Use Model Drawing in Four-Step Process

Use Model Drawing in Four-Step Process
Who What Unit Bar Read one sentence at a time to adjust unit bars. 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

Extra Information If a child understands that the details are what is needed to answer the main idea of the question, he will NOT include the extra information in the details. Try to keep students focused on what the question is asking them to find. However, if the child includes the extra information in the drawing, placing the ? in the model will help them understand that the extra information is NOT needed.

Put Together Addition

] Austin has 22 toys. Jeff has 33 toys.
Austin has 22 toys. Jeff has 33 toys. How many toys do they have together? How many toys do they have together? 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

Juan has 32 games for his Gameboy Devion has 52 games for his
Juan has 32 games for his Gameboy. Devion has 52 games for his Gameboy. Cody has 24 games for his. Juan gave 15 of his games to Cody. Which number sentence shows Cody’s number of games? Gameboy. Cody has 24 games for his. Juan gave 15 of his games to Cody. Which number sentence shows Cody’s number of games? Step 2 Step 1 32 Juan Devion Cody games | X Cody’s # games 15 52 24 15 ξ| ? Step 3 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. Theo has 4 old coins: W, X, Y, and Z. Does this provide any information to add to the model? Read the next sentence. “Coin Y is worth $2.” How can we show this in the drawing? Let’s label Coin Y with $2. Read the next sentence. “Coin Z is worth 3 times the value of coin Y.” Which model is this sentence about? How do we show that it is 3 times coin Y? Let’s label each with $2. What is the value of coin Z? Let’s label the value at the end of the bars. Read the next sentence. “Coin W is worth 4 times the value of coin Y.” How do we show it 4 times on the drawing? Let’s label each part of the model of coin w. What is the value of coin W? Read the next sentence. “The 4 coins are worth $30 altogether.” What is the action in this sentence? Let’s show the action of addition with the bracket from Coin W to Coin Z. What label will we use to show the total? Let’s read the next sentence. “What is the value of coin Y?” What are we being asking to find. Let’s label it with a ?. We have shown all of our sentences on the model so go to step 3. Step 3 Think about what the question is asking. How could we find the value of coin Y? How many coins are there? How many values do we know? If we know the total value of all 4 coins, and the value of 3 of the coins, how could we find the value of the 4th coin? What operation could we do to figure out the answer to the question? Let’s write the computation to find the answer. Step 4 What operations did you use to find the answer? What could we write to describe what we did? Step 4

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

X| J ? Step 2 Step 1 25 Jelly beans jar 6 Step 3 Step 4
Ms. Hernandez has 10 chocolates and 25 jelly beans in a bag. She ate 6 of the jelly beans. 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? 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? Step 2 Step 1 25 X| J Ms. H Jelly beans Jelly beans jar 6 ? 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?

] Fourth Grade | ? John wanted to buy a bicycle that cost $285
and a helmet that cost $39. He was able to get $19 taken off the price of the bicycle because he John wanted to buy a bicycle that cost $285 and a helmet that cost $39. He was able to get $19 taken off the price of the bicycle because he used a coupon from the newspaper. With the coupon, how much did the bicycle cost John not including tax? used a coupon from the newspaper. With the coupon, how much did the bicycle cost John not including tax? Step 2 Step 1 $285 | John bicycle money X ] Bicycle cost $19 ? 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? $285 - $19 Subtracted $19 from $285. $266 Fourth Grade

] Fourth Grade | ? |§§§§ John wanted to buy a bicycle that cost $285
and a helmet that cost $39. He was able to get $19 taken off the price of the bicycle because he John wanted to buy a bicycle that cost $285 and a helmet that cost $39. He was able to get $19 taken off the price of the bicycle because he used a coupon from the newspaper. With the coupon, how much did the bicycle cost John not including tax? used a coupon from the newspaper. With the coupon, how much did the bicycle cost John not including tax? Step 2 Step 1 $285 | John bicycle money helmet money X ] Bicycle cost $19 ? |§§§§ $39 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? $285 - $19 Found the difference between $19 and $285. $266 Fourth Grade

