Kindergarten Unit 3 Developing the Understanding of ... · Kindergarten Unit 3 Developing the Understanding of Addition and Subtraction Mathematics . 2017 – 2018 LBUSD

Kindergarten Unit 3 Developing the Understanding of Addition and Subtraction Mathematics

2017 – 2018 LBUSD 1

Unit Goals – Stage 1 Number of Days: 39 November 27 – February 2, 2018 Unit Description In this unit students continue to use counting to discover how numbers relate to one another. They learn to count forward beginning from a given number instead of beginning at one. They identify visual patterns on a hundreds chart. Students are introduced to addition and subtraction with small numbers. They begin to work with problem situations of “putting together” and “taking apart”. They extend their understanding of “one more” and “one less” of a number to “adding one” and “subtracting one”. They show their understanding in various ways such as by using language, objects, making drawings, or writing equations. Materials: 5 and 10 frames, 2 sided counters, Rekenrek, number path, unifix/linking cubes, and other counting objects Standards for Mathematical Practice SMP.1 Make sense of problems and

persevere in solving them. SMP.2 Reason abstractly and

quantitatively. SMP.3 Construct viable arguments and

critique the reasoning of others. SMP.4 Model with mathematics. SMP.5 Use appropriate tools strategically SMP.6 Attend to precision. SMP.7 Look for and make use of structure. SMP.8 Look for and express regularity in

repeated reasoning. Standards for Mathematical Content Clusters Addressed Counting and Cardinality [m] K.CC.A Know number names and the

count sequence [m] K.CC.B Count to tell how many [m] K.CC.C Compare numbers Operations and Algebraic Thinking [m] K.OA.A Understand addition as putting

together and adding to, and understand subtraction as taking apart and taking from

Students will be able to independently use their learning to… • Make sense of never-before-seen problems and persevere in solving them. • Construct viable arguments and critique the reasoning of others.

Making Meaning UNDERSTANDINGS Students will understand that… • Counting will answer, “How many?” • Objects and drawing can be used to represent

numbers and to represent problems.

ESSENTIAL QUESTIONS Students will keep considering… • Why is counting important? • What is the difference between counting

forward in the count sequence and counting backwards in the count sequence?

• How can I show and share my thinking? Acquisition

KNOWLEDGE Students will know… • The definition of academic vocabulary words

more, less and the same as. • Counting can begin with any number and going

forward in the count increases the amount counted and going backwards in the count decreases the amount counted.

• Joining groups together increases the total number of the group.

• Separating the group decreases the number in the original group.

• Numbers are written to represent quantity.

SKILLS Students will be skilled at and/or be able to… • Count forward from a number other than one. • Count two groups to determine which has

more, less or the same. • Show, draw or write a number to answer “how

many more to ten” from a given number 1 – 9. • Use objects and draw picture representations

to show quantity, joining groups together and separating groups and then record it with a drawing or number sentence.

• Explain their picture and symbol representations and their thinking.


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Assessed Grade Level Standards Standards for Mathematical Practice SMP.1 Make sense of problems and persevere in solving them. SMP.2 Reason abstractly and quantitatively. SMP.3 Construct viable arguments and critique the reasoning of others. SMP.4 Model with mathematics. SMP.5 Use appropriate tools strategically SMP.6 Attend to precision. SMP.7 Look for and make use of structure. SMP.8 Look for and express regularity in repeated reasoning. Standards for Mathematical Content Counting and Cardinality [m] K.CC.A Know number names and the count sequence K.CC.1 Count to 100 by ones and by tens. K.CC.2 Count forward beginning from a given number within the know sequence (instead of having to begin at 1). K.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). [m] K.CC.B Count to tell how many K.CC.4 Understand the relationship between numbers & quantities; connect counting to cardinality. c. Understand that each successive number name refers to a quantity that is one larger. K.CC.5 Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. [m] K.CC.C Compare numbers K.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. Operations and Algebraic Thinking [m] K.OA.A Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from K.OA.1 Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanation, expressions, or equations. K.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. K.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 (e.g., 5 = 2 + 3 and 5 = 4 + 1). K.OA.4 For any number from 1 to 9, 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. Key: [m] = major clusters; [s] = supporting clusters; [a] = additional clusters


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Evidence of Learning – Stage 2 Assessment Evidence Unit Assessment / Answer Key Students will complete selected response and constructed response items to indicate level of mastery/understanding of the unit standards as outlined in this guide. [m] K.CC.A

• Students will count forward from a given number and write the number that represents the total count. • Students will write numbers 0 -20 in the correct count sequence.

