Math 3 a 1 Addition Subtraction Algorithm Estimation Compatible Numbers Section 1 of 3 2015 Les

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

Third Grade Curriculum

+ / - Algorithm / Estimation / Compatible Numbers

TEKS 3.4A

Section 1 of 3 - Addition

Topic / Page
Addition / Part I:Addition using Place Value (Partial Sums)
Guided Practice 1
Guided Practice 2
Student Pages: Guided Practice 1-2
Guided Practice 1 and 2 IMN Strips
Oh, So Many Ways… record sheet
Place Value Chart
Part II: Addition using Properties
IMN Strips: Vortex Warm-Up
Part III: Addition using number line representation
Living Number Lines activity
Living Number Lines Card Sets
Part IV:Addition of Three- Digit Numbers (no regrouping)
Part V: Addition Algorithm with Three-Digit Numbers (regrouping)
Guided Practice 3: 3 digit with regrouping
Guided Practice 4: 3-digit with regrouping
Student Pages: Guided Practice 3 and 4 / 2
4
8
9
10-11
16
17
18
23
24
25
26
29
31
33
42
43

Additional Resources:

MATH_3_A_2 NUMBER LAB 2015_RES.docx

MATH_3_A_3 EQUALITY VORTEX 2015_RES.notebook

MATH_3_A_4 ADD SUBTRACT ALGORITHM MINI 1 2015_RES.docx

MATH_3_A_5 ADD SUBTRACT ALGORITHM MINI 2 2015_RES.docx

Addition

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 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)

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.

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).

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.

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 Practice1: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:

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)

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)

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.)

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.

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

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).

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)

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 Practice2: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 collected164 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.

Main Idea:Details / Known:

Strategy: Use the same questioning from Guided Practice 1 and attach the “Oh, So Many Ways…” record sheetunder 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

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?

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 collected164 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)

Property of Cy-Fair ISD Elem. Math Dept. (3rd Grade) 2015-20161

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

Property of Cy-Fair ISD Elem. Math Dept. (3rd Grade) 2015-20161

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

Oh, So Many Ways…
Algorithm
Set - Up / Relating to Base-Ten / Relating to Place Value / Relating to Properties / Relating to Number Lines / Relating to Relationships
Oh, So Many Ways…
Algorithm
Set - Up / Relating to Base-Ten / Relating to Place Value / Relating to Properties / Relating to Number Lines / Relating to Relationships
Oh, So Many Ways…
Algorithm
Set - Up / Relating to Base-Ten / Relating to Place Value / Relating to Properties / Relating to Number Lines / Relating to Relationships

Property of Cy-Fair ISD Elem. Math Dept. (3rd Grade) 2015-20161

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

Ones
Tens
Hundreds

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.

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

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

Available in resources:

MATH_3_A_EQUALITY VORTEX 2015_RES.notebook

IMN: Ask students to create/draw on the left side of their IMN at least 2 statements/equationsthat 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.

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 = 20

8 + 12 = 20

Circle the addends 12 + 8 and 8 + 12.

12 + 8 = 20

8 + 12 = 20

What do we know about what is in the circles? (they are equal). So if 12 + 8 is equal to 8 + 12, could we write12 + 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

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

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

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

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)

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

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)

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