math pre-k modeling addition & subtraction through five...

Modeling Addition and Subtraction through FiveMath, PreK

This unit is designed to be done late in the school year, after a great deal of Counting and Cardinality work.

The Massachusetts pre-kindergarten standards apply to children who are at the end of the preschool age group, i.e., older four- and younger five-year olds. The standards can be promoted through play and exploration activities and embedded in almost all daily activities. For this age group, foundations of mathematical understanding are formed out of children’s experiences with real objects and materials.

This unit addresses Critical Area #1 for Pre-Kindergarten in the 2011 MA Curriculum Framework for Mathematics: develop an understanding of whole numbers to 10, including concepts of one-to-one correspondence, counting, cardinality and comparison.

The focus of this unit is for children to begin to understand that adding items to a set or sets results in more than the original number of items and taking items away results in less than the original number of items. They will use concrete objects to model addition and subtraction problems through five (MA.PK.OA.1) and use comparative language (more/less than and equal to) to compare and describe collections of objects ( MA.PK.CC. 5).

These Model Curriculum Units are designed to exemplify the expectations outlined in the MA Curriculum Frameworks for English Language Arts/Literacy and Mathematics incorporating the Common Core State Standards, as well as all other MA Curriculum Frameworks. These units include lesson plans, Curriculum Embedded Performance Assessments, and resources. In using these units, it is important to consider the variability of learners in your class and make adaptations as necessary.

This work is licensed by the MA Department of Elementary & Secondary Education under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License (CC BY-NC-SA 3.0). Educators may use, adapt, and/or share. Not for commercial use. To view a copy of the license, visit http://creativecommons.org/licenses/by-nc-sa/3.0/

Draft 8/2013 of 63

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Table of ContentsIntroduction................................................................................................................................................................................................................. 3

Lesson 1 Find a Partner................................................................................................................................................................................................8

Lesson 2 Leap Frog..................................................................................................................................................................................................... 11

Lesson #3 Treasure Hunt........................................................................................................................................................................................... 15

Lesson #4 Classroom Store........................................................................................................................................................................................ 19

Lesson #5 Fishing Game............................................................................................................................................................................................. 22

Lesson #6 Mother May I............................................................................................................................................................................................ 25

Lesson #7 Build & Change It.......................................................................................................................................................................................28

Lesson #8 Mystery Box.............................................................................................................................................................................................. 31

Snack Attack (CEPA 1)................................................................................................................................................................................................ 34

Lesson 9 Tip the Chips................................................................................................................................................................................................ 39

Lesson #10 Mitten Match.......................................................................................................................................................................................... 43

Lesson 11 Bears in a Cave.......................................................................................................................................................................................... 46

Lesson 12 Bowling..................................................................................................................................................................................................... 49

Lesson 13 Ladybug..................................................................................................................................................................................................... 52

Lesson #14 Domino Train........................................................................................................................................................................................... 55

Weather Report (CEPA 2).......................................................................................................................................................................................... 59

This work is licensed by the MA Department of Elementary & Secondary Education under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License (CC BY-NC-SA 3.0). Educators may use, adapt, and/or share. Not for commercial use. To view a copy of the license, visit http://creativecommons.org/licenses/by-nc-sa/3.0/ Draft 8/2013 of 63


IntroductionThe main task during the preschool year is helping the children create a strong link between their sense of relative quantity and their ability to count. Key to this is children developing the concept of conservation (i.e., the sense that a quantity, once counted, doesn’t change unless items are added or taken away). This unit extends that foundational concept by having children explore what transforms a set into a new quantity. In other words, children need to develop an intuitive sense that if they have added items to a set or combined sets, they now have more than they started with, and if they take items away from a set, the set is now less than the original.

One of the ways children begin to understand this concept is by beginning to understand part-whole relationships. If children understand that a quantity can be subdivided into parts without changing, then they understand that each of the parts is less than the whole, and that the whole is more than each of the parts.

It is important to understand what this unit is not about. Preschool children are not yet at the representational stage (i.e., they don’t relate well to number sentences). This unit does not require children to read number sentences nor require them to record their results as number sentences, nor does this unit require children to remember or memorize the facts to five. It is also important to remember that real-world problems come in four types- Combine, Separate, Part-Whole, and Compare - not as addition or subtraction problems. Adding to is a Combine problem, and is typically thought of as addition. Taking away from is a Separate problem, and is typically thought of as subtraction. Part-Whole and Compare problems lend themselves to either addition or subtraction solutions.

In terms of methodology, preschool instruction should be hands on and embedded within normal classroom routines and centers whenever possible, with a limited dependence on whole-group instruction. In many cases, the activities in this unit can be presented as classroom options, then scaffolded on an individual or small group basis as children choose to engage in the activities. Most of these activities can be chosen by children more than once. Keeping them available makes that possible, and children are more likely to benefit from the activities if they choose when and how long to engage in them. Voluntary repetition will enhance the children’s mastery of the underlying concepts. Activities should stay available to children even when the unit is concluded, if they seem to be continuing to choose and benefit from them.

Two of the strategies children might use in solving the problems in this unit are (a) for Adding to problem, counting on (i.e., counting from the initial set rather than counting from 1) or (b) for Taking Away problem, counting back (i.e., counting backwards from the starter set rather than first taking away the amount and then counting the remainder). Both of these strategies require a more advanced number sense than some of the preschoolers may have yet developed. Therefore these strategies should be encouraged, but not required.

Finally, most of the activities in this unit lend themselves to working with quantities greater than 5. If children appear ready to work with larger quantities they should be allowed to, but note the expectations in the assessments are limited to children mastering these concepts for quantities of five or less.




ESTABLISHED GOALS GG1. PK.OA.MA1 – Use concrete objects to model real-world addition (putting together) and subtraction (taking away) problems up through five.G2. PK.CC.MA.5 – Use comparative language such as more/less than, equal to, to compare and describe collections of objects.

MP1. Make sense of problems and persevere in solving them.MP3. Construct viable arguments and critique the reasoning of others.MP4. Model with mathematics.MP5. Use appropriate tools strategically.MP6. Attend to precision.MP7. Look for and make sense of patterns.

SL.4. Describe personal experiences; tell real or imagined stories.SL.5. Create representations of experiences or stories (e.g., drawing, constructions with blocks or others or other materials, clay models) and explain them to others.

TransferChildren will be able to independently use their learning to… T

MeaningUNDERSTANDINGSChildren will understand that…U1. Adding to a quantity increases the amount. Taking away from a quantity decreases the amount.U2. Quantities can be divided into parts without changing the total amount.U3. There are various strategies for solving addition and subtraction problems.

ESSENTIAL QUESTIONS QQ1. “What changes make sets larger or smaller?”Q2. “What strategies can I use to figure out how many I now have?”Q3. “How can I decide if one set is larger than another if they don’t look the same?”Q4. “How can I separate a number into two or more parts?”Q5. “In what ways can I show how many I have?”

AcquisitionChildren will know…K.1. Combining two or more sets of objects or adding to a set of objects makes a new, larger quantity. This process is called addition.K.2. Taking objects away from a set creates a new, smaller quantity. This process is called subtraction.K.3. Adding or subtracting zero doesn’t change a quantity.K.4. A quantity can be taken apart in multiple ways without changing the whole.K.5. The order of parts doesn’t change the whole.K.6. Children will understand the terms larger, smaller, putting together, more than, less than, equal to, compare, quantity and count.

Children will be skilled at… SS1. Transforming unequal sets to make them equal by adding to or taking away from.S2. Knowing which displayed objects to count to answer the problem.S3. Creating a model (drawings, manipulatives, role-play) for put002D together and take-away word problems.S4. Remembering the whole when working with its parts (e.g., five subdivided into two and three is still five).

Stage 2 - EvidenceEvaluative Criteria1. Able to identify missing part of 5.2. Able to identify greater than, less than, and

most.3. Notes on strategies (counting on, counting

all, use of models).