[m] K.CC.B

• Students will count objects within 20 arranged in various configurations (line, array, circle, or scattered) to answer “how many”. • Students will be able to write the number that represents “one more” of a given set of objects.

[m] K.CC.C

• Students will identify a group of objects as being greater than, less than or equal to another group of objects. [m] K.OA.A

• Students will solve addition and subtraction words problems using drawings to show their thinking. • Students will show a number up to 10 decomposed into pairs in more than one way through drawings and write a number sentence (7 =

3 + 4) to match. • Students will draw to show how many more are needed to make 10 from a given number 1 – 9 and write a number sentence to match.

Other Evidence Formative Assessment Opportunities • Opening Task –EM Session 6 pg. 27 – 28 • GoMath! Show What You Know – Ch. 4 pg. 130; Ch. 5 pg. 166; Ch. 6 pg. 222 • GoMath! Performance Tasks: Ch. 4 Ella’s Art Project, Bees and Flowers • GoMath! Standards Practice book – for quizzes or homework • GoMath! – Getting Ready for SBAC – pages SB 5 – 6 • Cooperative Group Tasks – • District Unit 3 Resource (to be used if you are taking the online Unit Assessment) – exit tickets and quizzes

English (Word or PDF) Spanish (Word or PDF) • Using Formative Assessment for Differentiation

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Learning Plan – Stage 3 Teacher Resources

We encourage using the following resources throughout the unit • Mathematics Framework for California Public Schools - Kindergarten • Early Mathematics – A Resource for Teaching Young Children (EM) – If you do not have this book, download it to your desktop from

this link. You can then print selected pages if desired. • Think Central • Which One Doesn’t Belong? • Cooperative Group Mats and Directions • Standards Posters • myPD course #2821: GoMath! Digital Resources • myPD course #7401: Standards for Mathematical Practice • myPD course #7455: Lesson Planning Tools • myPD course #3578: Understand the Problem: Notice and Wonder Strategy • Introduction to the Rekenrek/Math Rack

Coach’s Note: • Rule of thumb: Minimize the emphasis on writing equations in chapters 5 and 6. • As students continue their work with counting and cardinality, continue to have students count collections. Keep this available during

choice time. Counting is developed first, then the number-symbol is connected to the quantity. Please refer to the first link listed above, Mathematics Framework for California Public Schools, pg 58 – 64.

• Mastering the Math Rack will be referenced beginning on days 2 – 6. Please refer back to your notes from the 10/30 and the power point of the training sent on 11/3 to refresh your memory.

• Introduce the Number Bond conceptually first, so students will understand what the numbers in the box represents.

Used when showing “put together” or composing an amount. This shows parts to whole which begins to lay a foundation for addition.

Used when showing “take apart” or decomposing an amount. This shows whole to part which begins to lay a foundation for subtraction.


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Learning Plan – Stage 3 Suggested Sequence of Key Learning Events and Instruction

Days Learning Target

Success Criteria Go Math! Lessons and Activities and Core Resources Supplemental Resources:

Daily I will group 2 or 3 dots to tell how many without counting by…

• Participating in daily Number Talks

• Using the structure of the 5-frame.

• Answering questions such as: o How many dots do you

see? o How do you see them?

• What do you mean?

• myPD course #2702 “Number Talks: Dot Card Images”

• myPD course #2939: Using Five-Frames

Coach’s Note:

• Contact the Math Office if you are new to the grade level and need Kindergarten Number Talk Cards.

• myPD course #7446 Elementary Number Talks

• myPD course #2165 Beginning of the Year Number Talks Kinder through 5th

Daily I will build counting fluency over time by…

• Correctly counting the sequence from one.

• Knowing when to stop the count.

• Answering “How many?”

Coach’s Note: • The Additional Daily Routines in this row are to

supplement the daily Number Talks. These routines can be used during times of transition or as a part of your Opening/Calendar. Choose a few from the given list in the next column.

• Name Attendance Pocket Chart & Name Cards &Ten Frame Chart (3 frames)

• Class Circle Count • Special Number (use

smaller numbers in unit 1) • Pick 2 Names Activity,

more/less /equal • Rapid Finger Count

60 minutes

per week

two 30 minute blocks

or three 20 minute blocks

I will persevere in problem solving to help me understand math by …

• Playing ST Math interactive games on the computer.

• Visualizing math concepts.

ST Math Objectives • Number and Objects to 20. • Understanding addition and subtraction within 5. • Understanding addition and subtraction within 10.

