Use Model Drawing Procedure in Four-Step Process

Use Model Drawing Procedure in Four-Step Process
Step 1: Main Idea Step 2: Details Who What Unit Bars Read one sentence at a time to adjust unit bars. Place ? Main Idea of Question Step 3 Step 4 Read the problem. What is the main idea of the question? Write the main idea of the question. Step 2 is about the details. Who is the problem about? What is the problem about? Re-read the problem one sentence at a time pausing at “ands” or commas. Label and adjust the models as you go. Read the first sentence. Jeff has 9 toys. Label the unit bar to show Jeff had 9 toys. Read the next sentence. Austin has 5 toys. Label Austin’s unit bar adjusting to represent the numbers. Ask: How many toys does Jeff have? Is the number of Austin’s toys larger or smaller than Jeff’s? How can you show’s Austin’s quantity as larger? Label Austin’s quantity. Read the next sentence. Label to show the action of putting together and place the ?. What operation can we use to solve the problem? Show the computation. How did you solve the problem? What is another way that you can could say how you solved the problem? Work the computation (s). Describe how the problem was solved.

Four Step Process Model Drawing Main Idea Details Strategy How
Read the problem. Write the main idea in the question. Details Write who the problem is about (related to main idea.) Write what the problem is about (related to main idea.) Draw unit bars of equal length. Re-read the problem one sentence at a time adjusting the unit bars to match the story and identify the question on the model. Strategy Work the computation (s). How Describe how the problem was solved. Model Drawing

Put Together The first problems will be addition problems. Addition

] Austin has 9 toys. Jeff has 3 toys.
Austin has 9 toys. Jeff has 3 toys. How many toys do they have together? How many toys do they have together? Step 1 Step 2 9 ] Austin Jeff toys Toys together ? 3 |ξξ Step 3 Step 4 Step 1 Read the problem. What is the main idea of the question? Write the main idea of the question. Step 2 is about the details. Who is the problem about? What is the problem about? Now, DRAW a UNIT BAR for each what (variable). Re-read the problem one sentence at a time pausing at “ands” or commas. Label and adjust the models as you go. Read the first sentence. Austin has 9 toys. Label the unit bar to show 9. Read the next sentence. Jeff has 3 toys. Look at Jeff’s unit bar. If Jeff has 3 toys, should his unit bar be larger or smaller than Austin’s? What made you say that Jeff’s should be smaller? Let’s make Jeff’s bar smaller like this. Label Jeff’s unit bars to show 3. Let’s read the next sentence. “How many toys do they have together?” Think about what the questioning is asking. What are we looking for? Are we looking for just Ann’s toys? Are we looking for just Jeff’s toys? Are we looking for both of their toys? Let’s show what we are looking for by linking them together with a brace and placing the ?. We have shown all of our sentences on the model so go to step 3. Step 3 What operation could we do to figure out the answer to the question? What should we do? Why? Let’s write the computation and find the answer. Step 4 What operation did you use to find the answer? What could we write to describe what we added? 9 + 3 Add 9 and 3. 12 Second Grade

Austin has 22 toys. Jeff has 33 toys. How many toys do they have?
Step 1 Step 2 22 ] Austin Jeff toys Toys together ? 33 Step 4 Step 3 Read the problem. What is the main idea of the question? Write the main idea of the question. Step 2 is about the details. Who is the problem about? What is the problem about? Re-read the problem one sentence at a time pausing at “ands” or commas. Label and adjust the models as you go. Read the first sentence. Austin has 5 toys. Label the unit bar to show Austin having 5 toys. Read the next sentence. Jeff has 9 toys. Label Jeff’s unit bar adjusting to represent the numbers. Ask: How many toys does Jeff have? Is the number of Jeff’s toys larger or smaller than Austin’s? How can you show’s Jeff’s quantity as larger? Label Jeff’s quantity. Read the next sentence. Label to show the action of putting together and place the ?. What operation can we use to solve the problem? Show the computation. How did you solve the problem? What is another way that you can could say how you solved the problem? 22 + 33 Add 22 and 33. 55

Take Away The next problems we work are subtraction. The action in these problems is take away. Subtraction

