollar symbol and cent symbol will not be used together to represent the value of
an amount of money.
 How many quarters are in one dollar? (4 quarters)
 How many pennies are in one dollar? (100 pennies)
17. Display a half-dollar from a Bag of Coins for the class to see.
Ask:
 What is the name of this coin? (half-dollar)
 What is the value of this coin? (fifty cents)
 How would you represent one half-dollar using numbers and symbols? (50¢)
18. Trace a half-dollar on the sheet of chart paper, write the name of the coin (half-dollar),
record the value of the coin in words (fifty cents), and, inside the coin, write the value of
the coin using 50 and the cent symbol ¢ (50¢).
50¢
one half-dollar
fifty cents
50¢
Ask:
 How many half-dollars are drawn? (one half-dollar)
 How many half-dollars are needed to equal one dollar?(2 half-dollars)
19. Display an additional half-dollar from a Bag of Coins for the class to see.
20. Trace two half-dollars on the sheet of chart paper, write the quantity and name of the
coins (two half-dollars), record the value of the coins in words (one dollar), with the cent
symbol ¢ (100¢), and with the dollar symbol $ ($1.00), and inside the coin, write the
value of the coin using 50 and the cent symbol ¢ (50¢).
50¢
50¢
two half-dollars
one dollar
100¢
$1.00
Ask:
 What is the value of each coin? (50¢)
 How many half-dollars do you have? (two half-dollars)
 How would you count this collection of coins? (by 50s)
21. Instruct students to replicate the model and count the coins in front of them. Chorally
count the coins aloud “50, one dollar” using the displayed coins.
Ask:
 What is the value of this collection of coins? Answers may vary. One dollar; one
hundred cents; etc.
22. Explain to students that coins represent fractions of a whole dollar. It takes two halfdollars or two halves to make a whole dollar or one whole.
23. Display the chart paper with the coin tracings for the class to see and reference for the
duration of the lesson. Facilitate a class discussion comparing the size of each coin and
the value of the coin. Explain to students that the size of a coin does not reflect the value
of the coin.
24. Place students in pairs and distribute handout: Quarter/Half-Dollar Recording Sheet to
each student.
25. Instruct student pairs to complete the handout: Quarter/Half-Dollar Recording Sheet
and reference the chart papers with the coin tracings as needed. Allow time for students
to complete the handout. Monitor and assess student pairs to check for understanding.
Facilitate a class discussion about student responses and how four quarters have the
same value as two half-dollars.
**Journal
What’s the teacher doing?
 Modeling and guiding students to
better understand the value of a
quarter and half-dollar.
 Asking higher order thinking
questions.
 Facilitate classroom discussion.
 Monitor to check for understanding.
What are the students doing?
 Practice identifying the quarter and
half-dollar.
 Practice skip counting by quarters and
half-dollar.
 Complete Quarter/Half-Dollar
Recording Sheet and journal entry.
 Actively participating in class
discussion.
Phase Four: Elaborate
MATERIALS
 Bag of Coins (Previously Created)
 Cup
 Paper Plate
Day 8 Activity:
Unlike Coin Collections
Topics:
 Unlike coin collections
 Coin collection value
 Cent “¢” symbol

HANDOUTS
Coin Spill Recording Sheet
 Dollar symbol
 Decimal
Elaborate
Student pairs spill coins onto a paper plate. They then count and record the value of the
collection using symbols and words.
Instructional Procedures:
1. Display the following coins: 3 dimes, 2 nickels, and 3 pennies. Model the “addition
method” of counting coins for students by arranging the coins in order from the greatest
valued coin to the least valued coin, and then point to each dime as you orally count the
set of dimes: “10, 20, 30,” stop, and record the sum of “30” below the set of dimes.
D
D
D
N
N
P
P
P
30¢
Ask:
 What is the next set of coins? (nickels)
 How should the nickels be counted? (by fives)
2. Model pointing to each nickel as you orally count the set of nickels; “5, 10,” stop, and
record the sum of “10” below the set of nickels.
D
D
D
N
30¢
N
P
P
P
10¢
Ask:
 What is the last set of coins needing to be counted? (pennies)
 When counting pennies, what number do you count by? (ones)
3. Model pointing to each penny as you orally count the set of pennies; “1, 2, 3,” stop, and
record the sum of “3” below the set of pennies.
D
D
D
30¢
N
N
P
10¢
P
P
3¢
30 + 10 + 3 = 43¢
4. Explain to students that by keeping a running total each time you count “like coins” all
you have to do is add them together to get the sum of the coin collection.
Ask:
 What is the number sentence that represents this collection of coins? (30 + 10
+ 3 = 43¢)
 What is the total of the collection? (43¢)
 How can the value of this collection be represented two ways? (43¢ or $0.43)
5. Place students in pairs and distribute a cup, paper plate, and Bag of Coins to each pair.
Instruct students to grab a handful of coins from their bag and place them in their cup.
Model the size handful you expect them to grab. (about 8 coins) and model how to
count the coins.
6. Instruct students to begin the activity. Allow time for students to complete 2 spills.
Monitor and assess student pairs to check for understanding and to observe counting
strategies.
7. Distribute a sheet of paper to each student. Instruct students to repeat the activity 4
more times, recording their first spill on the Spill Recording Sheet paper by tracing
around each of the coins they are assigned to count, and marking each coin with the first
letter of its name to distinguish the coin recorded. Allow time for students to record their
spills. Monitor and assess student pairs to check for understanding.
8. Instruct students to count their recorded coin collection and record how they counted the
sum using the cents symbol and/or decimal notation. Allow time for students to complete
the record. Monitor and assess students to check for understanding and to observe
counting strategies.
Example:
D
D
N
P
P
P
10¢
20¢
25¢
26¢
27¢
28¢
28¢
or
10 + 10 + 5 + 1 + 1 + 1 = 28¢
**Journal
What’s the teacher doing?
 Setting clear expectations on how to
complete coin spill activity.
 Modeling how to count various coins
and how to record it.
 Asking guiding questions.
 Monitoring to check for understanding.
What are the students doing?
 Working independently to complete
coin spill activity.
 Answering questions asked during
classroom discussion.
 Following teacher’s expectations on
how to complete the activity.
 Practicing coin counting.
Phase Three: Engage

MATERIALS
Bag of coins (previously created)