At breakfast, the temperature outside was 68 degrees F.
At lunchtime it had gone up 5 degrees F, At breakfast, the temperature outside was 68 degrees F. At lunchtime it had gone up 5 degrees F, and then by dinnertime it had gone down 2 degrees F. What was the temperature at dinnertime? and then by dinnertime it had gone down 2 degrees F. What was the temperature at dinnertime? Step 2 Step 1 68 5 temperature Temperature dinnertime X 2 ? Step 3 Step 4 This problem is division problem working with larger numbers and is the more difficult type of division to model. 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. Juan made paper roses for his girlfriend. Does this provide any information to add to the model? Read the next sentence. “He made 9 paper roses each day.” Think about how we can show this action on the bar. The bar represents Juan’s paper roses. Lets show the 9 paper roses that he made on day 1 like this, on day 2 like this, on day 3 like this. Let’s represent this continuing by … Labeling with Day 1, Day 2, etc. helps us to understand the action in the problem and to also choose an operation to use. Let’s read the next sentence. “How many days did it take him to make 117 roses?” Think about what the question is asking. What does the 117 represent? Let’s label the model. What are we looking for? Since we are looking for the days, I am going to label the question ? with a D.. We have shown all of our sentences on the model so go to step 3. Step 3 What’s the action? What operation could we do to figure out the answer to the question? What operation might we use? Let’s write the computation to find the answer. Step 4 What operation did you use to find the answer? What could we write to describe what we did? 68 +5 73 -2 Find the sum of 68 and 5. Find the difference of 73 and 2. 71 73

At breakfast, the temperature outside was 68 degrees F.
At lunchtime it had gone up 5 degrees F, At breakfast, the temperature outside was 68 degrees F. At lunchtime it had gone up 5 degrees F, and then by dinnertime it had gone down 2 degrees F. What was the temperature at dinnertime? and then by dinnertime it had gone down 2 degrees F. What was the temperature at dinnertime? Step 2 Step 1 68 5 temperature Temperature dinnertime 73 73 X 2 ? Step 3 Step 4 This problem is division problem working with larger numbers and is the more difficult type of division to model. 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. Juan made paper roses for his girlfriend. Does this provide any information to add to the model? Read the next sentence. “He made 9 paper roses each day.” Think about how we can show this action on the bar. The bar represents Juan’s paper roses. Lets show the 9 paper roses that he made on day 1 like this, on day 2 like this, on day 3 like this. Let’s represent this continuing by … Labeling with Day 1, Day 2, etc. helps us to understand the action in the problem and to also choose an operation to use. Let’s read the next sentence. “How many days did it take him to make 117 roses?” Think about what the question is asking. What does the 117 represent? Let’s label the model. What are we looking for? Since we are looking for the days, I am going to label the question ? with a D.. We have shown all of our sentences on the model so go to step 3. Step 3 What’s the action? What operation could we do to figure out the answer to the question? What operation might we use? Let’s write the computation to find the answer. Step 4 What operation did you use to find the answer? What could we write to describe what we did? 68 +5 Find the sum of 68 and 5. Find the difference of 73 and 2. 73 -2 73 71

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

] ] There are 18 children in Ms. Fry’s homeroom class.
There are more boys than girls. There are 18 children in Ms. Fry’s homeroom class. There are more boys than girls. What additional information is needed to find how many more boys than girls are in Ms. Fry’s homeroom? What additional information is needed to find how many more boys than girls are in Ms. Fry’s homeroom? Step 2 Step 1 B ] Ms. Fry’s Boys Girls info-more boys than girls ] 18 ? G 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?

