KINDERGARTEN Unit 5: Investigating Addition and Subtraction
9 Weeks
In this unit students will:
 Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
 Students will model simple joining and separating situations with sets of objects, or eventually with equations.
 Demonstrate the understanding of how objects can be joined (addition) and separated (subtraction) by representing addition and subtraction situations in
various ways.
 Solve problems presented in a story format (context) with a specific emphasis on using objects or drawings to determine the solution
 Understand that set of (5) objects can be decomposed- broken into two sets (3 and 2) and still be the same total amount (5).
 Count to 100 by ones and tens
Unit Resources:
Unit 5 Overview Video
Sample Post Assessment
Parent Letter
Number Talks Calendar
Vocabulary Cards
Prerequisite Skills Assessment
Topic 1: Investigating Addition and Subtraction
Big Ideas/Enduring Understandings:
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Part-Part-Whole problems involve three quantities: two parts that are combined into one whole
Problems can be solved in different ways.
Problems can be modeled using objects, pictures, and words.
Various combinations of numbers can be used to represent the same quantity.
Counting tells how many things are in a set.
The last number word, when counting, names the quantity for that set.
Sets of objects can be compared to determine more than, fewer than or equal.
Numbers are related to each other through a variety of number relationships. For example, 6 is one more than 5 and 4 less than 10, is composed of 3 and 3
as well as 4 and 2, and can be recognized quickly in patterned arrangements of dots.
Essential Questions:
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How can I represent and solve problem situations using objects, pictures, words and numbers?
What happens when I join quantities together?
What happens when sets are joined or separated?
How can I use different combinations of numbers to represent the same quantity?
How can using benchmark numbers help me when adding or subtracting?
How can I use models to represent addition and subtraction?
How can using benchmark numbers help me when adding or subtracting?
Why is it important that I can build the number combinations for the number 5?
What happens when I decompose a quantity? How do you know when your answer makes sense?
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Does the order of addends change the sum? How do you know when your answer makes sense?
How do you know how many objects you have?
How do you know if you have more or less than your partner?
Content Standards
Content standards are interwoven and should be addressed throughout the year in as many different units and activities as possible in order to emphasize the natural connections
that exist among mathematical topics.
MGSEK.CC.1 Count to 100 by ones and by tens.
MGSEK.CC.6 Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group,
e.g.,by using matching and counting strategies. (Limit category counts to be less than or equal to 10)
MGSEK.CC.7 Compare two numbers between 1 and 10 presented as written numerals.
These standards for quarter 3 only will be within 5. The completed standard OA.1-4 (within 10) will be taught in quarter 4.
MGSEK.OA.1 Represent addition and subtraction with objects, fingers, mental images, drawings1, sounds (e.g., claps), acting out situations, verbal explanations,
expressions, or equations. (within 5)
MGSEK.OA.2 Solve addition and subtraction word problems, and add and subtract within 5 e.g., by using objects or drawings to represent the problem.
(Addition and subtraction situation problems for Kindergarten are: Joining problems with Result Unknown, Separating problems with Result Unknown, Put
Together/Take Apart with Total Unknown and Both Addends Unknown. The following chart is highlighted for Kindergarten. The other types of word problems are
for First and Second Graders)
MGSEK.OA.3 Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition
by a drawing or equation. (drawings need not include an equation). (within 5)
MGSEK.OA.4 For any number from 1 to 5, find the number that makes 5 when added to the given number, e.g., by using objects or drawings, and record the
answer with a drawing or equation.
MGSEK.OA.5 Fluently add and subtract within 5.
Join/Combine
1
Problem Types (Highlighted types are Kindergarten Situations)
Result Unknown
Change Unknown
Two bunnies sat on the grass. Three
Two bunnies were sitting on the grass.
more bunnies hopped there. How
Some more bunnies hopped there. Then
many bunnies are on the grass now?
there were five bunnies. How many
2+3=?
bunnies hopped over to the first two?