Jeff has 9 toys. He gave 3 toys away. How many toys does he have now?
Step 1 Step 2 ] 9 __ X Jeff toys Toys now 3 ? Step 3 Step 4 Step 1 Read the problem. What is the main idea of the question? Write the main idea of the question. Step 2 is about the details. Who is the problem about? What is the problem about? Re-read the problem one sentence at a time pausing at “ands” or commas. Label and adjust the models as you go. Read the first sentence. Jeff has 9 toys. Label the unit bar to show 9. Read the next sentence. He gave away 3 toys. Let’s show the 3 toys that Jeff gave away by using a line and X to show that the toys were given away. Label this part with a 3. Let’s read the next sentence. “How many toys does he have now?” Think about what the question is asking. What are we looking for? What part of the model are we looking for? Let’s put a brace and a ? to show this on the model. We have shown all of our sentences on the model so go to step 3. Step 3 What is Jeff doing? Is he going to have more toys or fewer toys? What operation could we do to figure out the answer to the question? What should we do? Why? Let’s write the computation and find the answer. Step 4 What operation did you use to find the answer? What could we write to describe what we subtracted? What is another way that we might describe what we did? 9 - 3 Subtract 3 from 9. Found the difference between 9 and 3. 6 Second Grade

Subtraction Compare The next problems are subtraction problems and the action is compare.

|ξ Second Grade Jeff has 6 toys. Mary has 4 toys.
Jeff has 6 toys. Mary has 4 toys. How many more toys does Jeff have than Mary has? How many more toys does Jeff have than Mary has? Step 2 Step 1 6 Jeff Mary toys 4 more toys Jeff than Mary ] ? 4 |ξ - - - Step 3 Step 4 Sample Script Step 1 Read the problem. What is the main idea of the question? Write the main idea of the question. Step 2 is about the details. Who is the problem about? What is the problem about? Re-read the problem one sentence at a time pausing at “ands” or commas. Label and adjust the models as you go. Read the first sentence. Jeff has 6 toys. Label the unit bar to show 6. Read the next sentence. Mary has 4 toys. Should the bar be bigger than Jeff’s or smaller than Jeff’s? What helps you know that the Mary’s bar should be smaller than Jeff? Let’s show the Mary’s 4 toys on her unit bar by marking off part of her unit bar to make it smaller. Label Mary’s unit bar with a 4. Let’s read the next sentence. “How many more toys does Jeff have than Mary has?” Think about what the question is asking. What are we looking for? What is the action in the story? Let’s draw an arrow like this to show what we are comparing. In order to compare this to Jeff’s, let’s draw a dotted line on Jeff’s model to show 4. Now label the part of the model that 4 is 4. What part of the model are we looking for? Let’s put a brace and a ? to show this on the model. We have shown all of our sentences on the model so go to step 3. Step 3 What operation could we do to figure out the answer to the question? What should we do? Why? Let’s write the computation and find the answer. Step 4 What operation did you use to find the answer? What could we write to describe what we subtracted? 6 - 4 Subtract 4 from 6. 2 Second Grade

|ξ Jeff has 26 toys. Mary has 14 toys.
Jeff has 26 toys. Mary has 14 toys. How many more toys does Jeff have than Mary has? How many more toys does Jeff have than Mary has? Step 2 Step 1 26 Jeff Mary toys 14 more toys Jeff than Mary ] - - - ? 14 |ξ Step 3 Step 4 Read the problem. What is the main idea of the question? Write the main idea of the question. Step 2 is about the details. Who is the problem about? What is the problem about? Re-read the problem one sentence at a time pausing at “ands” or commas. Label and adjust the models as you go. Read the first sentence. Jeff has 9 toys. Label the unit bar to show Jeff had 9 toys. Read the next sentence. Austin has 5 toys. Label Austin’s unit bar adjusting to represent the numbers. Ask: How many toys does Jeff have? Is the number of Austin’s toys larger or smaller than Jeff’s? How can you show’s Austin’s quantity as larger? Label Austin’s quantity. Read the next sentence. Label to show the action of putting together and place the ?. What operation can we use to solve the problem? Show the computation. How did you solve the problem? What is another way that you can could say how you solved the problem? 26 - 14 Subtract 14 from 26. 12

