5E Lesson Plan Math
Grade Level: 2nd
Lesson Title: Number Relationships
Subject Area: Math
Lesson Length: 10 days
THE TEACHING PROCESS
Lesson Overview
This unit bundles student expectations that address patterns and relationships in numbers, including
basic addition and subtraction facts, fact families, odd and even numbers, place value, and the value
of coins in a collection. According to the Texas Education Agency, mathematical process standards
including application, 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 used concrete models to explore basic addition and subtraction
fact strategies and fact families. Students explored patterns within numbers as they generated
numbers greater than or less than a given number and experienced skip counting by 2, 5, and 10.
Students used these skip counting relationships to determine the value of a collection of coins, and
recorded the value of the collection using the cent symbol notation. Students also explored
determining an unknown in any position of an equation.
During this unit, students focus on developing mathematical strategies based on patterns and number
sense to strengthen their understanding of number relationships and fluency with computations.
Students explore number relationships in strategies based on place value and properties of operations
in order to develop automaticity in the recall of basic addition and subtraction facts, meaning
executing the fact with little or no conscious effort. Students use fact family relationships to solve
problems with an unknown in any position, such as start unknown, change unknown, and result
unknown problems. Students also mentally calculate sums and differences for numbers using place
value as they explore “10/100 more/less” relationships. Students discover patterns in odd and even
numbers through the pairing of objects and determining if the number can be paired without
leftovers. Students use skip counting patterns and relationships between the values of coins to
determine the value of a collection of like or mixed coins up to one dollar. Students extend their
representation of the value of coins to include either the cent symbol notation or the dollar sign and
decimal point notation.
After this unit, in Unit 03, students will extend and apply the patterns and relationships in numbers
and operations to solve a variety of addition and subtraction problem situations, including situations
involving the value of a collection of coins.
In Grade 2, recalling basic addition and subtraction facts, using fact families to solve problems, and
place value relationships within numbers are foundational building blocks to the conceptual
understanding of 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. Place value relationships within numbers is also included 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 along with the standards that address determining and
representing the value of a collection of coins. Determining if a number is odd or even is identified
within the Grade 2 Texas Response to Curriculum Focal Points (TxRCFP): Grade level connections.
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.
According to many researchers, patterns and relationships are found in numerous mathematical and
numerical concepts including the value of numbers, operations, and money. In discussing the
concept of patterns, Heddens and Speer (2006) state,
The study of patterns is central to all mathematical learning. If students have developed an
appreciation for patterns and can recognize them in different contexts, then transfer of learning will
proceed more smoothly. Students who understand the importance of patterns begin to look for
patterns in places that others might not look. (p. 109)
Understanding the patterns in skip counting and the relationships within and between values of 5, 10,
and 25 are essential to students’ success in determining the value of a collection of coins. Van de
Walle (2006) states,
For [coin] values to make sense, students must have an understanding of 5, 10, and 25. More than
that, they need to be able to think of these quantities without seeing countable objects… A child
whose number concepts remain tied to counts of objects [one object is one count] is not going to be
able to understand the value of coins. (p. 150)
To support students in developing essential understandings and skills needed for future success in
mathematics, the foundational skills related to basic facts and patterns are critical. The National
Mathematics Advisory Panel (2008) advises,
Research has demonstrated that declarative knowledge (e.g., memory for addition facts), procedural
knowledge (or skills), and conceptual knowledge are mutually reinforcing, as opposed to being
pedagogical alternatives… to obtain the maximal benefits of automaticity in support of complex
problem solving, arithmetic facts and fundamental algorithms should be thoroughly mastered, and
indeed, over-learned, rather than merely learned to a moderate degree of proficiency. (p. 34)
Heddens, J. W. & Speer, W. R. (2006). Today’s mathematics, concepts, classroom
methods, and instructional activities. Hoboken, NJ: Wiley Jossey-Bass Education
National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the
national mathematics advisory panel. Washington, DC: U.S. Department of Education.
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/txrcfp-texasresponse-curriculum-focal-points-k-8-mathematics-revised-2013
Van de Walle, J., & Lovin, L. (2006). Teaching student-centered mathematics grades k – 3. Boston,
MA: Pearson Education, Inc.
