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Third Grade Curriculum

Third Grade Addition/Subtraction Process Table of Contents

One Step Part I: Put together – Addition – Guided Practice 1Guided Practice 1 – Teacher Demo/Student PagePart II: Take Away – Subtraction – Guided Practice 2Guided Practice 2 – Teacher DemoGuided Practice 2 – IMN StripsGuided Practice 3 – Teacher Demo/Student PagePart III: Missing Part – Subtraction - Guided Practice 4Guided Practice 4 – Teacher DemoGuided Practice 4 – IMN StripsGuided Practice 5 – Teacher Demo/Student PagePart IV: Compare – Subtraction – Guided Practice 6Guided Practice 6 – Teacher DemoGuided Practice 6 – IMN StripsGuided Practice 7 – Teacher Demo/Student Page+/- Process Flipbook IMN – Teacher Guide+/- Process Flipbook IMN – Student Pages

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Third Grade

Addition/Subtraction Process Single Step

Property of Cy-Fair ISD Elem. Math Dept. (3rd grade) 2014-2015

Additional Resources:

MATH_3_A_ADD SUBTRACT PROCESS SINGLE STEP MINI PRACTICE 1_RES.doc

MATH_3_A_ADD SUBTRACT PROCESS SINGLE STEP MINI PRACTICE 2_RES.doc

MATH_3_A_ADD SUBTRACT PROCESS SINGLE STEP MIXED PRACTICE_RES.doc

MATH_3_A_FOOTBALL ACTIVITY_RES

MATH_3_A_MIXED REVIEW PLACE VALUE AND PROCESS 2014_RES.DOC

J. st. 38End

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TEKS: 3.5a: Students are expected to represent one and two-step problems involving addition and subtraction of whole numbers to 1,000 using pictorial models, number lines, and equations.

Vocabulary: action, put together, sum, join, add, addend, subtract, difference, minus, take away, compare, missing part, number sentence, expression, process statement, operation

Student Background: In second grade, the students showed number bonds through fact families. Students have also experienced unit bars in both addition and subtraction. The teacher notes will focus on subtraction, but briefly show an addition problem as a review because second graders were to be proficient at this skill.

Teacher Background: Teachers will need to represent addition and subtraction in multiple ways, including pictorial models, number lines and equations. On number line questions, sometimes the operation is included with the number above the arrow and sometimes not. This is to give the kids exposure to seeing it both ways. Also, the words unit bar, strip diagram and model drawing will be used interchangeably.

Remember to use your action posters to help bridge the model drawing and the actions. Also, it is suggested that you save the work from each problem so you can compare the types of subtraction once completed. Examples of saving work may include capturing the image on the smart board, projecting the work on to chart paper and completing the work on the chart paper or working the problem on the guided practice page using the Elmo/Ladybug.

Part I: AdditionGuided Practice 1

Step 1: Main Idea: # stickers beginning of day

Step 2: Details:

Property of Cy-Fair ISD Elem. Math Dept. (3rd grade) 2014-2015 1

Jessica had 38 stickers in her pencil bag at the end of the day. If she gave fifty-six stickers to her friends at school during the day, which method would determine how many stickers Jessica had at the beginning of the day?

A. Find the difference of 56 and 38 C. Subtract 38 from 56B. Find the sum of 56 and 38 D. Add 38 and 65

12 13 14 15 16 17

Step 3: Strategy:

“Let’s examine our model drawing. What action do you notice?” (put together) “What operation will we use?” (addition) “How do you know that our action is put together?” (We have a part of stickers from end of day and part of stickers she gave away. If we put them together, we will find a total)

“Could we represent the details from our problem in a different way? (students will give various answers) “How might a number line help us represent the details?” (It will visually show our model drawing.) “Let’s think about what we know.”

“What do we know about number lines?” (numbers are in order, least to greatest, numbers get bigger) “Let’s draw a number line on the board.”

Ask students to come up and add numbers to the number line. For example, “Who can come up and place the number 15 on this number line?” (Student places 15) “Great! Who can come up and place the number that comes before 15?” (Student places 14) Continue until the number line looks like this.

“What do you notice about the numbers on the number line?” (They are getting bigger in one direction and smaller in the other direction.) “How would this relate to addition and subtraction?” (When we add whole numbers, we get bigger numbers. When we subtract whole numbers, we get smaller numbers.) “Let’s look at the number line we have drawn already. To represent addition, we will draw an arrow moving forward above the number line.”