HANDOUTS
Coin Counting (1 per student)
Price Tag Cards
Day 9 Activity:
Wrap it up – Coin Collections/Value
Topics:
 Unlike coin collections
 Coin collection value
Engage
Students explore counting collections of unlike coins.
Instructional Procedures:
1. Prior to instruction, create a card set: Price Tag Cards for every 2 students and a
teacher set: Price Tag Cards for each teacher by copying on cardstock, cutting apart,
and laminating. Each page consists of 2 card sets (16¢ and 21¢), to be used by 2 pairs
of students.
2. Place students in pairs and distribute a card set: Price Tag Cards and a Bag of Coins to
each pair.
3. Instruct student pairs to use their Bag of Coins to collect the price on each of the cards
from card set: Price Tag Cards, and count the collection of coins out loud. Remind
student pairs that they must both agree that the sum of the coins matches the price on
the card before moving to the next card. Allow time for students to complete the activity.
Monitor and assess student pairs to check for understanding.
4. Display the 16¢ price tag from teacher resource: Price Tag Cards. Invite a student pair
to share the coins they collected to represent this price tag. Display the coins named by
the students. Instruct the class to count the displayed collection aloud. As they orally
count, touch each coin to confirm the count and value.
5. Invite another student pair to share the coins they collected to represent this price tag.
Display the coins named by the second pair of students. Instruct the class to count the
new displayed collection aloud. As they orally count, touch each coin to confirm the
count and value.
 Display the 21¢ price tag from teacher resource: Price Tag Cards. Repeat the
discussion by inviting two student pairs to share the coins they collected to represent this
price tag. Display the coins named by each pair of students. Instruct the class to count
the displayed collection aloud. As they orally count, touch each coin to confirm the count
and value
Topics:
 Unlike coin collections
 Coin collection value
 Cent “¢” symbol
 Dollar symbol
 Decimal
Elaborate
Students practice counting a collection of coins and record the total of the collection using
appropriate labels.
Instructional Procedures:
1. Distribute handout: Coin Counting and a Bag of Coins to each student. Instruct
students to use their coins to help them reorganize and count pictured coin sets. Allow
time for students to complete the handout independently. Monitor and assess students to
check for understanding.
2. Facilitate a class discussion about the handout.
Ask:
 How did you represent the value of the collections in a variety of ways?
Answers will vary depending on the coin collection.
 Who can describe how the representations are alike? Answers will vary.
How are they different? Answers will vary.
**Journal
What’s the teacher doing?
 Facilitate discussion to check for
understanding.
 Explain Price Tag and Coin
Counting Activity.
What are the students doing?
 Model counting coins.
 Answer guiding questions.
 Work in pairs and independently on
completing Price Tag and Coin
Counting Activity.
Phase Five: Evaluate
MATERIALS

HANDOUTS
Performance Assessment #2 (1 per
student)
Day 10 Activity:
Performance Assessment #2
As part of a Butterfly Project, a student may buy one butterfly larva to take home in a special
box to hatch, observe, and release. Each butterfly larva costs 80¢. Todd thinks he has
enough money in his backpack to buy one butterfly larva. The coins below represent the
coins Todd had in his backpack.
a) Record the value of Todd’s coin collection using two different representations. (Cents or
Dollars)
b) Describe how the symbol(s) of each representation is used to name the value of Todd’s
coin collection.
c) Does Todd have enough money to buy one butterfly larva? Explain why or why not.
2) Tanya counted the coins she had in the bottom her lunch bag and realized she had the
same amount of money as Todd, but she had a different collection of coins.
a) Create a visual representation of the coins that Tanya could have had in her lunch bag.
b) Explain in words how the collections represent the same value.
What’s the teacher doing?
 Set clear testing expectations.
What are the students doing?
 Work independently in completing
performance assessment.
Phase One: Engage the Learner


Materials:
Plastic zip bags (1 bag per 2
students)
Playing cards (1 deck per 2
Handouts:



students)
Dry erase boards
Dry erase markers
Shark Swimathon by Stuart J.
Murphy
Day 11 Activity:
Instructional Procedures:
1. Prior to instruction, the teacher will put together plastic zip bag (sandwich sized) with
playing cards (face cards and “10” cards removed). One deck per 2 students will be
distributed.
2. During instruction, distribute dry erase boards and markers to each student. Read, Shark
Swimathon by Stuart J. Murphy to the class. As the story is read, stop and pause while
students compute the differences from the story on dry erase boards. Students explain their
computation method and review the traditional algorithm.

Ex: Traditional addition (Standard)
Begin adding on the right, and then move to the left. Regroup each partial answer, if
necessary, by writing each digit in the appropriate place-value column.
398
+427
Add the ones. (8 ones + 7 ones = 15 ones)
1
Regroup. (15 ones = 1 ten + 5 ones)
398
+427
5
Add the tens. (1 ten + 9 tens + 2 tens = 12
1 1
tens)
398
+ 427
25
Add the hundreds. (1 hundred + 3 hundreds
11
+ 4 hundreds = 8 hundreds)
398
+ 427
825
825 is the total.
3. Place students in pairs. Distribute the plastic zip bags with playing cards inside for each
pair. Instruct students to separate the deck into two equal piles and place one pile of cards
face down in front of each partner. Explain to students that they will practice basic math fact
strategies by playing a card game with their partner. Each student will turn over one playing
card from the top of their pile of cards and place it on the table for their partner to see. Each
student will then mentally add their number and their partner’s number, and say the sum
aloud. The student who correctly determines the answer of the basic fact the fastest will
explain the strategy they used to their partner, collect both cards, and place them on the
bottom of their pile of cards. Student pairs will repeat the process with the next card in their
pile of playing cards until one student has no cards left.
4. Invite two students to demonstrate the game. Instruct each student to turn over the card
from the top of their pile of playing cards, mentally add both cards together, and say the
answer aloud. Facilitate a discussion with the student that solved the basic fact the fastest
regarding their strategy used.
Ask:
 What strategy did you use to find the sum of the two cards? Explain. Answers
may vary. I used doubles; I made a combination of ten; etc.
Invite other students to share strategies appropriate for the numbers demonstrated.
 What other strategies could have been used to add these two numbers?
Explain. Answers may vary. Doubles; doubles plus 1; make 10; adding on; etc.
5. Allow time for students to play the game. Monitor and assess student pairs to check for
understanding. Facilitate individual discussions to ensure students are sharing their strategy
with their partner.
6. When a pair of students has completed one round of play, instruct students to shuffle,
then redistribute the cards equally and begin a new round of play. Explain to students that
instead of adding the 2 numbers together, this time they will subtract the smaller number
from the larger number. Remind students to discuss the fact strategies used to answer
quickly.
TEACHER NOTE
The purpose of the Engage activity is to explore multiple strategies that can be used to
solve basic math facts. These strategies will be used to support students’ exploration of
flexible methods that can be used in addition and subtraction of 2-digit numbers.
What’s the teacher doing?
What are the students doing?
 Reviewing classroom expectations
 Computing the sums and differences
and rules.
from the read aloud and the math
fluency playing card game.
 Activating student’s prior knowledge
by allowing them to solve problems
 Following the rules on playing card
in their own way on their dry erase
activity.
board.
 Listening to their partner’s strategy in
 Leading a discussion on student’s
computing the sum and difference from
computation methods.
the activity.
 Facilitating student’s addition and
 Answering guiding questions to help
subtraction fluency activity.
improve their math fluency skills.
 Listening to students as they
explain their computation methods.
 Making notes and observations on
who may need extra practice on
basic math fluency skills.
Phase Two: Explore/Explain