|ξ ] Ben More adult than children tickets
Ben sold tickets to the game. 2 student tickets, He sold 8 adult tickets, . Ben sold tickets to the game. He sold 8 adult tickets, 2 student tickets, and 5 children tickets. How many more adult than children tickets did he sell? and 5 children tickets. How many more adult than children tickets did he sell? Step 1 Step 2 8 Ben Adult tickets Child tickets 5 More adult than children tickets - - - ] ? 5 |ξ Step 3 Step 4 Read the problem. What is the main idea of the question? Write the main idea of the question. Step 2 is about the details. Who is the problem about? What is the problem about? Re-read the problem one sentence at a time pausing at “ands” or commas. Label and adjust the models as you go. Read the first sentence. Jeff has 9 toys. Label the unit bar to show Jeff had 9 toys. Read the next sentence. Austin has 5 toys. Label Austin’s unit bar adjusting to represent the numbers. Ask: How many toys does Jeff have? Is the number of Austin’s toys larger or smaller than Jeff’s? How can you show’s Austin’s quantity as larger? Label Austin’s quantity. Read the next sentence. Label to show the action of putting together and place the ?. What operation can we use to solve the problem? Show the computation. How did you solve the problem? What is another way that you can could say how you solved the problem? 8 - 5 Found the difference between 8 and 5. 3

| ξ |ξ ] Ben More adult than children tickets
Ben sold tickets to the game. 2 student tickets, He sold 8 adult tickets, . Ben sold tickets to the game. He sold 8 adult tickets, 2 student tickets, and 5 children tickets. How many more adult than children tickets did he sell? and 5 children tickets. How many more adult than children tickets did he sell? Step 2 Step 1 8 Adult tickets Student tickets Child tickets 5 Ben - - - More adult than children tickets ] ? 2 | ξ 5 |ξ Step 3 Step 4 Read the problem. What is the main idea of the question? Write the main idea of the question. Step 2 is about the details. Who is the problem about? What is the problem about? Re-read the problem one sentence at a time pausing at “ands” or commas. Label and adjust the models as you go. Read the first sentence. Jeff has 9 toys. Label the unit bar to show Jeff had 9 toys. Read the next sentence. Austin has 5 toys. Label Austin’s unit bar adjusting to represent the numbers. Ask: How many toys does Jeff have? Is the number of Austin’s toys larger or smaller than Jeff’s? How can you show’s Austin’s quantity as larger? Label Austin’s quantity. Read the next sentence. Label to show the action of putting together and place the ?. What operation can we use to solve the problem? Show the computation. How did you solve the problem? What is another way that you can could say how you solved the problem? 8 - 5 Found the difference between 8 and 5. 3

Missing Part Subtraction

| Second Grade Jeff has 8 balls. Five balls are baseballs and
Jeff has 8 balls. Five balls are baseballs and the rest are soccer balls. How many are soccer balls? the rest are soccer balls. How many are soccer balls? Step 2 Step 1 8 | Jeff balls S B soccer balls ] 5 ? Step 3 Step 4 Step 1 Read the problem. What is the main idea of the question? Write the main idea of the question. Step 2 is about the details. Who is the problem about? What is the problem about? DRAW a UNIT BAR for each what (variable). Re-read the problem one sentence at a time pausing at “ands” or commas. Label and adjust the models as you go. Read the first sentence. Jeff has 8 balls. Label the unit bar 8. Read the next sentence. “Five balls are baseballs and …let’s STOP at AND to label our model. Let’s label part of the pictorial model to show 5 baseballs like this. Let’s draw a line a little more than half way to show 5. Let’s label it B to make the model clearer. What does this part of the model show? Let’s label is S for soccer. Finish reading the rest of the sentence after AND. “…and the rest are soccer balls.” Let’s label it S for soccer to make the model more understandable. Let’s read the next sentence. “How many are soccer balls?” Think about what the question is asking. What part of the model are we looking for? Let’s put a brace and a ? to show this on the model. We have shown all of our sentences on the model so go to step 3. Step 3 What operation could we do to figure out the answer to the question? What should we do? Why? Let’s write the computation and find the answer. Step 4 What operation did you use to find the answer? What could we write to describe what we subtracted? 8 - 5 Found the difference between 8 and 5. 3 Second Grade