Missing Part Subtraction

] | Jeff has 204 balls. Fifteen balls are baseballs
and the rest are soccer balls. Jeff has 204 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 ] 204 | 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

Abby went to the mall with $15 in her purse. After she bought a book
and popcorn, Abby went to the mall with $15 in her purse. After she bought a book and popcorn, she had $7 left. If the book costs $6, which of these shows one way to find the amount that Abby spent on the popcorn? she had $7 left. If the book costs $6, which of these shows one way to find the amount that Abby spent on the popcorn? Step 2 Step 1 $15 B P L Way-money spent popcorn money Abby B P $6 $7 ? Step 3 Step 4 Sample Script Step 1 Read the problem and picture what is going on in the story. What is the main idea of the question? Record what they are asking you to find. Step 2 is about the details. Who is in this problem ? What is the problem talking about? How do you know? How many variables do we have? How many unit bars do we need to DRAW? 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 4 bags. Look at the model. We only have one unit bar. What could we do to show 4 equal bags? We can draw 3 more unit bars to show 4 equal parts. What can you label each unit bar with to remind us what we are talking about? (bag) Read the next sentence. “Each bag has 5 toys.” How many toys are in each bag? How should we label the model to show each bag having 5 toys? Label each part of the model with 5. Let’s read the next sentence. “How many total toys does Jeff haves?” 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 on the model we are looking for total toys. We have shown all of our sentences on the model so go to step 3. Step 3 What action is happening in the main idea? (put together equal sets) What operation could we do to figure out the answer to the question? Is their another operation we could use? Is it okay to work the problem two ways? Let’s write the both computations to find the answer. NOTE: By showing both computations, we are not only differentiating instruction but ALSO showing the CONNECTION between addition and multiplication one more time. Step 4 How did you solve the problem in step 3? What operation did you use to find the answer? What is the answer to a multiplication problem? What could we write to describe what we did? What could be the benefit of working the problem in two ways?

] 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!

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

Warner Elementary has 1,125 students enrolled in PK to 5th grade.
Warner Elementary has 1,125 students enrolled in PK to 5th grade. McFee Elementary has 238 fewer students in PK to 5th grade. What is the total number of students in the 2 newest Cy-Fair schools? McFee Elementary has 238 fewer students in PK to 5th grade. What is the total number of students in the 2 newest Cy-Fair schools? Step 2 Step 1 1125 ] Warner McFee Students ? Students 2 new schools 238 887 ζ| Step 3 Step 4 1,125 + 887 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? 1,125 - 238 Subtracted 238 from 1,125. Added 887 and 1,125. 887 2,012

Donny had 148 baseball cards. Mel had 26 more baseball cards than
Donny had 148 baseball cards. Mel had 26 more baseball cards than Donny. Bruce had 11 fewer baseball cards than Mel. How many baseball cards did Bruce have? Bruce had 11 fewer baseball cards than Mel. How many baseball cards did Bruce have? Step 2 Step 1 148 Donny Mel Bruce Bb cards Baseballs-Bruce 148 26 148 26 |ξ ? 11 Step 3 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. Theo has 4 old coins: W, X, Y, and Z. Does this provide any information to add to the model? Read the next sentence. “Coin Y is worth $2.” How can we show this in the drawing? Let’s label Coin Y with $2. Read the next sentence. “Coin Z is worth 3 times the value of coin Y.” Which model is this sentence about? How do we show that it is 3 times coin Y? Let’s label each with $2. What is the value of coin Z? Let’s label the value at the end of the bars. Read the next sentence. “Coin W is worth 4 times the value of coin Y.” How do we show it 4 times on the drawing? Let’s label each part of the model of coin w. What is the value of coin W? Read the next sentence. “The 4 coins are worth $30 altogether.” What is the action in this sentence? Let’s show the action of addition with the bracket from Coin W to Coin Z. What label will we use to show the total? Let’s read the next sentence. “What is the value of coin Y?” What are we being asking to find. Let’s label it with a ?. We have shown all of our sentences on the model so go to step 3. Step 3 Think about what the question is asking. How could we find the value of coin Y? How many coins are there? How many values do we know? If we know the total value of all 4 coins, and the value of 3 of the coins, how could we find the value of the 4th coin? What operation could we do to figure out the answer to the question? Let’s write the computation to find the answer. Step 4 What operations did you use to find the answer? What could we write to describe what we did? Step 4 Found sum of 148 and 26. Found the difference between 174 and 11. 148 + 26 174 - 11 163 174