Unit Objectives:
Students will…
 focus on developing mathematical strategies based on patterns and number sense to
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strengthen their understanding of number relationships and fluency with computations
explore number relationships in strategies based on place value and properties of operations
in order to develop automaticity in the recall of basic addition and subtraction facts,
meaning executing the fact with little or no conscious effort
use fact family relationships to solve problems with an unknown in any position, such as
start unknown, change unknown, and result unknown problems
mentally calculate sums and differences for numbers using place value as they explore
“10/100 more/less” relationships
discover patterns in odd and even numbers through the pairing of objects and determining if
the number can be paired without leftovers
use skip counting patterns and relationships between the values of coins to determine the
value of a collection of like or mixed coins up to one dollar
extend their representation of the value of coins to include either the cent symbol notation or
the dollar sign and decimal point notation
Standards addressed:
TEKS:
2.1A-Apply mathematics to problems arising in everyday life, society, and the workplace.
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.
2.5A-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.
2.7A-Determine whether a number up to 40 is even or odd using pairings of objects to
represent the number.
2.7B-Use an understanding of place value to determine the number that is 10 or 100 more or
less than a given number up to 1,200.
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.1E
internalize new basic and academic language by using and reusing it in meaningful
ways in speaking and writing activities that build concept and language attainment
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.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.4D
use prereading supports such as graphic organizers, illustrations, and pretaught
topic-related vocabulary and other prereading activities to enhance comprehension of written text
ELPS.c.5C
spell familiar English words with increasing accuracy, and employ English spelling
patterns and rules with increasing accuracy as more English is acquired
Misconceptions:
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Some students may think you can use the dollar symbol, decimal, and cent symbol in the
same representation because the labels “dollars” and “cents” are both stated when describing
the value of coins and bills rather than either using the dollar symbol with a decimal or using
the cent symbol.
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Some students may think they must add or subtract in the order that the numbers are
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 the cent symbol is only used to record values less than one dollar
and the dollar symbol is only used to record values greater than or equal to one dollar rather
than realizing that equivalent coin values can be recorded using different symbolic
representations (e.g., 75¢ or $0.75).
Some students may think the concept of even and odd numbers is related only to skip
counting rather than the relationships in pairs and doubles.
Underdeveloped Concepts:
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Some students may correctly recall the sum of two basic fact addends but have difficulty
applying the commutative property of addition to recall the sum when the addends are
reversed (e.g., 4 + 5 and 5 + 4 seen as different facts).
Some students may correctly determine related addition number sentences but have
difficulty determining the subtraction number sentences within a fact family.
Some students may recognize the traditional views of coins but not recognize new or
commemorative views (e.g., state quarters, buffalo nickels, etc.).
Some students may not realize why collections of coins that look different may have the
same value.
Students may not have grasped the inverse relationships of addition and subtraction, which
may cause confusion when solving problems involving the start unknown or change
unknown.
Without fluency in grouping strategies, some students may not be able to take advantage of
mental math strategies for successful fact retrieval, composing/decomposing numbers,
number line representations, and compound counting with coins.
Vocabulary:
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Addend – a number being added or joined together with another number(s)
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
Even number – a number represented by objects that when paired have zero left over
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
Odd number – a number represented by objects that when paired have one left over
Place value – the value of a digit as determined by its location in a number such as ones,
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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:
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Addition
Hundreds place
Cent symbol (¢) Less than, fewer than
Change unknown
Nickel
Decimal point
Number sequence
Dime
Ones place
Dollar
One thousands place
Dollar sign ($)
Pairing
Greater than, more than
Part-part-whole Value
Penny
Quarter
Result unknown
Skip counting
Start unknown
Subtraction
Tens place
Half-dollar
List of Materials:
Engage/Day 1Word problem cards
Manipulatives/ counters of different types
Explore/Day 2&3Rulers or Yardsticks
Markers
Two Color Counters
Egg Cartons
Decks of Playing Cards
Scratch paper
Explain 2/Day 5Unifix or other locking cubes
Take It/Make It/Break It/Trace It paper
Explore/Explain 3/Day 6100’s charts
Blank grid paper
play coins/money
Sales Flyers
Explore/Explain 4/Day 7About 24 cards with numbers written on 1 side in the centuries (i.e. 234), and answers to
Corresponding spinner tasks on back (exe is shown in the activity description)
More than/less than spinner (10 +/-, 100 +/-)
6 small 10 x 10 grids
Elaborate 1/ Day 8100’s chart play coins/money
Other ideas for activities: http://www.pinterest.com/wyliespecialist/cscope-math-gr-2-1st-6-wks/
INSTRUCTIONAL SEQUENCE
Phase __Engage 1_____
Prior to instruction:
Print the Word Problem Cards and gather different types of manipulatives
Place a Word Problem Card at each station and different types of manipulatives
Activity:
TW supply manipulatives/counters of different kinds throughout the room.
