KINDERGARTEN Unit 5: Investigating Addition and Subtraction9 WeeksIn 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 Parent Letter Number Talks Calendar Vocabulary Cards Prerequisite Skills AssessmentSample Post Assessment

Topic 1: Investigating Addition and Subtraction Big Ideas/Enduring Understandings:

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:

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? Does the order of addends change the sum? How do you know when your answer makes sense?

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How do you know how many objects you have? How do you know if you have more or less than your partner?

Content StandardsContent 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.

Problem Types (Highlighted types are Kindergarten Situations)Result Unknown Change Unknown Start Unknown

Join/Combine

Two bunnies sat on the grass. Three more bunnies hopped there. How many bunnies are on the grass now?

2 + 3 = ?

Two bunnies were sitting on the grass. Some more bunnies hopped there. Then there were five bunnies. How many bunnies hopped over to the first two?

2 + ? = 5

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

Separate/Decompose

Five apples were on the table. I ate two apples. How many apples are on

Five apples were on the table. I ate some apples. Then there were three apples. How

Some apples were on the table. I ate two apples. Then there were three apples.

1 Drawings need not show details, but should show the mathematics in the problem. 3 Limit category counts to be less than or equal to 10.2

Kindergarten Unit 5 2015-2016

the table now? 5 – 2 = ? many apples did I eat?5 – ? = 3

How many apples were on the table before?? – 2 = 3

Total Unknown Addend Unknown Both Addends Unknown1

Put Together / Take Apart2

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 = ?

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 + 05 = 1 + 4, 5 = 4 + 15 = 2 + 3, 5 = 3 + 2

Vertical Articulation of Addition and Subtraction

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First Grade Addition & Subtraction StandardsMGSE1.OA.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problemMGSE1.OA.3 Apply properties of operations as strategies to add and subtract.2

MGSE1.OA.4 Understand subtraction as an unknown-addend 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 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.

Second Grade Addition & Subtraction StandardsMGSE2.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.

MGSE2.NBT.7 Add and subtract within 1000, using 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.

Third Grade Addition & Subtraction StandardsMGSE3.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.

2 Students need not use formal terms for these properties. Problems should be within 20.3 See standard 1.OA.6 for a list of mental strategies.

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Addition and Subtraction Instructional StrategiesFor 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.

Number Sense Trajectory – Putting It All Together

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Traj

ecto

ry

SubitizingBeing able to visually recognize a quantity of 5 or less.

ComparisonBeing able to compare quantities by identifying which has more and which has less.

CountingRote procedure of counting. The meaning attached to counting is developed through one-to-one correspondence.

One-to-OneCorrespondenceStudents can connect one number with one object and then count them with understanding.

CardinalityTells 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 InclusionNumbers 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.

Each concept builds on the previous idea and students should explore and construct concepts in such a sequence

Num

ber R

elati

onsh

ips Spatial Relationship

Patterned Set RecognitionStudents can learn to recognize sets of objects in patterned arrangements and tell how many without counting.

One and Two-More or LessStudents 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 MisconceptionsStudents 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 progress from the concrete level, to the pictorial level, then to the abstract level when learning mathematics.

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Evidence of LearningStudents will be able to:

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

Additional AssessmentFormative Assessment Lesson (FAL) https://ccgpsmathematicsk-5.wikispaces.com/K-5+Formative+Assessment+Lessons+%28FALs%29Adopted ResourcesMy Math:Chapter 4: Composing and Decomposing Numbers to 104.1 Make 4 and 54.2 Take Apart 4 and 5

Chapter 5: Addition5.1 Addition Stories5.2 Use Objects to Add5.3 Use the + Symbol5.4 Use the = Symbol5.5 How many in All?

Chapter 6: Subtraction6.1 Subtraction Stories6.2 Use Objects to Subtract6.3 Use the – Symbol6.4 Use the = Symbol6.5 How Many are Left?

*These lessons are not to be completed in seven days as it is way too much material. They are designed to help support you as you teach your standards.