2+?=5
Drawings need not show details, but should show the mathematics in the problem.
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Limit category counts to be less than or equal to 10.
2
Start Unknown
Some bunnies were sitting on the grass.
Three more bunnies hopped there. Then
there were five bunnies. How many
bunnies were on the grass before?
?+3=5
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Separate/
Decompose
Put Together / Take
Apart2
Five apples were on the table. I ate
two apples. How many apples are on
the table now? 5 – 2 = ?
Five apples were on the table. I ate some
apples. Then there were three apples. How
many apples did I eat?
5–?=3
Total Unknown
Addend Unknown
Three red apples and two green apples
are on the table. How many apples are
on the table?
3+2=?
Five apples are on the table. Three are red
and the rest are green. How many apples
are green?
3 + ? = 5, 5 – 3 = ?
Vertical Articulation of Addition and Subtraction
First Grade Addition & Subtraction Standards
Second Grade Addition & Subtraction
MGSE1.OA.1 Use addition and subtraction within 20 Standards
to solve word problems involving situations of adding
to, taking from, putting together, taking apart, and
comparing, with unknowns in all positions, e.g., by
using objects, drawings, and equations with a symbol
for the unknown number to represent the problem
MGSE1.OA.3 Apply properties of operations as
strategies to add and subtract.2
MGSE1.OA.4 Understand subtraction as an unknownaddend problem.
MGSE1.OA.5 Relate counting to addition and
subtraction.
MGSE1.OA.6 Add and subtract within 20.
a. Use strategies such as counting on; making ten (e.g.,
8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number
leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9);
using the relationship between addition and
2
3
MGSE2.OA.1 Use addition and subtraction within
100 to solve one and two step word problems by
using drawings and equations with a symbol for the
unknown number to represent the problem.
Problems include contexts that involve adding to,
taking from, putting together/taking apart
(part/part/whole) and comparing with unknowns in
all positions.
MGSE2.OA.2 Fluently add and subtract within 20
using mental strategies.3 By end of Grade 2, know
from memory all sums of two one-digit numbers.
MGSE2.NBT.5 Fluently add and subtract within 100
using strategies based on place value, properties of
operations, and/or the relationship between
addition and subtraction.
Some apples were on the table. I ate two
apples. Then there were three apples.
How many apples were on the table
before?
?–2=3
Both Addends Unknown1
Grandma has five flowers. How many can
she put in her red vase and how many in
her blue vase?
5 = 0 + 5, 5 = 5 + 0
5 = 1 + 4, 5 = 4 + 1
5 = 2 + 3, 5 = 3 + 2
Third Grade Addition & Subtraction
Standards
MGSE3.NBT.2 Fluently add and subtract within
1000 using strategies and algorithms based on
place value, properties of operations, and/or the
relationship between addition and subtraction.
MGSE2.NBT.7 Add and subtract within 1000, using
Students need not use formal terms for these properties. Problems should be within 20.
See standard 1.OA.6 for a list of mental strategies.
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subtraction (e.g., knowing that 8 + 4 = 12, one knows
12 – 8 = 4); and creating equivalent but easier or
known sums (e.g., adding 6 + 7 by creating the known
equivalent 6 + 6 + 1 = 12 + 1 = 13).
b. Fluently add and subtract within 10.
concrete models or drawings and strategies based
on place value, properties of operations, and/or the
relationship between addition and subtraction;
relate the strategy to a written method.
Addition and Subtraction Instructional Strategies
For numbers 0 – 5 (this quarter), Kindergarten students choose, combine, and apply strategies for answering quantitative questions. This includes quickly
recognizing the cardinalities of less sets of objects, counting and producing sets of given sizes, counting the number of objects in combined sets, or counting the
number of objects that remain in a set after some are taken away. Objects, pictures, actions, and explanations are used to solve problems and represent
thinking. Although GSE states, “Kindergarten students should see addition and subtraction equations, and student writing of equations in kindergarten is
encouraged, but it is not required”, please note that it is not until First Grade when “Understand the meaning of the equal sign” is an expectation.