Assessment EvidenceCurriculum Embedded Performance Assessment 1 (CEPA 1) Snack Attack ( pp 35-39)Curriculum Embedded Performance Assessment 2 (CEPA 2) Weather Report (pp 61-67)

Stage 3 – Learning PlanSummary of Key Learning Events and Instruction


Lesson 1 Find a Partner

Brief Overview of Lesson: Circle activity; children are handed number cards; find partner to combine to make target number.

The teacher introduces the part-whole concept at whole-group time. Children need to practice adding to their own number to find a partner. Later the teacher will introduce variations of finding partners by taking away from one number or having one quantity be represented only with a numeral, the other with a pictured quantity. As you plan, consider the variability of learners in your class and make adaptations as necessary.

Prior Knowledge Required: Count objects up to 5, one to one correspondence

Estimated Time (minutes): 15 minutes

Resources for Lesson: number cards (i.e. cards with a numeral and a picture representation)



Unit: Modeling Addition and Subtraction through FiveContent Area/Course: MathLesson #1 Find a PartnerTime (minutes): 15 minutes

By the end of this lesson children will know and be able: Children will know that two addends equal the sum (i.e. the part/whole concept). Children will be able to remember the whole while working with its parts. Children will also be able to add and subtract up through five.

Essential Question(s) addressed in this lesson: What strategies can I use to figure out how many I now have?

Standard(s)/Unit Goal(s) to be addressed in this lesson:

PK.OA.MA1 – Use concrete objects to model real-world addition (putting together) and subtraction (taking away) problems up through five.SMP 1 Make sense of problems and persevere in solving them.SMP 7 Look for and make use of structure.

Instructional Tips/ Strategies/Notes for Teacher Children need to be able to count to 5 and have one to one correspondence up to 5. Without this prior knowledge children may need additional support. Pre-teach the strategy of how to find a partner using an easier objective such as finding matching quantities rather than having to combine or subtract quantities. This will help establish the routine of the activity. Teachers should model the lesson and give several examples prior to children finding partners. Ideas for differentiation: use a higher target number for higher learners, use concrete objects for learners who have had limited exposure to counting to 5 as well as for ESL students.

Anticipated Child Preconceptions/Misconceptions:



Children may try to find their partner by matching the number of objects on his/her card rather than adding/subtracting the two sets together to get the whole target number. Children may have a hard time noticing, as they count, whether they have gone beyond the target number.

Lesson Sequence Opening Message: Gather children on the rug. Introduce the unit by asking the children, “We have learned to count to 5. Now we will learn how to add and subtract numbers. Isn’t that exciting? Our first lesson will be on addition. Who knows what addition means?” Share ideas and give a simple example such as “I have 2 cookies and Kate has 2 cookies. Together we have 4 cookies. That’s addition!” Begin by having children review counting 1-5. Inform them that they are going to play a partner game where they will be counting and combining numbers.

1. Teacher chooses three children to model activity.2. Teacher writes the number 5 on the board and asks, “What number is this?”3. Teacher hands out one number card to each child.4. Teacher says, “Two of these numbers can be added together to equal 5.”5. What strategy could I use to find the answer? (discuss)6. Teacher says, “Use one of the strategies to find the answer.”7. Children respond and share their strategy. 8. Teacher asks, “Why was the other number not chosen?” Discuss.9. Repeat with three more children.10. If successful, hand out cards to all children and have them attempt to find their partners. Remind children that “partner” means 2 people.

Lesson Closing: Children should find their partner and sit together on rug. Have partners stand up and share their number combinations and strategy. Notice which pairs of children used the same combination of numbers.



Lesson 2 Leap Frog

Brief Overview of Lesson:

This lesson includes a board game for two or more children. The game is a parallel path game where a 20-hop path is subdivided in groups of five. Children move from start to finish rolling 0-5 die. As you plan, consider the variability of learners in your class and make adaptations as necessary.

Prior Knowledge Required: Recognizing quantities and numbers 0-5; ability to count with 1:1 correspondence

Estimated Time (minutes): 15 minutes for demonstration plus open choice or set up at work station

Resources for Lesson: Egg carton sections turned bottom side up with a small green piece of construction paper glued to each dimple to make

“lily pads”. Cartons laid end to end, to make two parallel paths of 20 lily pads. Before the first egg carton is a green piece of

construction paper to represent the “meadow”; after the last egg carton is a blue piece of construction paper to represent the “pond” (see illustration on page 13).

Toy frogs or counters to use as game pieces Die marked with 1-3 dots (one dot on two sides, two dots on two sides, three dots on two sides)

Die marked with 0-2 dots (zero dots on two sides, one dot on two sides, two dots on two sides)



Unit: Modeling Addition and Subtraction through FiveContent Area/Course: MathLesson # 2 Leap FrogTime (minutes): 15 minutes for demonstration plus open choice or set up at work station.

By the end of this lesson children will know and be able to: Compare their frog’s position relative to their partner’s, the start and stop of each 5-jump section, and to the end of the path. Gradually children will be able to predict where their roll of the dice will land them before moving their piece.

Essential Question(s) addressed in this lesson: What strategies can I use to figure out how many I have? How can I decide if one set is larger than another if they don’t look the same?

Standard(s)/Unit Goal(s) to be addressed in this lesson: PK.OA.MA1 – Use concrete objects to model real-world addition (putting together) and subtraction (taking away) problems up through five.SMP 6: Attend to precision

Instructional Tips/ Strategies/Notes for Teacher:Much of the teacher effort should be in encouraging prediction questions regarding relative position – how many they need to catch up or to win; where they think they will land when they move their piece and how they know; etc. Ideas for differentiation: Have higher level learners use dice with numerals instead of dots.

Anticipated Child Preconceptions/Misconceptions Children count the space their marker is on when moving the indicated amount.

Lesson Sequence:



Opening Message: Gather children in a circle on the rug. Ask the children “Who remembers the new math game we played yesterday? “Children respond with “Find a Partner”. Remind students that we had to combine numbers to find our partners. “What do we call it when we combine numbers?” Children respond “Addition.” “Today we are going to learn how to play a new addition game called Leap Frog. Let me show you how”. Lesson Sequence:

1. Lay out the egg cartons end to end, with “lily pads” up, to make a continuous path of 20. Place the blue mat at one end with two frogs sitting on it, and place the green mat at the other end. Say to the children: “These two frogs want to get from meadow to the pond by hopping on the lily pads (point to each prop as mention). The dots on the dice will tell the frogs how many hops they can make. Who would like to play with me?”

2. A child joins the teacher, and they choose which frog to be.3. “Here is your path (point down one row of lily pads), and here is mine. Okay, I’m going to roll the dice and see how many hops to make” – roll

and demonstrate how to add the dice by counting the dots on both. Model how to hop from one lily pad to the next to reach the sum of the dice.

4. “Now it’s your turn.” Keep alternating turns. Pause occasionally to make strategic comments, such as:5. “I notice you’re 3 hops ahead of me. I hope I roll more than three, so I can get ahead of you”, or6. “Oh, you rolled a 4. You have 2 more hops to make on this carton. Where do you think your frog will be after you’ve moved 4 spaces?”7. “Do you think if you roll a 3 you will be ahead of me?”8. After one person’s frog makes it to the pond, let the other person continue to roll until their frog gets there as well.9. “If we wanted, we could play again, having our frogs hop back to the meadow. This game will be in the math center for those who decide they

would like to play.”Lesson Closing: Ask children to share what they learned today. Ask them to respond to the essential question: How strategies can I use to figure how many I now have?

Lesson 2 Resource



Downloaded from www. naeyc.org 10/2012



Lesson #3 Treasure Hunt

Brief Overview of Lesson: Using a sand table with buried objects, children search to find items and determine whether they have found all items of each set of objects. Children must determine what number represents the missing part of a target number of items. As they search, they need to mentally add the items that were found to the unburied objects to decide whether they have found them all. As you plan, consider the variability of learners in your class and make adaptations as necessary.

Prior Knowledge Required: Recognition of numerals 2-5; ability to count with 1:1 correspondence.

Estimated Time (minutes): 15 minutes to introduce to whole group with additional experience through center activity

Resources for Lesson:

Sand table

Sets of small objects with five in each set

Number/numeral cards 2-5.