12 13 14 15 16 17

+1

38

38

+56

38

+56

This would represent 12 + 1 = 13.

“To represent subtraction, we will draw an arrow moving backward on the number line.”

This would represent 13 – 1 = 12.

“Now let’s use what we know about number lines and model drawing to solve the problem. What operation did we choose for this problem?” (Addition) “Why?” (Because we are putting together) “Since we know our operation is addition, which way will we move on the number line?” (forewards) “What number do you think we should put on the number line first?” (38) “Why?” (because it is the first part we’re given) “Let’s label 38 on our number line near the middle of the number line. Why?” (because we have already determined that it is addition and we need to move foreward)

“How much do we need to move forward?” (56) “Would this be a large distance from 38 or small?” (large) “Why?” (because 56 is a large amount)

“As in our unit bar, we use a ‘?’ to represent what we are trying to find. Where might we put the ‘?’ on our number line?” (where the arrow is pointing)


12 13 14 15 16 17

-1

?

# stickers beginning of day

38

+56

?

38 + 56 =

Find the sum of 38 and 56Add 38 and 56

J. st. 38End

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“Let’s record the number line in our strategy section of our window pane.”

“What will our number sentence look like?”

Step 4: How/Why?

Completed 4-step:

Guided Practice 1


38 + 56 =

Find the sum of 38 and 56 Add 38 and 56

Jessica had 38 stickers in her pencil bag at the end of the day. If she gave fifty-six stickers to her friends at school during the day, which method would determine how many stickers Jessica had at the beginning of the day?

A. Find the difference of 56 and 38 C. Subtract 38 from 56B. Find the sum of 56 and 38 D. Add 38 and 65

Way to find # j.b in jar?

Ms. H Way to find # j.b in jar?

Part II: Take AwayGuided Practice 2

Ms. Hernandez has 10 chocolates and 25 jelly beans in a bag. She ate 6 of the jelly beans. She put the rest of the jelly beans in a jar. Which way can be used to find how many jelly beans are in the jar?

A. Add 10, 25 and 6 C. Subtract 6 from 25B. Subtract 10 from 25 D. Subtract 6 from 10

Begin the 4-step process.

Step 1: Main IdeaRead the problem.“What is the main idea of the question? What do they want you to find?” (way to find # j.b in jar)

Step 2: Details/Known

“What can we use to represent the details from our problem?” (draw a unit bar)

“Who is our problem about?” (Ms. Hernandez)

.

“What is our problem about?” (jelly beans)


Ms. H j.b. Way to find # j.b in jar?

25 Ms. H j.b.

Way to find # j.b in jar

Now have students draw a unit bar.

Ask, “Why are we not using chocolates?” (the question is not about chocolates)

Ask the students, “What should happen next?” (Re-read the problem one piece of information at a time. Label and adjust unit bars.)

Ask a student to read the first sentence. (Ms. Hernandez has 10chocolates and……..) “Why did we stop at the word and?” (because itseparates information.) “What do we need to do with thatinformation?” (nothing, b/c the question is not about chocolate.)

Now, read the second part of the sentence. (…..and 25 jelly beans in abag.) Ask, “What should we do with this information?” (Put 25 on the top of the unit bar.) Why? (Because there are a total of 25 jellybeans.)

“Read the next sentence.” (She ate 6 of the jelly beans.) “What does this information mean?” (6 jellybeans are gone) “What action is happening?” (take away) “How much of the bar do we take off for 6 jelly beans?” (a small amount since it is only 6 out of 25 jelly beans.) “Now, to represent a take away problem, let’s circle and draw an arrow going out of the unit bar for the 6 jelly beans eaten and label as ‘A’ for ate.”


Read the next sentence. (She put the rest of the jelly beans in a jar.)

Ask, “How do we mark the unit bar to show the jelly beans in the jar?” (Put a “J” for jar on the other part of the bar.) Read the last sentence. (Which way can be used to find how many jelly beans are in the jar?) “Where do we put the ?” (on the side of the unit bar labeled ‘J’.) “Why?” (because we do not know how many jelly beans are in the jar)

Step 3: Strategy

“Let’s examine our model drawing. What action do you notice?” (take away) “What operation will we use?” (subtraction) “How do you know that our action is take away?” (We have a total and part of our total was eaten. It is no longer there.)


