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Lesson Study Group Report

Title of Lesson: Multi-digit Computation ReviewLevel of Lesson: 3rd Grade Members of the Lesson Study Team: Rachel Heend, Kate Wessman & Sarah RaeDate of 1st Presentation of Lesson: 10/16/13 Teacher: Sarah RaeLocation: Mathew Whaley Elementary Audience: Kate Wessman & Rachel Heend; Miranda Katsibas’s classDate of 2nd Presentation of Lesson: 10/17/13 Teacher: Kate Wessman Location: Mathew Whaley Elementary Audience: Sarah Rae & Rachel Heend; Jennifer Lampert’s class

What changes were made between the 1st teaching and the 2nd lesson? Explore Stage: The teacher does not begin by modeling with the Base

Ten Blocks. The Base Ten Blocks will still be available as an adaptive scaffold, but not necessarily used during this stage. The teacher still models the first problem with student direction. In our revised lesson, students are then given three more questions to work out independently with large group “check-in” to make sure concepts are solidified. For students who work at a faster pace, the teacher provides additional problems for them to do that will not be reviewed as an entire group.

Explain Stage: For our revised lesson, the teacher begins by asking students guiding questions about number sentences instead of having students solve the problems independently. Next, the teacher models the first problem (1. Which problem is true: C. 8 = 6+2) from the worksheet with student directions. The teacher explains that a number sentence is true when the quantities on either side of the “=” are equal. The teacher then proceeds to model a second (3. Which problem is true: B. 4+5 = 3+6) and third (6. Which number makes the following sentence true 4+8 = 12; 12 - __ =4: C. 8) problem, which represent the next two concepts covered in the Explain stage. The teacher discusses how addition and subtraction are inverse relations. After all three problem types have been modeled by the teacher and completed by the students, the students will complete five more problems independently. If multiple students finish early, students will compare answers in pairs.

Elaborate Stage: First, the teacher walks the class through the problem solving process that is also posted on the board. We have

included a version of our word problem solving process in the Lesson Study. The teacher then models the first multi-digit computation word problem on the worksheet, eliciting student guidance. Students then complete the rest of the word problems in partners as teacher monitors progress.

Why were these changes made? How successful were the changes?Changes Made: Since this lesson study is a review, most of the students already knew

the process for multi-digit computation, and the Base Ten Blocks were not needed and even slowed them down in some cases.

We decided to give fewer problems to the students for each stage so that they would not be overwhelmed by the amount, and so that they could focus on a select few problems to ensure understanding.

We had students do additional problems independently while they waited for the large group “check-in’s” to account for those students who were working at a faster pace, but also to make sure that everyone understood the concepts.

For the Explain Stage, we chose to have the teacher model three problems, which covered the three different types of questions the students would be asked on their test for evaluating whether or not the number sentence is true.

We chose to go over the entire word problem solving process first because the students unsure how to approach the word problems on their own. Walking through the steps first and then modeling the process helped the kids understand the steps they should be taking. We also had students do the word problems in partners for extra support.

Results of Changes: Providing fewer problems for the students to do each stage proved

beneficial. With our first lesson, the students seemed overwhelmed by the quantity, but with fewer, they felt less pressure to complete all the problems. Also, we were able to completely get through every stage of the lesson. Decreasing the amount of problems was an effective time management strategy.

Starting each stage by modeling and walking through the problems was also very helpful to ensure that the students understood the concepts/procedures. The modeling was a helpful adaptation for students with special needs.

For students who worked faster, having extra problems available allowed those students to challenge themselves and remain engaged without disrupting the work of other students.

The combination of independent and group work was also a success because those who worked faster could provide support for those struggling with the concepts.

Modeling the entire process for solving word problems led by student directions also ensured that students understood the steps and could apply these strategies during independent work.

What changes were made for the final revision? Why were these changes made?

Students seemed to struggle the most with the Elaboration Stage solving the word problems. For both lessons, we had an hour and half to complete the learning cycle. With that time allotted, we decided that the Elaboration Stage should be addressed on a second day in order to devote more time to the word problem solving process.

We also decided to make laminated cards of the word problem process for each student. While students are doing their problems they can refer to their own cards instead of having to go to the board to look at the process.

If possible, we think that having students work through the stages of this lesson plan in differentiated groups would be a more efficient and productive use of class time. This may entail having multiple teachers/aides or having the students rotate so that each group has a mini-lesson with the teacher for the Explain stage and independent or partner work for the Explore and Elaborate rotations.

FINAL DRAFTMatthew Whaley Elementary School

3rd Grade Math Lesson Plan – Multi-Digit Computation

Rachel HeendSarah RaeKate Wessman

Context: This lesson is designed for a 3rd grade class at Matthew Whaley Elementary School. This class contains 20 students, 3 of which are identified as gifted and 2 are English Language Learners. This is a review lesson on multi-digit computations for addition and subtraction, 0-9,999.