Mathematically proficient students communicate precisely by engaging in discussion about their reasoning using appropriate mathematical language. The
terms students should learn to use with increasing precision with this cluster are: join, add, separate, subtract, and, same amount as, equal, less, more,
compose, and decompose
OA.1 asks students to demonstrate the understanding of how objects can be joined (addition) and separated (subtraction) by representing addition and
subtraction situations in various ways. This objective is primarily focused on understanding the concept of addition and subtraction, rather than merely reading
and solving addition and subtraction number sentences (equations). Create written addition or subtraction problems with sums and differences less than or equal
to 10 using the numbers 0 to 10. It is important to use a problem context that is relevant to kindergarteners. After the teacher reads the problem, students choose
their own method to model the problem and find a solution. The teacher and students should use the words equal and is the same as interchangeably.
The standard OA.2 asks students to solve problems presented in a story format (context) with a specific emphasis on using objects or drawings to determine the
solution. This objective builds upon their understanding of addition and subtraction from K.OA.1, to solve problems. Once again, numbers should not exceed 10.
Provide contextual situations for addition and subtraction that relate to the everyday lives of kindergarteners. A variety of situations can be found in children’s
literature books. Students then model the addition and subtraction using a variety of representations such as drawings, sounds, acting out situations, verbal
explanations and numerical expressions. Manipulatives, like two-color counters, clothespins on hangers, connecting cubes and stickers can also be used for
modeling these operations.
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Have students decompose numbers less than or equal to 5 during a variety of experiences to promote their fluency with sums and differences less than or equal to
5 that result from using the numbers 0 to 5. For example, ask students to use different models to decompose 5 and record their work with drawings or equations.
Students are to understand that a set of (5) objects can be broken into two sets (3 and 2) and still be the same total amount (5). In addition, this objective asks
students to realize that a set of objects (5) can be broken in multiple ways (3 and 2; 4 and 1). Thus, when breaking apart a set (decomposing), students develop the
understanding that a smaller set of objects exists within that larger set Next quarter, have students decompose 6, 7, 8, 9, and 10 in a similar fashion. As they come
to understand the role and meaning of arithmetic operations in number systems, students gain computational fluency, using efficient and accurate methods for
computing.
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Trajectory
Number Sense Trajectory –Putting It All Together
Subitizing
Being able to
visually
recognize a
quantity of 5
or less.
Comparison
Being able to
compare
quantities by
identifying
which has more
and which has
less.
Counting
Rote procedure of
counting. The
meaning attached
to counting is
developed
through one-toone
correspondence.
One-to-One
Correspondence
Students can
connect one
number with one
object and then
count them with
understanding.
Cardinality
Tells how many things are
in a set. When counting a
set of objects, the last word
in the counting sequence
names the quantity for that
set.
Hierarchical Inclusion
Numbers are nested
inside of each other
and that the number
grows by one each
count. 9 is inside 10 or
10 is the same as 9 + 1.
Number
Conservation
The number of
objects remains the
same when they are
rearranged spatially.
5 is 4&1 OR 3&2.
Number Relationships
Each concept builds on the previous idea and students should explore and construct concepts in such a sequence
Spatial Relationship
Patterned Set Recognition
Students can learn to recognize
sets of objects in patterned
arrangements and tell how
many without counting.
One and Two-More or Less
Students need to understand the relationship of number as it relates
to +/- one or two. Here students should begin to see that 5 is 1
more than 4 and that it is also 2 less than 7.
Understanding
Anchors
Students need to see
the relationship
between numbers and
how they relate to 5s
and 10s. 3 is 2 away
from 5 and 7 away
from 10.
Part-Part-Whole
Relationship
Students begin to
conceptualize a
number as being
made up from two
or more parts.