Materials:
12 Ways to Get to 11 by Eve
Merriam (Optional)



Handouts:
Two-Digit Addition Recording Sheet 1 (1
per teacher and 1 per student)
Two-Digit Addition Recording Sheet
Sample Key (1 per teacher)
Two-Digit Subtraction Recording Sheet
1 (1 per teacher and 1 per student)
Day 12 Activity:
Instructional Procedures:
Optional: The teacher may introduce this lesson with the book, 12 Ways to Get to 11 by
Eve Merriam. (This book talks about the different ways to get to the number 11. This book
will lead into the lesson nicely as you explain that there are many strategies that lead to the
same result).
1. Students will demonstrate two-digit addition number sentences modeling with an open
number line and then explain the strategy used with a base-ten representation and a
numerical explanation.
2. Facilitate a class discussion to demonstrate the process of solving and recording addition
problems using a number line model, and then use words and a base-ten representation to
write a numerical explanation of the strategy.
3. Display teacher resource: Two-Digit Addition Recording Sheet 1 for students to see.
Refer to the displayed addition word problem: Madeline bought 47 pencils on Saturday.
Beth bought 14 pencils more than Madeline on Sunday. How many pencils did Beth buy?
47 + 14 = ?
4. Invite several students to share strategies that could be used to solve the problem.
Facilitate a discussion to compare the strategies shared and to reinforce the understanding
that there are multiple flexible methods that could be used to solve two-digit addition
problems. (Students may choose to draw a quick picture, use a standard algorithm, baseten blocks, linking cubes, or another strategy).
5. Explain to students that while there are many strategies, for demonstration purposes, the
class will all record the same strategy in the top portion of handout: Two-Digit Addition
Recording Sheet 1.
6. Demonstrate solving the problem on the number line by beginning with 47, adding one
group of ten from the addend 14, and then adding 4 from addend 14. Instruct students to
replicate the number line model on their handout: Two-Digit Addition Recording Sheet 1
7. Demonstrate recording the strategy number sentence: 47 + 10 + 4 = 61. Refer to the
number line model as you record each addend of the strategy number sentence.
8. Facilitate a discussion to explain to students how to write a numerical explanation of the
strategy using words and a base-ten representation to justify the solution.
Ask:
 According to the number line model, what starting number was used? (47)
 How could 47 be represented using base-ten blocks? (Draw 4 10-longs and 7
units.)
Instruct students to write the first step of the strategy in words and to draw a base-ten
model of 47 using 4 10-longs and 7 units in the “Numerical Explanation” section of
the recording sheet.
 What was the next step in the strategy modeled on the number line? (Add the
10 from the addend 14.)
 How could this step be represented using base-ten blocks? (Draw 1 additional
10-long.)
 How many 10-longs and units are represented now? (5 10-longs and 7 units)
Instruct students to write this step of the strategy in words and to draw the base-ten
model with the additional 10-long.
 What was the next step in the strategy modeled on the number line? (Add 4
from the addend 14.)
 How could this step be represented using base-ten blocks? (Draw 4 additional
units.)
Instruct students to write this step of the strategy in words and to draw the base-ten
model with the additional 4 units.
 How many 10-longs and units are represented? (5 10-longs and 11 units)
 Will regrouping be appropriate? (yes) Explain. Answers may vary. When there are
10 or more units, they can be regrouped into a 10-long; etc.
 How could this step be represented using base-ten blocks? (Circle 10 units to
represent the regrouping and draw an additional 10-long.)
Instruct students to write this step of the strategy in words and to show the
regrouping on the base-ten model.
 How many 10-longs and units are now represented? (6 10-longs and 1 unit)
 What number does the base-ten model represent? (61)
 Does this number match the total determined on the number line model? (yes)
 According to the number line and the base-ten model, what is the sum of 47 +
14? (61)
Instruct students to record the answer in the “Answer” section of the recording sheet.
9. Refer students to the bottom portion of the handout: Two-Digit Addition Recording
Sheet 1. Remind students of the earlier discussion where multiple strategies were shared.
Instruct students to complete the bottom portion of the recording sheet individually. Explain
to students that they will record a different number line model, strategy answer sentence,
and numerical explanation for the same problem: 47 + 14 = ?.
10. Monitor and assess students to check for understanding. Facilitate individual
discussions to guide students’ wording of their numerical explanation as necessary. Allow
time for students to complete all sections of the recording sheet.
11. Facilitate a class discussion to review flexible methods that may be used to solve
addition problems and the connection to the base-ten number system. Encourage students
to discuss the similarities and differences in each strategy, highlighting efficient strategies
and encouraging students to understand their peers' thinking.
Ask:
 Who can explain how a strategy they used is connected to the base-ten
number system? Answers may vary. The strategy involved separating the addends
by the tens place and the ones place; the strategy involved adding the tens place first
and then the ones place; the strategy involved regrouping when the number in the
ones place was ten or higher; etc.
 Of the strategies shared, which strategy or strategies could be considered
efficient? Answers may vary.
 What makes the strategy efficient? Answers may vary. The strategy included
jumping by larger numbers; the strategy did not take many steps to complete; the
strategy involved friendly numbers so the sum could be found mentally; etc.
12. Repeat the steps above with the handout: Two-Digit Subtraction Recording Sheet 1.
TEACHER NOTE
The purpose of the lesson is not to teach technical language of flexible strategies but for
students to experience solving problems using flexible strategies. Students may use
language such as jumping by multiples of ten, jumping by larger friendly numbers, using
landmark numbers, splitting addends in to smaller friendly number combinations, or jumping
too far and coming back (e.g. to add 49, students may jump 50 then subtract 1). The
following technical language, for teacher use only, explains some flexible methods of
addition, including:
 Aggregation: Add on the tens, then add on the ones, or add on the ones, then add on the
tens.
 Partial Sums: Add the tens together, add the ones together, and then add the new
subtotals together.
 Compensation: Add or subtract extra to reach a landmark number or friendly number, and
then compensate at the end.
 Leveling: Move an amount from one addend to the other to get to landmark numbers or
friendly numbers.
Note, there are some mathematicians that do not distinguish between some methods, such
as compensation and leveling, and/or aggregation and partial sums, but think of them as
similar strategies. Therefore, do not teach the technical language but focus on how the
student is solving the problem and their understanding of their strategy. The purpose of
including the above definitions is to familiarize teachers with various methods discussed
among mathematicians such as Clements, Sarama, Fosnot, Dolk, Van De Walle, etc.
What’s the teacher doing?
 Facilitate a discussion on the
process of solving addition problems
on a number line.
 Model how to use the base-ten
blocks and a numerical explanation
to explain the strategy.
 Monitor student’s work as they come
up with strategies to solve the
addition problem.
 Listen to student strategies and lead
the class into a discussion with
guiding questions.
What are the student’s doing?
 Working independently to solve doubledigit addition problems.
 Share strategy on solving their addition
problem.
 Listen to others share different
strategies that led to the same answer.
 Answer guiding questions and
participate in classroom discussion.
Phase Three: Explain/Explore