Objective: Students will accurately compute addition and subtraction problems involving multi-digit computations, for numbers between 0 and 9,999. Students will successfully regroup in subtraction problems and carry over numerals to the next place value for addition. Students will use information provided in word problems to set up and solve multi-digit computations. Students will apply the identity property and the concept of inverse relations to answer questions about mathematical statements.

VA SOL: 3.1) The student will read and write six-digit numerals and identify the place value and value of each digit; 3.2) The student will recognize and use the inverse relationships between addition/subtraction and multiplication/division to complete basic fact sentences; 3.4) The student will estimate solutions and solve single-step and multistep problems involving the sum or difference of two whole numbers, each 9,999 or less, with or without regrouping; 3.20) The student will investigate the identity and the commutative properties for addition and multiplication.

Materials/Resources:White boards and dry erase markers (one of each per student)Pencil (one per student)Who Has? Game Cards (25 cards)Teacher copy of numeric computations for Explore PhasePractice Problems worksheet on mathematical statements for Explain Phase (one per student)Word Problems worksheet for Elaborate Phase (one per student)Large teacher copy and student copies of “Problem Solving Process”Exit Tickets (one per student)Base-10 Blocks to use as needed

Approximate Time Required: 90 minutes

Content and Instructional Strategies:1. Introduce the goal of the lesson, which is to successfully prepare to compute

addition and subtraction problems on the upcoming exam, and for the future

at large! Introduce and model how to use the “Who Has?” cards for basic addition and subtraction facts.

2. Time students as they complete one round of the game as practice. If students struggle with a problem, model “adding up” or “counting down” strategies. Write their time on the board. Then challenge students to beat their time in a second round.

3. Time students as they complete a second round of the game. Write this time on the board.

4. Ask students guiding questions for explore stage: When you subtract, do you get a larger number or a smaller number? What does it mean to regroup? When you regroup, is it still the same number? Where do I begin for this problem? Correct any misconceptions.

5. Model the problem 6007 – 4258 on the board and allow students to direct the process of regrouping and solving.

6. Allow students to practice solving on their own. Allow students to use the base-10 blocks as necessary as an adaptation. Provide students one question at a time, have them solve independently on their white boards, and then discuss the process as a class after adequate time. The next three problems are 103 + 87, what is the difference between 235 and 147, and what is the sum of 623 and 464. Discuss the cueing words of “difference” and “sum” in the last two questions.

7. Review mathematical concepts that will be on the exam. Ask the guiding questions of: What makes a number sentence true? How are addition and subtraction related? What is the identity property? Model the first three problems on the “Practice Problems” worksheet, eliciting student responses.

8. Have students complete the remaining five practice problems independently. Review the answer as a large group after adequate time. Take note of areas of confusion and emphasize the related concept.

9. Review the “problem solving process” from a large teacher copy and distribute individual student copies. Call on students to read aloud each step.

10. Using the problem solving steps, model the first word problem on the Word Problem Worksheet, eliciting student direction.

11. Have students complete the remaining four word problems in partners. Review answers as a large group after adequate time.

12. Distribute “Exit Tickets” for students to complete individually. Collect “Exit Tickets” when students finish to assess and inform the teacher if there needs to be clarification of a concept before the exam is given tomorrow.

Evaluation: Exit Cards, Formative observation of student work and responses in discussion to inform concepts that need reinforcement during lesson

Differentiation/Adaptations: For the Engage stage of this lesson, the teacher will model how to play the

“Who Has?” game with slowed speech and repetition, as well as ask for questions

before the activity begins to make sure every student knows what to do. The cards are written only as numeric problems, so ELL students will not be bogged down with language. All cards follow the pattern, “I have ____, Who has ______?” The facts in the activity are simple enough that they should be mental math for every student, but students can use their fingers or draw a picture quickly if need be. The teacher will prompt with “adding up” or “counting down” strategies as necessary.

For the Explore, Explain, Elaborate and Evaluate stages, additional problems will be provided as needed for students who are moving quickly and waiting for other students to finish. For students that are having difficulties, manipulatives (such as base-10 blocks) will be available for support, students will be allowed to ask a partner and/or the teacher for assistance, and whiteboards will be used to go through problems slowly, step-by-step. Repetition and acting out for word problems will also be especially beneficial for ELLs.