SW receive a word problem card that describes different scenarios where adding or
subtracting will be used to solve the problem.
SW build the numbers with manipulatives/counters then model what is happening in the
story as they add on or take away manipulative/counters.
This activity is used as a formative assessment to see how the students solved the
problems. Do not let them say, “I just know it.”
SW show their work on paper and any strategies they used to solve the problem and build
their model.
SW then travel to the different areas of the room, where the manipulative/counters were
placed with problem cards, and look for similarities and differences in strategies used by
fellow students.
Near Doubles, Doubles, Make Ten, Splitting Strategies, Counting On, Counting Back,
Compensation, and Related Facts are all possible strategies used by students so TW look
for these and label them accordingly then group them by similar strategy as students visit
the areas again to see these visuals. These can be used as visual examples of each of these
strategies, to place in the room, etc.
Teacher Notes on strategies can be found at this link
http://www.decd.sa.gov.au/northernadelaide/files/links/mathematicsdefinitions.pdf
What’s the teacher doing?
Observing students as they travel through the areas in
the room and work.
Looking for similar strategies used by students in
their drawings and models.
Sorting the models and drawings to put like styles
together and label any that are:
Near Doubles, Doubles, Make Ten,
Splitting Strategies, Counting On, Counting
Back, Compensation, and Related Facts
Recording any students that are struggling
with the understanding of any specific
strategies and/or the problems, overall.
What are the students doing?
Visiting the areas with
manipulative/counters and word problem
cards
Building models of the word problems with
the manipulatives/counters
Drawing their model and showing work for
solving the problem on the card
Visiting the areas again to look for
similarities and differences in strategies
used by other students
Visiting the areas another time, once teacher
has labeled and grouped strategies
Phase _____Explore_1________
Prior to Instruction:
Gather yardsticks and/or rulers for each student or pair of students
Prepare egg cartons with 12 of the 2 color counters in each carton
Gather decks of playing cards and scratch paper
All of these activities should be introduced as different ways to model addition and
subtraction and can be used in conjunction with the above word problem cards from the
Engage phase of this lesson to model for students then each of these Explore activities can
be used as centers/workstations within the classroom for students to visit.
Activity 1: “Yardstick Number Line”
TW give each child a ruler or yardstick, depending on the available space. Let each child
choose a marker to use. You can bring in old game board pieces, coins, erasers or other
token markers.
TW call out a number and have each child place his chosen marker on that number.
TW call out another number and have the child physically move his marker the number of
steps to get to that number.
TW explain to the students that the number of steps he moved his marker is the difference
of the two numbers. This activity provides the child with a visual understanding of
subtraction. (exe: the teacher called out 10 first so students placed a marker on 10 then the
next number was 5 so students moved their marker to the 5 which means that they jumped
back 5 spaces so the difference between 10 and 5 is 5)
SW will then practice adding and subtracting on the yardstick/ruler as a number line and
jumping forward and back.
Activity 2: “Broken Eggs”
TW place twelve two colored counters in an egg carton with Yellow side up (not broken).
TW then open the egg carton with counters in it and say, "we are going to make believe
that these counters are eggs inside of this egg carton. All of these eggs are in one piece
because they are on the yellow side, so that will mean they are not broken. The red
counters represent broken eggs."
TW then say, "they are in one piece now." Drop the carton and say, "oops, I dropped my
eggs, let's see if they are still in one piece." Open it and show the class.
