Kindergarten Unit 3: Comparing Numbers6 WeeksIn this unit students will:

Students will count to 100 by ones Students will write numbers up to 20 Students use numbers, including written numerals, to represent quantities and to solve quantitative problems, such as counting objects in a set up to 20 Students will count out a given number of objects Students will quickly recognize the cardinalities of small sets of objects

Unit Resources:Unit 3 Overview Video Parent Letter Parent Guides Number Talks Calendar Vocabulary Cards Prerequisite Skills Assessment Sample Post AssessmentTopic 1: Comparing NumbersBig Ideas/Enduring Understandings:• Counting tells how many things are in a set.• The last number word, when counting, names the quantity for that set.• Counting objects in a different order does not change the quantity.• Each successive number name refers to a quantity that is one greater.• A number can be represented by a set of objects and then by a numeral.• 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.• The numbers 5 and 10 are benchmark numbers. (Is a number closer to 5 or 10? How close?)Essential Questions:• How do you know if you have more or less than your partner?• When do we use counting skills in everyday life?• How can you know a quantity without counting each object?• How do we use counting in our everyday lives?• What is an efficient way to count an amount greater than ten?• Why do I need to be able to count objects?• How do I use numbers every day?Student Relevance: Counting to determine how much of something is needed or the amount that each person has to compare

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.

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Know number names and the count sequence.MGSEK.CC.1 Count to 100 by ones and by tens.MGSEK.CC.2 Count forward beginning from a given number within the known sequence (instead of having to begin at 1).MGSEK.CC.3 Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).Count to tell the number of objects.MGSEK.CC.4 Understand the relationship between numbers and quantities; connect counting to cardinality.a. When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.(one-to-one correspondence)b. Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.c. Understand that each successive number name refers to a quantity that is one larger.MGSEK.CC.5 Count to answer ‘how many?” questions.a. Count to answer “how many?” questions about as many as 20 things arranged in a variety of ways (a line, a rectangular array, or a circle), or as many as 10 things in a scattered configuration.b. Given a number from 1-20, count out that many objects.c. Identify and be able to count pennies within 20. (Use pennies as manipulatives in multiple mathematical contexts.)Compare numbersMGSEK.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.Classify objects and count the number of objects in each category.MGSEK.MD.3 Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. (Limit category counts to be less than or equal to 10)

Vertical ArticulationFirst Grade StandardsMGSE1.NBT.1 Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.MGSE1. NBT.3 Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

Second Grade StandardsMGSE2.NBT.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.MGSE2.NBT.4. Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.

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Comparing Numbers Instructional Strategies Have students say number words as a chant or a rote procedure plays a part in students constructing meaning for the conceptual idea of counting. They

will learn how to count before they understand cardinality, i.e. that the last count word is the amount of the set.

Counting on or counting from a given number conflicts with the learned strategy of counting from the beginning. In order to be successful in counting on, students must understand cardinality. Students often merge or separate two groups of objects and then re-count from the beginning to determine the final number of objects represented. For these students, counting is still a rote skill or the benefits of counting on have not been realized. Games that require students to add on to a previous count to reach a goal number encourage developing this concept. Frequent and brief opportunities utilizing counting on and counting back are recommended. These concepts emerge over time and cannot be forced.

One of the first major concepts in a student’s mathematical development is cardinality. Cardinality, knowing that the number word said tells the quantity

you have and that the number you end on when counting represents the entire amount counted. The big idea is that number means amount and, no matter how you arrange and rearrange the items, the amount is the same. Until this concept is developed, counting is merely a routine procedure done when a number is needed.

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To determine if students have the cardinality rule, listen to their responses when you discuss counting tasks with them. For example, ask, “How many are

here?”. The student counts correctly and says that there are seven. Then ask, “Are there seven?”. Students may count or hesitate if they have not developed cardinality. Students with cardinality may emphasize the last count or explain that there are seven because they counted them. These students can now use counting to find a matching set.

Students develop the understanding of counting and cardinality from experience. Almost any activity or game that engages children in counting and comparing quantities, such as board games, will encourage the development of cardinality.

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Like counting to 100 by either ones, writing numbers from 0 to 20 is a rote process. Initially, students mimic the actual formation of the written numerals while also assigning it a name. Over time, children create the understanding that number symbols signify the meaning of counting.

Numbers have meaning when children can see mental images of the number symbols and use those images with which to think. Practice count words and

written numerals paired with pictures, representations of objects, and objects that represent quantities within the context of life experiences for kindergarteners. For example, dot cards, dominoes and number cubes all create different mental images for relating quantity to number words and numerals. Students should study and write numbers 0 to 10 in this order: numbers 1 to 9, the number 0, and then numbers 10.

When comparing numbers, students will also identify whether the number of objects in one group is less than the number of objects in another group. Remember that with this standard students are comparing the objects using matching and counting strategies.