Appendix: Who Has? Cards Answers:

1) START CARD: Who has 9+10?2) I have 19. Who has 7-5?3) I have 2. Who has 20+3?4) I have 23. Who has 8-0?5) I have 8. Who has 2+4?6) I have 6. Who has 7+7?7) I have 14. Who has 15-8?8) I have 7. Who has 6+5?9) I have 11. Who 13+3?10) I have 16. Who has 5-4?11) I have 1. Who has 18+3?12) I have 21. Who has 5+8?13) I have 13. Who has 16-4?14) I have 12. Who has 25+1?15) I have 26. Who has 9+9?16) I have 18. Who has 10-5?17) I have 5. Who has 10+5?18) I have 15. Who has 22+2?19) I have 24. Who has 0-0?20) I have 0. Who has 9-6?21) I have 3. Who has 5+4?22) I have 9. Who has 9+8?23) I have 17. Who has 12-8?24) I have 4. Who has 25-5?25) I have 20. Who has 9+1?

END (at start card) I have 10.

Name: ________________________ 1. Which problem is true?

A. 3 + 4 = 6B. 7 + 2 = 8C. 8 = 6 + 2D. 9 = 4 + 3

2. Which problem is true?A. 2 + 4 = 8B. 3 + 2 = 6C. 8 + 5 = 12D. 9 = 6 + 3

3. Which problem is true? A. 6 + 5 = 14 +2B. 4 + 5 = 3 + 6C. 6 + 7 = 11 + 4D. 3 + 6 = 2 + 5

4. Which problem is true? A. 4 + 9 = 12 + 1B. 3 + 4 = 5 + 3C. 6 + 3 = 7 + 4D. 2 +1 = 3 + 9

5. Which problem is true? A. 8 + 5 = 11 + 3

B. 6 + 4 = 9 + 1 C. 2 + 7 = 3 + 8D. 1 + 5 = 2 + 3

6. Which number makes the following sentence true?

4 + 8 = 12; so 12 - ____ = 4A. 6B. 7C. 8D. 9


7 + 3 = 10; so 10 - ____ = 3 A. 6B. 7C. 8D. 9

8. 5 + 0 = ____A. 5B. 6C. 0D. 4

EXPLORE PROBLEMS – completed on mini white boards

Easy

48 74 62

+ 35

+ 86 - 44

Answer 83 160 18

Medium

*103

351 745 1002

+ 87 - 72 - 346 + 459

Answer 190 279 399 1,461

Hard

*6,007 5,607 3,425 4,003

- 4,258

- 3,459 + 6,687

- 2,435

Answer 1749 2148 10,112 1,568

*What is the difference between 235 and 147? Answer: 88

*What is the sum of 623 and 464? Answer: 1,087

*Note: for the REVISED lesson, only the questions in the first column of Medium and Hard will be asked, as well as the last two problems in sentence form. The other problems will be available for students getting through problems quickly.

Name: _________________

Complete the following word problems and show your work!

1) The Matthew Whaley PTA sold 133 t-shirts last year. The PTA made an awesome new t-shirt design and sold 421 this year. How many more t-shirts did the PTA sell this year than last year?

2) Mrs. Lampert’s class decided to get an ant farm with 37 ants. But then the ants hatched 25 baby ants! How many ants does Mrs. Lampert’s ant farm have all together now?

3) Mrs. Katsibas has been saving up to take a trip to Mexico. If the trip costs $1,490 and Mrs. Katsibas has already saved $855, how much more does she need to be able to book her trip?

4) Christina is organizing her art drawer. She found 22 colored pencils, 40 crayons, and 31 markers. She decides to put the colored pencils and markers in a separate container. How many items did she put in the container?

_________________________________________________________________________________________________

5) Bobby and Laura want to add their money together to buy their mom a nice jacket for her birthday that costs $89.00. If Bobby saved $45.00 and Laura saved $24.00, how much more money do Bobby and Laura need before they can buy the jacket?

_________________________________________________________________________________________________

LESSON STUDYTEMPLATE:

First Revision

PLANNING TOOL FOR TEACHERS

Mathematics Science Partnership GrantThe College of William and Mary

Authors of this Lesson: Rachel Heend, Sarah Rae, Kate Wessman

School/District: Matthew Whaley Elementary School, WJCC

Strand: VA SOL: 3.1, 3.2, 3.4, 3.20

Grade Level: 3

Title of Lesson: Multi-Digit Computation Review

PLANNING AND PREPARATION

First Teaching: Wednesday October 16th – Miranda Katsibas’s 3rd gradeSecond Teaching: Thursday October 17th – Jennifer Lampert’s 3rd grade

Demographics of Ms. Katsibas’s class:

TOTAL Black White Hispanic Asian OtherFemale 10 3 6 0 1 0Male 10 2 5 3 0 0

Title I: No LEP: 2 Special Needs: 0 Gifted/Talented: 3Free/Reduced Rate: N/A

LESSON LOGISTICS


Lesson Objectives: Students will…use inverse relationships between addition/subtraction to solve related basic fact sentences; write three related basic fact sentences when given one basic fact sentence for addition/subtraction; determine whether to add or subtract in practical problem situations; add or subtract two whole numbers, each 9,999 or less; solve practice problems involving the sum/difference of two whole numbers, each 9,999 or less, with or without regrouping, using calculators, paper and pencil, or mental computation; explain the commutative and identity property for addition; write number sentences to represent equivalent mathematical relationships.

