Third Grade Curriculum - Pearson Schoolstorage.schoolnet.com/cfisd/MATH_3_A_ADDITION SUB… · Web viewProperty of Cy-Fair ISD Elem. Math Dept. (3rd Grade) 2015-2016 ... at least

MATH_3_A_1 ADDITION SUBTRACTION ALGORITHM ESTIMATION COMPATIBLE NUMBERS SECTION 1 OF 3 2015_LES

Third Grade Curriculum+ / - Algorithm / Estimation / Compatible Numbers

TEKS 3.4ASection 1 of 3 - Addition

Topic Page

AdditionPart I: Addition using Place Value (Partial Sums)Guided Practice 1Guided Practice 2Student Pages: Guided Practice 1-2Guided Practice 1 and 2 IMN StripsOh, So Many Ways… record sheetPlace Value ChartPart II: Addition using PropertiesIMN Strips: Vortex Warm-UpPart III: Addition using number line representationLiving Number Lines activityLiving Number Lines Card SetsPart IV: Addition of Three- Digit Numbers (no regrouping)Part V: Addition Algorithm with Three-Digit Numbers (regrouping)Guided Practice 3: 3 digit with regroupingGuided Practice 4: 3-digit with regroupingStudent Pages: Guided Practice 3 and 4

248910-111617182324252629

31

334243

Additional Resources:MATH_3_A_2 NUMBER LAB 2015_RES.docx

MATH_3_A_3 EQUALITY VORTEX 2015_RES.notebookMATH_3_A_4 ADD SUBTRACT ALGORITHM MINI 1 2015_RES.docxMATH_3_A_5 ADD SUBTRACT ALGORITHM MINI 2 2015_RES.docx

Addition

Property of Cy-Fair ISD Elem. Math Dept. (3rd Grade) 2015-2016


TEKS: 3.4a The student is expected to solve with fluency one-step and two-step problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction.

Vocabulary: sum, add, number sentence, expression, group, ungroup, regroup, algorithm, addend, equation, parenthesis as grouping symbols

ELPS Vocabulary: lab, earned, bank account, parenthesis, base ten, quarterback.

Teacher Background: The concepts of place value, relationships, and multiple representations are continuously interwoven into the verbage and strategies associated with addition. One goal of third grade is to have students become fluent in addition. Because students were to be proficient in 2nd grade, not fluent, in addition with regrouping, it is suggested that you do some pre-assessing of your students to determine where you might begin teaching students. Using compatible numbers is imbedded in addition, subtraction and estimating solutions. Please note that the strip diagrams drawn are only one way the representations could be done.

Student Background: In second grade, students were expected to be proficient, not fluent, in addition with regrouping using 2 and 3-digit numbers. Students were also able to use ¾ inch grid paper to help align their digits when adding. It is suggested that students still be allowed to use grid paper if necessary.

Essential Question: Why is it necessary to regroup when adding?

Misconception Man: Students may forget to regroup their ten or hundred and/or forget to add it in to their total.

Materials: base ten blocks, base ten mats (8 ½ X 11 provided in notes (Pg. 17), suggested to print on legal paper or create on construction paper), Oh, So Many Ways… record sheet (Pg. 16) copied for each student, virtual

Property of Cy-Fair ISD Elem. Math Dept. (3rd Grade) 2015-2016 1


manipulatives (Website Pg. 40) Number Lab record sheet and cards (Resource file), masking tape, yarn, IMN Strips

Part I: Addition using Place Value (Partial Sums)

1. Have students play Number Lab.

Available in resources: MATH_3_A_NUMBER LAB 2015_RES.DOC

*Please note that this activity is to allow students to practice representing numbers in multiple different ways. The goal is to allow them to experience the putting together action with different values WITHOUT solving the algorithm for the process.

2. What is something you noticed while playing Number Lab? (answers will vary, guide students to notice that we broke the numbers apart) Why do you think we broke apart numbers, or decomposed, just to put the numbers back together again? (Answers will vary – guide students to notice that we could find the total of each place value. We can then put those together when we need to).