| Jeff has 24 balls. Fifteen balls are baseballs
and the rest are soccer balls. Jeff has 24 balls. Fifteen balls are baseballs and the rest are soccer balls. How many are soccer balls? How many are soccer balls? Step 1 Step 2 24 | Jeff balls soccer balls B ] S 15 ? Step 3 Step 4 Step 1 Read the problem. What is the main idea of the question? Write the main idea of the question. Step 2 is about the details. Who is the problem about? What is the problem about? DRAW a UNIT BAR for each what (variable). Re-read the problem one sentence at a time pausing at “ands” or commas. Label and adjust the models as you go. Read the first sentence. Jeff has 24 balls. Label the unit bar 24. Read the next sentence. “Fifteen balls are baseballs (pause at the AND) Let’s label part of the pictorial model to show the 15 baseballs like this. Let’s draw a line a little more than half way to show 15. Label this part of the model with 15. Let’s label it B to make the model clearer. Finish reading the rest of the sentence after AND. “…and the rest are soccer balls.” What does this part of the model show? Let’s label it S for soccer to make the model more understandable. Let’s read the next sentence. “How many are soccer balls?” Think about what the question is asking. What part of the model are we looking for? Let’s put a bracket and a ? to show this on the model. We have shown all of our sentences on the model so go to step 3. Step 3 What operation could we do to figure out the answer to the question? What should we do? Why? Let’s write the computation and find the answer. Step 4 What operation did you use to find the answer? What could we write to describe what we subtracted? 24 - 15 Found the difference between 24 and 15. 9

Add and Subtract Multiple Step Operations
At the end of second grade, we begin to do some multi-step problems so we will model 1. Add and Subtract

] Second Grade X| ? Max had 5 marbles. He gave his friend 3 marbles.
He bought 7 new Max had 5 marbles. He gave his friend 3 marbles. He bought 7 new marbles at the store. Which number sentence shows how to find how many marbles he has now? marbles at the store. Which number sentence shows how to find how many marbles he has now? Step 2 Step 1 5 7 X| Max marbles ] NS-Max marbles now 3 ? Step 3 Step 4 Sample Script Step 1 Read the problem. What is the main idea of the question? Write the main idea of the question. Step 2 is about the details. Who is the problem about? What is the problem about? DRAW a UNIT BAR for each what (variable). Re-read the problem one sentence at a time pausing at “ands” or commas. Label and adjust the models as you go. "Max has 5 marbles." What label shall we give the unit bar? (5) Read next sentence "He gave his friend 3 marbles." What is the action here? (Take Away.) Adjust bar. Read next sentence. "He bought 7 new marbles at the store." This could get confusing if we put the 7 on the bar where we have crossed off a part. Let's go ahead and subtract. So now this little piece of the bar is worth "2." Let's bring that little "2" bar down. Then we can perform can neatly add the 7 bar on the end. How long should this bar be? Notice that to keep the picture neat, the subtraction is performed; the remainder brought down; and then the 7 added. This is an option - or the subtraction can be done, as in the previous slide, on the left side of the bar. 1) I subtracted 3 from 5. 5 - 3 2 + 7 2) I added 2 and 7. 2 9 Second Grade