TW give the class a problem that represents your broken eggs. "I started with twelve eggs
and I dropped the eggs and broke ______, now I have _____ left. So I could say 12____=_____."
TW give the carton to a student to shake up.
SW then open the carton and depending on which are broken (say, "there are still 12 eggs
in the carton, but 5 are broken. So how many good eggs do we have left?")
TW have the children respond with the answer and the subtraction problem they used to
get that answer. Repeat the steps above with more students.
Activity 3: “Go Fish Adding Game”
The object of the game is to get as many pairs of cards as you can that total 20. The
winner of the game is the player with the most pairs of cards that equal 20.
Each player is dealt five cards. The remaining cards are placed face down in a deck in the
center of the table or play area.
If you have any pairs that total 20 in your first hand, put them down in front of you and
replace those cards with cards from the deck.
As you find combinations of numbers that equal 20, each player will use a pencil to write
that addition problem on his or her own lined sheet of paper. Place all of your
combinations of ten in one pile after you have written that combination on your paper.
Take turns. On a turn, ask one of the other players for a card that will go with a card in
your hand to make 20. (Note: a "WILD" card can be whatever number you would like it to
be to make a pair that adds up to 20.)
If you get a card that makes 20, put the pair of cards down. Then take one card from the
deck. Your turn is over.
If you do not get a card that makes 20 because the other player did not have the card you
asked for, take a card from the deck. Then your turn is over.
If the card you take from the deck makes 20 with a card in your hand, put the pair down
and take another card.
If there are no cards left in your hand but still cards in the deck, take two cards.
The game is over when there are no more cards left unpaired. Whoever has the most pairs
of 20 at the end of the game wins!
What’s the teacher doing?
What are the student’s doing?
Modeling each of the activities/games
Observing the teacher as they model the
activities/games
Setting up each of the activities/games in an
area of the room that students can visit later
Assisting in modeling of the activities/games
Listening and observing students as they
participate in the activities/games
Participating in trying out each activity/game that
will be in a center within the room for later use
Writing the addition and subtraction problems that
represent each of the addition and/or subtraction
problems from the games
Verbalizing the equations that they are writing down
by stating
I drew a five and I already had a 10 and another 5 so
I now have 20” or “I drew the 5 card and added to
my 10 and my other 5 card to make a sum of 20”
Phase ______Explain_1___________
Prior to Instruction:
Gather two colors of markers, pencils or crayons for each student and paper
Activity:
Using equations from the past days TW start by color coding with the kids and have them
highlight or underline the largest number in each of five problems, with both colors then
one of the smaller numbers with a color and the other number with the second color or you
can do this for them with boxes or circles of the colors to get them started.
TW show them and discuss, repeatedly, that these are the members of the family and they
must all three be there and the largest number has both colors because it takes the other
two to make it.
Once they work with the color coding, several times, they should get in the habit of
knowing that the subtraction will always start with the largest number (two colors) and the
addition will always end with the largest number ( two colors).
15
3
3
15
18
18
Addend + addend= sum
18
3
15
Minuend-subtrahend=difference
18
5
13
Color coding for add/sub check or
sub/add check
Good color
58
5
3
8
3
coding if you
are teaching it
as work
opposite
direction (up)
and opposite
sign to check .
5
It is fine to continue using the colors as long as needed if you are always talking them
through the process also.
What’s the teacher doing?
What are the students doing?
Collecting equations from student papers done in the
centers during the Explore 1 activities.
Observing the teaching models.
Modeling those equations with different addends
missing.
Color coding the largest number and the smaller
numbers as modeling is done.
Using paper, whiteboards or desk tops to record and
color code the example equations being modeled.
Asking questions and answering questions during the
modeling process.
Phase ______Explain 2________________________
Prior to Instruction:
Print and copy the Take It/Make It/Break It/ Trace It page for each student
Gather enough blocks for each student to have at least 40
Activity:
TW list all number combinations that students can think of for equaling 11 without any
operation signs0 11
1 10
2 9
3 8
4 7
5 6
6 5
7 4 ….. and so on
TW then ask if there’s something the numbers all have in common on those lists?
TW continues:
If I decided that I wanted an operation to make all of these into number
sentences and for them to all equal the same thing, horizontally (draw lines
under the numbers across column one and two to show horizontally as you
repeat that term) what operation could I use?