Materials:
Plastic zip bags (1 bag per 2
students)
Playing cards (1 deck per 2
students)


Handouts:
Two-Digit Addition Recording Sheet 2
(1 per teacher and 1 per student)
Two-Digit Subtraction Recording Sheet
2 (1 per teacher and 1 per student)
Day 13 Activity:
Students demonstrate two-digit addition number sentences modeling with an open number
line and then explain the strategy used with a base-ten representation and a numerical
explanation.
Instructional Procedures:
1. Prior to instruction, select the following cards from a deck of Fact Practice Playing
Cards: 4, 7, 1, and 4 of any suit.
2. Place students in pairs. Explain to students that they will work with a partner to create
and solve two-digit addition word problems using playing cards. Students will model their
strategy for solving the addition problem on a number line, record the strategy number
sentence, and then use words and a base-ten representation to write a numerical
explanation of the strategy.
3. Display teacher resource: Two –Digit Addition Recording Sheet 2 for students to see.
Distribute handout: Two-Digit Addition Recording Sheet 2 to each student and a deck
of Fact Practice Playing Cards to each pair. Instruct students to separate the deck of
playing cards equally, one pile for each student.
4. Explain to students how to create a two-digit addition problem using playing cards.
Display the previously selected playing cards for the class to see. Instruct students to
imagine the first student in a pair had drawn the 4 card and then the 7 card, and the
other student in a pair had drawn the 1 card and then the 4 card. Explain to students that
the first student’s cards, 4 and 7, will form the addend 47. The second student’s cards, 1
and 4, will form the other addend, 14.
Ask:
 How could 47 and 14 be written as an addition number sentence? (47 + 14 = ?
or 14 + 47 = ?)
 Could the addends be written in either order? (yes) Explain. Answers may vary.
Two numbers can be added in either order, and it does not affect the sum; etc.
5. Refer to the displayed teacher resource: Two-Digit Addition Recording Sheet 2 to
facilitate a class discussion on how to complete the recording sheet. Explain to students
that they will write the word problem and number sentence they create in the section of
the recording sheet labeled “Problem Number Sentence.” Explain that the section
labeled “Answer,” will be filled in after the problem has been solved.
6. Explain to students that after writing their word problem and recording their number
sentence, each partner will solve the problem individually and record their strategy in the
section of their recording sheet labeled “Open Number Line.” Students will then record
their strategy number sentence in the section labeled “Strategy Number Sentence” and
record the answer in the section labeled “Answer.”
7. Once both partners have recorded their strategy on the number line and as a number
sentence, each student will share their strategy with their partner. Each student will be
allowed time to explain their strategy and justify their solution to their partner. Students
will then use words and a base-ten model to write a numerical explanation of their
strategy in the section labeled “Numerical Explanation.”
8. Monitor and assess student pairs to check for understanding. Allow time for students to
complete 2 addition problems.
9. Facilitate a class discussion to review flexible methods that may be used to solve
addition problems and the connection to the base-ten number system. Invite students to
share their recording sheets with the class. Encourage students to discuss the
similarities and differences in each strategy, highlighting efficient strategies and
encouraging students to understand their peers' thinking.
Ask:
 Who can explain how a strategy they used is connected to the base-ten
number system? Answers may vary. The strategy involved separating the addends
by the tens place and the ones place; the strategy involved adding the tens place first
and then the ones place; the strategy involved regrouping when the number in the
ones place was ten or higher; etc.
 Of the strategies shared, which strategy or strategies could be considered
efficient? Answers may vary.
 What makes the strategy efficient? Answers may vary. The strategy included
jumping by larger numbers; the strategy did not take many steps to complete; the
strategy involved friendly numbers so the sum could be found mentally; etc.
10. Distribute handout: Two-Digit Subtraction Recording Sheet 2 and have students
repeat the following steps above using subtraction.
What’s the teacher doing?
What are the students doing?
 Model how to use the playing cards
 Create two-digit numbers using playing
to create two-digit numbers for
cards and using those numbers to write
student’s word problems.
a word problem.
 Monitor and assist students as they
 Work with a partner in explaining
create their own word problems.
strategies used in solving their
partner’s word problem.
 Work with students having difficulty
writing their word problems.
 Practice using different strategies in
solving the problems.
 Set clear expectations on how to use
the playing cards and how to work
with a partner.
Phase Four: Elaborate
Materials:




Handouts:
Addition Practice Sample Key (1 per
teacher)
Addition Practice (1 per teacher and 1
per student)
Subtraction Practice Sample Key (1 per
teacher)
Subtraction Practice (1 per teacher and
1 per student)
Day 14 Activity:
Students demonstrate two-digit addition number sentences, modeling with an open number
line and then explaining the strategy used with a base-ten representation and a numerical
explanation.
Instructional Procedures:
1. Display teacher resource: Addition Practice. Distribute handout: Addition Practice to
each student.
2. Explain to students that they will work independently to solve the story problems on
handout: Addition Practice. Refer to the displayed teacher resource: Addition
Practice to facilitate a discussion on how to complete each section of the handout.
3. Allow time for students to work the first problem independently. Monitor and assess
students to check for understanding.
4. Facilitate a class discussion to review the first problem with the class.
Ask:
 What is the unknown or question in the problem? (The number of words in Sam’s
story.)
 What number sentence could be used to answer the question? (275 + 25 = ?)
Allow time for students to self-correct, if necessary.
 How could this problem be solved using an open number line? Answers may
vary.
Facilitate a class discussion inviting multiple students to share their strategy. Allow
students to display their recording sheet and explain their open number line, strategy
number sentence, and numerical explanation. Instruct the class to evaluate the student’s
displayed recording sheet to ensure that the strategy has been explained thoroughly.
Allow time for students to self-correct, if necessary.
5. Instruct students to continue working independently to complete the remaining problem
on the handout.
6.
7.
Monitor and assess students to check for understanding.
Allow students to complete and practice handout: Subtraction Practice.
What’s the teacher doing?