] Second Grade | X ? Max had 5 marbles. He gave his friend 3 marbles.
He bought 7 new marbles at the store. Max had 5 marbles. He gave his friend 3 marbles. He bought 7 new marbles at the store. Which number sentence shows how to find how many marbles he has now? Which number sentence shows how to find how many marbles he has now? Step 2 Step 1 5 | X Max marbles NS-Max marbles now 3 7 ] 2 ? Step 3 Step 4 SAME PROBLEM AS PREVIOUS, CHANGE DRAWING TECHNIQUE TO BRINGING THE BAR DOWN AFTER THE FIRST OPERATION. THEN PERFORMING THE SECOND OPERATION. Step 1 Read the problem. What is the main idea of the question? Write the main idea of the question. Step 2 is about the details. Who is the problem about? What is the problem about? DRAW a UNIT BAR for each what (variable). Re-read the problem one sentence at a time pausing at “ands” or commas. Label and adjust the models as you go. "Max has 5 marbles." What label shall we give the unit bar? (5) Read next sentence "He gave his friend 3 marbles." What is the action here? (Take Away.) Adjust bar. Read next sentence. "He bought 7 new marbles at the store." This could get confusing if we put the 7 on the bar where we have crossed off a part. Let's go ahead and subtract. So now this little piece of the bar is worth "2." Let's bring that little "2" bar down. Then we can perform can neatly add the 7 bar on the end. How long should this bar be? Notice that to keep the picture neat, the subtraction is performed; the remainder brought down; and then the 7 added. This is an option - or the subtraction can be done, as in the previous slide, on the left side of the bar. 1) I subtracted 3 from 5. 5 - 3 2 + 7 2) I added 2 and 7. 2 9 Second Grade

] Second Grade X | | X Cathy has 9 pencils. She gave John 4 pencils.
Sue gave Cathy 2 pencils Cathy has 9 pencils. She gave John 4 pencils. Sue gave Cathy 2 pencils at lunch. How could you find how many pencils Cathy has altogether? at lunch. How could you find how many pencils Cathy has altogether? Step 2 Step 1 9 2 Cathy John Sue pencils X | ] Find pencils Cathy 4 ? 4 | X 2 Step 3 Step 4 DEMONSTRATION PROBLEM WITH EXTRA INFORMATION. When subtracted 4 went from the left to keep the bar neat. When add 4 to John's bar, be sure don't just label John's bar 4. She gave John some, we don't know how many pencils he had to start with. 9 - 4 5 + 2 Subtract 4 from 9. Then add 5 and 2. 5 7 Second Grade

] Second Grade X | Cathy has 9 pencils. She gave John 4 pencils.
Sue gave Cathy 2 pencils Cathy has 9 pencils. She gave John 4 pencils. Sue gave Cathy 2 pencils at lunch. How could you find how many pencils Cathy has altogether? at lunch. How could you find how many pencils Cathy has altogether? Step 2 Step 1 9 2 Cathy pencils X | ] Find pencils Cathy 4 ? Step 3 Step 4 DEMONSTRATION WITH EXTRA INFORMATION EXCLUDED. Here only Cathy's unit bar is made - this is from observing the main idea - the only pencils we are concerned about are Cathy's. Note: You could also subtract the 4 from the 9 unit bar by crossing off on the right. Bring the new "5" bar down and add 2 to the "5" bar. 9 - 4 5 + 2 Subtract 4 from 9. Add 2 to the difference. 5 7 Second Grade

What's a another way? Second Grade Y | P R ]
Tammy has a box of ten markers. She has red, yellow, and purple Tammy has a box of ten markers. She has red, yellow, and purple markers. Three of the markers are yellow, and four are purple. How could you find how many markers are red? markers. Three of the markers are yellow, and four are purple. How could you find how many markers are red? Step 2 Step 1 10 Tammy box of markers Y | P R red markers 3 4 ] ? Step 3 Step 4 PURPOSE: TO DEMONSTRATE HOW THE PUZZLE GROUPING PIECE IS GOING TO WORK. Puzzle mixer to get group. We are going to give you a puzzle piece. Your group will all have the same color puzzle pieces and your piece will complete the windowpane problem solving format. Once found group - Together read problem. 1) Together decide on main idea. If you have the "Main Idea" puzzle piece, you write in the group's main idea. Ask questions: Who? What? Unit bar. Read one sentence or phrase at a time. Adjust unit bars, label, place quetsion mark. Person with this puzzle piece does the recording. 3) Decide on the operations and perform them. The person with this puzzle piece does the writing. 4) Together decide on the "how." The person with this puzzle piece records this section. **Puzzle pieces passed out after this problem by Ilesia, Alice and Vicki. Groups can pick up their own sheets of chart paper when the time comes. 10 - 3 7 - 4 Subtract 3 from 10. Subtract 4 from the difference. 7 3 What's a another way? Second Grade