Comparing Numbers Common Misconceptions
Students may over-generalize the vocabulary in word problems and think that certain words indicate solution strategies that must be used to find an answer. They
might think that the word more always means to add and the words take away or left always means to subtract. When students use the words take away to refer
to subtraction and its symbol, teachers need to repeat students’ ideas using the words minus or subtract. For example, students use addition to solve this Take
from/Start Unknown problem: Seth took the 8 stickers he no longer wanted and gave them to Anna. Now Seth has 11 stickers left. How many stickers did Seth
have to begin with?
If students’ progress from working with manipulatives to writing numerical expressions and equations, they skip using pictorial thinking. Students will then be
more likely to use finger counting and rote memorization for work with addition and subtraction. Counting forward builds to the concept of addition while
counting back leads to the concept of subtraction. However, counting is an inefficient strategy. Teachers need to provide instructional experiences so that students
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progress from the concrete level, to the pictorial level, then to the abstract level when learning mathematics.
Evidence of Learning
Students will be able to:
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Count to 100 by ones and tens
Identify objects that are greater than, less than or equal to another set of objects
Compare 2 numerical numbers between 1 and 10
Represent addition and subtraction within 5
Solve addition and subtraction word problems within 5
Decompose numbers less than or equal to 5
Given a number, add a number to equal 5
Fluently add and subtract within 5
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Additional Assessment
Formative Assessment Lesson (FAL) https://ccgpsmathematicsk-5.wikispaces.com/K-5+Formative+Assessment+Lessons+%28FALs%29
Adopted Resources
My Math:
Adopted Online Resources
My Math
Chapter 4: Composing and Decomposing Numbers to
10
4.1 Make 4 and 5
4.2 Take Apart 4 and 5
http://connected.mcgraw-hill.com/connected/login.do
Chapter 4: Moving on the Number Line
4.3 Jumping on the Number Line
4.4 Jumping Forwards and Backwards
Teacher User ID: ccsde0(enumber)
Password: cobbmath1
Student User ID: ccsd(student ID)
Password: cobbmath1
Chapter 5: Making and Breaking Numbers
5.1 Grouping and Counting
5.2 Above, Below and In All
Chapter 5: Addition
5.1 Addition Stories
5.2 Use Objects to Add
5.3 Use the + Symbol
5.4 Use the = Symbol
5.5 How many in All?
Chapter 6: Subtraction
6.1 Subtraction Stories
6.2 Use Objects to Subtract
6.3 Use the – Symbol
6.4 Use the = Symbol
6.5 How Many are Left?
Think Math:
Examplar
http://www.exemplarslibrary.com/
 Bowl of Apples
 Buttons for Snowman
User: Cobb Email
Password: First Name
*These lessons are not to be completed in seven days as it is
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way too much material. They are designed to help support
you as you teach your standards.
Additional Resources
These next three websites are for students to practice adding and subtracting:
http://www.education.com/games/math/kindergarten/
http://www.abcya.com/addition.htm
http://www.turtlediary.com/kindergarten-games/math-games/learn-to-add.html
Mathematics TEKS Toolkit
http://www.utdanacenter.org/mathtoolkit/instruction/lessons/3_hundred.php
Estimation 180 is a website of 180 days of estimation ideas that build number sense. http://www.estimation180.com/days.html
Illustrative Mathematics provides instructional and assessment tasks, lesson plans, and other resources. https://www.illustrativemathematics.org/
http://www.gregtang.com
Suggested Manipulatives
Vocabulary
Suggested Literature
number lines
five frames
ten frames
100 chart
Dot cards (subitizing)
dice and dominos
rekenreks
number generators such as: dice, dominos, dot cards
objects to count (counters, snap/unifix cubes, bears,
pattern blocks, plane shapes, attri-links, coins)
Addition
Subtraction
Compose
Decompose
Equal
Same
Left
Combine
Take Away
Compare
Greater than
Less than
Quack and Count
Animals on Board
Ready, Set, Hop
Jack the Builder
Five Silly Fishermen
Rooster’s Off to See the World
Let’s Count it Out
Jessie Bear
Math for All Seasons
Napping House
Monster Math Picnic
Fat Frogs on a Skinny Log
Task Descriptions
Scaffolding Task
Constructing Task
Practice Task
Culminating Task
Formative Assessment
Lesson (FAL)
Kindergarten Unit 5
Tasks that build up to the learning task.