What are the students doing?
Ask guiding questions.
Monitor and assist students to
check for understanding.
 Review strategies to help students
solve the story problems.
Phase One: Explore/Explain



Materials:



Work independently.
Practice solving problem strategies.
Participate in class discussion.
Handouts:
Directional Addition/Subtraction (1 per
teacher and 1 per student)
Directional Addition/Subtraction Story
Problem (1 per teacher and 1 per
student)
Hundreds chart
Day 15 Activity:
Instructional Procedures:
1. Review the different strategies used from the previous lessons and explain to the
students that the hundred chart can also be used as a tool to help solve addition and
subtraction problems.
2. Distribute a 100s chart and 2 counters to each student.
3. Explain to students that they can mathematically communicate the directional arrow of a
mystery number. Demonstrate how to create a number sentence to symbolically represent
the actions taken to get from 34 to 46 (e.g., 34
represents 34 + 10 + 1 + 1 = 46;
when written in standard form becomes 34 + 12 = 46).
4. Display a two-digit number along with an arrangement of directional arrows for the class
to see (e.g., 56
).
Ask:
 Using your 100s chart, can you discover the mystery number being described
with the starting number and directional arrows? Explain your thinking.
Answers may vary. I started at the number 56, moving down two rows would be 20
more than 56, which is 76. Moving one unit to the right would be one more than 76,
which is 77. The mystery number is 77; etc.
5. Repeat the directional mystery number activity with several more times with different
starting numbers and varying directional arrows.
6. Display the following number sentences for the class to see. Instruct students to use their
100s chart and counter to find the solutions to check for understanding. Following each
example, allow students to share how they solved each number sentence.
62 – 10 – 1 – 1 = ?
23 + 10 + 10 + 10 + 2 = ?
98 – 10 – 10 – 10 – 10 – 2 = ?
87 – 12 = ?
66 + 23 = ?
7. Display the following number sentence for the class to see.
49 + 10 + 10 + 1 + 1 + 1 = ?
8. Instruct students to use their 100s chart and counter to find the solution to the number
sentence. Allow students time to find the solution.
Ask:
 What makes this problem different from the previous addition number
sentences? Answers may vary. There are not enough spaces on the row to move
right three times; etc.
 If you are at the end of the row and still need to move right, what do you do? (I
loop to the left end of the row below.)
9. Display the following number sentence for the class to see.
31 – 10 – 1 – 1 – 1 – 1 = ?
10. Instruct students to use their 100s chart and counter to find the solution to the number
sentence. Allow students time to find the solution.
Ask:
 What makes this problem different from the previous subtraction number
sentences? Answers may vary. There are not enough spaces on the row to move
left four times; etc.
 If you are at the beginning of a row and still need to move left, what do you do?
(I loop to the right end of the row above.)
11. Explain to the students that you have a number sentence and that you need to identify
the starting number and directional arrows for the given number sentence. Display the
following number sentences for the class to see:
44 + 10 + 10 + 1 + 1 + 1 = 67
12. Place students in pairs. Instruct student pairs to identify the starting number and
directional arrows.
Ask:
 Who can explain the process used to figure out the starting number and
directional arrows? Answers may vary. I started at the beginning of the number
sentence and identified the starting number, 44. Next, I said that plus 10 is an arrow
pointing down, plus 10 is an arrow pointing down, plus 1 is an arrow pointing right,
plus 1 is an arrow pointing right, and plus 1 is another arrow pointing right; etc.
 Did anyone find the solution another way? Answers may vary. I worked backward
to determine the directional arrows and then the starting number. I started at 67 and
worked the numbers in opposite direction. Plus 1 is an arrow pointing right, plus 1 is
an arrow pointing right, and plus 1 is another arrow pointing right. Then plus 10 is an
arrow pointing down, and plus another 10 is another arrow pointing down. Finally the
starting number is 44; etc.
 If you began at 44 and used arrows, how would it look? (44
) Invite
a student to volunteer to model the arrows for the class.
13. Distribute handout: Directional Addition/Subtraction Story Problem to each student.
Instruct students to complete handout individually. Allow time for students to complete the
activity. Monitor and assess students and check for understanding.
14. Distribute handout: Directional Addition/Subtraction Story Problem to each student.
Use teacher resource: Directional Addition/Subtraction to model completing problem
number 1. Allow students time to brainstorm as a class about the question a learner should
be asking in order to complete the activity.
Ask:
 What number is your problem starting with? What does the number represent?
(Paul is starting with 21 cars).
 How is the number changing in the problem? How do you know? Answers may
vary. Paul got 14 more cars. I will need to add the new cars to the old ones; etc.
 How can you write this problem using a number sentence? (21 + 14 = ?)
 How can you show this number using directional arrows?
 When you use your 100s chart and follow the directional arrows, what number
do you end with? (35)
 Does the ending number make sense for this problem? Answers may vary. The
ending number makes sense because Paul got more cars and 35 is more than 21,
etc.
15. Instruct students to work with a partner to discuss each story problem. Partners should
take turns asking the questions that will guide them through each part of the activity. Each
student should record the answers on the handout. Monitor the assess students to check for
understanding.
16. Facilitate a closing discussion. Allow students to share how they used the guiding
questions to help them complete the activity. Guide students to discuss how the 100s chart
and the directional arrows helped them find the solution to the problems.
What’s the teacher doing?
What are the students doing?
 Model how to use the 100’s chart to
 Practice using the 100s chart to solve
solve addition and subtraction
two-to three-digit addition and
problems.
subtraction story problems in whole
group and independently.
 Practice this strategy as a whole
class.
 Build fluency and critical thinking skills
by using different models to solve word
 Monitor and assist students to
problems.
check for understanding.
Phase One: Explore/Explain
Materials:




Handouts:
One-Step/Multi-Step Practice Problems
(1 per teacher and 1 per student)
One-Step/Multi-Step Practice Problems
Key (1 per teacher)
One-Step/Multi-Step Practice Problems
2 (1 per teacher and 1 per student)
One-Step/Multi-Step Practice Problems
2 Key (1 per teacher)
Day 16 Activity:
Instructional Procedures:
1. Review the different models used to help solve math problems.
Ask:
 What types of models have we used to figure out math problems? Answers may
vary. (ten-frames, number lines, quick pictures, 100s chart, etc.)
2. Explain to students that today they will be practice using part-part-whole models to help
solve subtraction problems. Read the following story problem out loud:
Cindy had 36 pencils. She gave 17 pencils to Anthony.
How many pencils does Cindy have left?
Ask:

What information is given in the problem? (number of pencils Cindy has and how
many pencils she gave to Anthony).