3. IMN: Ask students to write/draw on the left side of their IMN, at least 2 things they think about when they hear the word ADDITION.

4. Have students share their thoughts with their elbow partner and then with the class. Record students’ thoughts on an Anchor Chart labeled Addition. Students may add to/modify/refine what they have put in their IMN during or after the class addition discussion.

Guided Practice 1: *Please note the Guided Practice questions are given as IMN strips. Students can glue each guided practice question on a separate page in their IMN to allow enough space for multiple representations of the addition processes using the Oh, So Many Ways… record sheet



in their strategy section. Lessons on following days will refer back to these questions and guide students through the creation of differing multiple representations for the addition process (TEKS 3.4A).

Guided Practice 1: Place Value representation of 3-digit by 3-digit addition

Deja has saved $135 in her bank account. This summer she walked the neighbor’s dog and earned another $104. If she put all of that money into her bank account, how much does she have in her account now?

IMN strips (Pg. 14)



Have students visualize the problem and begin the “Four step Problem solving” process with the students.

Main Idea: Details / Known:

Strategy: (Attach Oh, So Many Ways… record sheet under windowpane. It will be used as the strategies. Leave room at the bottom for the How/Justify.)

Strategy:

1. Let’s think about what we know. Based on our strip diagram, which action will we be doing? (put together – refer to action posters). Which math operation does that represent? (Addition). Remember we are focusing on how we can represent this addition. We will focus on solving the work at another time. How would we set up our numbers to show addition? (place one on top of the other – Record in “Algorithm Set-Up” section of record sheet)


earnedsavedD has ______ $ now104135

?

D $


2. Now that we know the numbers, let’s build our numbers with

our base-ten blocks. (Give one place value mat to each pair of students and allow them to build both numbers on the mat one on top of the other)

3. How would we represent these base-ten blocks in a picture? (Draw picture of each number using base-ten models and record in “Relating to Base-Ten” section of record sheet.)

4. Now that we can see our base-ten representation, what do we know about the value of each of the digits of these numbers? (1 group of 100 equals 100 and 3 groups of 10 equals 30 and 5 groups of one equals 5, 1 group of 100 equals 100 and 4 groups of one equals 4) How could we write these numbers to show the value of each digit? (Expanded form – write 100 + 30 + 5, 100 + 4 next to the base-ten pictures) Do we need to write any tens for 104? (No) Are there any tens in 104? (No) Actually there are. There are ten groups of ten which make a group of 100, but since there are no left over or individual groups of ten left, we do not need to write any.


135+104

135+104

135+104

100+ 30+5

100 +4


5. Where should we start our addition? (ones place) Why? (because we need to see if we need to regroup) I see we have 5 groups of one and 4 groups of one, so how many groups of ones do we have altogether? (9 ones). Write 9 under the ones

6. Now, if we have 3 groups of ten and no groups of ten how many groups of ten do we have altogether? (3 groups of ten) What is the value of those 3 groups of ten? (30 - Write 30 under the tens).

7. Let’s find out how many groups of a hundred we have. If we have 1 group of a hundred and 1 group of a hundred, how many groups of a hundred do we have? (2 groups of a hundred) What is the value of those 2 groups of a hundred? (200-- Write 200 under the hundreds)


135+104

100+ 30+5

100 +4

100+ 30+5

100 +4 30+9

135+104

100+ 30+5

100 +4 9

135+104


8. We have the sum of 2 groups of a hundred (or 200), the sum of 3 groups of ten (or 30), and the sum of 9 groups of one (or 9). This is called finding the partial sums. We are able to use the place values to put together the partial sums of 135 and 104. We will refer to our place values when practicing the algorithm later in our lesson. Right now we are just practicing showing different representations of how to add.

Note: We will complete the rest of the ‘Oh So Many Ways’ record sheet later in the lesson. The last column will be completed in the subtraction notes.

How/Justify: Found partial sums of 135 and 104

Guided Practice 2: Place Value representation of 3-digit by 3-digit addition

The 3rd grade boys and girls at Metcalf Elementary had a competition to see how much trash they could pick up on the playground. The boys collected 164 pieces of trash and the girls collected 237 pieces of trash. How many pieces of trash did the boys and girls collect?