“Now let’s use what we know about number lines and model drawing to solve the problem. What operation did we choose for this problem?”


6A J

25 ?Ms. H j.b.


6A

25 Ms. H j.b.


25

? 25

-6

(Subtraction) “Why?” (Because we are taking away) “Since we know our operation is subtraction, which way will we move on the number line?” (backwards) “What number do you think we should put on the number line first?” (25) “Why?” (because it is the largest number) “What is another reason?” (It is our total, that is the number we started with.) “Let’s label 25 as the last number on our number line. Why?” (because we have already determined that it is subtraction and we need to move backward)

“How much do we need to move backward?” (6) “Would this be a large distance from 25 or small?” (small) “Why?” (because 6 is a small portion of 25) “As in our unit bar, we use a ‘?’ to represent what we are trying to find. Where might we put the ‘?’ on our number line?” (where the arrow is pointing)

“Let’s record the number line in our strategy section of our window pane.”


6A J

25 ?Ms. H

j.b.Way to find # j.b in jar?

-6

? 25

“What number sentence can we write to find the number of jelly beans that are still in the jar?”

25 – 6 =

“Let’s look back at the model. Is there another number sentence we can write to show the relationship between 25 and 6?” (25 is the total, and we already have 6, so we can see that 6 plus something (?) is 25. This relates back to what you learned in second grade. Fact families or number bonds all have a relationship and share the same numbers.”

6 + = 25

“How could we represent 6 plus something(?) on a number line?” (draw 6 and 25 on the number line) “How do we know where to place the numbers?” (6 is on the left and 25 is on the right) “Why?” (because 6 is smaller than 25) “Do we put 6 and 25 close together or far apart?” (far apart because there are many numbers between them)


+ ?

6 25

? 25

25 – 6 =

6 + = 25

Step 4: How/Why?

See how many different statements students can write.

* Subtract 6 from 25* Difference of 6 and 25* Sum of 6 and a number is equal to 25

? 25

Ask, “Now which answer choice matches one of our “How” statements?” (C. Subtract 6 from 25)


6A

25 Ms. H j.b.


25 – 6 =

6 + = 25

-6

6A

25 Ms. H j.b.


-6

Guided Practice 2

1. Ms. Hernandez has 10 chocolates and 25 jelly beans in a bag. She ate 6 of the jelly beans. She put the rest of the jelly beans in a jar. Which way can be used to find how many jelly beans are in the jar?

A. Add 10, 25, and 6 C. Subtract 6 from 25

B. Subtract 10 from 25 D. Subtract 6 from 10


IMN Strips Guided Practice ProblemsGuided Practice 2












Guided Practice 3

2. Look at the following representation. Which problem could represent this strip diagram?

$674

M $ $419

A. Marret earned $674 mowing lawns in June and $419 in July. How much money did Marret earn during these two months mowing lawns?

B. Marret had $419 in his bank account. He spent $674 on a new flat screen TV. How much money does Marret have left in his bank account?

C. Marret spent $419 on a new X-Box and $674 on a new computer. How much money did Marret spend?

D. Marret earned $674 babysitting his cousin one summer. He bought a computer pad for $419. How much money does Marret have left?


?

?

?

Guided Practice 3 Answer

2. Look at the following representation. Which problem could represent this strip diagram?

$674

M $ $419

A. Marret earned $674 mowing lawns in June and $419 in July. How much money did Marret earn during these two months mowing lawns?

B. Marret had $419 in his bank account. He spent $674 on a new flat screen TV. How much money does Marret have left in his bank account?

C. Marret spent $419 on a new X-Box and $674 on a new computer. How much money did Marret spend?

D. Marret earned $674 babysitting his cousin one summer. He bought a computer pad for $419. How much money does Marret have left?

Problem represent strip diagram? M $ $419

Answer choices

?A. M $ X $674 Ju $419 Jl

$419B. M $ X

$674 BA ?C. M $ X

$419 X-B $674 C

$674D. M $ M


?

?

Drew unit bar for each answer choice

Looked to see which unit bar matched my details

$419 C. P.

$674

Method # not pink j.b.?