ST Math Tips • Set goals: 3% progress

per week • Review your classroom

reports regularly • Monitor/Celebrate

progress • Monitor/Intervene students

with alerts • Assign a few homework

objectives at a time

Before the Unit

Give the “Show What You Know” Diagnostic Assessment Ch. 4 pg. 130, Ch. 5 pg. 166 and Ch. 6 pg. 222 Determine if students need intervention for the unit prerequisite skills.

*Use the Diagnostic Table for intervention options: On-level, Strategic, Intensive and Independent Rule of Thumb: Rather than doing Vocabulary Builder as a separate activity, incorporate vocabulary, where appropriate in daily lessons.

It is not necessary to administer all 3 of the diagnostic assessments at the same time.


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1 I can recreate images with up to three objects by…

Opening Task – EM Session 6: Mental Representations for Images of 5 • Telling “how many” were

shown. • Using counters and tiles to

show arrangement.

• Early Mathematics (EM) Session 6: pgs. 27 – 28 (see Coach’s Notes below)

Coach’s Note • Activate – Instead of the EM Activate use the Number

Talks dot images just completed. • Discuss how they saw the dots (counted, “just knew”

etc.) • Engage – Begin from pg. 28. Tell students they are

going to use the strategy of taking a “good guess” known as estimating, counting or “just knew” to recreate the dot images from the Number Talk cards.

• Use the 2-sided counters instead of colored tiles for this session.

• Start with the day 1 cards and choose strategically. Work only within 3 dots for this Opening Task.

• Ask questions such as: o How many? o Why was it easy? o Did you have to count? o Were there the same amount of dots as in the last

image? o Does changing the arrangement, or the way the

dots are shown, change the number of dots?

Procedural Skills and Fluency • Continue to use shapes

for Freight Train sets; small and large circles, squares, triangles, rectangles, and hexagons.

2 – 5 I can recreate images with up to five objects by…

• Subitizing and/or counting. • Using counters and tiles. • Explaining how I saw the dots

or tiles arranged. • Answering questions such as:

o How many were there altogether?

o How were they arranged? (Students should be using position words learned from the previous unit in their explanation)

• EM Session 6 pgs. 28 – 34 • Mastering the Math Rack (MMR) pgs. 32 – 33 Coach’s Note • Continue with dot images from Opening Task. Move on

to four dot images if the students can recreate three with ease.

• On the remaining days consider: o Introducing the color tiles to represent the dots.


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o Use day 16 card 2 of 3 when first having students recreate five. Do not go beyond day 16 in the Dot Images cards.

o Consider doing the Develop section as a whole class and model being the “Card Flasher”. Pick students who need the support and practice to be the card flasher before releasing the students to work with partners.

• If this is the students first experience with the Rekenrek, allow the students to explore it for a few minutes and continue the lesson doing a “Notice and Wonder” with them. Refer to the salmon color sheet “Introducing the Rekenrek/Math Rack” distributed at the 10/30 training for introductory procedures.

• Introduce the vocabulary for the Rekenrek: o start position o beads in play o beads out of play

6 – 10 I can

recognize and show quantities up to 10 by…

• Using the Rekenrek to: o Moving beads from start

position to beads in play. o Counting the beads to put

in play. o Pushing all the red beads

as a group (subitize) and counting on.

o Noticing the beads that are not in play.

o Drawing the beads in play and out of play on my Rekenrek Recording Sheet and writing the number that tells how many.

o Explaining how I pushed the correct amount into play.

• MMR pgs. 26 – 27 Coach’s Note • If this is the students’ first experience with the

Rekenrek, see the last two bullets in the previous learning target.

• Ask the following types of questions if needed: o What do you notice about the red and white

beads? o How many? o How many altogether?

• On the following days use the recording sheet to have students record how they showed the amount on their Rekenrek and then write the number. This will take the students through C – R – A. Blackline master pg. 122.

Conceptual Understanding: • Continue to count

collections and record on Counting Collections Recording sheet.


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• Using the benchmark 5 and 10 to show or explain how many.

• Using a 5 or 10 frame.

11 - 13 I can count forwards to ten and backwards from ten by…

• “Finger walking” across my arm (EM).

• Participating in the activity “Going up, going down”

• Answering questions such as: o How many more floors to

the tenth floor? o How do you know the

elevator is going up/down? o How do you know the

number is smaller/bigger? o Does that mean we add

cubes or take away cubes? o How many need to be

added/taken away? o What number comes

after___? Or what number is next?

o What number comes before ___?

o What happens to the amount when counting forward/backwards?