Pocket chart with rows of 5 pockets on left labeled “Not Hidden” and 5 pockets on the right labeled “Found”.

Alternatively, two waterproof boards to set side by side with circles to indicate where objects sit.



Unit: Modeling Addition and Subtraction through FiveContent Area/Course: MathLesson 3: Treasure HuntTime (minutes) : 15 minutes during whole group time, then available as center activity.

By the end of this lesson children will know and be able: Identify a missing part of 5.

Essential Question(s) addressed in this lesson: What strategies can I use to figure out how many I have? How can I separate a number into 2 or more parts?

Standard(s)/Unit Goal(s) to be addressed in this lesson:PK.OA.MA1 – Use concrete objects to model real-world addition (putting together) and subtraction (taking away) problems up through five.PK.CC.MA.5 – Use comparative language such as more/less than, equal to, to compare and describe collections of objects.SMP1: Make sense of problems and persevere in solving them.SMP7: Look for and make use of structure.

Instructional Tips/ Strategies/Notes for Teacher: At the sand table, encourage children to make predictions and share their reasoning, and remind them to re-bury items that they were not searching for rather than adding them to the chart.

Periodically change the target number card and the number of items put out.



Ideas for differentiation: Higher level learners can be given quantities larger than 5 to search for. For struggling students this can be taught in a small group setting to monitor understanding.


Common errors children make during this activity: Children may not be able to predict whether all of a certain type have been found and keep looking. Children may put items in the chart as they are found, rather than doing one type completely before moving on to another type. Children may not pay attention to the target number to tell how many are in the total set. Children may not arrange like objects on the same side-by-side row, and may tend to place found items on the left side with the not-hidden

ones rather than create a separate set on the right.

Opening Message: Move sand table to an accessible area where all children can see demonstration.“Ahoy there Mateys! Today we are going on a Math Treasure Hunt! Gather around the sand table and I’ll show you how to play.”

Lesson Sequence:1. Set up the chart with some of the objects on the “Not Hidden” side and the other objects buried in the sand table. 2. Point out the chart and read aloud the labels “Not Hidden” and “Found” and the target number/numeral card (e.g., 5) at the top. “This number

means there are 5 of each item. Over here on the “Not Hidden” side, I see some ducks. How many ducks do you see?” Have one of the children count. “But there should be 5 ducks. How many ducks do you think are hidden in the sand somewhere?” Take suggestions from the group, and ask them how they came up with that number.

3. Have a child dig in the sand and find a duck. If the child finds something other than a duck, have them re-bury it. “Oh, there’s one of them. Since that is one of the missing ducks, we should put it over here, on the “Found” side.” Have the child place the duck in the leftmost pocket.



4. “Do you think there are any more missing ducks?” Take suggestions, and ask children why they think so. 5. Repeat this process until children conclude that all the ducks have been found. 6. Repeat with the objects on the second row, so children can get used to the routine.7. If children seem to have the concept, say: “There are some other objects missing. If you choose to work at the sand table, you will be able to

look for the other items.8. At the sand table, after all the items have been found, have the children transfer them all to the “Not Hidden” side, then decide how many of

each type to hide in the sand for the next round.Lesson Closing: Ask children to share their thinking about what they learned in the game today.



Lesson #4 Classroom Store

Brief Overview of Lesson): Children shop for items using a punch card with five icons. The goal of the learning activity is to determine whether they have enough icons on their card to obtain a desired item or items. In this Classroom Store lesson, children compare the price of the item to the number of picture icons on their card and decide whether theirs is the same or more than the price. After each purchase, a hole punch is used to “remove” icons corresponding to the purchase price, and children can decide whether they have enough icons left to make another purchase. As you plan, consider the variability of learners in your class and make adaptations as necessary.

Prior Knowledge Required: Identify numbers 1-5 and be able to count from 1-5

Estimated Time (minutes): 15 minutes to introduce to whole group with additional experience through center activity

Resources for Lesson Thematic items to sell Punch card Hole punch Numbered stickers



Unit: Modeling Addition and Subtraction through FiveContent Area/Course: MathLesson #4: Classroom StoreTime (minutes): 15 minutes to introduce to whole group with additional experience through center activity

By the end of this lesson children will know and be able to: Combining two or more sets of objects or adding to a set of objects makes a new, larger quantity. This process is often called addition.Taking objects away from a set creates a new, smaller quantity. This process is often called subtraction.

Essential Question(s) addressed in this lesson: What strategies can I use to figure out how many I now have?

Standard(s)/Unit Goal(s) to be addressed in this lesson: PK.OA.MA1 – Use concrete objects to model real-world addition (putting together) and subtraction (taking away) problems up through five.SMP1. Make sense of problems and persevere in solving them.SMP3. Construct viable arguments and critique the reasoning of others.

Instructional Tips/ Strategies/Notes for Teacher: *Children will receive one punch card per day.Ideas for differentiation: Children who have mastered counting 1-5 can be challenged with a punch card with 10 icons.Teacher will assist struggling learners when they visit the store.

Opening Message:“How many of you have ever gone shopping? Tell me about it. Did you buy one item or more than one item? What did you use to buy this or these items? Today we are going shopping in the Classroom Store this is a center in our Dramatic Play Area”.



Lesson Sequence: Invite children to come to the rug and sit in a circle and place items for sale in the center of the carpet. Show children the ticket with five stickers. Explain to them that you want to buy one of the items and that your ticket is your money. Show children the different numbers on each of the item. Choose one of the items to buy. Explain to children that the item cost ___ tokens and you must hole punch that many tokens on your ticket. Put the item in your shopping bag. Have children help you count the remaining number of tokens on your card. Tell children that you want to buy something else and have them help you find something you can afford. Take a few suggestions before choosing an item. Punch the tokens on your ticket and place the item in your shopping bag. Show children your ticket and explain that you are all done shopping because you have used all your tokens. Hand a new ticket to a child and the hole punch to another child and have them model the activity for the class. Explain to the children that the activity is called Class Store and show them where it is located within the classroom. Explain to them that

they will get a new ticket every day.



Lesson #5 Fishing Game

Brief Overview of Lesson: A “fish pond” contains face-down cards that have a certain number of fish pictured on the bottom. Children have a given number of cardboard fish bowl mats to fill. Children place captured fish cards in fish bowls until each bowl contains the target number of fish. Through this lesson, children practice combining parts to make a whole, having to decide how many more fish are needed to reach the target number for each fish bowl. As you plan, consider the variability of learners in your class and make adaptations as necessary.

Prior Knowledge Required: Able to count with 1:1 correspondence

Estimated Time (minutes): 15 minutes to introduce at group time plus choice options or set up as work station


Cards with pictures of fish on them, 0 to 5 and attached paper clip

Fishing pole with magnet on end of the fishing line

Large blue mat to serve as “pond” for fish cards

Fish bowl mats large enough for fish on cards placed in the fish bowl to remain visible

Number card showing target number and picture to match.



Unit: Modeling Addition and Subtraction through FiveContent Area/Course: MathLesson # 5: Fishing GameTime (minutes): 15 minutes to introduce at group time, then added to choice options or set up as work station.

By the end of this lesson children will know and be able to: Combine quantities to add up to a target number up to 5.

Essential Question(s) addressed in this lesson: What strategies can I use to figure out how many I have?’ How can I separate a number into 2 or more parts?

Standard(s)/Unit Goal(s) to be addressed in this lesson: PK.OA.MA1 – Use concrete objects to model real-world addition (putting together) and subtraction (taking away) problems up through five.PK.CC.MA.5 – Use comparative language such as more/less than, equal to, to compare and describe collections of objectsSMP1: Making sense of the problems and persevere in solving themSMP6: Attend to precision

Instructional Tips/ Strategies/Notes for Teacher:Encourage children to predict where to put their recent catch to equal the target number before they combine and count the total quantity.

Encourage children to count on (e.g., 3…4, 5”) rather than counting all (“1, 2, 3…4, 5”).

If children make a combination that is too many, ask them to predict what quantity they should actually add to make the target.

Ideas for differentiation: For beginning counters, set a lower target such as 3. For more advanced children, consider using a target higher than 5.



