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KINDERGARTEN Unit 6: Further Investigation of Addition and Subtraction (within 10)4 WeeksIn this unit students will: For numbers 0 – 10, 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.

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 10 objects can be decomposed- broken into two sets (3 and 7) and still be the same total amount (10). Unit ResourcesUnit 6 Overview Video Parent Letter Number Talks Calendar Vocabulary Cards Prerequisite Skills AssessmentSample Post Assessment

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

Addition and subtraction problems are placed in four basic categories: Joining problems, Separating problems, Part-Part Whole problems, and Comparing problems.

A joining problem involves three quantities: the starting amount, the change amount, and the resulting amount. A separating problem involves three quantities; the starting amount, the change amount (the amount being removed), and the resulting amount;

however, the starting amount is the largest amount with the change amount being removed which leaves the resulting amount. Compare problems involve the comparison between two different quantities. The third quantity does not actually exist but is the difference between the

two quantities. When one quantity is compared to another, the first quantity is either more than, less than, or equal to the second quantity. 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. 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. Problems can be modeled using objects, pictures, and words.

Essential Questions:

1Kindergarten Unit 6 2015-2016

Does the order of addends change the sum? How can I prove that groups are equal? How can I find the total when I put two quantities together? How can I find what is left over when I take one quantity away from another? How can I solve and represent problems using objects, pictures, words and numbers? How can I use different combinations of numbers to represent the same quantity? How can strategies help us solve problems? How can you model a math problem with objects or pictures? How do you know when your answer makes sense? What happens when I decompose a quantity? What happens when I join quantities together? What happens when some objects are taken away from a set of objects? What is the difference between addition and subtraction? Why is it important that I can build the number combinations for the number 5? 10?

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.OA.1 Represent addition and subtraction with objects, fingers, mental images, drawings1, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. MGSEK.OA.2 Solve addition and subtraction word problems, and add and subtract within 10 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).MGSEK.OA.4 For any number from 1 to 10, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.MGSEK.OA.5 Fluently add and subtract within 5.MGSEK.NBT.1 Compose and decompose numbers from 11 to 19 into ten ones and some further ones to understand that these numbers are composed of ten ones and one, two, three, four, five, six , seven, eight, or nine ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8)

Problem Types (Highlighted types are Kindergarten Situations)

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 6 2015-2016

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 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

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

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


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.


Addition and Subtraction Instructional StrategiesProvide 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. Kindergarten students should see addition and subtraction equations written by the teacher. Although students might have a difficult time at first, teachers should encourage them to try writing the equations. Students’ writing of equations in Kindergarten is encouraged, but it is not required.

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. Students discuss their solution strategies while the teacher represents the situation with an equation written under the problem. The equation should be written by listing the numbers and symbols for the unknown quantities in the order that follows the meaning of the situation. The teacher and students should use the words equal and is the same as interchangeably.

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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.


For OA.3 and OA.4, have students decompose numbers less than or equal to 10 during a variety of experiences to promote their fluency with sums and differences less than or equal to 10 that result from using the numbers 0 to 10. For example, ask students to use different models to decompose 10 and record their work with drawings or equations. Students are to understand that a set of (10) objects can be broken into two sets (3 and 7) and still be the same total amount (10). In addition, this objective asks students to realize that a set of objects (10) can be broken in multiple ways (3 and 7; 4 and 6). Thus, when breaking apart a set (decomposing), students develop the understanding that a smaller set of objects exists within that larger set. 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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OA.5 Students are fluent when they display accuracy (correct answer), efficiency (a reasonable amount of steps in about 3 seconds without resorting to counting), and flexibility (using strategies such as the distributive property). Students develop fluency by understanding and internalizing the relationships that exist between and among numbers. Oftentimes, when children think of each “fact” as an individual item that does not relate to any other “fact”, they are attempting to memorize separate bits of information that can be easily forgotten. Instead, in order to fluently add and subtract, children must first be able to see sub-parts within a number (inclusion, K.CC.4.c). Once they have reached this milestone, children need repeated experiences with many different types of concrete materials (such as cubes, chips, and buttons) over an extended amount of time in order to recognize that there are only particular sub-parts for each number. Therefore, children will realize that if 3 and 2 is a combination of 5, then 3 and 2 cannot be a combination of 6. NBT.1 This standard is the first time that students move beyond the number 10 with representations, such as objects (manipulatives) or drawings. The spirit of this standard is that students separate out a set of 11-19 objects into a group of ten objects with leftovers. This ability is a pre-cursor to later grades when they need to understand the complex concept that a group of 10 objects is also one ten (unitizing). Ample experiences with ten frames will help solidify this concept. Research states that students are not ready to unitize until the end of first grade. Therefore, this work in Kindergarten lays the foundation of composing tens and recognizing leftovers.