What number are you asked to find? (the number of pencils Cindy has left).
What is your plan or strategy to help you solve this problem? (Possible answer:
I can use a model to help me understand the problem.)
Why is subtraction used to solve this problem? (Possible answer: The whole is
36 and one part is 17. I need to find the unknown part, so subtraction can be used to
find the answer.)
Can you add 17 + 36 to solve this problem? Why or why not? No; Possible
answer: The model and the number sentence show that I need to find a part. I cannot
add the whole and part to find an unknown part.
3. Show students how to use the part-part-whole model.
Read
What information am I given?
Cindy has 36 pencils.
She gave 17 pencils to Anthony.
Plan
What is my plan or strategy?
I can use a model.
Solve
17
?
36
36 – 17 = ?
19 pencils left
4. Distribute white boards and dry erase markers to each student. Then read another story
problem for the students to try.
Charlotte has a box of 48 crayons.
Her baby brother broke 30 crayons.
How many crayons were not broken?
Ask:
 What information are you given? Charlotte has 48 crayons. 30 crayons were
broken.
 How can you use a model to help you solve the problem? Possible answer: I can
use the model to show the information that I know: the whole, 48 and one part, 30.
The model helps me see that I need to find the other part.
 How will you write a number sentence? Possible answer: I will subtract the part
from the whole and draw a box for the unknown part, or the difference.
 How will you find the other part? Answers may vary. Some students may use the
standard algorithm while others may use alternative methods.
Read
What information am I given?
Charlotte has 48 crayons.
Plan
What is my plan or strategy?
I can use a model.
Her baby brother broke 30 crayons.
Solve
30
?
48
48 – 30 = ?
18 crayons are not
broken
5. Show students a multi-step problem that will require them to use higher order thinking.
Students must use both addition and subtraction to solve the problem. Read the story
problem out loud.
There are 90 guests at the party.
28 guests are dancing and 51 guests are eating.
The rest are taking pictures
How many guests are taking pictures?
Ask:




What information are you given? There are 90 guests at the party. 28 are dancing,
and 51 are eating.
How can you use a model to help you solve the problem? Possible answer: I can
use the model to show the information that I know: the whole, 90 and two parts, 28
and 51. The model helps me see that I need to find the other part.
How will you write a number sentence? Possible answer: I will subtract the two
parts from the whole and draw a box for the unknown part, or the difference.
How will you find the other part? Answers may vary. Some students may use the
standard algorithm while others may use alternative methods.
Read
What information am I given?
There are 90 guests.
28 are dancing and 51 are eating.
Plan
What is my plan or strategy?
I can use a model.
Solve
28
51
90
?
 90 – 28 - 51 = 11 or
 51 + 28 = 79
90 – 79 = 11
11 guests are taking pictures
6. Distribute handout: One-Step/Multi-Step Practice Problems and One-Step/Multi-Step
Practice Problems 2 to students for additional practice. Have them work independently and
monitor to check for understanding.
What’s the teacher doing?
 Facilitate a discussion on the
process of solving addition and
subtraction problems using a partpart-whole model.
 Model how to use the part-partwhole model.
 Monitor student’s work as they
practice using the model strategy.
 Listen to student strategies in
solving multi-step problems.
What are the students doing?
 Working independently to solve onestep and multi-step addition and
subtraction problems.
 Answer guiding questions and
participate in classroom discussion
 Work independently on practicing how
to solve one-step and multi-step
addition and subtraction story problems.
Phase One: Engage the Learner



Materials:
set of Matching Game cards
1 piece of bulletin board paper
folded into 4ths with the labels
number sentence, problem
situation, pictorial, and answer and
justification.
9 by 18 manila paper 1 per group of
4 students
Handouts:
Day 17 Activity:
Activity 1 Option 1:
Tell the class that now they are going to play a Matching Game. Give one card to each
student. Tell the students that the cards will all look different some have a number
sentence, some have a number line, some have a problem situation on them and some
have a 100s chart. Have them look closely and read their card. They will stand up holding
their card under their chin facing out where others can see it. Have them make two lines
facing each other. They will then look/study the cards across from them, looking for a card
that will go with their card. Tell them that they are looking for four cards plus their own totals
five cards that represent the same problem situation. If they see someone they can walk
over to them and see if they both agree. When everyone has a group have each group
place their cards in a pocket chart. Go over each group of cards and let the students agree
or disagree with their placement.
Activity 1 Option 2:
Prior to the lesson make 5 sets of the Matching Game. Put the students in pairs and give
each pair a set of Matching Game cards. Have the students lay all of the cards face up in
front of them. Then the student pairs try to find the cards that go together.
Activity 2:
Write problem situations using a situation board.
Use a piece of bulletin board paper and fold it into fourths and label each quadant.
Write an addition sentence on the displayed paper in the top left box for the students to see:
Number Sentence
Problem Situation:
24 + 34 = _____
Pictorial
Answer and Justification
Have the students read the number sentence out loud together.
Have the students turn and talk (one minute) to a neighbor about what 2 items are being
added together.
Have different student volunteers tell what 2 items they talked about with their neighbor.
Tell them that they are now going to help you write a problem situation for the number
sentence.
Ask:
*What two items should we use to be added together? (Ex. 24 bananas and 34 oranges)
*How can we use these two items in a story?(someone is having a party or someone is
buying fruit at the grocery store)
*What question could we ask for the fruit to be added together?
Have volunteers use the fruit to tell the addition problem situation. (Ex. Sam is having a
party. He went to the grocery store and brought 24 bananas and 34 oranges. How many
pieces of fruit did he buy?)
Write the problem situation the students come up with under the number sentence on the
displayed paper.
Ask:
*How can we solve this addition problem? (add the numbers together)
*What strategies can we use? (base ten pictorial, place value discs, or open number line)
Choose a strategy and have a student draw it on the displayed paper.
For the answer and justification box have the students tell how they know that the answer is
correct.
Explore
Activity 2:
Tell the students that they will be given a number sentence and they are to create a
storyboard like the one that was just made.
Put the students in groups of 4. Give each group an addition or subtraction number
sentence. Give each group a 9 by 11 sheet of manila paper. Tell them they are going to
work together to make a situation board. They should draw quadrants (4 sections) on the
paper and label each with number sentence and which type, problem situation,
strategy used to solve the number sentence, a pictorial of how they solved the situation
problem. They should work together to complete the chart.
Activity 3:
Have each group share their storyboard.
What’s the teacher doing?


Leading students through the four
sections of storyboard example.
Rotating to each group and
monitors the groups and assists,
when needed.
What are the students doing?