Part III: Missing PartGuided Practice 4


Step 1: Main Idea

Read the problem.“What is the main idea of the question? What do they want you to find?” (method # not pink j.b)



Ms. Hernandez had 10 chocolates and 25 jelly beans in a bag. Six of the jellybeans were pink. Which method will determine the number of jelly beans that were not pink?

A. Subtract 6 from 10 C. Add 10 and 25 and 6

B. Add 25 and 6 D. Subtract 6 from 25

Ms. H Method # not pink j.b.?

Ms. H j.b. Method # not pink j.b.?

“What do we want to use to record our details?” (draw a who, what, unit bar)

“Who is our problem about?” (Ms. Hernandez)

.

“What is our problem about?” (jelly beans)

Now have students draw a unit bar.

Ask, “Why are we not drawing a unit bar for chocolates?” (The question is not about chocolates.)

Ask the students, “What should happen next?” Re-read the problem one sentence at a time. Label and adjust unit bar.

Ask a student to read the first sentence. (Ms. Hernandez has 10 chocolates


25Ms. H j.b. Method # not

pink j.b.?

6

25

P


and………) “Do we need this information about chocolate?” (No) “Why?” (because our problem does not have to do with chocolates)

Continue reading after the ‘and’ (……25 jelly beans in a bag. ) Ask, “What should we do with this information?” (Put 25 on top of the unit bar.) “Why?” (Because there is a total of 25 jelly beans.)

Read the next sentence. (Six of the jellybeans were pink.)

Ask, “What should we do with this information?” (label the unit bar for the 6 jelly beans that are pink.) “How much of the model do we mark off for 6 jelly beans?” (a small amount since it is only 6 out of 25.)


6 ?

25

P


Read the next sentence. (Which method will determine the number of jellybeans that were not pink?)

Ask, “Where should we place the question mark?” (in the empty box on the unit bar) “Why?” (because we want to know how many jelly beans were not pink)

Step 3: Strategy

“Let’s examine our model drawing. What action do you notice?” (find a missing part) “What operation will we use?” (subtraction) “How do you know that our action is find a missing part?” (We have a total and the part that is pink. We want to find out the part that is not pink.)

“Could we represent the details from our problem in a different way? (students will give various answers) ”How might a number line help us represent the details?” (It will visually show our model drawing.) “Let’s think about what we know.”

“What do we know about number lines?” (numbers are in order, least to greatest) “Let’s draw a number line.”

“Now let’s use what we know about number lines and model drawing to solve the problem. What operation did we choose for this problem?” (Subtraction) “Why?” (Because we have a missing part) “What number do


NP

25

25

you think we should put on the number line first?” (25) “Why?” (because it is the largest number) “What is another reason?” (It is our total.) “Let’s label 25 as the last number on our number line. Why?” (because we have already determined that it is subtraction and we need to move backward)

“Since we know it is subtraction, which way will we move on the number line?” (backwards) “How much?” (6) “Would this be a large distance from 25 or small?” (small) “Why?” (because 6 is a small portion of 25) “As in our unit bar, we use a ‘?’ to represent what we are trying to find. Where might we put the ‘?’ on our number line?” (where the arrow is pointing)

“Let’s record the number line in our strategy section of the window pane.”

? 25

“What number sentence can we write to find the jelly beans that are not pink?”


? 25

-6

P NP

Ms. H j.b.


-6

25

25 – 6 =

“Let’s look back at the unit bar. Is there another number sentence we can write to show the relationship between 25 and 6? Use your knowledge of fact families and number bonds to help you.” (25 is the total, and we already have 6, so we can see that 6 plus something (?) is 25.”

6 + = 25

“How could we represent 6 plus something (?) on a number line?” (draw 6 and 25 on the number line) “How do we know where to place the numbers?” (6 is on the left and 25 is on the right) “Why?” (because 6 is smaller than 25) “Do we put 6 and 25 close together or far apart?” (far apart because there are many numbers between them)

? 25

“Does anyone remember why we can write 6 + = 25?” (25 is our total and we already have 6 of the 25. We need to find how many more we need.)

Step 4: How/Why?See how many different statements students can write.


25 – 6 = or

6 + = 25

+ ?

6 25

P NP

Ms. H j.b.