Number Sense Trajectory – Putting It All Together

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. Additional Assessment Formative Assessment Lesson (FAL): Snail in the Well https://ccgpsmathematicsk-5.wikispaces.com/K-5+Formative+Assessment+Lessons+%28FALs%29Adopted ResourcesMy Math:Chapter 4: Composing and Decomposing Numbers to 104.3 Make 6 and 74.4 Take Apart 6 and 74.5 Problem Solving Strategy4.6 Make 8 and 94.7 Take 8 and 94.8 Make 104.9 Take Apart 10

Chapter 5: Addition

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

Think Math:Chapter 5: Making and Breaking Numbers 5.7 Modeling Addition Problems5.13 Modeling Subtraction Problems

Chapter 6: Stories in Numbers, Words, and Pictures6. 1 Pairs that Make 106.2 Taking Away from 10


http://www.exemplarslibrary.com/

http://connected.mcgraw-hill.com/connected/login.do

https://ccgpsmathematicsk-5.wikispaces.com/K-5+Formative+Assessment+Lessons+(FALs)

5.6 Problem -Solving Strategy5.7 Adds to Make 10

Chapter 6: Subtraction6.6 Problem -Solving Strategy6.7 Subtract to Take Apart 10

Chapter 7: Compose and Decompose Numbers 11 to 197.1 Make Numbers 11 to 157.2 Take Apart Numbers 11 to 157.3 Problem- Solving Strategy7.4 Make Numbers 16 to 197.5 Take Apart Numbers 16 to 19

*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.

User: Cobb EmailPassword: First Name

Web 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.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 frames 100 chartDot cards (subitizing) dice and dominos

Vocabulary AdditionSubtractionComposeDecomposeEqualSame

Suggested Literature Quack and CountAnimals on BoardReady, Set, HopJack the BuilderFive Silly FishermenRooster’s Off to See the World


http://www.gregtang.com/

https://www.illustrativemathematics.org/

http://www.estimation180.com/days.html

http://www.utdanacenter.org/mathtoolkit/instruction/lessons/3_hundred.php

http://www.turtlediary.com/kindergarten-games/math-games/learn-to-add.html

http://www.abcya.com/addition.htm

http://www.education.com/games/math/kindergarten/

rekenreksnumber generators such as: dice, dominos, dot cardsobjects to count (counters, snap/unifix cubes, bears, pattern blocks, plane shapes, attri-links, coins)

LeftCombineTake AwayCompareGreater thanLess than

Let’s Count it Out Jessie Bear Math for All SeasonsNapping House Monster Math Picnic Fat Frogs on a Skinny Log

Task DescriptionsScaffolding 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 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.

State Performance Tasks

Task NameStandards Task Type/

Grouping Strategy Content Addressed Brief Description

Balancing ActMGSEK.OA.1-5 3-Act Task

Whole GroupAddition and subtraction through word problems

Students make different combinations to build the same quantity

Ten Flashing Fireflies

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

Addition and subtraction through word problems

Students use addition and subtraction while solving a story problem.