Related Standards of Learning (SOL)

Previous year(s): VA SOL 1.1, 1.4, 1.5, 1.6, 1.15, 2.1, 2.5, 2.6, 2.7, 2.8, 2.19

Current Year: VA SOL 3.1, 3.2, 3.4, 3.20

Following Year: VA SOL 4.1, 4.4, 4.5

Prerequisite Mathematics Understanding

Potential Roadblocks

Understanding when it is appropriate to subtract or add in word problems; grasp of “mathematics vocabulary” and synonyms for operations

Confusion with synonyms for operations (ex: add, plus, sum); being able to decipher which operation is appropriate in word problems

Understanding how “Base-10” blocks can be utilized to solve computations

When subtracting, the student subtracts the smaller number from the larger number

Basic single-digit computations (mental math)

Understanding place value principles

Confusion or lack of understanding of how to regroup

Confusion in ordering numbers for subtraction sentences

Misconceptions or difficulty with basic, single-digit computations (mental math)

Confusions related to place value, especially involving “0”

Curriculum Resources:

Day, Malloy, Altieri, Carter, & Cuevas. (2012). Virginia: Math connects. Macmillian/McGraw-Hill.

Katsibas, M. (2012). 3rd grade computation test. Williamsburg, VA.

Williamsburg-James City County Public Schools. (2013). Unit 3: Multi-digit computation. Williamsburg, VA.

Supplies/Materials:

For this lesson, we will need individual white board tablets, individual dry erase marker, white board erasers, the “Who Has?” cards, the “Exit Tickets”, pencils for students, nametags, Base-10 blocks, and teacher copies of word problems/sentence facts.

I. Engage: 10 Minutes Teacher Activity Student Activity (thoughts, words,

actions)- Teachers will introduce

themselves and the lesson goal. They will distribute nametags for students to fill out.

- Teacher will introduce the game “Who Has?” dealing with mental math addition and subtraction and model how to play.

- Teacher will distribute “Who Has?” cards to practice and time students as they complete a full round. If students are incorrect, guide them towards correct answer.

- After the students successfully complete one round, the teacher will shuffle the cards and redistribute for the “time trial” round.

- Teacher will time students during this round and see if they beat their goal time.

- Students will sit at their desks and fill out nametag to wear for the lesson.

- Students will observe the teacher’s modeling of “Who Has?”

- Students will each receive a “Who Has?” card and participate in the practice round.

- After the students successfully complete one round, they will receive a new “Who Has?” card and participate in the “time trial”, with the goal of beating their initial time.

- Students will complete the cards and see if they beat their goal time.

Ex) start card- “Who has 11 +3?”“I have 14. Who has 17 – 5?” etc.

Adaptations/Enrichments:The teacher will model how to play the game with slowed speech and repetition, and ask for questions before the activity begins so that every student knows what to do. The cards are written only as numeric problems so that the ELL students will not be bogged down with language. All cards follow the pattern “I have ____, Who has _______.” The facts in this activity are simple enough that they should be mental math for every student, but students can use their fingers or draw a picture quickly if need be.

II. Explore – 15 min

Teacher Activity Student Activity(thoughts, words, actions)

- Teacher begins by asking guiding questions to students about regrouping for multi-digit computations.

- Teacher does multi-digit computation example (modeling) led by students’ directions.

- Students are given three more multi-digit computations to explore on their own. Teacher will review as a class.

- Students will respond to guiding questions; ex:

- “When you take numbers away or add numbers to the next place value”

- “It’s the same number!” - “You place the bigger number on top”

- Students attempt to complete the first computation problem then compare answers as a large group to check for accuracy

- “You can’t subtract 7 from 9 so you need to regroup.”

- “You need to give me 1 group of 10 from the next number so I can subtract.”

- Students will complete three more problems independently with large group check in after each one.

Guiding Questions: - What does it mean to regroup? - When do you have to regroup? - When you regroup, is it the same

number? - When you subtract, do you get

more or less? How about when you add?

- How can you set this problem up?

Adaptations/ Enrichments:

- Provide additional problems as needed (We are only teaching 4, but all the others we are no longer including for all students will be available for those who move faster and are going ahead)

- Provide larger digit problems for enrichment - Use of whiteboards to explain reasoning, draw pictures; “act it out” as necessary

for ELL’s

III. Explain 15 minutes Teacher Activity Student Activity

(thoughts, words, actions) Teacher begins by asking students guiding

questions (see below). Teacher models the first problem from

worksheet with student assistance. Teacher models the second problem from the

worksheet, which introduces another step in the process

Teacher models the third problem on the worksheet, which introduces a third concept the students will need to complete the rest of the worksheet.