] ? 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

Put Together Equal Sets
Multiplication

] Jeff has 4 bags. Each bag has 5 toys.
Jeff has 4 bags. Each bag has 5 toys. How many total toys does Jeff have? ] How many total toys does Jeff have? Step 1 Step 2 4 5 total toys bags of toys Jeff 5 5 5 ? Step 3 Step 4 5 + 5 Sample Script Step 1 Read the problem and picture what is going on in the story. What is the main idea of the question? Record what they are asking you to find. Step 2 is about the details. Who is in this problem ? What is the problem talking about? How do you know? How many variables do we have? How many unit bars do we need to DRAW? 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 4 bags. Look at the model. We only have one unit bar. What could we do to show 4 equal bags? We can draw 3 more unit bars to show 4 equal parts. What can you label each unit bar with to remind us what we are talking about? (bag) Read the next sentence. “Each bag has 5 toys.” How many toys are in each bag? How should we label the model to show each bag having 5 toys? Label each part of the model with 5. Let’s read the next sentence. “How many total toys does Jeff haves?” 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 on the model we are looking for total toys. We have shown all of our sentences on the model so go to step 3. Step 3 What action is happening in the main idea? (put together equal sets) What operation could we do to figure out the answer to the question? Is their another operation we could use? Is it okay to work the problem two ways? Let’s write the both computations to find the answer. NOTE: By showing both computations, we are not only differentiating instruction but ALSO showing the CONNECTION between addition and multiplication one more time. Step 4 How did you solve the problem in step 3? What operation did you use to find the answer? What is the answer to a multiplication problem? What could we write to describe what we did? What could be the benefit of working the problem in two ways? Added 5 four times. 5 x 4 Found the product of 5 and 4. 20 20

NS-party plates Ms Cassidy bought ?
Mrs. Cassidy bought 9 packages of party plates to use for a special party. Each package contained 8 party plates. The party plates cost $48 altogether. Mrs. Cassidy bought 9 packages of party plates to use for a special party. Each package contained 8 party plates. The party plates cost $48 altogether. Which number sentence can be used to find how many party plates in all Mrs. Cassidy bought? Which number sentence can be used to find how many party plates in all Mrs. Cassidy bought? Step 1 Step 2 $48 Ms C Plates 8 8 8 8 8 8 8 8 8 NS-party plates Ms Cassidy bought P1 P2 P3 P4 P5 P6 P7 P8 P9 ? 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. Theo has 4 old coins: W, X, Y, and Z. Does this provide any information to add to the model? Read the next sentence. “Coin Y is worth $2.” How can we show this in the drawing? Let’s label Coin Y with $2. Read the next sentence. “Coin Z is worth 3 times the value of coin Y.” Which model is this sentence about? How do we show that it is 3 times coin Y? Let’s label each with $2. What is the value of coin Z? Let’s label the value at the end of the bars. Read the next sentence. “Coin W is worth 4 times the value of coin Y.” How do we show it 4 times on the drawing? Let’s label each part of the model of coin w. What is the value of coin W? Read the next sentence. “The 4 coins are worth $30 altogether.” What is the action in this sentence? Let’s show the action of addition with the bracket from Coin W to Coin Z. What label will we use to show the total? Let’s read the next sentence. “What is the value of coin Y?” What are we being asking to find. Let’s label it with a ?. We have shown all of our sentences on the model so go to step 3. Step 3 Think about what the question is asking. How could we find the value of coin Y? How many coins are there? How many values do we know? If we know the total value of all 4 coins, and the value of 3 of the coins, how could we find the value of the 4th coin? What operation could we do to figure out the answer to the question? Let’s write the computation to find the answer. Step 4 What operations did you use to find the answer? What could we write to describe what we did? 9 x 8 Found the product of 9 and 8. 72