Anticipated Child Preconceptions/Misconceptions:Children may not initially realize they can put multiple cards in the same bowl.

Children may have a hard time with multiple addends (e.g., using three cards to equal the target number).

Even if children can count the total set, they may not be able to judge whether it is too many or too few (e.g., may know they have 7 but not realize that is more than the target number, 5).

Lesson Sequence:1. Set out the “fishing pond” with fish cards facing down. 2. Tell children: “Today you’re going fishing. The fish are all swimming here in the pond.” Turn over one of the fish cards to show fish pictures.

“See? This card has some fish on it. How many fish do you see?” Help children count.3. “You’re going to be filling each of these fish bowls with this many fish.” Point to empty fish bowl mats and target number/numeral card. Help

children identify the target number. 4. “You’ll be using this fishing pole to catch your fish, and then you’ll have to decide which fish bowl to put them in. Remember, you can’t have

more than this many fish in any bowl.” Again, point to the target number. “Who would like to catch some fish for me?”5. Let children take individual turns catching fish, counting fish on the card, and deciding where to place it. Help them realize they can put

multiple cards on the same bowl mat, as long as the total isn’t more than five. Ask questions such as:6. “Can this mat take any more fish? How many more?” “What strategies did you use find the answer?” (Teacher can discuss/model with student:

counting on, addition, subtraction.7. “How many fish are together in this bowl now? Is 7 more or less than 5?” How do you know?8. “There are 3 on the first card and 2 on the other, so together we have 3…” (see if children can continue the count from 3, rather than starting

over from 1).

Lesson Closing: Ask children to share what they learned in this lesson. Have students share their thinking about the essential question: What strategies can I use to figure out how many I now have?



Lesson #6 Mother May I

Brief Overview of Lesson: This call-and-response outdoor group movement game is based on the Mother May I children’s game. It focuses on children listening to verbal more than/less than commands that involve combining or taking away, e.g., “You may hop forward 1 more than 3 hops” or “You may crawl forward 2 less than 3 crawls”). Children must transform the called number by adding to it or taking away from it to know how many moves to make. As you plan, consider the variability of learners in your class and make adaptations as necessary.

Prior Knowledge Required: Children need to understand vocabulary more/less and be able to count from 0-5, counting 1-5


Resources for Lesson: None



Unit: Modeling Addition and Subtraction through FiveContent Area/Course: MathLesson # 6 Mother May ITime (minutes): 20 minutes

By the end of this lesson children will know and be able:

Combining two or more sets of objects or adding to a set of objects makes a new, larger quantity. This process is often called addition.Taking objects away from a set creates a new, smaller quantity. This process is often called subtraction.

Essential Question(s) addressed in this lesson:

What changes make sets larger or smaller? What strategies can I use to figure out how many I now have?


PK.OA.MA1 – Use concrete objects to model real-world addition (putting together) and subtraction (taking away) problems up through five.SMP1. Make sense of problems and persevere in solving them.SMP6. Attend to precision.

Instructional Tips/ Strategies/Notes for Teachers: Pre-teach vocabulary Model activity Discuss problem solving strategies

Ideas for differentiation: provide a number line for students who may require more visual support.



Anticipated Child Preconceptions/Misconceptions Children may assume that the “less” command means to go backwards.

Opening Message“We’ve been working on lots of fun math games using manipulatives to add and subtract. Today we are going to use our bodies.”

Lesson Sequence 1. Bring children outside and line them up on a starting line (fence, chalk line, wall etc.).2. Explain to children that they are going to work as a group to move towards a designated finish line.3. Give the children the command, “You may hop forward 1 more than 3 hops.” 4. Model for children how to use their fingers to find the answer.5. Choose one child to tell you how many hops the class may take and if possible have child explain their answer. 6. Allow children to move 4 hops toward the finish line.7. Give the children the command, “you may crawl 1 less than 2.”8. Choose one child to tell you the answer and have them explain their answer.9. Allow children to move.10. Continue giving commands and allowing children to move until the class reaches the finish line.

Lesson Closing: After the game is over, bring them back together and have the children explain what they did in the game. Encourage them to talk about the commands you gave by asking questions such as: How did you know how many hops, crawls, etc. to take? as they tried to get to the finish line. Use one of the commands as an example to facilitate the conversation. Encourage the children to explain their mathematical thinking.



Lesson #7 Build & Change It

Brief Overview of Lesson: Children predict how many will need to be added to or taken off a five frame. Children add the target quantity and check their predictions. Children can do this activity during choice time that involves continuously changing their current number to a new target number.

Prior Knowledge Required: Children will need to be able to use 1 to 1 correspondence and count from 1-5.



Overhead

Transparent sheet with a five frame

Transparent tokens

Child’s set five frame or ten frame

Number cards 0-5 or 0-10

Counters



Unit: Modeling Addition and Subtraction through FiveContent Area/Course: MathLesson # 7 Build & Change ItTime (minutes): 15 minutes

By the end of this lesson children will know and be able to: Understand that adding to a quantity increases the amount (addition) and taking away from a quantity decreases the amount (subtraction).

Essential Question(s) addressed in this lesson: What strategies can I use to figure out how many I have? How can I decide if one set is larger than another if they don’t look the same? In what ways can I show how many I have?


PK.OA.MA1 – Use concrete objects to model real-world addition (putting together) and subtraction (taking away) problems up through five.SMP1. Make sense of problems and persevere in solving them.SMP5. Use appropriate tools strategically.

Instructional Tips/ Strategies/Notes for Teacher Pre-teach/Model first whole group using an over-head projectorDiscuss rules of partnershipsIdeas for differentiation: A challenge activity is for children who need more challenge to use a ten frame and number cards 0-10Teacher can instruct struggling learners in a small group to monitor understanding.

Anticipated Child Preconceptions/Misconceptions :

This work is licensed by the MA Department of Elementary & Secondary Education under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License (CC BY-NC-SA 3.0). Educators may use, adapt, and/or share. Not for commercial use. To view a copy of the license, visit http://creativecommons.org/licenses/by-nc-sa/3.0/ Draft 8/2013


Children may start with a starter set and continue to add on to it rather than changing it.

Opening Message: Invite all children to join you on the rug area. Explain to them that you are going to be working together to count and change numbers. In Find a Partner and Leap Frog we had to put together numbers. “What was that called?” Children respond with “addition”. Now we will learn how to take away from a number. This is called subtraction. In today’s game you will have to decide whether to add or subtract. Put on your thinking caps! “

Lesson Sequence 1. Show children an image of a five frame.2. Turn over one card from a deck and show children the number.3. Place that many tokens on the frame (be sure to use transparent tokens).4. Confirm with children that the number of tokens matches your first card.5. Turn over a second card and show the number to children.6. Discuss if the number shown is larger or smaller than the first number.7. Show children how to change the number of tokens on the five-frame by either adding more tokens or taking away tokens to equal the number on the second card. Ask: are there more or less tokens on the five-frame now? How many do we now have? Ask the essential question: “What strategies can I use to figure out how many I now have?8. Review the procedure again in detail.9. Clear the five-frame and start the process again.10. After several demonstrations have children come up to the overhead and try it on their own.11. Activity could potentially be set up as a shelf activity, for a child or group of children to do independently.

Lesson Closing- Have students go to the rug for a whole group wrap-up. Ask: what did you learn today? How did you know if you had to add or take away tokens on the five-frame? Ask students to think and share about the essential question: What changes make sets larger or smaller?”



Lesson #8 Mystery Box

Brief Overview of Lesson: This lesson involves the teacher placing a certain quantity in an opaque box. When the lid is closed, a certain number of items are shown that are being added to the box. Children must answer the question: how many are in the box now? The children are then asked whether they added or subtracted. Children also visualize quantities being transformed where they can see what is being added to or taken away but they cannot see the set that has been created. As you plan, consider the variability of learners in your class and make adaptations as necessary.