Reading and trying to find the problem
situations and the other cards that go
together.
Listening and participating during the
storyboard example.
Working with their group to complete
their storyboard.
Phase One: Explore/Explain the Concept





Materials:
pocket chart
1 set of day 2 cards
1 set of 3 addition number
sentences
1 set of 3 subtraction number
sentences
1 copy of the problem situation
recording sheet per student

Handouts:
1 copy of the problem situation
recording sheet per student
Day 18 Activity:
Activity 1:
In a pocket chart:
Display a number sentence 3 different ways (Ex. 24+12=___, 24+___=36,
____+12=36).
Ask:
*Can someone tell the class what we call an addition number sentence that
is missing the sum? (result unknown)
* Can anyone make up a problem situation for the first number sentence?
(the problem situation has to have two parts, but no total/sum)
*Can anyone tell us what we call an addition number sentence that is
missing
the second addend? (change unknown)
*Can anyone make up a problem situation for the second number
sentence? (the problem situation has to have one part and the total)
*Does anyone know what we call an addition number sentence that is
missing the first addend? (start unknown)
* Can anyone make up a problem situation for the third number sentence?
(the problem situation has to have a part and a sum/total)
*The teacher can record an example of the problem situation the students make up of
each to put in the pocket chart.
Display a subtraction number sentence 3 different ways (Ex. 85-63=____,
85-___=22, ____-63=22)
Ask:
*Does anyone know what we call a subtraction problem that is missing the
difference? (result unknown)
*Can someone make up a problem situation for the first subtraction
number sentence? ( the problem situation has to have a minuend and a
subtrahend)
*Does anyone know what we call a subtraction problem that is missing the
subtrahend. (change unknown)
*Can anyone make up a problem situation for the second number
sentence? (the problem situation has to have a minuend and the
difference)
*Does anyone know what we call a number sentence that is missing the
minuend? (start unknown)
*Can anyone make up a problem situation for the third number sentence?
(the problem situation has to have a subtrahend and the difference)
Activity 2:
Put the students in groups of four. Give each group a number sentence card. Have the
group work together to make up a problem situation for their number sentence card.
Have them record all of their information on the problem situation recording sheet and
use one of the following ways to solve their number sentence with a pictorial of:
* place value discs *base tens * open number line * part-part-whole chart
When everyone is finished have each group present what they recorded on their recording
sheet to the class.
What’s the teacher doing?
1. Rotating to each group and monitoring
the groups and assisting, when needed.
What are the students doing?
*Listening, answering questions and
participating during the pocket chart activity.
*Listening and sharing ideas with their group
to complete their situation board.
Phase Three: Evaluate Students’ Understanding of the Concept
Materials:
 2 sheets of paper per group
 1 set of the Mix and Match cards
Day 19 Activity:
Handouts:
Solving multi-step problem situations.
Explore the Concept
Activity # 1
Present the class with the following number sentence:
349 + 12 – 30 = _______
Turn and Talk to your neighbor about the action words that could be used in a problem
situation about this number sentence
Have the students come up with each part of the number sentence and write it on the board.
Phase Two: Explore/Explain the Concept
Activity 3:
Put the students in groups of 4. Give each group a multi-step number sentence and 2
sheets of paper. Tell the students that each group will be acting out the problem situation
they come up with for the rest of the class and then showing the steps they used to solve
the problem. These are the directions for the groups:
1st Read the number sentence.
2nd Talk to each other about the actions/operations taking place.
3rd Decide how to act out the problem situation. One student should be the
reader and the others should act out what is happening in the story.
4th Use the paper to make labels of the amounts from the
problem situation. For example, if the problem says the dog ate 25 pieces
of cheese then write that and label it 25 pieces of cheese.
5th Practice acting out the problem.
6th Write a number sentence, then work the problem and record the steps you
used to solve it.
When all of the student groups are finished have them present their multi-step problem to
the rest of the class.
Mix and Match Activity
Display the mix and match cards in a pocket chart.
Have the students read the cards and number sentences to themselves.
Turn and Talk to your neighbor and explain which problem situations would go with number
sentences.
Have different students come up and match a problem situation and a number sentence and
explain why they go together.
When all of the cards are matched assign groups of students a set of cards (problem
situation and number sentence) to work together to solve the number sentence. They can
use their math journal to record the number sentences and the steps they take to solve the
problems.
As the groups finish, groups can swap cards to work another number sentence
What’s the teacher doing?
What are the student’s doing?
* Rotating through and monitoring the
groups to help as needed.
* Working with their group to make up and act
out their problem situation.
* Working with their group to make up and
act out their number sentence.
Phase Five: Evaluate
Materials:

Handouts:
Performance Assessment #3 (1 per
student)
Day 20 Activity:
Performance Assessment #3:
Provide a variety of concrete tools based on place value. Present the following situation and
tasks:
1) Select one of the following number sentences.



? + 500 = 750
1000 – ? = 750
550 + ? – 200 = 750
a) Create a problem situation related to the Butterfly Project that could be represented by
the number sentence.
b) Create a concrete or pictorial model that demonstrates how place value could be used to
solve the problem.
c) Orally describe the model, strategies, and processes used to solve the problem.
d) Orally justify the reasonableness of the solution.
What’s the teacher doing?
 Monitoring the student’s progress.
What are the students doing?
 Working individually to complete the
performance assessment.
Phase One: Engage
Materials:
 Bags of base-ten blocks
 Dry erase Markers
 Tissues
 Germ-X
 Holey Cards (optional)
Day 21 Activity:
Prior to the lesson:

Handouts:
Addition 2-digit no regrouping
*Option: Create a bag of manipulatives for every 4 students by placing manipulatives in a
plastic bag. Create a variety of manipulative bags with each containing one type of
manipulative.
Engage
Activity:
Start off by having student’s complete holey cards of single digit addition. If holey cards are
not available, have the addition sheet printed that is provided within the lesson for them to
complete first.
This is an informal assessment to gauge where each child is.
Explore/Explain
Class Activity:
1. Pass out base-ten blocks to students. They can share with a neighbor if they do not
have enough blocks.
2. Pass out dry erase markers, tissues and germ-x to each group of students.
3. Tell students to create two numbers with their blocks. Wait for all of them to have
both numbers created.
4. Then have them draw a plus sign on their table in between the two numbers and an
equal line underneath.
EX:
5. Allow them time to work on this problem. Once a majority of the students have
figured out the answer, go step by step with them, showing them how to find the
answer of the ones column with their cubes. Write the answer under the ones place.
Then show them how to find the answer to the tens column with their base-ten sticks.
Write the answer under the tens place.
6. The answer should then be complete for a two-digit plus two-digit number. (You don’t
necessarily have to put the words tens and ones on the top of the problem unless
your students need to see that.)
7. Complete this activity a couple of times until you feel they understand the two-digit
plus two-digit.
Teachers Note: These problems do not require regrouping on Day 21.
Elaborate
1. Allow students to use base-ten blocks to complete the following worksheet.
This should be something easy that relates to the activity that was just
completed. Different option worksheets are provided.
What’s the teacher doing?
 Teacher is walking around checking
the student’s answers on their
desks.
 Modeling the addition problem and
sum on board.
 Teacher needs to set expectations
for the materials.
What are the students doing?
 Students are working on the problems
on their desks with base-ten blocks.
 Students will complete the worksheet
related to the activity.
Phase Two: Explore/Explain