Fourth Grade Aaron exercises every day of the week. If he does 25
Aaron exercises every day of the week. If he does 25 jumping jacks each day, how many jumping jacks will he do in 1 week? jumping jacks each day, how many jumping jacks will he do in 1 week? Step 2 ? Step 1 Aaron jump jacks 25 25 25 25 25 25 25 Jumping jacks 1 week 1 2 3 4 5 6 7 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? 25 X 7 Found the product of 25 and 7. 175 Fourth Grade

 crayons ? Ms. Lee has 12 boxes of crayons. Each box has 16 crayons.
Ms. Lee has 12 boxes of crayons. Each box has 16 crayons. How many crayons does she have? How many crayons does she have?  Step 2 12 Step 1 Ms. Lee boxes of crayons crayons 16 16 16 … 16 ? Step 3 Step 4 This problem is working with larger numbers and represents a 4th of 5th grade problem. 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. Ms. Lee has 12 boxes of crayons. Look at the model. If the unit bar represents one box of crayons, we would need to draw 11 more unit bars to show 12. Because this is a larger number, we can just indicate a pattern in the model to show to 12 boxes. Now place a bracket and label it with 12 to show that the model represents 12 boxes of crayons. (NOTE: It would have been fine to draw several lines on the unit bar to show 12 parts also.) Read the next sentence. “Each box has 16 crayons.” How should we label the model to show each box having 16 crayons? Label each part of the model with 16. Let’s read the next sentence. “How many crayons does she have?” 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 operation might we use? Let’s write the computation to find the answer. Step 4 What operation did you use to find the answer? What could we write to describe what we did? 16 X 12 Multiplied 16 by 12. 32 16 . 192

Take Away Equal Sets Division

 D ? Juan made paper roses for his girlfriend. He made
Juan made paper roses for his girlfriend. He made 9 paper roses each day. How many days did it take him to make 117 roses? 9 paper roses each day. How many days did it take him to make 117 roses?  Step 2 Step 1 117 9 days to make roses Juan paper roses 9 9 D ? Day 1 Day 2 Day 3 … Step 3 Step 4 This problem is division problem working with larger numbers and is the more difficult type of division to model. 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. Juan made paper roses for his girlfriend. Does this provide any information to add to the model? Read the next sentence. “He made 9 paper roses each day.” Think about how we can show this action on the bar. The bar represents Juan’s paper roses. Lets show the 9 paper roses that he made on day 1 like this, on day 2 like this, on day 3 like this. Let’s represent this continuing by … Labeling with Day 1, Day 2, etc. helps us to understand the action in the problem and to also choose an operation to use. Let’s read the next sentence. “How many days did it take him to make 117 roses?” Think about what the question is asking. What does the 117 represent? Let’s label the model. What are we looking for? Since we are looking for the days, I am going to label the question ? with a D.. We have shown all of our sentences on the model so go to step 3. Step 3 What’s the action? What operation could we do to figure out the answer to the question? What operation might we use? Let’s write the computation to find the answer. Step 4 What operation did you use to find the answer? What could we write to describe what we did? Divided 117 by 9. 13 9 )117