Prior Knowledge Required: 1:1 correspondence; ability to count on or count back

Estimated Time (minutes): 15 minutes to introduce at group time, then added to choice options or set up as work station

Resources for Lesson

Opaque bag or box

Counters



Unit: Modeling Addition and Subtraction through FiveContent Area/Course: MathLesson #8 Mystery BoxTime (minutes): 15 Minutes to introduce during group time then added to choice options or set up as work station

By the end of this lesson children will know and be able to: Predict total up to five when quantities added or taken away but final amount invisible.Combining two or more sets of objects or adding to a set of objects makes a new, larger quantity. This process is often called addition.Taking objects away from a set creates a new, smaller quantity. This process is often called subtraction.

Essential Question(s) addressed in this lesson: What changes make sets larger or smaller?What strategies can I use to figure out how many I now have?

Standard(s)/Unit Goal(s) to be addressed in this lesson:PK.OA.MA1 – Use concrete objects to model real-world addition (putting together) and subtraction (taking away) problems up through five.SMP1. Make sense of problems and persevere in solving them.SMP6. Attend to precision.

Instructional Tips/ Strategies: Make sure children share their reasoning about how they came up with their answer. Look explicitly for accurate counting on or counting back skill.

Ideas for differentiation: Consider allowing struggling learners to use counters if they cannot visualize the change or cannot count on or count back. Higher level learners can use a recording sheet to draw a visual representation.Consider displaying numeral cards to help children remember how many were in the box originally and how many were added or taken away.



If children are perplexed by the changes, try modeling how to count on or count back: “There were five in the box and I took one out so now there are…? And I take out another so now there are…?”

Anticipated Child Preconceptions/:When counting on or counting back, children may mistakenly use the base number as the first jump; for example, if 2 were in the box, may say: “2, 3, 4…4!”

Lesson Sequence:

Opening Message:Begin by telling the children that we have been lots of time counting. Ask children “What changes make sets larger or smaller?”“What strategies can I use to figure out how many I now have?

Pull out the mystery box: “Today we’re going to play a guessing game. It’s a lot like the game Build It/Change It. We will be adding and subtracting.1. Start by letting everyone see the quantity of counters being added to the box, one at a time. Have children count aloud as each in put in.2. “Now watch carefully.” Close the lid so children can’t see inside, then show a certain number of items being added to the box, one at a time. 3. “How many do you think are in the box now?” Call on children, ask for their prediction, and ask them why they chose that number. Ask

children what strategies they used to find out how many counters are in the Mystery Box.4. Reveal the counters in the box. Have one of the children count the counters.5. “Remember, there are now ____ counters in the box. Now watch.” Close the lid and remove a certain number of items from the box one at a

time.6. Again ask how many counters do we have now? and ask children to share their reasons for their prediction. Reveal the counters in the box. 7. Repeat several more times. Periodically ask: “Did we add, or subtract?”How did you know what to do? Define the terms if needed.8. Let the children know the activity will be in a work station so they may play the game with each other.



Snack Attack (CEPA 1)

During the daily snack routine, children will use snacks to solve addition and subtraction problems up through five. Children will each be given a random amount of snack items and asked to determine whether or not they have enough or too much based on the target number. Children will represent the number they received by drawing that many circles on a laminated snack mat and either add tallies to show how many more they need or X out the circles that are too many. Children will be encouraged to explain their representation to a partner while the teacher circulates the room and asks them how many more they need or how many they may need to put back. Teachers will ask how they know using their mat as a model. The teacher will also ask whether they used addition or subtraction. This CEPA is designed to be used as a formative assessment.

Resources for the CEPA:

Snack Items Snack Mat Recording Sheet Dry Erase Markers

Standard to be addressed in this CEPA:

PK.OA.MA1 – Use concrete objects to model real-world addition (putting together) and subtraction (taking away) problems up through five. PK.CC.MA.5 – Use comparative language such as more/less than, equal to, to compare and describe collections of objects. SL.5. Create representations of experiences or stories (e.g., drawing, constructions with blocks or others or other materials, clay models)

and explain them to others. MP6. Attend to precision.



1. The day before the first Snack Attack is given, do a mock role play of the procedure at circle. Show a target number of 3. Have three children receiving a pretend snack, one is given too many, one not enough, and one the right amount. Have them first count their snack then draw that amount of circles on their snack mat. One child at a time, show the target number and ask do you have more than this, less than this or is yours equal to this? Have group discuss how each child would reach the target number. Teacher will hold up the child’s mat and show how to change the drawing by adding tallies or using X’s to take away circles. The teacher asks the group was this addition or subtraction. Group discusses.

2. Teachers will decide on a daily number ranging from 1-5 and have a visual display of the numeral as well as a representation. Snack Attack will be done every other day for a two week cycle (i.e. for each child 2x more than, 2x less than, 2x equal to). On days when target number is 4 or 5, assess less than or equals. On days when the target number is 1 or 2 assess more than or equals (i.e. give either too many or the right amount). Make sure that each child has had two “equals to” experiences by the end of the sequence.

3. On Snack Attack day the teacher should tell the group “Remember, today we’re doing Snack Attack. Before you eat your snack, you need to make yours equal to this much.

4. After washing hands each child will be given an individual snack mat and a dry erase marker. The teacher will then circulate and give each child a random amount of snack pieces (i.e.: goldfish, pretzels, crackers). The amount should be no more than five. Teachers will conduct the activity and record data every other day for a two week cycle (per child 2 x more than, 2x less than, 2x equal to).

5. Teacher will ask the children to count their snack pieces, and then draw an equivalent representation on their mats.

6. Children should decide how the amount they were given compares to the day’s number and either draw tally marks to show how many more they need or draw X’s through items that are too many.

7. Teacher announces: “When I come around, I will be asking whether yours is MORE THAN this much, or whether yours is LESS THAN this much. Then you can tell me how to change yours so it is EQUAL to this much.



8. Teacher will then ask children to explain their drawing to their neighbor, explaining how many more or how many less they need or whether they already have the right amount.

9. While the children are conversing, teacher should circulate and ask each child to explain how their quantity compares to the target number using the appropriate vocabulary: (i.e.: more than, less than, equal to). The children should then tell how many more they should be given or how many they should put back. (Note: snack being returned should go into a separate container and be discarded) Finally, the children will then be asked if they used addition or subtraction to reach the daily number.10. Include in notes any strategies used by children.11. Teachers will conduct the activity and record data every other day for a two week cycle. (per child 2 x more than, 2x less than, 2x equal to)12. Teacher says “Snack Attack” and children are allowed to eat their snack.



CEPA 1 Rubric: Snack AttackName: ____________________________________________________ Date: _____________

Skill Does Not Attempt

1

BeginningFrequent Support Needed

2

ProgressingLittle Support Needed

3

Mastered Demonstrated Skill without Additional Support

4Make a comparison between two quantities to indicate more than/less than or equal toChild drawing shows adding to and taking away from with objects to make two quantities equal.Ability to connect adding to and taking away from to the terms addition and subtraction

Notes on strategies (counting on, counting all, using fingers, using visual chart)



CEPA 1 Checklist

Snack Attack Checklist

KEY: Com Compares own quantity to target quantity in terms of whether it is more than-less than-equal to.Eq Makes own quantity equal to target.Voc Interprets action as addition or subtraction.

CHILD’SNAME

Given more than Given more than Given less than Given less than Given equal to Given equal to COMMENTSCom Eq. Voc. Com Eq. Voc. Com Eq. Voc. Com Eq. Voc. Com Eq. Voc. Com Eq. Voc.



Lesson 9 Tip the Chips

Brief Overview: Children compare quantities to make more-less-same judgments. Using two-sided counters or beans, children toss the counters and move their color to their side of the mat. They then decide who has more, who has less.

As you plan, consider the variability of learners in your class and make adaptations as necessary.

Prior Knowledge Required: Children will need to know how to count from 0-5; 1:1 correspondence.

Estimated Time: 15 minutes to introduce at group time, then added to choice options or set up as work station.


Two colored chips Sorting mat Cup Recording sheet



Unit Modeling Addition and Subtraction through FiveContent Area/Course: MathLesson # 9 Toss the ChipsTime (minutes): 15 minutes

By the end of this lesson children will know and be able to: A quantity can be taken apart in multiple ways without changing the whole.The order of parts doesn’t change the whole

Essential Question(s) addressed in this lesson: How can I separate a number into two or more parts?