Materials:
Base-ten blocks
Math journal


Handouts:
Addition 2-digit regrouping
Addition 2-digit regrouping 2



Dry Erase Markers
Germ-X
Tissues
Day 22 Activity:
Engage:
Activity:
Start off by having students complete holey cards of single digit addition. If holey cards are
not available, have the addition sheet printed that is provided within the lesson for them to
complete first.
Explore/Explain
1. Pass out base-ten blocks to all students. They can share with a neighbor if they
do not have enough blocks.
2. Pass out dry erase markers, tissues and germ-x to each group of students.
3. Tell students to create two numbers with their blocks. Wait for all of them to have
both numbers created.
4. Then have them draw a plus sign on their table in between the two numbers and
an equal line underneath.
5. Allow them time to work on the problem independently as you walk around
checking answers.
6. Once the majority has finished the problem, walk them through the answer and
how you would answer the problem.
How many ones can you have in the ones place? 9
What happens if we have more than 9 ones in the ones place?
Answers may vary.
(Teacher will create the number and show more than 9 ones will be carried
over into the tens place as however many tens.)
7. Show them how adding the ones place can only be added up to the number 9
before it rolls over to the tens column.
8. Like the example below, 8 + 2=10. Once you reach 10 in the ones place, you
have to roll the 10 into the tens place and add a “0” in the ones place showing it
did have a value.
9. Then explain how you carry your “1” from the ones place over to the tens place. It
is now 60 + 10 +10=80.
10. Take some time working on this while the students are writing the problems on
their desk.
Elaborate
1. Allow students to use base-ten blocks to complete the following worksheet.
This should be something easy that relates to the activity that was just
completed. Different option worksheets are provided.
What’s the teacher doing?
What are the students doing?
 Assisting students in creating their
 Participating in completing activity.
number.
 Collaborating with peers to check
 Setting expectations for materials.
answers.
 Checking for understanding.
 Facilitating classroom discussion.
Phase Two: Explore/Explain


Materials:
Unifix Cubes
Holey Cards (optional)


Handouts:
Subtraction 2-digit no regrouping
Subtraction 2-digit no regrouping 2
Day 23 Activity:
Engage
Activity:
Start off by having students complete holey cards of single digit subtraction. If holey cards
are not available, have the subtraction sheet printed that is provided within the lesson for
them to complete first.
Explore/Explain
1. Pass out unifix cubes to all the students. They can share with a neighbor if they
do not have enough cubes.
2. Have students create two different numbers. (Low ones to start out with)
What do you notice about the two rows? That one is shorter/longer than
the other.
3. Show them, side-by-side, how one row of cubes is longer than the other.
4. Once all the students have their cubes side-by-side, tell them to break off the
extra cubes that don’t match up with the other.
How many cubes are left? Answers may vary.
5. The left over is the answer to that subtraction problem.
6. Start with the simple digit subtraction and move onto the 2-digit subtraction with
no borrowing for this day.
Teacher’s Note: If they don’t understand the unifix cubes, use a number line to show
subtraction. Have the students start with the bigger number on the number line and bounce
back the smaller number. The number they land on is the answer. There is a copy of a
number line included just in case.
Elaborate:
1. Allow students to use unifix cubes or number line to complete the following
worksheet. This should be something easy that relates to the activity that was just
completed. Different option worksheets are provided.
What’s the teacher doing?
 Modeling with unifix cubes.
 Setting expectations for materials.
 Facilitating classroom discussion
amongst students.
What are the students doing?
 Creating numbers with unifix cubes
and subtracting the cubes from the
rows.
 Collaborating with peers to find
answer.
Phase Two: Explore/Explain



Materials:
Number line
Math Journal
Holey Cards (optional)
Handouts:
Day 24 Activity:
Engage
Activity:
Start off by having students complete holey cards of single digit subtraction. If holey cards
are not available, have the subtraction sheet printed that is provided within the lesson for
them to complete first.
Project a number line onto the board. Have student create a number line in their math
journal.
Explore/Explain:
1. Remind the students about the subtraction they did yesterday with the unifix cubes.
2. Pass out tissues, dry erase markers, and germ-x.
3. Explain to them that the bigger number will always go on top because if you have a
smaller number, you can’t take away a bigger number.
4. If the bigger number on top has a smaller ones place number than the bottom, you
have to “borrow” from the tens place.
What does it mean to borrow? Answers will vary.
What number are you borrowing from? The tens place number
Why would you borrow from the tens place and not the ones? Because
the 7 is really a 70 and you can take away 10 and still have a number.
What is the new number in the tens place? Ex. 6
What is the new number in the ones place? Ex. 15
Can you subtract the ones place now? Yes
5. This means taking one ten from the tens place and moving it over to the ones place.
Your ones number on top now becomes bigger than your ones number on bottom.
6. Subtract the top number in the ones place from the bottom number in the ones place.
7. Subtract the top number in the tens place from the bottom number in the tens place.
Elaborate:
1. Allow students to use unifix cubes or number line to complete the following
worksheet. This should be something easy that relates to the activity that was just
completed. Different option worksheets are provided.
What’s the teacher doing?
What are the students doing?
 Teacher is monitoring students.
 Students are collaborating with peers
to find answers to the problems.
 Teacher is setting material
expectations.
 Teacher is facilitating classroom
discussion.
Phase Five: Evaluation
Materials:

Handouts:
Performance Assessment #4 (1 per
student)
Day 25 Activity:
Evaluation
Performance Assessment #4
Directions: Present a set of basic addition and subtraction fact cards or use technology to
assess students using the following tasks:
1) Consider each fact card.
a) Quickly identify the sum or difference for each basic fact presented.
b) Select one addition and one subtraction fact. Orally explain the strategy used to solve the
fact and how this strategy helped in quickly finding the sum or difference.
TEK(s): 2.1C, 2.1D, 2.1F, 2.1G, 2.4A
ELPS ELPS.c.1A, ELPS.c.2D, ELPS.c.2E, ELPS.c.3B, ELPS.c.3C, ELPS.c.3H
What’s the teacher doing?
 Monitoring students
What are the students doing?
 Students are working independently
on completing assignment