IMN strips (Pg. 15)Have students visualize the problem and begin the “Four Step Problem Solving” process with the students.



? Find pieces of trash boys and girls collected

164

G t237

B t

?

100+ 30+5

100 +4200+ 30+9

135+104


Strategy: Use the same questioning from Guided Practice 1 and attach the “Oh, So Many Ways…” record sheet under windowpane. It will be used as the strategy section. Leave room at the bottom for the How/Justify.

How/Justify: Found partial sums of 164 and 237



Guided Practice

1. Deja has saved $135 in her bank account. This summer she walked the neighbor’s dog and earned another $104. If she put all of that money into her bank account, how much does she have in her account now?

2. The 3rd grade boys and girls at Metcalf Elementary had a competition to see how much trash they could pick up on the playground. The boys collected 164 pieces of trash and the girls collected 237 pieces of trash. How many pieces of trash did the boys and girls collect together?



IMN Strips: Guided Practice 1 (7 per page)

Deja has saved $135 in her bank account. This summer she walked the neighbor’s dog and earned another $104. If she put all that money into her bank account, how much does she have in her account now?









IMN Strips: Guided Practice 2 (6 per page)









Oh, So Many Ways…AlgorithmSet - Up

Relating to Base-Ten

Relating to Place Value

Relating to Properties

Relating to Number Lines

Relating to Relationships

Oh, So Many Ways…AlgorithmSet - Up






Oh, So Many Ways…Algorithm Set - Up







cut


One

sTe

nsH

undr

eds



Part II: Addition using Properties

*Please note: this lesson is to allow students to practice representing numbers in multiple ways and begin allowing them to experience the putting together action with different values without solving the algorithm. Additionally, the students will NOT need to identify the Commutative and Associative properties, rather they will need to apply the concepts to the manipulation of numbers.

1. Using the smart board, play the Equality Vortex as a class.

2. What is something you noticed while playing Equality Vortex? (answers will vary)

Available in resources: MATH_3_A_EQUALITY VORTEX 2015_RES.notebook

3. IMN: Ask students to create/draw on the left side of their IMN at least 2 statements/equations that would enter the Equality Vortex for 12 + 8 = 20 based on what they just experienced in the Vortex Game. (Available as an IMN Strip Pg. 24)

Please Note: The following instruction is done using the grouping symbol of parenthesis. This is done solely for the purpose of showing how the numbers could be grouped together. Order of Operations should NOT be done in 3rd Grade.

4. Write 12 + 8 = 20 on chart paper. What is another way we could write this equation? If students need help, have them think of Fact Families or number bonds. (8 + 12 = 20, write underneath 12 + 8 = 20). Does it matter what order we write the addends, the parts you add? (No, they can be written in any order because they still equal 20).

12 + 8 = 208 + 12 = 20

5. Circle the addends 12 + 8 and 8 + 12.

12 + 8 = 208 + 12 = 20

6. What do we know about what is in the circles? (they are equal). So if 12 + 8 is equal to 8 + 12, could we write 12



+ 8 = 8 + 12 (Yes) Why? (answers will vary, guide students to connect that since 12 + 8 equals 20, and 8 + 12 equals 20 then they equal each other) In addition, we can write the addends in any order and this is called the Commutative Property of Addition. (Label the top of the anchor chart, Commutative Property of Addition)

12 + 8 = 8 + 12

7. Write 12 + 8 on the top of a new chart paper. Let’s try to think even deeper about these addend numbers. What more do we know about these numbers? (we can decompose them and break them down). How we could break them down? What could we decompose 12 into so that the numbers are easy to work with? (guide students to 10 and 2). If 12 is the same as 10 + 2, could we replace the 12 with 10 + 2? (yes). Write 10 + 2 + 8 underneath 12 + 8.

12 + 8 = 20 10 + 2 + 8 = 20

8. We want everyone to know that the 10 + 2 are working as a team or group to make 12, so we put these grouping symbols around the numbers (add grouping symbols around 10 + 2). Grouping symbols could also look like ( ), [ ], or { }.