Standard(s)/Unit Goal(s) to be addressed in this lesson: PK.CC.MA.5-Use comparative language such as more/less than, equal to, to compare and describe collections of objects.MP5. Use appropriate tools strategically.

Instructional Tips/ Strategies Cover the cup to prevent chips from tossing into the air Model how to gently spill the cup over onto the mat

Ideas for differentiation: Extend the activity for higher learners by increasing chips to 10 and using 10 frames.Teacher will model and encourage key vocabulary use with struggling/ESL learners.

Anticipated Child Preconceptions/Misconceptions: NoneOpening Message: Gather children on the rug in a circle. “We have been doing lots of counting! Encourage children to share some of their counting experiences in your class in recent days. Ask them to share how they knew how many they had. What strategies did they use to count the objects?



“Today we are going to play another partner game. Think about the game Find a Partner. What does it mean to have a partner? What do partners do?” Encourage children to discuss taking turns, listening to their partner, working together to solve the problem.Lesson Sequence 1.”Today you are going to play another counting game with your partner called “Tip the Chips” This is called a chip” Show children a chip. “What do you notice about the chip” Encourage children to recognize the color red on one side and the color yellow on the other side.

2. Next show the children the counting mat. The mat should indicate where to separate the counters – one side red the other side yellow. Tell children: “This is our counting mat. When we toss our counters on this mat where are they going to go? How are we going to know where to separate them?” Elicit responses from the children.

3. “Let me show you how to play.” Teacher will then choose a child to model the activity with. “___________ will you be my partner?”

“Step number one is for us to toss the chips. Before we toss the chips let’s count to see how many chips we have altogether? What strategies can I use to figure out how many I now have? Teacher will place 3-5 chips in the cups. What does it mean to toss?” Model for children how to gently shake the cup and spill the chips onto their counting mat. Discuss with the children the right way to toss and the wrong way. What would happen if I toss them high in the air? Encourage the discussion of keep the chips on the counting mat to make sure the chips do not get lost.

4. “Step 2 is for __________ and I to separate the counters of the counting mat. Model how partners decided who has what color. _____________ would you like to count the red or the yellow? Remember good partners work together.

5.”Step 3 is count how many red we have and how many yellow we have. Then decide who has more/less.

Lesson Closing: Encourage children to share what they learned (mathematically) today. Ask the essential question: What changes make sets larger or smaller?

Name: _________________________________

Tip the Chips



Toss the chips in your cup. Sort them on your mat. What color did you have more of? What color did you have less of? Put chips back in your cup and repeat.

RED YELLOW

Lesson #10 Mitten Match



Brief Overview: Children will place a top hat (with numbers 1-5 and pictures) on the snowman and find two mittens that will equal the number. As you plan, consider the variability of learners in your class and make adaptations as necessary.

Prior Knowledge Required:

Children will need to know how to count a set of objects with one to one correspondence from 1-5.



Large laminated snowman (may use Velcro on hat and mittens to make it vertical) Top hats with numbers 1-5 (with pictures to show quantity) Mittens with 0-5 spots



Unit: Modeling Addition and Subtraction through FiveContent Area/Course: MathLesson # 10 Mitten MatchTime (minutes): 15 minutes to introduce at group time, then added to choice options or set up as work station.

By the end of this lesson children will know and be able: Combining two or more sets of objects or adding to a set of objects makes a new, larger quantity. This process is called addition.

Essential Question(s) addressed in this lesson:

What strategies can I use to figure out how many I have?How can I separate a number into 2 or more parts?In what ways can I show how many I have?What changes make sets larger or smaller?

Standard(s)/Unit Goal(s) to be addressed in this lesson (type each standard/goal exactly as written in the framework):

MP1. Make sense of problems and persevere in solving them.MP7. Look for and make use of structure.

Instructional Tips/ Strategies Do task initially as a whole group activity Add Velcro to snowman and pieces to make vertical Observe/assess whether children can manipulate and combine numbers to equal a whole. Check to see if children understand that combining two numbers will make a larger number.

Ideas for differentiation: Increase target number for higher level learners. Struggling learners can work in a partnership with higher level learners.


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Anticipated Child Preconceptions/Misconceptions: Children may think they should find mittens with the same numbers as the hat.

Opening Message: “Today we are going to play a new counting game called Mitten Match. Instead of using chips to do the counting we are going to use mittens.”

Lesson Sequence:1. “What do you notice about these mittens” Encourage children to discuss the dots on the mittens. 2.”Today we are going to use two mittens to dress our snowman. Step number one is to pick a hat for the snowman’s head. What do you notice about the hats?” Discuss the numbers that are on each snowman’s hat. Model by picking a hat for snowman’s head. “What number did I pick?”3. “Step number two is to find two mittens that equal the number on your snowman’s hat”. “The number I chose for my snowman’s hat is 4. What two mittens together equal the number 4?” As the children respond be sure to model by counting the dots on the mittens. 4. Ask children what strategy they used to find the answer. And if there could be more than one way to separate the number into two parts. 5. Teacher will also model the wrong answer, such as 1 mitten with 3 dots and another mitten with 2 dots. Allow the children to talk and discuss why or why not these mittens should go on the snowman.

Challenge: use numbers of mittens that when subtracted from one another equal the number on the hat.



Lesson 11 Bears in a CaveBrief Overview: Children are given a missing-part game to play during choice time, where they try to use their knowledge of the total to guess what part of the whole set is not visible. Included are cases where all of the pieces are visible or all are hidden, invoking the concept of zero. Difficulty can be adjusted by changing the size of the set to less than or more than five.In this game, a target number of bears start outside the cave. One or more children hide their eyes while some of the bears are hidden in the cave. Children open their eyes and try to guess how many bears are hiding. As you plan, consider the variability of learners in your class and make adaptations as necessary.

Prior Knowledge Required: Children will need to count 0-5; children will need to understand the relationship between numbers, that two sets equal a whole


Resources for Lesson: bears, bowl



Unit: Modeling Addition and Subtraction through FiveContent Area/Course: MathLesson # 11: Bears in a CaveTime (minutes): 15 minutes to introduce at group time, then added to choice options or set up as work station.

By the end of this lesson children will know and be able to: A quantity can be taken apart in multiple ways without changing the whole.The order of parts doesn’t change the whole.

Essential Question(s) addressed in this lesson: Q2. “What strategies can I use to figure out how many I now have?”Q4. “How can I separate a number into two or more parts?”

Standard(s)/Unit Goal(s) to be addressed in this lesson (type each standard/goal exactly as written in the framework):

MP1. Make sense of problems and persevere in solving them.MP7. Look for and make use of structure.

Instructional Tips/ Strategies Preteach/Model first using whole group experience prior to working independently Children must also be taught how to work within a small group or as a partner Emphasize taking turns.

Ideas for differentiation: consider making counters available to children to help model the total, seen, and/or hidden parts of the problem.Increase target number for higher level learners.

Anticipated Child Preconceptions/Misconceptions : Children may report only the number of bears they see, not the amount of bears that are hidden in the cave.



Lesson Sequence :Opening Message:1. Gather children on the rug in a circle. “Boys and girls, we’ve been doing lots of counting in school. Before we start a new counting game, I want you to show me what great counters you are.” Do a quick review of counting to 5 using 3 different types of manipulatives.2.” During the last activity Mitten Match we worked on counting dots on a mitten to equal the number on the snowman’s hat. Today we are going to do some more counting with bears.”3. Model activity with a child as your partner. “___________ and I are going to show you how to play this partner game.” ______________ can you remind me what good partner’s do?”4. “First I’m going to place 3 bears in row. Let’s count them together 1-2-3. How many bears do I have? Then I’m going to take this cave and cover some of the bears in the cave. So everyone close your eyes while I hid the bears. Remember not to peek. When the bears are sleeping I’ll tell you to open your eyes and try to guess how many bears are in the cave.” Ready? When all children eyes are closed begin to cover some of the bears in the cave.5. “Let’s see how many bears are in the cave!” “_______________ is my partner. _________ can you tell me how many bears you think are in the cave?” “How do you know?” “Does anyone else have the same idea as ____________” “Does anyone have a different idea”. Allow children to share their responses as well as their strategies. 6. Once children have had the opportunity to share their responses, uncover the bears in the cave and discuss whether their answers were accurate. Model the activity once more showing how partners take on different roles. Model with a different quantity up to 5 and discuss with children what we did as partners as well as allow the remaining children to assist in finding the answer.