If no responses, TW prompt with addition and subtraction as a possibility
and if there are responses try them while also modeling with blocks but be
sure to show subtraction at some point with the first two.
So If I use the first numbers, 11 and 0 ( show a stick of 11 blocks) and I
take away the second number (show that you are taking away 0
blocks) how many do I have left over? (also fill in the subtraction
and equals sign on the list of numbers)
Now let’s try the second set of numbers (show a stick of 10 blocks) If I
have 10 and I take away 1 how many do I have left over? Does that
answer of 9 match our first answer of 11? No, so this operation is
not what I want because I wanted what? (kids should recall that
you wanted the number sentences to all equal the same thing)
TW then give students 2-3 minutes with a partner (assign one person
to each color of blocks and teach them to say “take it” when they
get the blocks then “make it” when they combine the blocks and
“trace it” when they write the number sentences down)to figure out
an operation that you think will work to meet our two goals of
equaling the same thing and figuring out the operation to use on all
of these.
They should come up with addition or prompt them to that if not coming
to that conclusion on their own.
Using the blocks, model each of the number sentences together to check
the answers by having each group “take it” then “make it” with a
certain assigned fact from the list and “trace it” on the board.
Now what if I had 6 houses for these facts and I needed to find a place for
every fact that you’ve made here? They all equal the same thing
but are they all part of one large fact family? No, because they are
not the same numbers in each of the number sentences (point out
some examples)
So, do any of them have the same numbers in the number sentences?
See if you can take your assigned facts and find the other fact/number
sentence that has the same numbers and stand with those people
now.
How many groups of people do we have now? Six so those are the facts
that could move into the houses and why is that?
Well now that everyone has somewhere to live, some of the numbers need
to leave and “break free” for school, work, play and all different
reasons.
If we added to bring everyone together, what operation could we use with
those numbers to help “break” them off for leaving?
So we “take it” to get the blocks, “make it” to put them together for
addition, “trace it” to show the number sentence then “break it” to
take one of the numbers away from the whole. (model this several
times while saying the phrases)
You will have 2-3 minutes with your whole family group to decide what
two subtraction “break it” problems you can make. Remember that
the largest number, both colors combined, has to come first in both
subtraction problems.
Students now “trace it” a group at a time, depending on time, the
subtraction problems that their group could make as they say
“make it” and make the whole stick with two numbers then “break
it” to show what number is taken away. (one child writes as one
does the blocks)
TW also ask students to line blocks next to each other to see that in some cases the blocks
line up exactly with each block having a partner and in some cases it does not and there are
left overs that have no partner. Use this as a way to lead students to the understanding of
odds and evens and extend with students looking at each addend as blocks and breaking
them up to see if they are odd or even, the sum and if it is odd or even. As students work
through this they will start to notice pattern such as two odds added can make an even
because each has a partner, two evens can add to an even but not an odd. What does it take
to make an odd sum, etc. and have students discuss these using correct terminology as they
explain the situations.
Students will now complete 2 problems on a large paper, for evaluation. Students who
were successful with the color coding could benefit from the “Make it, Take It” color
coded mat.
Draw, on the board, 5 sets of blocks with varying numbers of red and blue (exe: 3 red, 2
blue…..4 red, 7 blue….6 red, 3 blue…2 red, 8 blue)
Model 2 red, 5 blue but be sure to also do double digit added to single digit:
Take it
Break it
Make it
Trace it
5+2=7
2+5=7
7-2=5
7-5=2
Also going on to show, the ones that are ready, how any number can be written as the
magic number was to quickly recall all of the facts for that number and match like
terms for fact families can be done.
EXE:
5 0
8
0
When memorizing facts, have
4 1
7
1
kids write these ladders and
3 2
6
2
add the + signs instead of just
2 3
5
3
writing facts, then have them
1 4
4
4
find the number sentences
0 5
3
5
with like terms for fact
2
6
families.
1
7
0
8
What’s the teacher doing?
Modeling and explaining the processes.
What are the students doing?
Working with students who need help as others
are attempting the different ideas being
presented.
Attempting the models with blocks, on paper
and discussing with peers and the teacher, the
processes they are doing.