12 + 8 = 20 (10 + 2) + 8 = 20

9. Circle 12 + 8. How much does 12 + 8 equal? (20). Circle (10 +2) + 8. How much does 10 + 2 equal (12), then add 8 more (20). So if this group (point to 12 + 8 circle) equals 20 and this group (point to (10 + 2) + 8 circle) equals 20, than what do we know about each group? (they are equal). Rewrite the number sentences horizontally and ask students what symbol they can place in between. Place an equal sign in between the number sentences.

12 + 8 = (10 + 2) + 8

10. Point to the (10 + 2) + 8. Do any of the numbers in this group have the same place value and could be put together easily? (2 and 8). Let’s rewrite it showing the 8 and the 2 working together. What would we use to show



these two numbers are working together? (Parenthesis or grouping symbols). Write 10 + (2 + 8) underneath (10 + 2) + 8 circle.

(10 + 2) + 8 10 + (2 + 8)

11. Let’s think through this new grouping of numbers. Since 2 and 8 are grouped in parenthesis, let’s start there. What is the sum of 2 and 8? (10) Now, add it to the 10 that is in the number sentence already. So 10 + 10 equals what? (20).

(10 + 2) + 8 10 + (2 + 8) 10 + 10 = 20

12. What can we say about the values we have found? (they are equal) Write 10 + (2 + 8) next to (10+2) + 8 and put an = between the two groups.

12 + 8 = (10 + 2) + 8 = 10 + (2 + 8)

13. Point to the 10 + (2 + 8) group, How much was 2 + 8? (10) We could rewrite this as 10 + 10. (write next to number sentence) What is 10 + 10 equal to? (20) What could we say about both groups of numbers? (they are equal, put an equal sign between the groups)

12 + 8 = (10 + 2) + 8 = 10 + (2 + 8) = 10 + 10

14. What do we now know about 10 + 10, if I put them together, what do I get? (20) So, 10 + 10 = 20. Add this to your chart.

12 + 8 = (10 + 2) + 8 = 10 + (2 + 8) = 10 + 10 = 20

15. We have just discovered another property, or characteristic of putting numbers together! Each group of numbers equaled 20, right? (Yes) Did it matter how we grouped the numbers together to get that 20? (No). In addition, we can group numbers with the same value in different ways, but they still equal the same amount.



This is called the Associative Property of Addition. (title anchor chart Associative Property of Addition) Please note: In the Associative Property, the sequence of numbers does NOT change, only the grouping.

16. Let’s relate addition to properties for larger numbers. Turn to Guided Practice 1 in IMN and review problem. The problem puts together 135 and 104. If our Commutative Property of Addition says the order of the addends does not matter, how else could we write our number sentence? (135 + 104 = 104 + 135)

17. The Associative Property of Addition is different though. It says we can group the addends in different ways, as long as we keep them in the same order. Let’s think about how we could decompose 135 + 104 in a different way to help us think through putting them together? (answers may vary, 135+(100+4) = (135+100)+4 = 235+4 = OR (100+35) + 104. Don’t solve, we will return later to do this as we are focusing on the representations)

18. Turn to Guided Practice 2 in IMN and review problem. Have students try to complete the associative and commutative properties with a partner. Review as a class and allow students to revise their work if necessary.


135+104=104+135100+ 30+5

100 +4200+ 30+9

135+104

135+(100+4)=(135+100)+4=235+4=

135+104=104+135100+ 30+5

100 +4200+ 30+9

135+104


IMN: 0n the left side of IMN have students describe the Associative and Commutative Properties of Addition in their own words.