Lesson 12 Bowling

Brief Overview: Children mark five tally marks for standing pins and “bowls.” They then wipe of the number of pins that fell and mark those on the other side. They roll again and adjust the marks (challenge: use ten tally marks for “ten-pins”). As you plan, consider the variability of learners in your class and make adaptations as necessary.

Prior Knowledge Required: Children will need to know the quantities 0-5 (see PK Counting and Cardinality standards). Children will need to know how to represent the quantities 0-5 with tally marks.


Resources for Lesson: Bowling pins, pin mat, 3 small balls. Dry erase board divided into “Still Standing” and “Knocked Over” columns, marker, and eraser.


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Unit: Modeling Addition and Subtraction through FiveContent Area/Course: MathLesson # 12 BowlingTime (minutes): 15 minutes to introduce at group time, then added to choice options or set up as work station.

By the end of this lesson children will know and be able to:Decompose the quantity 5 into two parts different ways.

Essential Question(s) addressed in this lesson: How can I separate a number into two or more parts?In what ways can I show how many I have?

Standard(s)/Unit Goal(s) to be addressed in this lesson: PK.OA.MA1 – Use concrete objects to model real-world addition (putting together) and subtraction (taking away) problems up through five.SL.5. Create representations of experiences or stories (e.g. drawing, constructions with blocks or others or other materials, clay models) and explain them to others.MP4. Model with mathematics

Instructional Tips/Strategies Model the activity at whole group using a child as a partner Remind children to leave their answers on the board for you to check. Give children a large-motor game to play that involves starting with a target quantity and moving some of them to another category – the

parts change, but the whole remains the same.

Ideas for differentiation: Higher level learners will use 10 pins. Teacher/Aide will support struggling learners with the role of score keeper.




Children may need reminders that they need to adjust both sides of the score board after each roll, and to re-set the score board with each new turn.

Lesson Sequence :Opening Message:1. Gather children on the rug: “Today we are going to bowl and keep track of our score.”2. “How many of you have ever been bowling before?...What is the object of the game” Continue to build background knowledge about bowling

especially what a bowling pin is, how you roll more than once, how you keep track of how many pins you’ve knocked down as you go along. “Here’s the mat, on which we will place these 5 pins.”

3. “Today you will play bowling with a partner. One of you will be the bowler and the other will be the score keeper and in charge of setting up the pins. Then you’ll switch jobs. The bowler is going to stand this far away and roll the ball to knock down as many pins as he/she can. The bowler gets three tries to try to knock down all of the pins.” Ask children to turn and talk to a partner to review what a good partner does and what each will do.

4. “Let’s look at the score board. This side will show how many bowling pins are still standing, and on the other side we will show how many bowling pins have been knocked over. How many pins are standing to begin with?” Have scorer mark 5 tallies on the Still Standing side. “And how many are Knocked Down right now?” Help them understand why that side is kept blank at the start.

5. “Let’s watch _____________ bowl”. Child rolls first ball. “How many bowling balls did __________ knock down on the first try? How many pins are still standing? How can _____ show that on the score board?” Show scorer how to remove tallies from Still Standing side and add tallies to the Knocked Over side. “Does that 2 and that 3 still equal 5? How can we tell?” Solicit strategies, encouraging the counting-on strategy. “Okay, _____ bowled 1 ball. How many more turns can he take to try to get them all down?”

6. Continue to finish first turn, then model how to re-set the pins and scoreboard. Play twice more and have the children discuss what they noticed. Have discussions about how the amount shown on each side of the score board changes, but the total is always five.

7. Make the game available for the children to choose. As children bowl, encourage them to notice how the pins down and pins still standing continue to equal five (and that the tallies show the whole amount decomposed into two parts). Also have them compare the two amounts and make more-than/less-than judgments.



Lesson 13 Ladybug

Brief Overview: Children choose a number card and manipulate dots on both ladybug wings to show how the numbers combined equal that number represented on their number card. As you plan, consider the variability of learners in your class and make adaptations as necessary.

Prior Knowledge Required: 1:1 counting up to 5 (see Counting and Cardinality standards).


Resources for Lesson: Enough ladybug mats for group of children to each have two; number cards 0-5, supply of black dots.



Unit: Modeling Addition and Subtraction through FiveContent Area/Course: MathLesson #13 LadybugTime (minutes): 15 minutes to introduce at group time. Then added to choice options or set up as work station.

By the end of this lesson children will know and be able to: That a quantity can be decomposed in multiple ways without changing the whole

Essential Question(s) addressed in this lesson: How can I decide if one set is larger than another if they don’t look the same?How can I separate a number into two or more parts?In what ways can I show how many I have?


PK.OA.MA1 – Use concrete objects to model real-world addition (putting together) and subtraction (taking away) problems up through five.SMP1. Make sense of problems and persevere in solving them.SMP7. Look for and make use of structure.

Instructional Tips/Strategies Preteach/model using whole group experience prior to working independently.

Ideas for differentiation: Increase the target number for higher level learners. Continue to model in a small group for struggling learners until they show independence.

Anticipated Child Preconceptions/Misconceptions: Children may look at their number card and create the same number of dots on their ladybug and state that it is the only way to represent the

number. Help children notice turn-around facts, when same parts are used on two ladybugs, but on opposite wings.



Lesson Sequence

Opening Message:

1. Gather children on the rug. “We have been working a lot with numbers. Today we are going to continue to practice our counting using spots on a ladybug.” Show children a real picture of a ladybug to show them that ladybugs have spots.

2. “Before we start, let’s work on counting together.” Practice counting 3 different manipulatives.3. “Right now your ladybugs don’t have any spots on them. This card will show how many dots we’re going to put on our first ladybug.” Turn over

one of the number cards. “What number are we going to make?” (e.g., 4). 4. “Okay, everyone get 4 spots.” Pause and help children check to make sure they have 4.5. “Now you have to decide how many dots to put on this wing and how many on the other.” Help children arrange dots, making sure they use

them all and don’t add any additional ones.6. “So let’s look at how many different ways we made 4.” Have children share the two amounts they made. Occasionally pause and say: “Let’s

see, is that still four? Periodically model a counting-all strategy (“1,2,3,,,,4”) and sometimes model a counting-on strategy (“3…4”).7. “You have one more ladybug. I would like you to put the same number of dots on that ladybug, but don’t put them the same way you did on

the first one.”8. Review with the children their two results, emphasizing how different combinations equal the same total – “So on this ladybug you put 2 on

this side and 2 on this side, and that equaled 4, and on this one you put 1 on this side and 3 on that side, and that also equaled 4.”9. Continue to model with a different number card and encourage children to discuss and compare the different strategies they are using to

represent the given number.10. Let the children know where the materials will be available in the room for their continued use. When children are working, emphasize how

the total number of dots continues to match the target number even when the number of dots on each wing varies.



Lesson #14 Domino Train

Brief Overview of Lesson Children take turns picking from a pile of 0-5 dominoes to create sets equal to the target number. Children add to or take away from to make a target quantity. As you plan, consider the variability of learners in your class and make adaptations as necessary.

Challenge: Children may have to take away from rather than add to reach the target number.

Prior Knowledge Required: 1:1 counting up to five (see Counting and Cardinality standards).

Estimated Time (minutes): 15 minutes to introduce at group time, then added to choice options or set up as work station.

Resources for Lesson

Domino sets with 6-dot dominoes removed

Numeral card showing target number

Numeral card showing target number



Unit: Modeling Addition and Subtraction through FiveContent Area/Course: MathLesson # 14 Domino TrainsTime (minutes): 15 minutes to introduce at group time, then added to choice options or set up as work station.