Observing students as they attempt the
problems to see who needs more help.
Observing teaching models being done.
Creating the models in concrete, pictorial and
abstract number forms.
Phase _____Explore/Explain 3________
Prior to Instruction:
Gather the play money and coins for each student to have at least 10 of each coin and
a variety of bills as needed
Print and Copy the 100’s chart for each student
Gather crayons for students to use
Activity: Money Exchange Game/Roll to …
SW play this game then TW transition them to the Making Change game to bring in
the explanation of adding the money amounts and making change as the subtraction.
To transition to a conversation of numbers to money and value in money, ask
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What is the purpose of money?
Why are coins an important form of money?
Why is it important to understand the value of money?
Ask students about the value of each of the coins and what they already know
about the coins.
What does it mean to spend money or buy something or pay for something?
(money is going away/subtracting)
What does it mean to earn money or be given money? (addition)
1. Students roll die to determine who begins. Highest number
begins the game.
2. Player rolls and takes appropriate coins. e.g. 4 = 4 pennies
3. Students exchange coins as needed. e.g. 5 pennies =1 nickel
5 nickels = 1 quarter
4. The winner is the first student to reach $1.00.
Extensions: 10 pennies = 1 dime
10 dimes = 1 dollar
5 pennies = 1 nickel
2 nickels = 1 dime
10 dimes = 1 dollar etc.
Making Change
1. Tell students that the grid represents 100 pennies which make up a
dollar. You may wish to do some whole class samples first.
2. Students cut out 6 items from the flyers that cost less than $1.00.
3. They glue the item with it’s price and one of the grids side by side
on the blank paper.
4. Using the play money, they reproduce the cost of the item. Next,
using the crayon they color in the equivalent number of boxes to
match the price of the item.
5. Students then look at what’s left and record that amount as their
change due beside the grid on the paper.
Source: The Power of Ten by Trevor Caulkin
Extra Activity:
TW ask how many ways can you make 20? (students will likely think of at least 3 ways of
adding numbers)
SW look over a 100's chart and use play money to see if they can think of more ways to
make 20.
SW lay pennies on the 1 then 2 and so on until they get to 20. Next have them lay nickels
on the 5 then pennies on the numbers after until they get to 20 and count out loud 5 then
6,7,8 and so on to 20. Do several combinations of these.
TW have student volunteers walk through the combinations again they record addition
problems for them (exe: nickel then pennies to 20 would be 5+15 more pennies and so on.)
SW with then record several addition problems that they can prove on the hundreds chart.
Repeat the process with subtracting money on the 100’s chart in the same manner.
What’s the teacher doing?
Modeling the activity
Observing students as they attempt the
activities
What are the students doing?
Observing the teacher as the activity is modeled
Attempting the activity with partners, groups and
on their own.
Recording equations and working with the money
and charts to justify the equations
Reviewing and assisting students that need
more help
Phase _____Explore/Explain 4______
Prior to Instruction:
Create cards as shown in the example below with different numbers of varying
centuries (100’s, 200’s,300’s etc.)
Create spinner as shown in the example below (students can use an opened paper clip
to spin with the a paper broken into the four sections instead of making spinners)
Activity: More Than, Less Than spinner game
Shuffle number cards and place face up.
2. Player 1 picks a card and writes the number on his/her paper.
3. The player spins the spinner and changes the number on the card
according to what the spinner tells him/her to do. Record on paper.
4. The player then verifies if the answer is correct by looking on the back
of the card. If it is he gets 1 point.
5. The card goes to the bottom of the pile.
6. The other players repeat the same in turn.
7. Play continues until a player gets a predetermined number of points, such as 10.
How can we use this 100’s chart to work with these
numbers? (even though the numbers might be past 100,
we can see that 134 up 10 is 144 so it the number is 234
it must go up to 244)
Source: Découvertes mathématiques by Éditions Accords Inc.
What’s the teacher doing?
What are the students doing?
Modeling the activity
Observing the modeling then working on the activity
with a partner as students get assistance in small
groups
Assisting students that are still struggling
in small groups or one on one
Phase _____Elaborate 1__
Prior to Instruction:
You will be using the centers and materials that were already presented
Print and copy 100’s charts for each student
Gather coins for students to where each student has at least 10 of each coin
Activity:
SW go through the centers/workstations created earlier in the lesson and do the activities
with money amounts replacing any numbers.