-6

25

? 25

“Which answer choice matches one of our “How’s?” (D – Subtract 6 from 25)

Guided Practice 4


Ms. Hernandez has 10 chocolates and 25 jelly beans in a bag. Six of the jellybeans were pink. Which method will determine the number of jelly beans that were not pink?

A. Subtract 6 from 10 C. Add 10 and 25 and 6B. Add 25 and 6 D. Subtract 6 from 25

25 – 6 = or

6 + = 25

* Subtract 6 from 25* Difference of 6 and 25* Sum of 6 and a number is 25

P NP

Ms. H j.b.


-6

Guided Practice 5


Kai and Lena were collecting coins to help raise money for new playground equipment at their school. Together they collected 746 coins. If there were 323 pennies, which number line represents how you could find the number of coins that were not pennies?

A. B.

C. D.

746

323

? ? 746

323

746 323

?

323

746

?



746 – 323 =

Drew unit bar Drew number line to

show the difference of 746 and 323 and matched it to the answer choices.

2. Kai and Lena were collecting coins to help raise money for new playground equipment at their school. Together they collected 746 coins. If there were 323 pennies, which number line represents how you could find the number of coins that were not pennies?

A. B.

C. D.

746

323

? ? 746

323

746 323

?

323

746

?

Number line represent how find coins not pennies? KL c

p not p323 ?

746

# choc needed to equal j.b?

Part IV: CompareGuided Practice 6


Step 1: Main IdeaRead the problem.“What is the main idea of the question?” “What are you trying to find? (# choc needed to equal j.b.)


Ms. Hernandez has 10 chocolates. She would like to have the same number of chocolates as jelly beans. If she has 25 jelly beans, which method would help her find the number of additional chocolates she needs?

A. Find the sum of 10 and 25 C. Find the difference of 25 and 10B. Subtract 25 from 10 D. Add 10 and 25 and 8




“What do we want to do to record our details?” (draw a unit bar)

Who is our problem about? (Ms. Hernandez)

.

“What is our problem about?” (chocolates and jellybeans)

Then have students draw the who, what, and unit bar for each item.

Ask the students, “What should happen next?” Re-read the problem one piece of information at a time. Label and adjust unit bars.


Ms. H

Ms. H ch

Ms. H j.b.

10# choc needed to equal j.b? Ms. H ch

Ms. H j.b.

Ms. H ch.

Ms. H j.b. 25

10


Ask a student to read the first sentence. (Ms. Hernandez has 10 chocolates.)Ask, “What should we do with this information?” (Put 10 on the top of the chocolate unit bar) “Why?” (Because there are a total of 10 chocolates)

Read the next sentence. (She would like to have the same number of chocolates as jellybeans.) “What should we do with this information?” (Nothing on the unit bar, but we need to remember that she wants the same amount of candies to adjust our unit bar later.)

Read the next sentence. (If she has 25 jellybeans,) Ask, “What should we do with this information?” (put 25 on top of the jelly bean bar) “Is there something we need to do with the size of either of the unit bars?” (Make the jelly bean unit bar larger.) “How much larger?” (If 10 + 10 = 20, then we have to make the jelly bean unit bar a little more than double the first unit bar)

Read the next sentence. (Which method would help her find the number of additional chocolates she needs?)



“What do we need to do to our unit bars now?” (We can draw arrows to show that 10 is the same amount on both unit bars. Then extend the chocolate bar with a dotted box to match the size of the jelly bean box.) “Why are we extending the chocolate unit bar to match the jelly bean unit bar?” (because we want to have the same amount of chocolate as jelly beans. If we make the bars the same size, this shows the same amount for both candies.) “Where should we place the question mark?” (in the dotted box on the chocolate unit bar) “Why?” (because we want to know how many more chocolates we need to buy.)

Step 3: Strategy

“Let’s examine our model drawing. What action do you notice?” (subtraction) “What type of subtraction is it?” (comparing) “How do you know that?” (we compared the number of jelly beans to the number of chocolates to find how many more chocolates were needed)


“What do we know about number lines?” (numbers are in order, least to greatest) “Let’s draw a number line.”


Ms. H ch.

Ms. H jb. 25

10

?

10

25

Ms. H ch.

Ms. H jb. 25

10

?