As Teacher models, she will ask the students to guide her as she is solving it (Asking questions like, “What do I do now? What follows that? What does that tell us about the number sentence?”)

The most important part of this phase of the lesson is allowing students to express and brainstorm strategies they can use for solving, as well as to emphasize that there is no single “correct” strategy to use

Guiding Questions: What makes a number sentence (problem)

true? How are addition and subtraction related? How can it be used to solve related basic fact

sentences? What is the identity property?

Students respond to guiding questions:“When you add or subtract 0, the number stays the same.” “A number sentence is true if the numbers on both sides are equal to each other”

While the teacher models the first problem, students are asked to follow along and guide her through the process.

Students guide the teacher as she solves the next problem. They answer her questions as they go through the steps of the problem.

This cycle repeats as the teacher goes into inverse relationships and identity property.

After explanations, students complete an additional 5 problems on the worksheet.

Example problems:

Fact sentences: Which problem is true?

A. 3 + 4 = 6B. 7 + 2 + 8C. 8 = 6 + 2D. 9 = 4 + 3

Which problem is true?A. 6 +5 = 14 +2B. 4 +5 = 3 + 6C. 6 + 7 = 11 + 4D. 3 + 6 = 2 + 5

Inverse relationships: 4 + 8 = 12; so… 12 -__ = 4 “It has to be 8 because 4 + 8 is 12, so 12--8 will be 4!”

Adaptations/Enrichments:

Students struggling can use the base-10 blocks to help them visualize equivalencies (what makes a number sentence true), inverse relationships, and the identity property.

The teacher should make sure to provide very specific definitions to ELLs about all of these concepts, as well as provide further modeling if necessary.

IV. Elaborate (Summarize) 15 minutes


- Teacher talks students through problem solving process:

1. Read the Entire Problem 2. Underline the Question 3. Write the Question in a Telling Statement 4. Decide who or what is involved in the problem 5. Decide if the problem calls for a bigger or a smaller number. 6. Use your best math to solve the problem. 7. Write the answer and make sure it makes sense.

- Teacher introduces and models the first multi-digit computation word problem on

- Teacher will help the students during partner work as needed.

- Students will talk through the problem solving process

- Students will help the teacher with the first word problem.

- Students will complete numbers 2-5 with a partner

o The Matthew Whaley PTA sold 133 t-shirts last year. The PTA made an awesome new t-shirt design and sold 421 this year. How many more t-shirts did the PTA sell this year than last year?

Guiding Questions: - What is this question asking? Do

we need to add or subtract? Could we do it both ways?

- Should the answer be a bigger or smaller?

- Do we need to regroup? Why?


- Use of manipulatives for extra support- Partner work - Word problems with simple language for ELL support; modeling on a need basis - Enrichment through more complex word problems

V. Evaluate 15 Minutes


- Teacher will pass out exit ticket for students to complete independently

- Teacher will collect exit tickets when completed

- Students fill out exit ticket independently


- Allow them to use manipulatives if necessary- Repeat and act out word problem for ELLs; provide sentence models for

answering the word problem


26)START CARD: Who has 9+10?27)I have 19. Who has 7-5?

28)I have 2. Who has 20+3?29)I have 23. Who has 8-0?30)I have 8. Who has 2+4?31)I have 6. Who has 7+7?32)I have 14. Who has 15-8?33)I have 7. Who has 6+5?34)I have 11. Who 13+3?35) I have 16. Who has 5-4?36) I have 1. Who has 18+3?37) I have 21. Who has 5+8?38) I have 13. Who has 16-4?39) I have 12. Who has 25+1?40) I have 26. Who has 9+9?41) I have 18. Who has 10-5?42) I have 5. Who has 10+5?43) I have 15. Who has 22+2?44) I have 24. Who has 0-0?45) I have 0. Who has 9-6?46) I have 3. Who has 5+4?47) I have 9. Who has 9+8?48) I have 17. Who has 12-8?49) I have 4. Who has 25-5?50) I have 20. Who has 9+1?