SW do several as coin amounts using the correct decimal placement and cent/dollar sign
then do several as dollar amounts.
This new activity can also be included and/or used for students that have mastered other
activities and need moreActivity:
SW ask how many ways can you make 20? (students will likely think of at least 3 ways of
adding numbers)
SW look over a 100's chart and use play money to see if they can think of more ways to
make 20.
SW lay pennies on the 1 then 2 and so on until they get to 20. Next have them lay nickels
on the 5 then pennies on the numbers after until they get to 20 and count out loud 5 then
6,7,8 and so on to 20. Do several combinations of these.
TW have student volunteers walk through the combinations again they record addition
problems for them (exe: nickel then pennies to 20 would be 5+15 more pennies and so on.)
SW with then record several addition problems that they can prove on the hundreds chart.
Repeat the process with subtracting money on the 100’s chart in the same manner.
SW also decide if numbers (money amounts) are odd or even by pairing up equal coin
amounts to see if there are any left over that would make that amount odd.
What’s the teacher doing?
What are the students doing?
Working with students in small groups
and/or one on one to go back over
activities and concepts not mastered
Working with partners, groups and independently in
centers
Phase _____Evaluate__
Provide a set of 40 counters. Present the following real-world situations and tasks:
1) Eastland Elementary is having a book fair to raise money for new library books. For each
problem situation:
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Record a number sentence that could be used to solve the problem with the unknown
indicated.
Determine the solution to the problem.
Explain the strategy used to solve the problem and justify the reasonableness of the
solution.
a) There were only 3 bookmarks left on the display at the book fair. The librarian put some more
bookmarks on the counter, and now there are 12 bookmarks on the display. How many bookmarks
did the librarian put on the counter?
b) Reed had some quarters to spend at the book fair. His mother gave him 6 more quarters, and
now he has 14 quarters. How many quarters did Reed have to start with?
c) The librarian had some copies of the book, Skippy Jon Jones, to sell at the book fair. She sold 7
copies on the first day and counted 10 copies left to sell during the rest of the week. How many
copies of the book did the librarian start with?
d) The librarian started with 16 pet-shaped erasers to sell at the book fair. She sold some of the
erasers on Monday and counted 8 erasers left to sell. How many pet-shaped erasers did the
librarian sell on Monday?
2) Linda and Rafael have the following coins to spend at the book fair:
a) Record the value of Linda’s collection of coins using two different representations.
b) Describe how the symbol(s) of each representation is used to name the value of Linda’s coin
collection.
c) Rafael said his collection of coins was equal in value to Linda’s collection of coins. Determine the
value of Rafael’s collection of coins.
d) Orally explain whether Rafael is correct, and how you know.
3) Joaquin and Victoria each bought a new chapter book at the book fair. For each problem
situation:
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Record a number sentence and solution to each question.
Orally describe the pattern in the place value of the solutions as 10 or 100 is added to or
subtracted from the number of pages.
a) Joaquin decided to keep track of the number of pages he had read in the book. During the first
day, he read 73 pages. The second day he only read 10 more pages. The third day he read 100
more pages. How many total pages had Joaquin read by the second day? How many total pages
had Joaquin read by the third day?
b) Victoria decided to keep track of the number of pages she had left to read in the book. The
chapter book has a total of 859 pages. On the first day, she read 10 pages. On the next day, she
read 100 pages. How many pages does Victoria have left in her book on the first day? How many
pages did Victoria have left to read on the second day?
4) Shatina is helping the librarian count the items left at the end of the book fair. She counted 29
fancy pencils and 36 fancy pens. For each question:
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Use counters to model each number.
Orally describe the models and how they were used to determine whether each number
was odd or even.
a) Was the number of pencils left an even or odd number?
b) Was the number of pens left an even or odd number?
United States coin image(s) used following official guidelines from the United States Mint
What’s the teacher doing?
What are the students doing?
Working with students in small groups
and/or one on one to go back over
activities and concepts not mastered
Working with partners, groups and independently in
centers