164+(200+37)=(164+200)+37=364+37

164+237=237+164100 + 60 + 4

200 + 30 + 7300 + 90 +11

164+237


Resources: IMN Strips (10 per page)Write two statements or

equations that would enter the vortex.12 + 8

Write two statements or equations that would enter the

vortex.12 + 8


vortex.12 + 8


vortex.12 + 8


vortex.12 + 8


vortex.12 + 8


vortex.12 + 8


vortex.12 + 8


vortex.12 + 8


vortex.12 + 8



Part III: Addition using number line representation(Suggested that part III and IV be taught on the same day)

Living Number Lines: Experience Before LabelPreparation:

Pre-cut table card sets for each table and put in a baggie (Pg. 26-28)

6 long pieces of masking tape for table number lines Yarn to use to show distance for each table 3 long pieces of masking tape on floor to use as class

number lines

1. Give each table a different card set. Give each table a long piece of masking tape and a long piece of yarn. Have the students read their problem and create a number line based on the numbers that were given in their card set using the masking tape and yarn. Table groups may cut the tape or yarn if necessary.

2. Invite 3 different tables to bring up their number line and represent it on the floor number line. Bring all students to the floor and discuss how the number lines are both different and similar. (decomposing numbers in multiple ways)

3. How can number lines that are so different, with so many different numbers, represent the same question? What did we do to the numbers to get such different number lines? (we decomposed the numbers)

4. Return to Guided Practice 1 and review problem. How could we represent this algorithm as a number line? (show the number line of 135 plus 104). Could we decompose one of our addends to help us represent the number line differently? (Answers will vary. Show how to decompose 104 into 100 plus 4 that can then be added separately to 135, or decompose 135 into 100 plus 30 plus 5 that can then be added separately to 104). Add one or more representations to the Oh, So Many Ways… record sheet.


+4+100

135 135

+104


5. Return to Guided Practice 2 and review problem. How could we represent this algorithm as a number line? (show the number line of 164 plus 237). Could we decompose one of our addends to help us represent the number line differently? (Answers will vary. Show how to decompose 237 into 100 plus 100 plus 30 plus 7 that can then be added separately to 164, OR decompose 237 into 200 plus 30 plus 7 that can then be added separately to 164). Add one or more representations to the Oh, So Many Ways… record sheet.


730100100

164 164

237

164+(200+37)=(164+200)+37=364+37

164+237=237+164100 + 60 + 4

200 + 30 + 7300 + 90 +11

164+237


Resources: Living Number Lines

Table 1 Card SetJosue has $74. He made $226 helping his aunt paint her house. How much money

does Josue have now?

74 226?



74 100100 26

?

Table 3 Card Set



Josue has $74. He made $226 helping his aunt paint her house. How much money


74 20026 ?



74 100100 6

? 1010

Table 5 Card SetJosue has $74. He made $226 helping his



aunt paint her house. How much money does Josue have now?

74 20020 6?



74 100100 20

? 6



Part IV: Addition of 3-Digit Numbers Using the Algorithm (no regroupingIt is suggested that at this point, you do a pre-assessment of what students know about adding with 3-digit numbers using the algorithm without regrouping. For students who are proficient, see projects listed in resources. If students are not proficient at adding without regrouping, follow the lesson below. You may move into small group teaching at this point.

Students can work in pairs or table groups for this activity with base-ten blocks. It is suggested for the first question to have students use base-ten blocks while teacher records the algorithm. This connects the concrete to the abstract. Once students are comfortable using base-ten blocks, have them begin to draw the base-ten blocks while doing the algorithm.

Return to Guided Practice 1 in IMN. Re-read problem and review Main Idea, Details/Known, and set up of algorithm. Students could work in partners to complete the algorithm. Some students may use grid paper if necessary to help them align their place values.



1. Have students build 135 on base-ten mat.2. Have students build 104 underneath 135 on base-ten mat.


135+104

100+ 30+5

100 +4200+ 30+9

135+104=104+135

+4+100

135

135

+104

135+(100+4)=(135+100)+4=235+4=

D has _______ $ now104135

?

D $earnedsaved


Hundreds Tens Ones

3. What operation are we doing? (Addition) How do we know that? (we are putting together all the money to find what she has now, refer to action posters)

4. Where should we start adding our numbers? (Ones place) Why? (because we need to see if we have to regroup) How many ones did we have? (9) Where do we write it? (In the ones place value, under the addends).