Name: ________________________ 1. Which problem is true?

a. 3 + 4 = 6b. 7 + 2 = 8c. 8 = 6 + 2d. 9 = 4 + 3

2. Which problem is true?a. 2 + 4 = 8b. 3 + 2 = 6c. 8 + 5 = 12d. 9 = 6 + 3

3. Which problem is true? a. 6 + 5 = 14 +2b. 4 + 5 = 3 + 6c. 6 + 7 = 11 + 4d. 3 + 6 = 2 + 5

4. Which problem is true? a. 4 + 9 = 12 + 1b. 3 + 4 = 5 + 3c. 6 + 3 = 7 + 4d. 2 +1 = 3 + 9


5. Which problem is true? a. 8 + 5 = 11 + 3b. 6 + 4 = 9 + 1 c. 2 + 7 = 3 + 8d. 1 + 5 = 2 + 3


4 + 8 = 12; so 12 - ____ = 4a. 6b. 7c. 8d. 9


7 + 3 = 10; so 10 - ____ = 3 a. 6b. 7c. 8d. 9

8. 5 + 0 = ____a. 5b. 6c. 0d. 4

Easy

48 74 62

+ 35

+ 86 - 44

Answer 83 160 18

Medium

*103

351 745 1002

+ 87 - 72 - 346 + 459

Answer 190 279 399 1,461

Hard

*6,007 5,607 3,425 4,003

- 4,258

- 3,459 + 6,687

- 2,435

Answer 1749 2148 10,112 1,568

*What is the difference between 235 and 147? Answer: 88

*What is the sum of 623 and 464? Answer: 1,087

*Note: for the REVISED lesson, only the questions in the first column of Medium and Hard will be asked, as well as the last two problems in sentence form. The other problems will be available for students getting through problems quickly.

Name: _________________






_________________________________________________________________________________________________


LESSON STUDYTEMPLATE:ORIGINAL

PLANNING TOOL FOR TEACHERS

Mathematics Science Partnership GrantThe College of William and Mary

Authors of this Lesson: Rachel Heend, Sarah Rae, Kate Wessman

School/District: Matthew Whaley Elementary School, WJCC

Strand: VA SOL: 3.1, 3.2, 3.4, 3.20

Grade Level: 3


PLANNING AND PREPARATION

First Teaching: Wednesday October 16th – Miranda Katsibas’s 3rd gradeSecond Teaching: Thursday October 17th – Jennifer Lampert’s 3rd grade

Demographics of Ms. Katsibas’s class:

TOTAL Black White Hispanic Asian OtherFemale 10 3 6 0 1 0Male 10 2 5 3 0 0

Title I: No LEP: 2 Special Needs: 0 Gifted/Talented: 3Free/Reduced Rate: N/A

LESSON LOGISTICS


Lesson Objectives: Students will…use inverse relationships between addition/subtraction to solve related basic fact sentences; write three related basic fact sentences when given one basic fact sentence for addition/subtraction; determine whether to add or subtract in practical problem situations; add or subtract two whole numbers, each 9,999 or less; solve practice problems involving the sum/difference of two whole numbers, each 9,999 or less, with or without regrouping, using calculators, paper and pencil, or mental computation; explain the commutative and identity property for addition; write number sentences to represent equivalent mathematical relationships.

Related Standards of Learning (SOL)

Previous year(s): VA SOL 1.1, 1.4, 1.5, 1.6, 1.15, 2.1, 2.5, 2.6, 2.7, 2.8, 2.19

Current Year: VA SOL 3.1, 3.2, 3.4, 3.20

Following Year: VA SOL 4.1, 4.4, 4.5

Prerequisite Mathematics Understanding

Potential Roadblocks

Understanding when it is appropriate to subtract or add in word problems; grasp of “mathematics vocabulary” and synonyms for operations

Understanding how “Base-10”

Confusion with synonyms for operations (ex: add, plus, sum); being able to decipher which operation is appropriate in word problems

Confusion or lack of

blocks can be utilized to solve computations

When subtracting, the student subtracts the smaller number from the larger number

Basic single-digit computations (mental math)

Understanding place value principles

understanding of how to regroup Confusion in ordering numbers

for subtraction sentences Misconceptions or difficulty with

basic, single-digit computations (mental math)

Confusions related to place value, especially involving “0”

Curriculum Resources:

Day, Malloy, Altieri, Carter, & Cuevas. (2012). Virginia: Math connects. Macmillian/McGraw-Hill.

Katsibas, M. (2012). 3rd grade computation test. Williamsburg, VA.

Williamsburg-James City County Public Schools. (2013). Unit 3: Multi-digit computation. Williamsburg, VA.

Supplies/Materials:

For this lesson, we will need individual white board tablets, individual dry erase marker, white board erasers, the “Who Has?” cards, the “Exit Tickets”, pencils for students, nametags, Base-10 blocks, and teacher copies of word problems/sentence facts.

I. Engage: 10 Minutes

Teacher Activity Student Activity (thoughts, words,

actions)- Teachers will introduce

themselves and the lesson goal. They will distribute nametags for students to fill out.

- Teacher will introduce the game “Who Has?” dealing with mental math addition and subtraction and model how to play.

- Teacher will distribute “Who Has?” cards to practice and time students as they complete a full round. If students are incorrect, guide them towards correct answer.

- After the students successfully complete one round, the teacher will shuffle the cards and redistribute for the “time trial” round.

- Teacher will time students during this round and see if they beat their goal time.