• Lesson 4.4 Count and Order to 10 pgs. 145A – 147 • EM Session 8: pgs. 41 – 45 Engage and Develop

sections only • MMR pgs. 34 – 35 More or Less

(also sited on days 14-15)

Coach’s Note • EM session 8 will allow students to continue practicing

counting, exploring how numbers relate to one another, vertically and build conceptual understanding in context for addition and subtraction. Mouse Count will be used for this lesson.

• Some students may need explicit instruction to make the connection from the number path to the “elevator” and why the numbers increase as they go up. (Remember to change the wording to number path where number line is written.)

• Spend time helping the students to make sense of the problem with each draw of the card (SMP1). This is foundational to problem solving as students’ progress through the grades.

Conceptual Understanding: • Exit Ticket: “This is What I

See”

14 - 15 I can count to compare two groups and know which group is greater than, less than or equal to the other group by…

• Using various math tools such as the 5 frame, 10 frame, Rekenrek or number path.

• Drawing a picture or representation that would show an amount greater than, less than or equal to an amount in another group

• Lesson 4.6 Compare by Counting Sets to 10 pgs. 153A – 156

• Lesson 5.3 Problem Solving: Act Out Addition Problems pg. 177B Vocabulary Builder-only

• MMR pgs. 32 – 33, Show Me! • MMR pgs. 34 – 45 More or Less! Coach’s Note • For the students who are having difficulty, have them

use the same tool as you are showing, i.e., if showing

Conceptual Understanding: • Ch. 6 Game, Spin for

More pg. 224


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• Explaining why an amount is greater than, less than or equal to another set.

• Recreating it by drawing a representation and labeling the groups using numbers.

an amount on the 10 frame, have the student(s) also use a 10 frame to show the amount and as you change your tool so does the student.

• Take students through C- R –A by circling the amount that you show (10 frame, dot image, Rekenrek) on the number path rather than showing it on a math tool.

• Have a discussion on how the students were able to determine the total amount.

16 – 17 I can

complete a Performance Task by…

Formative Assessment Lesson #1: Ella’s Art Projects • Persevering through difficulties • Listening and following

directions

• Performance Task - Ch. 4 Ella’s Art Projects pgs. AG98 – AG102D

• On Day 2 have a chart prepared with a common error

to discuss from the FAL. • Allow students time to look and study the problem

before asking them to identify the error. If there isn’t any students that can identify the error ask questions to lead them to see the error rather than pointing out the error to them.

Coach’s Note • Have workshop activities ready for early finishers.

18 – 22 I can tell how many more I need to get to benchmark 5 or 10 by…

• Using manipulatives such as the Rekenrek, 10 frames or counters.

• Drawing and labeling a representation.

• Answering questions such as: o How many do you have? o How many more do you

need to get to 5? o How many more do you

need to get to 10? o How can you draw that? o How can you write that in a

number sentence?

• MMR pgs. 30 -31 Visualize It • MMR pgs. 34 – 35 More or Less Coach’s Note • When using More or Less lesson, have the students

find how many more to the benchmark numbers. • Consider a gradual release away from the Rekenrek

and/or 10 frame (concrete) to using the Number Path to represent the problem.

• Practice the counting on strategy.

Task “The Candy Shop”


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o What does the first number represent?

o What does the second number represent?

o What does this sign represent?

o Is ___ closer to 5 or 10? How do you know?

23 – 27 I can break apart (decompose) a given amount by…

• Using manipulatives. • Drawing a representation of

my decompositions. • Writing numbers to label the

groups to show the decomposition.

• Using a number bond to show the decomposition (see pg. 4 coach’s note 3rd bullet)

• Answering questions such as: o How many did you start

with/total? o How many are in each of

the groups? o How can you draw what

you did with ___? o Can you show how to label

this group? o How can what you drew be

written in a number sentence?

o What do these numbers represent? Show me with your manipulatives.

• Lesson 5.8 Hands On Algebra Number Pairs to 5 pgs. 197A – 200

• Lesson 5.9 Hands On: Algebra Number Pairs for 6 and 7 pgs. 201A – 204

• Lesson 5.10 Hands On: Algebra Number Pairs for 8 pgs. 205A – 208

• Lesson 5.11 Hands On: Algebra Number Pairs for 9 pgs. 209A – 212

• Lesson 5.12 Hands On: algebra Number Pairs for 10 pgs. 213A – 216

Coach’s Note Read the following Read About the Math:

o Lesson 5.9 pg. 201A o Lesson 5.11pg. 209A o Lesson 5.12 pg. 212A

• The following Advanced Learner activities can be used with all students for any number within 10. o pg. 207 o pg. 211 o pg. 215

• If students have not seen number sentences written with the total first followed by the equal sign (8=3+5) this would be an appropriate time to do so.