] Ecourage students to see multiple ways! Step 1 $81 V S C
Victoria’s parents spent $81 at the shoe store. Victoria’s shoes cost $24, and her sister’s shoes cost $29. Victoria’s parents spent $81 at the shoe store. Victoria’s shoes cost $24, and her sister’s shoes cost $29. The rest of the money was spent on her brother Carlos’ shoes. How much money was spent on Carlos’ shoes? The rest of the money was spent on her brother Carlos’ shoes. How much money was spent on Carlos’ shoes? Step 1 Step 2 $81 V. parents money V S C Money Carlos’ shoes $24 $29 ] ? Step 3 Step 4 $57 -$29 Subtracted $24 from $81. Subtracted $29 from $57. Sample Script Step 1 Read the problem. What is the main idea of the question? Write the main idea of the question. Step 2 is about the details. Who is the problem about? What is the problem about? DRAW a UNIT BAR for each what (variable). Re-read the problem one sentence at a time pausing at “ands” or commas. Label and adjust the models as you go. Read the first sentence. Lisa had $10 to spend by Wednesday. We need to show the total money that Lisa will spend in 3 days. To show that on the model, let’s put a brace from the money on Monday to the money on Wednesday and label that $10. Read the next sentence. “On Monday, she spent $3,” Stop at the comma and label the model. Label money for Monday as $3. Read the NEXT part of the sentence. And on Tuesday she spent $4. Look at the model for money on Tuesday. Since this is $4, should we make the unit bar larger or smaller? How can you decide? Since 4 is larger than 3, let’s add some more on to Tuesday’s model. Label this as $4. Let’s read the NEXT sentence. “How much money does she have left to spend on Wednesday? Think about what the question is asking. What part of the drawing are we looking for? Let’s put a ? to show this on the drawing. We have shown all of our sentences on the model so go to step 3. Step 3 What operation could we do to figure out the answer to the question? What should we do? Why? Let’s write the computation and find the answer. Step 4 What operation did you use to find the answer? What could we write to describe what we did? $81 _ $24 81 – $57 $28 Ecourage students to see multiple ways!

] ? Step 1 $24 Money Carlos’ shoes $29 $81 Step 3 Step 4 $24 + $29 $81
Victoria’s parents spent $81 at the shoe store. Victoria’s shoes cost $24, and her sister’s shoes cost $29. Victoria’s parents spent $81 at the shoe store. Victoria’s shoes cost $24, and her sister’s shoes cost $29. The rest of the money was spent on her brother Carlos’ shoes. How much money was spent on Carlos’ shoes? The rest of the money was spent on her brother Carlos’ shoes. How much money was spent on Carlos’ shoes? Step 2 Step 1 $24 ] Victoria Sister Carlos Shoes Money Carlos’ shoes $29 $81 ? Step 3 Step 4 Sample Script Step 1 Read the problem. What is the main idea of the question? Write the main idea of the question. Step 2 is about the details. Who is the problem about? What is the problem about? DRAW a UNIT BAR for each what (variable). Re-read the problem one sentence at a time pausing at “ands” or commas. Label and adjust the models as you go. Read the first sentence. Lisa had $10 to spend by Wednesday. We need to show the total money that Lisa will spend in 3 days. To show that on the model, let’s put a brace from the money on Monday to the money on Wednesday and label that $10. Read the next sentence. “On Monday, she spent $3,” Stop at the comma and label the model. Label money for Monday as $3. Read the NEXT part of the sentence. And on Tuesday she spent $4. Look at the model for money on Tuesday. Since this is $4, should we make the unit bar larger or smaller? How can you decide? Since 4 is larger than 3, let’s add some more on to Tuesday’s model. Label this as $4. Let’s read the NEXT sentence. “How much money does she have left to spend on Wednesday? Think about what the question is asking. What part of the drawing are we looking for? Let’s put a ? to show this on the drawing. We have shown all of our sentences on the model so go to step 3. Step 3 What operation could we do to figure out the answer to the question? What should we do? Why? Let’s write the computation and find the answer. Step 4 What operation did you use to find the answer? What could we write to describe what we did? $24 + $29 $81 - $53 Find the sum of $24 and $29. Subtracted the sum from $81. $53 $28

Use Model Drawing Procedure in Four-Step Process

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