- Students will sit at their desks and fill out nametag to wear for the lesson.

- Students will observe the teacher’s modeling of “Who Has?”

- Students will each receive a “Who Has?” card and participate in the practice round.

- After the students successfully complete one round, they will receive a new “Who Has?” card and participate in the “time trial”, with the goal of beating their initial time.

- Students will complete the cards and see if they beat their goal time.

Ex) start card- “Who has 11 +3?”“I have 14. Who has 17 – 5?” etc.

Adaptations/Enrichments:The teacher will model how to play the game with slowed speech and repetition, and ask for questions before the activity begins so that every student knows what to do. The cards are written only as numeric problems so that the ELL students will not be bogged down with language. All cards follow the pattern “I have ____, Who has _______.” The facts in this activity are simple enough that they should be mental math for every student, but students can use their fingers or draw a picture quickly if need be.

II. Explore – 15 min


- Teacher begins by asking guiding questions to students about regrouping for multi-digit computations.

- Teacher models multi-digit computation problems using base ten blocks.

- Teacher does multi-digit computation example led by students’ directions.

- Students are given multi-digit computations to explore on their own with the base ten blocks.

- Students will respond to guiding questions; ex:

- “When you take numbers away or add numbers to the next place value”

- “It’s the same number!” - “You place the bigger number on top”

- Students will help the teacher solve the first computation problem by telling her what steps she needs to take (i.e. setting up the problem, regrouping, etc.)

- “You can’t subtract 7 from 9 so you need to regroup.”

- “You need to give me 1 group of 10 from the next number so I can subtract.”

- Students will model problems on their own with base ten blocks

Guiding Questions: - What does it mean to regroup? - When do you have to regroup? - When you regroup, is it the same

number? - When you subtract, do you get

more or less? How about when you add?

- How can you set this problem up?


- Model additional problems as needed- Provide larger digit problems for enrichment - Use of whiteboards to explain reasoning, draw pictures; “act it out” as necessary

for ELL’s- Use of manipulatives for diverse learning styles - Buddy partners for extra support

III. Explain 15 minutes

Teacher Activity Student Activity (thoughts, words, actions)

Teacher gives the students one number sentence problem (ex: “Which one is true?” from post-unit assessment) to solve independently. Students are then asked to share how they went about solving it.

The teacher then models what makes a problem (number sentence) true

Teacher provides another example but this time asks the students to guide her as she is solving it (Asking questions like, “What do I do now? What follows that? What does that tell us about the number sentence?”)

The teacher will follow the same steps when asking students about inverse relationships and identity property.

The most important part of this phase of the lesson is allowing students to express and brainstorm strategies they can use for solving, as well as to emphasize that there is no single “correct” strategy to use

Guiding Questions: What makes a number sentence (problem)

true? How are addition and subtraction related? What is an inverse relationship between

addition and subtraction, and how can it be used to solve related basic fact sentences?

What is the identity property?

Students first solve problems independently, then share their strategies

While the teacher models, students are asked to follow along, solve and explain their strategy in their own words

Students guide the teacher as she solves the next problem. They answer her questions as they go through the steps of the problem.

This cycle repeats as the teacher goes into inverse relationships and identity property.

Students brainstorm:“When you add or subtract 0, the number stays the same.” “A number sentence is true if the numbers on both sides are equal to each other”

Example problems:

Fact sentences: Which problem is true?

E. 3 + 4 = 6F. 7 + 2 = 8G. 8 = 6 + 2H. 9 = 4 + 3

Which problem is true?E. 6 +5 = 14 +2F. 4 +5 = 3 + 6G. 6 + 7 = 11 + 4H. 3 + 6 = 2 + 5

Inverse relationships: 4 + 8 = 12; so… 12 -__ = 4 “It has to be 8 because 4 + 8 is 12, so 12--8 will be 4!”

Identity Property: 5 + 0 = 5 11 – 0 = 11

Adaptations/Enrichments:

Students struggling can use the base-10 blocks to help them visualize equivalencies (what makes a number sentence true), inverse relationships, and the identity property.

The teacher should make sure to provide very specific definitions to ELLs about all of these concepts, as well as provide further modeling if necessary.

IV. Elaborate (Summarize) 15 minutes


- Teacher introduces and models multi-digit computations through word problems.

- Teacher reads word problem and asks the class to walk her through the steps to solve the problem.

1) Identify if she should add or subtract

2) Set up problem 3) Regroup? 4) Solve

- Students work on word problem worksheet independently or with partner

- Students will help the teacher with the first word problem.

Ex) Mary collected 212 chocolates on Halloween. Ben collected 345. How many more chocolates does Ben have than Mary?

- “We need to find out how many more chocolates Ben got than Mary. We need to subtract.”

- “We could add from 212 until we got to 345!”