Adopted Online ResourcesMy Mathhttp://connected.mcgraw-hill.com/connected/login.do

Teacher User ID: ccsde0(enumber)Password: cobbmath1Student User ID: ccsd(student ID)Password: cobbmath1

Examplarhttp://www.exemplarslibrary.com/

Bowl of Apples Buttons for Snowman

User: Cobb EmailPassword: First Name

Think Math:Chapter 4: Moving on the Number Line4.3 Jumping on the Number Line4.4 Jumping Forwards and Backwards

Chapter 5: Making and Breaking Numbers5.1 Grouping and Counting5.2 Above, Below and In All

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Additional ResourcesThese next three websites are for students to practice adding and subtracting: http://www.education.com/games/math/kindergarten/ http://www.abcya.com/addition.htmhttp://www.turtlediary.com/kindergarten-games/math-games/learn-to-add.html

Mathematics TEKS Toolkit http://www.utdanacenter.org/mathtoolkit/instruction/lessons/3_hundred.phpEstimation 180 is a website of 180 days of estimation ideas that build number sense. http://www.estimation180.com/days.htmlIllustrative Mathematics provides instructional and assessment tasks, lesson plans, and other resources. https://www.illustrativemathematics.org/http://www.gregtang.comSuggested Manipulativesnumber lines five frames ten frames100 chartDot cards (subitizing)dice and dominosrekenreksnumber generators such as: dice, dominos, dot cardsobjects to count (counters, snap/unifix cubes, bears, pattern blocks, plane shapes, attri-links, coins)

VocabularyAdditionSubtractionComposeDecomposeEqualSameLeftCombineTake AwayCompareGreater thanLess than

Suggested LiteratureQuack and CountAnimals on BoardReady, Set, HopJack the BuilderFive Silly FishermenRooster’s Off to See the WorldLet’s Count it OutJessie BearMath for All SeasonsNapping HouseMonster Math PicnicFat Frogs on a Skinny Log

Task Descriptions

Scaffolding Task Tasks that build up to the learning task.Constructing Task Constructing understanding through deep/rich contextualized problem solving tasks.Practice Task Tasks that provide students opportunities to practice skills and concepts.Culminating Task 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.

Formative Assessment Lesson (FAL)

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 the standards.

3-Act Task A Three-Act Task is a whole-group mathematics task consisting of 3 distinct parts: an engaging and perplexing Act One, an information

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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 Standards Task Type/Grouping Strategy Content Addressed Brief Description

What the Heck is Rekenrek? MGSEK.CC.1-4

MGSEK.MD.3

Constructing TaskPartner

Subitizing, Modeling numbers, Understanding number relationships

Students make a Rekenrek. Students also practice modeling numbers through a

variety of activities.

Find the 5 th Tower MGSEK.CC.1-4MGSEK.G.1

MGSEK.MD.3

Culminating TaskWhole group/Small group

One to one correspondence, Understanding number relationships,

Numeral writing, Positional words, Ordinal words

Students use all the concepts they have learned in this unit to complete a task.

Addition/Subtraction Word Problems

MGSEK.OA.1-5 Constructing TaskIndividual. Whole, Small

Group

Addition and subtraction through word problems

Students answer different type addition and subtraction story problems

Building TrainsMGSEK.OA.1,3,4,5 Constructing Task

Whole or Small Group Number combinations to 5 and 10Students practice different ways of

building five using two different quantities

Going BananasMGSEK.OA.1-5 Practice Task

Whole, Small Group or Individual

Number combinations to 5 through problem solving

Students find different combinations to build 5 and 10

Shake and SpillAddition/Subtraction

MGSEK.OA.1,3,4,5 Constructing TaskWhole, Small Group or

IndividualNumber combinations to 10 (+/-)

Students build number combinations to 10

Summoning 5’s and 10’s

MGSEK.OA.1,3,4,5 Practice TaskPartners

Using 5 as a benchmark number, number combinations to 10

Students practice using the benchmark number 5 to build number combinations

to 10

Bo Peep’s Domino Dilemma

MGSEK.OA.1-5 Practice TaskWhole, Small Group or

IndividualNumber combinations to 5 and 10

Students use a variety of activities to build combinations to 10

The Bike Store MGSEK.OA.1-5 Performance TaskIndividual

Number combinations to 5 through problem solving

Students use different combinations to five to solve a problem.

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Dropping PenniesMGSEK.OA.1-5 Performance Task

IndividualNumber combinations to 5 through

problem solvingStudents practice building number

combinations to 5

The Candy StoreMGSEK.OA.1-5 Culminating Task

IndividualNumber combinations to 5 through

problem solving

Students use their knowledge gained to build number combinations to 5

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