D ? Juan made paper roses for his girlfriend. He made
Juan made paper roses for his girlfriend. He made 9 paper roses each day. How many days did it take him to make 117 roses? 9 paper roses each day. How many days did it take him to make 117 roses? Step 2 Step 1 117 paper roses 9 9 days to make roses Juan - - - - - - 9 … - - - … D ? Day 1 Day 2 Day 3 Step 3 Step 4 This problem is division problem working with larger numbers and is the more difficult type of division to model. 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. Juan made paper roses for his girlfriend. Does this provide any information to add to the model? Read the next sentence. “He made 9 paper roses each day.” Think about how we can show this action on the bar. The bar represents Juan’s paper roses. Lets show the 9 paper roses that he made on day 1 like this, on day 2 like this, on day 3 like this. Let’s represent this continuing by … Labeling with Day 1, Day 2, etc. helps us to understand the action in the problem and to also choose an operation to use. Let’s read the next sentence. “How many days did it take him to make 117 roses?” Think about what the question is asking. What does the 117 represent? Let’s label the model. What are we looking for? Since we are looking for the days, I am going to label the question ? with a D.. We have shown all of our sentences on the model so go to step 3. Step 3 What’s the action? What operation could we do to figure out the answer to the question? What operation might we use? Let’s write the computation to find the answer. Step 4 What operation did you use to find the answer? What could we write to describe what we did? Divided 117 by 9. 13 9 )117

Multi-Operation Multiplication and Division

Looking at the model, what are other ways? Fourth Grade
Manny bought pencils that were priced at 3 for 45¢. Manny bought pencils that were priced at 3 for 45¢. What was the total cost of 8 pencils? What was the total cost of 8 pencils? ? Step 2 45¢ Step 1 Manny pencils Total cost 8 pencils 1 2 3 4 5 6 7 8 Looking at the model, what are other ways? Step 3 Step 4 ___ 3)45¢ 15¢ 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? 15¢ X 8 Divided 45 by 3 and multiplied the quotient by 8. $1.20 Fourth Grade

Fourth Grade Manny bought pencils that were priced at 3 for 45¢.
Manny bought pencils that were priced at 3 for 45¢. What was the total cost of 8 pencils? What was the total cost of 8 pencils? ? Step 2 45¢ Step 1 Manny pencils Total cost 8 pencils 1 2 3 4 5 6 7 8 Step 3 Step 4 ___ 3)45¢ 15¢ 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? 15¢ X 8 Divided 45 by 3 and multiplied the quotient by 8. $1.20 Fourth Grade

Step 1 Step 2 NS-money spent ? Step 3 Step 4
Theo bought 2 books for $4 each and Theo bought 2 books for $4 each and 3 pencils for $1 each. Which number sentence can be used to find the total amount of money in dollars Theo spent? 3 pencils for $1 each. . sentence can be used to find the total amount of money in dollars Theo spent? Which number Step 1 Step 2 2 Theo Books Pencils NS-money spent $4 $4 ? 3 $1 $1 $1 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. Theo has 4 old coins: W, X, Y, and Z. Does this provide any information to add to the model? Read the next sentence. “Coin Y is worth $2.” How can we show this in the drawing? Let’s label Coin Y with $2. Read the next sentence. “Coin Z is worth 3 times the value of coin Y.” Which model is this sentence about? How do we show that it is 3 times coin Y? Let’s label each with $2. What is the value of coin Z? Let’s label the value at the end of the bars. Read the next sentence. “Coin W is worth 4 times the value of coin Y.” How do we show it 4 times on the drawing? Let’s label each part of the model of coin w. What is the value of coin W? Read the next sentence. “The 4 coins are worth $30 altogether.” What is the action in this sentence? Let’s show the action of addition with the bracket from Coin W to Coin Z. What label will we use to show the total? Let’s read the next sentence. “What is the value of coin Y?” What are we being asking to find. Let’s label it with a ?. We have shown all of our sentences on the model so go to step 3. Step 3 Think about what the question is asking. How could we find the value of coin Y? How many coins are there? How many values do we know? If we know the total value of all 4 coins, and the value of 3 of the coins, how could we find the value of the 4th coin? What operation could we do to figure out the answer to the question? Let’s write the computation to find the answer. Step 4 What operations did you use to find the answer? What could we write to describe what we did? Found the product of 4 and 2. Found the product of 3 and 1. Found the sum of the products. 4 x 2 8 3 x 1 8 + 3 11