Constructing understanding through deep/rich contextualized problem solving tasks.
Tasks that provide students opportunities to practice skills and concepts.
Designed to require students to use several concepts learned during the unit to answer a new or unique situation. Allows students to
give evidence of their own understanding toward the mastery of the standard and requires them to extend their chain of
mathematical reasoning.
Lessons that support teachers in formative assessment which both reveal and develop students’ understanding of key mathematical
ideas and applications. These lessons enable teachers and students to monitor in more detail their progress towards the targets of
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3-Act Task
the standards.
A Three-Act Task is a whole-group mathematics task consisting of 3 distinct parts: an engaging and perplexing Act One, an information
and solution seeking Act Two, and a solution discussion and solution revealing Act Three. More information along with guidelines for
3-Act Tasks may be found in the Guide to Three-Act Tasks on georgiastandards.org and the K-5 CCGPS Mathematics Wiki.
Unit 3 State Comparing Numbers Tasks (These will focus on sums and differences to 5)
Task Name
What the Heck is
Rekenrek?
Find the 5th Tower
Addition/Subtraction
Word Problems
Standards
MGSEK.CC.1-4
MGSEK.MD.3
MGSEK.CC.1-4
MGSEK.G.1
MGSEK.MD.3
MGSEK.OA.1-5
MGSEK.OA.1,3,4,5
Building Trains
MGSEK.OA.1-5
Going Bananas
Shake and Spill
Addition/Subtraction
Summoning 5’s and
10’s
Bo Peep’s Domino
Dilemma
Kindergarten Unit 5
MGSEK.OA.1,3,4,5
MGSEK.OA.1,3,4,5
MGSEK.OA.1-5
Task Type/
Grouping Strategy
Constructing Task
Partner
Culminating Task
Whole group/Small group
Constructing Task
Individual. Whole, Small
Group
Content Addressed
Brief Description
Students make a Rekenrek. Students also
practice modeling numbers through a
variety of activities.
One to one correspondence,
Students use all the concepts they have
Understanding number relationships,
learned in this unit to complete a task.
Numeral writing, Positional words,
Ordinal words
Students answer different type addition
Addition and subtraction through
and subtraction story problems
word problems
Subitizing, Modeling numbers,
Understanding number relationships
Constructing Task
Whole or Small Group
Number combinations to 5 and 10
Practice Task
Whole, Small Group or
Individual
Constructing Task
Whole, Small Group or
Individual
Number combinations to 5 through
problem solving
Number combinations to 10 (+/-)
Practice Task
Partners
Using 5 as a benchmark number,
number combinations to 10
Practice Task
Whole, Small Group or
Individual
Number combinations to 5 and 10
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Students practice different ways of
building five using two different
quantities
Students find different combinations to
build 5 and 10
Students build number combinations to
10
Students practice using the benchmark
number 5 to build number combinations
to 10
Students use a variety of activities to
build combinations to 10
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The Bike Store
Dropping Pennies
MGSEK.OA.1-5
MGSEK.OA.1-5
MGSEK.OA.1-5
The Candy Store
Kindergarten Unit 5
Performance Task
Individual
Performance Task
Individual
Culminating Task
Individual
Number combinations to 5 through
problem solving
Number combinations to 5 through
problem solving
Number combinations to 5 through
problem solving
10
Students use different combinations to
five to solve a problem.
Students practice building number
combinations to 5
Students use their knowledge gained to
build number combinations to 5
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