- “If we subtract we don’t need to regroup.”

- Students will work on word problems independently or with a partner. They may model problems with base ten blocks if needed. Students will set up numeric representations of the word problem to solve it.

Guiding Questions: - What is this question asking? Do

we need to add or subtract? Could we do it both ways?

- How can we use base ten blocks to model this problem?

- Should the answer be a bigger or smaller?

- Do we need to regroup? Why?


- Use of manipulatives for extra support- Partner work - Word problems with simple language for ELL support; modeling on a need basis - Enrichment through more complex word problems

V. Evaluate 15 Minutes


- Teacher will pass out exit ticket for students to complete independently

- Teacher will collect exit tickets when completed

- Students fill out exit ticket independently


- Allow them to use manipulatives if necessary- Repeat and act out word problem for ELLs; provide sentence models for

answering the word problem


51)START CARD: Who has 9+10?52)I have 19. Who has 7-5?53)I have 2. Who has 20+3?54)I have 23. Who has 8-0?55)I have 8. Who has 2+4?56)I have 6. Who has 7+7?57)I have 14. Who has 15-8?58)I have 7. Who has 6+5?

59)I have 11. Who 13+3?60) I have 16. Who has 5-4?61) I have 1. Who has 18+3?62) I have 21. Who has 5+8?63) I have 13. Who has 16-4?64) I have 12. Who has 25+1?65) I have 26. Who has 9+9?66) I have 18. Who has 10-5?67) I have 5. Who has 10+5?68) I have 15. Who has 22+2?69) I have 24. Who has 0-0?70) I have 0. Who has 9-6?71) I have 3. Who has 5+4?72) I have 9. Who has 9+8?73) I have 17. Who has 12-8?74) I have 4. Who has 25-5?75) I have 20. Who has 9+1?


Explain Problems:

1. Which problem is true?

E. 3 + 4 = 6F. 7 + 2 = 8G. 8 = 6 + 2H. 9 = 4 + 3

2. Which problem is true?a. 4 = 2 + 1

b. 8 + 2 = 9c. 3 + 7 = 10d. 10 = 5 + 6

3. Which problem is true?a. 2 + 4 = 8b. 3 + 2 = 6c. 8 + 5 = 12d. 9 = 6 + 3

4. Which problem is true? a. 6 + 5 = 14 +2b. 4 + 5 = 3 + 6c. 6 + 7 = 11 + 4d. 3 + 6 = 2 + 5

5. Which problem is true? a. 4 + 9 = 12 + 1b. 3 + 4 = 5 + 3c. 6 + 3 = 7 + 4d. 2 +1 = 3 + 9

6. Which problem is true? a. 8 + 5 = 11 + 3b. 6 + 4 = 9 + 1 c. 2 + 7 = 3 + 8d. 1 + 5 = 2 + 3

7. Which number makes the following sentence true?4 + 8 = 12; so 12 - ____ = 4

a. 6b. 7c. 8d. 9

8. Which number makes the following sentence true?7 + 3 = 10; so 10 - ____ = 3

a. 6b. 7c. 8d. 9

9. 5 + 0 = ____a. 5b. 6c. 0

d. 4

10. 11 – 0 = _____a. 10b. 0c. 11d. 9


Easy

48 74 62

+ 35

+ 86

- 44

Answer 83 160 18

Medium

103 351 745 1002

+ 87

- 72 - 346 + 459

Answer 190 279 399 1,461

Hard

6,007 5,607 3,425 4,003

- 4,258

- 3,459

+ 6,687 - 2,435

Answer 1749 2148 10,112 1,568

What is the difference between 235 and 147? Answer: 88

What is the sum of 623 and 464? Answer: 1,087

Elaborate Phase Problems:

Name: _________________




3) Mr. Pumpkin wants to figure out how many jumbo chocolate bars to buy for trick-or-treaters. Last Halloween, he needed 289 jumbo bars, but this year, 14 more children moved into the neighborhood. If he wants to give each child a jumbo chocolate bar, how many bars should he buy for this Halloween?

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5) Rosie scored 546 points over the course of her basketball season, up until the last game. In the team’s last game, Rosie scored another 18 points to finish the season. How many points did Rosie score in total for the whole season?

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6) The Matthew Whaley performance of “The Nutcracker” usually expects 170 audience members. But this year, everyone heard how great it was going to be, so we expect an additional 53 people to attend. How many audience members will we expect at “The Nutcracker?”

7) Mike collects Pokémon cards and has a collection of 97. For his friend Colin’s birthday, Mike gave him 9 cards as part of his present. How many Pokémon cards does Mike have now?

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10) Rory has a sneaky dog named Max! Rory bought Max two boxes of treats. Each box has 52 dog treats. But Max found the treats and already ate 14! How many treats does Rory have left to feed his sneaky dog?

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