5. Let’s look back at our base-ten blocks. Where would we add next? (tens place) How many groups of ten is that in all? (3) Where do we record that 3 groups of ten? (In the tens place value, underneath the addends)

6. Let’s look back at our base-ten blocks, again. Where would we add next? (Hundreds place) How many groups of a hundred do we have in all? (2) Where do we record those 2 groups of hundreds? (In the hundreds place value, underneath the addends)

How/Justify: found the sum of 135 and 104*Complete Oh, So Many Ways… record sheet.Part V: Addition Algorithm with Three-Digit Numbers (regrouping) It is suggested that at this point, you do a pre-assessment of what students know about adding with 3-digit


135+ 104

135 + 104 9

135 + 104 39

135 + 104 239


numbers using the algorithm with regrouping. For students who are proficient, see projects listed in resources. If students are not proficient at adding with regrouping, follow the lesson below. You may move into small group teaching at this point.

Using Technology Appropriately:Technology use in the classroom can be a powerful tool. Please remind students that with this power comes great responsibility. We are living in an age where our digital footprint can have huge implications on our future. A digital footprint is all of the information online about a person either posted by that person or others, intentionally or unintentionally. Filling out a form, leaving a blog comment, updating your status, checking into a location, emailing or IMing a friend, posting a photo, visiting a website, using a search engine… everything you do online leaves a trail. This trail is your digital footprint. Remind students that they can properly manage their digital footprint by respecting each other and the technology that has been put in their hands.

Experience Before Label

Use the following web address for virtual manipulatives http://www.glencoe.com/sites/common_assets/mathematics/ebook_assets/vmf/VMF-Interface.html

Choose Grade 3Choose Ones, Tens, Hundreds workmatChoose Base Ten Manipulatives

Display the website on the Smartboard for full class interaction.

Click the manipulative picture tabs at the top to get 2 hundreds, 13 tens and 15 ones.


http://www.glencoe.com/sites/common_assets/mathematics/ebook_assets/vmf/VMF-Interface.html

http://www.glencoe.com/sites/common_assets/mathematics/ebook_assets/vmf/VMF-Interface.html


The virtual manipulatives can be ungrouped by clicking the mouse arrow on the bottom left of the object. To group manipulatives, drag the manipulatives to each other.

1. What do you see/notice? (Answers will vary) Look at our ones place value. How many ones do we have? (15) Let’s think about what we know. What do we know about ones? (Answers may vary, guide towards the relationship that it takes a group of 10 ones to make a one group of ten). If we have 15 ones, could we make a group of ten? (Yes, demonstrate by grouping ten ones with the virtual manipulatives) What happened when we made a group of ten? (they connected to form a group of ten) What should we do with this group of ten? Does it belong in the ones place? (Move it to the Tens place– move manipulative but leave it separated from the other 13) It is suggested that you place it above the 13 tens to mirror the action of regrouping. How many ones do we have left? (5)

2. Let’s look at those tens now. How many groups of ten did we have? (13) But then what happened? (we created a new group of ten and moved it to the tens) So now how many groups of ten do we have? (14) Let’s think about what we know. What do we know about tens? (Answers may vary, guide towards the relationship that it takes a group of 10 tens to make a one group of a hundred). If we have 14 tens, could we make a group of 10 tens? (Yes, demonstrate by grouping 10 tens with the virtual manipulatives) What happened when we made a group of 10 tens? (they connected to form a group of a hundred) What should we do with this group of a hundred? Does it belong in the tens? (No, move it to the hundreds place – move manipulative to the hundreds but leave it separated from the other 2) Again, it is suggested to place it above the 2 hundreds to mirror the action of regrouping. How many groups of ten do we have left? (4)



3. Now, let’s look at the hundreds place. How many groups of a hundred did we have? (2) But then what happened? (we created a new group of a hundred and moved it to the hundreds place) So now how many groups of a hundred do we have? (3) Let’s think about what we know. What do we know about hundreds? (Answers may vary, guide towards the relationship that it takes a group of 10 hundreds to make one group of a thousand). If we have 3 groups of a hundred, could we make a group of 10 hundreds? (No) So how many groups of a hundred do we have? (3)

4. If we have 3 hundreds + 4 tens + 5 ones (write on board), how much does this picture represent? (345)

Guided Practice 3 : Concrete or pictorial 3-digit addition algorithm (with regrouping) Some students may need to use grid paper to line up their place values.