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Kindergarten children should be able to describe attributes of objects and classify these objects according to the identified attributes. Classifying objects is deciding how to categorize them and this is the most basic foundational skill of data analysis. Sorting objects into these identified categories is the beginning stages of organizing data. Going a step further and attaching a number to the set (10 or less in a set) is the bridge to displaying data in graphs and charts. Collecting data helps children answer questions about the world around them and this naturally follows the fundamental idea of data: to answer a question! Formulating questions and deciding how to represent information that has been collected requires one to decide what categories to create. Determining these categories and even changing categories to represent different attributes helps children make sense real world data. To develop this flexible reasoning about the characteristics of data, a student needs many experiences with categorizing attributes and representing the categories mathematically. Focusing on different attributes creates different classifications and later on in elementary, will produce different graphs.

Number Sense Trajectory – Putting It All Together

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Traj

ecto

rySubitizing

Being 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.

Common Misconceptions1. Some students might not see zero as a number. Ask students to write 0 and say zero to represent the number of items left when all items have been taken away. Avoid using the word none to represent this situation.2. Some students might think that the count word used to tag an item is permanently connected to that item. So when the item is used again for counting and should be tagged with a different count word, the student uses the original count word. For example, a student counts four geometric figures: triangle, square, circle and rectangle with the count words: one, two, three, and four. If these items are rearranged as rectangle, triangle, circle and square and counted, the student says these count words: four, one, three, and two.Evidence of Learning

Students will count to 120 by ones Students will write numbers up to 20 Students use numbers, including written numerals, to represent quantities and to solve quantitative problems, such as counting objects in a set Students will count out a given number of objects Students will quickly recognize the cardinalities of small sets of objects Students will compare sets of objects, greater than, less than, and equal to

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Students will sort and classify objectsAdditional Assessments

Adopted ResourcesMy Math:Chapter 1: Counting numbers to 5 1.6 Equal to 1.7 Greater than 1.8 Less than 1.9 Compare Numbers 0 to 5Chapter 2: Numbers to 10 2.7 Problem Solving 2.8 Compare Numbers 0-10Chapter 3: Numbers Beyond 10 3.8 Count to 50 by Ones 3.9 Count to 100 by Ones

*These resources are designed to help support you as you teach your standards.

Adopted Online Resources

My 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/

User: Cobb EmailPassword: First Name

Boots and Hats Buttons for Snowman

Think Math:(Review from Quarter 1)Chapters 1: Numbers to Ten 1.1 Number One 1.2 Number Two 1.3 Number Three 1.4 Number Four 1.5 Number Five 1.6 Working with Five 1.7 Number Six 1.8 Working with Six 1.9 Number Seven 1.10 Number Eight 1.11 Number Nine 1.12 Number Zero 1.13 Number Ten

Web ResourcesThese next three websites are for students to practice counting and comparing objects and numbers:http://www.primarygames.com/science/spacestation/index.htmhttp://www.kidport.com/GradeK/Math/MeasureGeo/MathK_Same.htmhttp://gamequarium.com/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

VocabularyGreater than

Suggested LiteratureDouble the Ducks

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five frames ten frames100 chartDot cards (subitizing)dice and dominosrekenreksSorting Circlesnumber generators such as: dice, dominos, dot cards objects to count and sort (counters, snap/unifix cubes, bears, pattern blocks, plane shapes, attri-links, coins)

Less thanEqual to

Quack and CountMath for All SeasonsNapping HouseGood Night OneMonster Math PicnicLet’s Count it OutJessie BearRooster’s Off to See theWorldFat Frogs on a Skinny Log Counting Crocodiles

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 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.

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State Tasks

Task Name Standards Task Type/Grouping Strategy

Content Addressed Brief Description

Got Dots Revisited (11-20)

MGSEK.CC.5a,b-7 Scaffolding TaskWhole/Small GroupPartner/Individual

Number relationships, Comparing sets, One to one

correspondence

Students engage in numerous activities to count objects

greater than ten.Numeral, Picture,

Word (11-20)MGSEK.CC.1-4 Scaffolding Task

Whole/Small GroupPartner/Individual

Counting, Numeral recognition, Number

relationships, Recognizing number words

Students engage in numerous activities to connect numerals,

picture representations and words.

The Cardinal Cup(revisited 11-19)

MGSEK.CC.2,4 Constructing TaskWhole Group/partner

Counting and number sequence

Students practice counting forwards and backwards.

One More/Less Than Dominos

MGSEK.CC.4a,5a,b,6 Scaffolding TaskSmall Group/Individual

Comparing sets, Number relationships

Students work with one more and one less when completing

the task.Not all State Tasks have been added due to the appropriateness of teaching these tasks until quarters 3-4.

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