10


? 25

-10

“Now let’s use what we know about number lines and model drawing to solve the problem. What operation did we choose for this problem?” (Subtraction) “Why?” (Because we are comparing) “What number do you think we should put on the number line first?” (25) “Why?” (because it is the largest number) “What is another reason?” (It is our total.) “Let’s label 25 as the last number on our number line. Why?” (because we have already determined that it is subtraction and we need to move backward)

“Since we know it is subtraction, which way will we move on the number line?” (backwards) “How much?” (10) “Would this be a large distance from 25 or small?” (small) “Why?” (because it is a small portion of 25) “As in our unit bar, we use a ‘?’ to represent what we are trying to find. Where might we put the ‘?’ on our number line?” (where the arrow is pointing)

“Let’s record the number line in our strategy section of the window pane.”

“What number sentence can we write to find how many more chocolates she needs to buy?”

25 – 10 =


? 25

-10

25 – 10 =

10 + = 25

Ms. H ch.

Ms. H jb.

25

10

?

10


? 25

-10

“Let’s look back at the unit bar. Is there another number sentence we can write to show the relationship between 25 and 10? Use your knowledge of fact families and number bonds to help you.” (25 is the total, and we already have 10, so we can see that 10 plus something (?) is 25.”

10 + = 25

“How could we represent 10 plus something(?) on a number line?” (draw 10 and 25 on the number line) “How do we know where to place the numbers?” (10 is on the left and 25 is on the right) “Why?” (because 10 is smaller than 25) “Do we put 10 and 25 close together or far apart?” (relatively far apart because there are several numbers between them)


+ ?

10 25

Ms. H ch.

Ms. H jb. 25

10

?

10

? 25

-10

Step 4: How

See how many different statements students can write.

“Let’s see which of our “How” statements matches our answer choices.” (C – Find the difference of 25 and 10.)

Look back at all 3 problems together with students to compare each type of subtraction.


Subtract 10 from 25 to find the difference

Find the difference between 25 and 10

Sum of 10 and another number is 25

25 – 10 =

10 + = 25


Guided Practice 6


Ms. Hernandez has 10 chocolates. She would like to have the same number of chocolates and jelly beans. If she has 25 jelly beans, which method would help her find the number of additional chocolates she needs.

A. Find the sum of 10 and 25 C. Find the difference of 25 and 10

B. Subtract 25 from 10 D. Add 10 and 25 and 8



A. Find the sum of 10 and 25 C. Find the difference of 25 and 10B. Subtract 25 from 10 D. Add 10 and 25 and 8


A. Find the sum of 10 and 25 C. Find the difference of 25 and 10C. Subtract 25 from 10 D. Add 10 and 25 and 8


A. Find the sum of 10 and 25 C. Find the difference of 25 and 10D. Subtract 25 from 10 D. Add 10 and 25 and 8


A. Find the sum of 10 and 25 C. Find the difference of 25 and 10E. Subtract 25 from 10 D. Add 10 and 25 and 8


A. Find the sum of 10 and 25 C. Find the difference of 25 and 10F. Subtract 25 from 10 D. Add 10 and 25 and 8


Guided Practice 7


Copeland Elementary collected 617 canned goods and 15 gallons of water during the food drive. Emmott Elementary collected 321 canned goods and 23 gallons of water. How could you find how many more canned goods Copeland Elementary collected than Emmott Elementary?

A. Add 617, 15, 321, and 23 C. Find the sum of 617 and 23

B. Find the difference of 617 D. Subtract 617 from 341 and 321



Copeland Elementary collected 617 canned goods and 15 gallons of water during the food drive. Emmott Elementary collected 321 canned goods and 23 gallons of water. How could you find how many more canned goods Copeland Elementary collected than Emmott Elementary?

A. Add 617, 15, 321, and 23 C. Find the sum of 617 and 23

B. Find the difference of 617 D. Subtract 617 from 341 and 321

How find more canned goods Copeland than Emmott?

617 C cg

321 E cg

617 – 321 =

321 + = 617

Subtract 321 from 617 Find the difference of

617 and 321617

321

?

?321


IMN Idea

Run pg 40 and 41 front/back.

Cut along dotted lines to create a flip book.

Model with students how to draw the unit bar with the action posters

Model the number lines and number sentences

? 3

6

2

?

6

2

?


Vanilla Not Vanilla

?

?

2 ?

5

3

?

2 + 3 =

6 - 2 =

5 – 3 =

6 - 2 =

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