Terrance is the quarterback on his football team. He threw the football 249 yards in the first half of his game and 385 in the second half of the game. How many yards did Terrance throw the football at the game?



Have students build 249 on base-ten mat.1. Have students build 385 underneath 249 on base-ten mat.

Hundreds Tens Ones


?

249+ 385

T y 249 385Yards T. throw football1st half 2nd half


2. What operation are we doing? (Addition) How do we know that? (we are putting together all of the yards Terrance threw, refer to action poster)

3. Where should we start adding our numbers? (Ones place) We have 9 groups of one and 5 groups of one. What is the sum of our ones? (14) What do you notice about 14? (It has 2 digits or the value is 10 or larger) Can we put 2 digits in the same place value? (No) What do we need to do? (regroup) Let’s think about what we know! What do we know about our relationship between our tens and ones? (it takes 10 ones to make a group of ten) Do we have at least ten ones to make a group of ten? (Yes) Let’s group those ten ones to make one group of ten, or one ten. (trade in a group of ten ones for a group of ten) Where would we put this new group of ten? (in the tens place) Place it in the tens (It is suggested students place it horizontally above the tens they already have. This allows us to see the new ten easier as well as mirrors the regrouping action used in the algorithm.)

Hundreds Tens Ones



4. After we have made our one group of ten, how many ones remain in the ones place? (4) In our algorithm we would put that 4 in the ones place. But now we have one new group of ten. Where do we put that new group of one ten? (above the tens place) Why? (because it is a group of ten or a ten)

5. Let’s look back at our base-ten blocks. Where should we add next? (Tens place) We have 4 groups of ten, 8 groups of ten and our 1 new group of ten. What is the sum of our tens? (13) What do you notice about 13? (It has 2 digits) Can we put 2 digits in the same place value? (No) What do we need to do? (regroup) Let’s think about what we know! What do we know about our relationship between our tens and hundreds? (it takes 10 groups of ten to make one group of a hundred) Do we have at least ten groups of ten to make a group of a hundred? (Yes) Let’s group those 10 tens to make one group of a hundred, or one hundred. (Trade in 10 groups of ten for 1 group of hundred) Where would we put this new group of a hundred? (Hundreds place) Why? (Because it is a hundred) Put it in the hundreds. (explain that we put it off to the side just so we can see it better).

Hundreds Tens Ones


1 249 + 385 4


6. After we have made our one group of 10 tens, how many groups of ten remain in the tens place? (3) In our algorithm we would put the 3 in the tens below the addends. But now we have one new group of a hundred. Where do we put the new group of one hundred? (above the hundreds place) Why? (because it is one group of ten tens or one hundred)

7. Let’s look back at our base-ten blocks. Where should we add next? (hundreds place) We have 2 groups of a hundred, 3 groups of a hundred and our new 1 group of a hundred. What is the sum of our hundreds? (6) What do you notice about it? (It has 1 digit) Can we put that digit into a place value? (yes) Do we need to make groups of anything? (No) How many hundreds do we have? (6)

8. Look back at your base-ten blocks. What number is now being represented? We have 6 groups of a hundred, 3 groups of tens, and 4 ones. (634)

Hundreds Tens Ones


11 249 + 385 34


9. Let’s look at our algorithm. We have 2 groups of a hundred, 3 groups of a hundred and our new 1 group of a hundred. What is the sum of our hundreds? (6) What do you notice about it? (It has 1 digit) Can we put the digit into a place value? (yes) Do we need to make groups of anything? (No) So, How many hundreds do we have? (6)

How/Justify: found the sum of 249 and 385

Return To Guided Practice 2Students can complete with partner.


11 249 + 385 634


The 3rd grade boys and girls at Metcalf Elementary had a competition to see how much trash they could pick up on the playground. The boys collected 164 pieces of trash and the girls collected 237 pieces of trash. How many pieces of trash did the boys and girls collect together?

Re-read problem and review Main Idea, Details/Known, and set up of algorithm.