By the end of this lesson children will know and be able: Add to and take away from to make combinations equal to target number between 1 and 5.

Essential Question(s) addressed in this lesson: What strategies can I use to figure out how many I now have?How can I separate a number into two or more parts?

Standard(s)/Unit Goal(s) to be addressed in this lesson: PK.OA.MA1 – Use concrete objects to model real-world addition (putting together) and subtraction (taking away) problems up through five.SMP1. Make sense of problems and persevere in solving them.

Instructional Tips/Strategies: Preteach/model first using whole group experience prior to working independently.Ideas for differentiation: For children who are comfortable with combinations up to 5, consider including the 6-dominoes – or go further using a double-nines set. Teachers/Aides will continue to work with struggling learners in a small group until they become independent.

Anticipated Child Preconceptions/Misconceptions: Children may not know that if the last segment is already the target number they can add a blank to it (zero). Children who cannot count backwards may have a hard time doing the take-away combinations. When children are checking their combinations they often have trouble hearing their target number in their count and may “overshoot”. Some children who have counted their combination and know it doesn’t match the target may not be know whether they have too many or too

few; in other words, they don’t have a more than-less than sense separate from modeled sets.



Lesson Sequence:1. “We’ve been practicing lots of ways to put numbers together to make a new number. Today I’m going to show you another way you can do

that.2. Lay out a pile of 0-5 dominoes, face up, pick up one of the dominoes that ends in 2 and show it to the children: “How many dots are there on

this side of the domino?...And how many on this side?” If necessary, hold out so children can touch each of the dots as they count.3. “We are going to make a long train with these dominoes. But there is a special rule for how we build this train: the parts of the dominoes that

are touching have to add up to this number” – hold up a target numeral card (e.g., 4). “What number is this?” 4. “So we want a total of 4 dots. Here on the end of this domino we have 2. How many more dots do we need to make 5?” Take suggestions and

ask for reasoning. Consider making manipulatives, number lines, or ten-frames available to the children to demonstrate their reasoning of the missing part. Encourage counting-all, counting-on, comparison, and counting-back strategies. For example, model how to counting on (e.g., “2…3, 4” rather than “1, 2, 3, 4”).

5. Have a child find a domino with 2 dots on one side, and place it at the end of the first domino. “Now on the end of the train we have ___ dots? Is that 4?” If not, say: “Is it less than 4 or more than 4?”

6. If need to add more, repeat above. If too much, say: “So we already have too many dots to make 4. On this train, if we have too many dots we can use the next domino to show how many dots need to be taken away to equal 4. How many dots would we have to take away from this 5 to make 4?” Have children suggest answers and give their reasons. Help children practice the counting backwards strategy. . Consider making manipulatives, number lines, or ten-frames available to the children to demonstrate their reasoning of the surplus amount. Consider whether to model one of the other strategies suggested above. For example, if children cannot count back, you might need to provide counters so children can model the end set and see how many they have to remove to reach the target number. Or you can have the children cover up the number of dots they want to remove and count the remaining set.



7. When get to an example where the last domino ends in the target number, say: “So we already have 4 dots. Does that mean we can’t add another domino to our train?” Help children realize that if they choose one of the dominoes blank on one side, they will still have 4. “So 4 dots plus zero dots is still 4?”

8. Continue extending the train until children appear comfortable with the routine, then let them know where the game will be available on the shelf of in a work station for their choice. As children work, encourage them to predict how many they are looking for and share their reasoning. Continue to scaffold their use of different strategies. For example, if children create a match that doesn’t work, ask follow-up questions about how much over or how much under they are, so they can strategically choose a replacement .



Weather Report (CEPA 2)Math PreK Unit – Modeling Addition and Subtraction through Five

Related to the skill of putting together and taking away is the understanding that a quantity can be subdivided into parts without the total quantity changing. In this activity, children are asked to name the missing part of data they have gathered, knowing that the total in each case is five (i.e., the five days that make up the school week). The split-page recording sheets represent putting together to make five using real-world data. Having to guess the missing part and explain their reasoning requires them to use patterned relationships to solve problems using a strategy that makes sense to them. Asking them to decide to compare the sunny to cloudy days each week or which week had the most sunny days requires the children to make comparative judgments (“This week had the most sunny days”). The final probe, where the children are asked to combine pairs of weeks where the sunny days equals a total of five more directly assesses their ability to combine sets up to five.



CEPA 2, Weather ReportTeacher Instructions:

Each day at group time, have a group make a judgment about whether they would say it’s sunny or cloudy (group consensus). Keep track of daily judgments (if weather reports are a daily circle event, may put on calendar or add to a weather graph. If not, teacher can simply record class decision on a displayed chart).

Data recording phase (end of each week that month): Teacher hands out a Weather Report recording sheet to each child (see Resources). Have children record under the sun icon the number of days that were sunny (can make tally marks, or draw). Do same for cloudy days under the cloud icon. Children can attempt to write the numerals corresponding to the two quantities in the boxes (they can use a class number line display as a reference) or they can leave blank.

End of the month:Assemble each child’s Weather Report book stapling the four folded pages inside the cover.At a small group work station, give each child their book and allow them to decorate the cover.Taking individual children aside, ask the following questions, and record the results (see attached resource):

[turn to the first page, but cover up one side of the page] “We had school five days each week.” “So there were 2 cloudy days this week. How many of the five days this week do you think were sunny?”

[reveal both sides so child can check his or her guess] Were there more sunny days or more cloudy days this week?” (periodically switch to asking “fewer” rather than “more”).

Repeat for each of the four pages, choosing different sides of the page to cover so you can check different part-whole combinations. Ask: “Which week this month had the most sunny days?” Finally, show the probe sheet that s a four-week display of sunny days, and ask the child “Which two boxes would you put together if you

wanted a total of five sunny days?....Can you show me how you know that is five?...Would you call what you just did addition or subtraction? What does the word addition/subtraction mean?”



CEPA 2, Weather ReportChild Instructions:

Data collection phase (end of each week that month): Children are handed the work page for recording the class data collected that week that is on display: sunny days on one side of the page, cloudy days on the other (children can use tally marks, or if they prefer draw the required number of icons).Teacher collects and saves pages.

End of the month:At the work station, children are given their assembled books and they are given time to decorate the cover of their book.Children are individually interviewed about the weather each week (see teacher instructions).



CEPA 2, Weather ReportRecording Sheet:

Child’s Name: ________________________________________WEEK 1 #visible _________ Missing Part Correct? Yes No More/Less judgment Correct? Yes NoWEEK 2 #visible ________ Missing Part Correct? Yes No More/Less judgment Correct? Yes NoWEEK 3 #visible ________ Missing Part Correct? Yes No More/Less judgment Correct? Yes NoWEEK 4 #visible ________ Missing Part Correct? Yes No More/Less judgment Correct? Yes NoMost sunny days question correct? Yes NoSunny days combined to make 5 questions correct Yes No Strategy used: ________________________________________Identifies as addition Yes No

SCORING RUBRICMISSING PARTCriterion 1: Accuracy of Missing Part Judgments

1. Consistently accurate.2. Accurate with larger starting quantity, errors with smaller starting quantities.3. Largely random.

Criterion 2: Strategy being used for Missing Part Judgmentsa) Randomly guessing.b) Counting all.c) Counting on.d) Counting back.

MORE-LESS



Criterion 1: Accuracy of More/Less Judgments1. Consistently accurate.2. Accurate with large differences, errors with small differences.3. Largely random.

Criterion 2: Strategy being used for More/Less Judgmentsa) Randomly guessing.b) Visual comparison.c) Doing 1:1 matching.d) Comparing counted quantities by name (e.g., 3 is more than 2).e) Referring to another modeled representation (e.g., number line; fingers).



CEPA 2, Weather Report documents and other resources needed

Weather Report Data page set up as follows: a line down the middle with a sun icon at top level and the “cloud” icon at top right side of the page space to write name & week space to record a numeral with space underneath for tallies or drawings

Cover sheetWeather Probe sheet showing four sets of suns



Weather This WeekName _________________________________________________

sunny dayscloudy days



math pre-k modeling addition & subtraction through five...

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