Got Your Number?MGSEK.OA.1-5 Practice Task

Individual or small Group Number relationships to 10Students play a card game to build

combinations to 10.

By The RiversideMGSEK.OA.1-5 Scaffolding Task

Individual, Whole or Small Group

Modeling number combinations through

problem solving

Students build different combinations for the same sum.

Capturing Bears (5/10)

MGSEK.OA.1-5 Practice TaskPartners

Number combinations to 5 and 10 and development of 8

Students use number combinations of 5 and 10 to play a game.


SMPs

Fishing TaleMGSEK.OA.1-5 Scaffolding Task

Individual, Whole or Small GroupNumber combinations to 5

through problem solvingStudents build number combinations to five

through story problems

Moving DayMGSEK.OA.1-5 Constructing Task

Individual, Whole and Small Group Number relationships to 10Students show different combinations to 10

How Many Ways to get to 10?

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

Making generalizations in number relationships to 10

Students come up with different combinations to build 10

A Day at the BeachMGSEK.OA.1-5 Practice Task

Individual, Whole or Small Group

Modeling number combinations to 10 through

problem solving

Students model different ways to make combinations up to 10.

At the Mechanics

MGSEK.OA.1-5Constructing Task

Individual, Whole and Small Group

Development with the understanding of equality

and number relationships to 10

Students manipulate the different quantities to make the number sentence true.

Field Trip for FivesMGSEK.OA.1-5 Practice Task

Individual, Whole or Small GroupNumber combinations to 5

through problem solvingStudents build number combinations to 5.

The Magic PotMGSEK.OA.1-5 Constructing Task

Individual, Whole and Small GroupMaking generalizations in

number relationships to 10Students look for patterns to solve word

problems through 10.

Equally Balancing Numbers

MGSEK.OA.1-5 Culminating TaskIndividual, Whole and Small Group

Number combinations to 10 through problem solving

Students use the knowledge gained to find patterns and build different number

combinations to 10.Peas-in-a-Pod MGSEK.NBT.1

CC.1-3,4abc,7MD.3

3-Act TaskWhole Group

Estimating, Number relationships, Comparing sets, One to one correspondence,

Categorizing

Students will use their number knowledge to count forwards and backwards and count

numbers higher than ten

“Teen” Frame Talk About (11-12)

MGSEK.NBT.1CC.3,4a,5a,b

Constructing TaskWhole Group/Partner

Number relationships Students work in a class discussion to understand the concept that a teen number is a

group of ten and some more“Teen” Frame Talk

About (13-19)MGSEK.NBT.1CC.3,4a,5a,b,6


Number relationships Students continue the work of the previous task with numbers 13-19.

Counting Cup MGSEK.NBT.1CC.3,4a,5a,b,6,

7MD.3

Practice TaskSmall Group or Partner

Estimating and one to one correspondence

Students practice counting forwards and backwards with various amounts of objects.


Moving a Cup of 10 MGSEK.NBT.1CC.3,4b,5a,b

Constructing TaskPartner

Counting, One to one correspondence, Unitizing

Students practice making ten and some more when building teen numbers.

Make a 10 and Carry On

MGSEK.NBT.1CC3,4a,5a,b,c,6

,7MD.3


Counting, Unitizing Students use pennies and dimes to create a group of ten and some more.

Race to 100 Pennies(revisited)

MGSEK.NBT.1CC.1,4b,5a,b,c,

6


Counting, One to one correspondence, Skip

counting, Unitizing

Students use their knowledge of building teen numbers to complete the activity using ten and

some more.10 and Some More MGSEK.NBT.1

CC.3,4a,5a,b,6,7

MD.3

Culminating TaskSmall Group/Individual

Counting, One to one correspondence, Number

relationships, Comparing sets

Students will use all the information gained from this and the previous unit to complete the

task by showing their understanding of teen numbers.


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