Conceptual Understanding: • Ch. 5 Game: Pairs that

Make 7 (any number within ten)

28 – 30 I can solve putting together and taking apart

• Identifying what is happening in the math story.

• Drawing a picture or representing what is happening in the math story.

• Lesson 5.3 Problem Solving: Act Out Addition Problems pg. 177 – 179 (see notes below)

• Lesson 5.4 Model and Draw Addition Problems pgs.181A – 184


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problems by…

• Labeling the picture or representation with numbers.

• Writing a number sentence to match the action in the math story.

• Explaining what was drawn or written as it relates to the math story

• Answering questions such as: o What happened in the

math story? o What does that mean? o What math tool could we

use to help us show what happened in the math story?

o How could we represent what happened in the story?

o Can that be written in a number sentence? Show me.

• Lesson 6.3 Problem Solving: Act Out Subtraction Problems pgs. 233 – 236

• EM Session 10: Joining and Separating Quantities to 10 pgs. 62 – 65 (also sited on days 33 – 38)

• MMR pgs. 36 – 37 Tell Me a Story (Mouse Count can be used)

Coach’s Note • Do not do the workbook pages for the GoMath! lessons

listed above. Read the problem orally, don’t show the picture, have students represent the problem or act it out. Students may count if they see the picture rather than thinking and making sense of the the story.

• Use context when having the students put the groups together.

• Continue to periodically repeat the Activate section (K.OA.1) to develop quotity, the ability to hold numbers in your head.

31 – 32 I can complete a Performance Task by…

Formative Assessment Lesson #2: Bees and Flowers • Completing the Performance

Task or Writing Activity • Persevering through difficulties • Participating in class

discussions.

• Performance Task – Chapter 5 Bees and Flowers pgs. AG 103 – AG146107D

• Prepare on chart paper a common error that was found

on the FAL for day 2 to discuss. • Allow students time to look and study the problem

before asking them to identify the error. • Ask questions such as:

o How many of you thought this way? (Point to chart.)

o How could we prove this is correct or incorrect? Coach’s Note • Have workshop activities ready for early finishers.


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33 – 38 I can put together two groups and tell how many altogether by…

• Using manipulatives. • Drawing a representation of

my decompositions. • Giving context to the numbers

in the equation. • Writing numbers to label the

groups to show the decomposition.

• Using a number bond to show joining groups.

• Writing a number sentence to show putting together or taking apart.

• Answering questions such as: o What does that

number/symbol represent? o What math tool could we

use to help us show what happened in the math story?

o How could we represent what happened in the story?

o Can that be written in a number sentence? Show me.

o Can you explain what the numbers in the number bond represent in the story?

• Lesson 6.7 Hands On: Algebra Addition and Subtraction pgs. 249A do

• EM Session 10: Joining and Separating Quantities to 10 pgs. 62 – 65 (also sited on days 28 – 30)

• Mastering the Math Rack (MMR) pgs. 36 – 37 Coach’s Note • Do not do the workbook pages for the GoMath! lesson

listed above. Read the problem orally, use cubes and have students draw/represent the problem. If appropriate, introduce the meaning of the minus sign and equal sign.

• Do the Activate section from EM Session 10 pg. 63 as it allows students practice with developing the ability to hold an amount in their head without visual support.

• Use the story Mouse Count for the activity sited in MMR. Share situations of put together and take apart. Have students use Rekenrek to solve.

• Examples of put together and take apart situations, (CCSS pg. 88): o There were 3 mice in the jar. The snake caught 2

more mice and put them in the jar. How many mice are in the jar now?

o The snake has 6 mice in the jar. 1 escapes. How many are in the jar now?

• Students can also represent the problem using a number path.

Fluency: • Addition and Subtraction

with Dice

39 Unit Assessment Select either the Online Assessment (Synergy) or paper pencil test. (The Assessment link is found on page 3 of this Unit guide).

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Kindergarten Unit 3 Developing the Understanding of ... · Kindergarten Unit 3 Developing the Understanding of Addition and Subtraction Mathematics . 2017 – 2018 LBUSD