1. Have students build 164 on base-ten mat.2. Have students build 237 underneath 164 on base-ten mat.

Hundreds Tens Ones


164

237

164+(200+37)=(164+200)+37=364+37

164+237=237+164100 + 60 + 4

200 + 30 + 7300 + 90 +11

164+237

?

B t237

G t

164

? Find pieces of trash boys and girls together


3. What operation are we doing? (Addition) How do we know that? (we are putting together the trash the boys and girls picked up – refer to action posters)

4. Where should we start adding our numbers? (Ones place)

5. What is the sum of our ones? (11) What do you notice about 11? (It has 2 digits or it is larger than 10) Can we put 2 digits in the same place value? (No) What do we need to do? (regroup) Let students share the process they would go through to regroup ten ones into a group of ten. Guide students through their thought processes.Hundreds Tens Ones

6. After we have made our one group of ten, how many ones

remain in the ones place? (1) Where would we put that 1? (In the ones place value, below the addends) But what happens to the one new group of ten? (put it above the tens place) Why? (because it is a group of ten or a ten)


1 164 + 237 1


7. Let’s look back at our base-ten blocks. Where should we add next? (Tens place)

8. What is the sum of our tens place? (10) What do you notice about 10? (It has 2 digits) Can we put 2 digits in the same place value? (No) What do we need to do? (regroup) Let students share the process they would go through to regroup ten groups of ten into a group of a hundred. Guide students through their thought processes

Hundreds Tens Ones

9. After we have made our one group of 10 tens, how many tens remain in the tens place? (0) In our algorithm, where would we put that 0? (in the tens below the addends) But where do we put the new group of one hundred we just grouped together? (above the hundreds place) Why? (because it is a group of ten tens or one hundred)

10. Let’s look back at our base-ten blocks. Where should we add next? (hundreds place)

11. How many hundreds did you count? (4) What do you

notice about 4? (it is 1-digit) Can we make any groups of 10 with them? (No) So we have 4 hundreds.

12. Look back at your base-ten blocks. What number is now being represented? We have 4 groups of a hundred, no groups of tens, and a one. (401)


11 164 + 237 01


Hundreds Tens Ones

13. Let’s look at our algorithm. What do we need to do? (add the hundreds) What is the sum of our hundreds? (4) What do you notice about it? (It has 1 digit) Can we put the digit into a place value? (yes) What do we need to make groups of anything? (No) How many hundreds do we have? (4)

How/Justify: found the sum of 164 and 237

*Complete Oh, So Many Ways… record sheet.

Guided Practice 4: Concrete or pictorial 3-digit addition algorithm (with 3 numbers and regrouping) Again, you may want to pre-asses students and teach in small group.

Students may complete with a partner and check with teacher

Dina’s grandfather is a truck driver. In September, he drove 574 miles. In October, he only drove 353 miles. In November, he drove four hundred sixty-five. How many miles did Dina’s grandfather drive in all three months?


11 164 + 237 401




Details / Known: Found sums of 574, 353 and 465

** Note: There are 13 hundreds. A group of ten hundreds can be grouped out of that 13 to create a thousand. There are no thousands in the place values in this problem to then group them with, so we write 13 hundreds and add the comma to break up the math periods.


Found the sums of 574, 353, and 465

?

465

927

465

574

G N

G O353

G S

?

1 1 574 927+353 +465 927 1,392

D’s grandfatherdrove ______ miles in 3 months


Guided Practice

3. Terrance is the quarterback on his football team. He threw the football 249 yards in the first half of his game and 385 in the second half of the game. How many yards did Terrance throw the football at the game?

4. Dina’s grandfather is a truck driver. In September, he drove 574 miles. In October, he only drove 353 miles. In November, he drove four hundred sixty-five miles. How many miles did Dina’s grandfather drive in all three months?


Documents

Third Grade Curriculum - Pearson Schoolstorage.schoolnet.com/cfisd/MATH_3_A_ADDITION SUB… · Web viewProperty of Cy-Fair ISD Elem. Math Dept. (3rd Grade) 2015-2016 ... at least