Alex bought lemons that were priced at 2 lemons for 18¢.
total cost of 5 lemons? What was the Alex bought lemons that were priced at 2 lemons for 18¢. What was the total cost of 5 lemons? Step 1 Step 2 $18 Alex lemons Cost 5 lemons 1 2 3 4 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. Theo has 4 old coins: W, X, Y, and Z. Does this provide any information to add to the model? Read the next sentence. “Coin Y is worth $2.” How can we show this in the drawing? Let’s label Coin Y with $2. Read the next sentence. “Coin Z is worth 3 times the value of coin Y.” Which model is this sentence about? How do we show that it is 3 times coin Y? Let’s label each with $2. What is the value of coin Z? Let’s label the value at the end of the bars. Read the next sentence. “Coin W is worth 4 times the value of coin Y.” How do we show it 4 times on the drawing? Let’s label each part of the model of coin w. What is the value of coin W? Read the next sentence. “The 4 coins are worth $30 altogether.” What is the action in this sentence? Let’s show the action of addition with the bracket from Coin W to Coin Z. What label will we use to show the total? Let’s read the next sentence. “What is the value of coin Y?” What are we being asking to find. Let’s label it with a ?. We have shown all of our sentences on the model so go to step 3. Step 3 Think about what the question is asking. How could we find the value of coin Y? How many coins are there? How many values do we know? If we know the total value of all 4 coins, and the value of 3 of the coins, how could we find the value of the 4th coin? What operation could we do to figure out the answer to the question? Let’s write the computation to find the answer. Step 4 What operations did you use to find the answer? What could we write to describe what we did? ____ )18 9 9 X 5 2 Find the quotient of 18 and 2. Find the product of 9 and 5. 45

Value of coin X Step 1 Step 2 ? Step 3 Step 4 8 2 + 6 30 -16 14 16
Theo has 4 old coins: W, X, Y and Z. Coin Z is worth 3 Coin Y is worth $2. . times the value of coin Y. Theo has 4 old coins: W, X, Y and Z. Coin Y is worth $2. Coin Z is worth 3 times the value of coin Y. Coin W is worth 4 times the value of coin Y. The 4 coins are worth $30 altogether. What is the value of coin X? Coin W is worth 4 times the value of coin Y. The 4 coins are worth $30 altogether. What is the value of coin X? Step 1 Step 2 $2 $2 $2 $2 $8 Theo Coin W Coin X Coin Y Coin Z ? Value of coin X $30 $2 $2 $2 $2 $6 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. Theo has 4 old coins: W, X, Y, and Z. Does this provide any information to add to the model? Read the next sentence. “Coin Y is worth $2.” How can we show this in the drawing? Let’s label Coin Y with $2. Read the next sentence. “Coin Z is worth 3 times the value of coin Y.” Which model is this sentence about? How do we show that it is 3 times coin Y? Let’s label each with $2. What is the value of coin Z? Let’s label the value at the end of the bars. Read the next sentence. “Coin W is worth 4 times the value of coin Y.” How do we show it 4 times on the drawing? Let’s label each part of the model of coin w. What is the value of coin W? Read the next sentence. “The 4 coins are worth $30 altogether.” What is the action in this sentence? Let’s show the action of addition with the bracket from Coin W to Coin Z. What label will we use to show the total? Let’s read the next sentence. “What is the value of coin Y?” What are we being asking to find. Let’s label it with a ?. We have shown all of our sentences on the model so go to step 3. Step 3 Think about what the question is asking. How could we find the value of coin Y? How many coins are there? How many values do we know? If we know the total value of all 4 coins, and the value of 3 of the coins, how could we find the value of the 4th coin? What operation could we do to figure out the answer to the question? Let’s write the computation to find the answer. Step 4 What operations did you use to find the answer? What could we write to describe what we did? 8 2 + 6 Found sum of 8, 2, and 6. Found the difference between 16 and 30. 30 -16 14 16

Use Model Drawing in Four-Step Process

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