Step-by-Step Model Drawing Solving Word Problems the Singapore Way

Norms Courtesy Be on time Cell phones on silent, vibrate, or off Be mindful of side-bar conversations Focus on the task at hand Collaborative Promote a sense of inquiry Frame meaningful questions Pay attention of self and others Assume positive intentions Be reflective (Anna)

Today’s Outcomes Participants will have a better understanding of why Model Drawing is an important strategy to teach K-5. Participants will have a better understanding of how to teach Model Drawing. (Anna)

A Focus on Problem Solving One of the key Elements missing in the United States instruction of Mathematics is a focus on Problem Solving. Singapore Math focuses on problem solving and creating equations from Primary up. Model Drawing is the way the teach this and build conceptual understandings (not just memorizing facts and formulas) https://www.youtube.com/watch?v=E5Bte7K_Mxg (Becky) Singapore once had similar Math scores as the US. So they revamped and they have 5 key Elements to their math program. Model Drawing focuses on Element 4- Multiple Models

C-P-A Concrete- Manipulatives Pictorial- Visual Models or Drawings Abstract- Symbols (Becky) Have teachers turn and talk about why we need these 3 stages and share with group. We need to use this model anytime we teach a new math concept. You can’t skip any of the steps or you will lose students. Often times teachers go from manipulatives right to a problem and we don’t understand why the students didn’t make the transition. It is because we skip the pictorial phase. The goal of model drawing is to provide a bridge between the concrete and abstract.

What is Computation? Computation is about students comprehending what they are doing, not simply following rules. Model Drawing does not address this but Number Talks or other Fluency work will help students with this part. (Becky) Important to remember, we can’t teach just procedures. We have to teach understanding. Sometimes it is easier to just teach the rules. We can’t do that because when students who have memorized get to upper level math fall apart because they don’t have a deep level of conceptual understanding. Students who fail Algebra 1 have a much higher percentage rate of dropping our of high school than other students. Algebra 1 data is the data that is used to predict dropout rates.

Math Comprehension Comprehension should be the goal in mathematics just like reading! What to do and why. (Anna) We can teach math like we do in reading in that here should be turn and talks, partner talks, small group instruction, mini-lessons, guided practice, independent practice, share time, and students should be able to justify and support their answers. Model drawing helps with this because it is built upon as students learn new and more difficult math concepts. Model Drawing can be used from beginning adding to understanding fractions and ratios. With model drawing student answers have to make sense in their number sentences (equations).

Everyone learns in different ways! Teachers have to use multiple strategies to teach the same concept because what makes sense to one student may not make sense to another. (Anna) Just like we don’t teach reading the same way to students, we can’t teach math. This is where Number Talks come into play, model drawing, and other problem solving strategies. Also this is where small group instruction has to come into play. After the mini-lesson and guided practice, you pull small groups to work with students while the other students work independently.

Two Stages of Model Drawing First they need to learn the process. Then they need to apply the process independently. (Anna) You need to use problems to teach the process. Discuss the process, it is about this to start with not solving the problems. Then they need to practice the process to solve the problems. Some students will learn the process after 2 or 3 models. Others will need 10 to 12. You may need to teach the process in small groups to those students who don’t understand it. Use easy problems to teach the process. You don’t want them worrying about computation when learning the process.

Process of Model Drawing Manipulatives K-2 Number Bonds/Part-Part Whole Boxes Discrete Model Continuous Model (Becky) Start with manipulatives like in any process(unifix cubes work best as they make bars), next are number bonds, use discrete model problems, before moving to continuous model. Have student use their manipulatives and record the Number Bonds. Have teachers do this with red and yellow chips. This is in the common core for Kindergarten and First Grade. Next use the Number Bonds to help you solve the problems in the Discrete Model. The goal of model drawing is to develop algebraic thinking, this is how it ties into Number Talks, which also develops algebraic thinking. Remember Algebra starts with Kindergarten. This strategy helps you organize data. It doesn’t help with computation always. Number Talks will do that for your students.

7 Steps https://www.youtube.com/watch?v=9Mrz1t2PvDQ Read the entire problem. Rewrite the question in sentence form, leaving a space for the answer. Write who or what is involved in the problem. Draw the unit bars. Chunk the problem, adjust the bars, and fill in the question mark. Compute and solve the problem. Write the answer in the sentence and make sure the answer makes sense. (Anna) Go over the 7 steps. As the problem becomes more complex, you will want the students to combine steps 4 &5. Go over chunking – you stop at every punctuation, in a complex sentence stop at (and, but, or, so) or any place where there is more than one piece of data.

Discrete Model Janet picked 3 daisies and 2 sunflowers from her garden. How many total flowers did Janet pick from her garden? Work with small numbers with students drawing 1 square to represent each object, put in a part-part whole box, or use grid paper. (Becky) Go through the problem with the teachers. Remind them they first teach the process, this is the first type of problem after number bonds. Remember you can use this same problem change the objects and change the numbers. P.11 Can use grid paper to work the problems. Or use unifix cubes

Continuous Model One bag of lettuce weighed 14 ounces. Another bag weighed 12 ounces. What was the total weight of the 2 bags of lettuce? When students understand cardinality, they can move to the continuous model. They have one unit bar and will write numbers inside the bar. (Anna) Have teachers work the problem and discuss why this is more difficult for students. Cardinality is understanding that a number can represent a set of things. P. 14 Now using this process let’s solve some problems. Are we smarter than 5th graders? These are problems our students will have to solve. They need to understand the process of Model Drawing by the time they reach 3rd grade.

Add to- Missing Sum/Result Unknown There were 5 baboons in a troop. 3 more baboons joined them. How many baboons are now in the troop?

Take From- Missing Difference There were 8 bees in a hive. 2 bees flew away. How many bees are still in the hive?

Compare-Difference Unknown(more) 6 wolves are grey and 4 wolves are red. How many more grey wolves are there than red wolves?

Compare- Difference Unknown(fewer) 6 cats have short hair and 8 cats have long hair. How many fewer cats have short hair than long hair?

Add to- Missing Sum Katie had 8 books on her shelf. Her father gave her 5 more. How many books does Katie now have all together?

Take From- Missing Subtrahend Jack bought one dozen donuts. He ate some of them. Now he has 4 donuts left. How many donuts did Jack eat?

Add Together/Take Apart- Missing Sum 8 baseballs, 7 soccer balls, and 3 basketballs were in a large barrel. How many balls are in the barrel?

Compare- Difference Unknown(more) The Orioles scored 11 runs and the Red Sox scored 7 runs. How many more runs did the Orioles score than the Red Sox?

Compare- Bigger Unknown(more) Tyrone read 11 more pages than Jackson. Jackson read 6 pages. How many pages did Tyrone read?

Compare- Smaller Unknown(more) In April, it rained 13 days. That’s 8 more days than it rained in July. How many days did it rain in July?

Compare- Difference Unknown(fewer) 14 kids play the trumpet and 5 kids play the clarinet. How many fewer kids play the clarinet?

Compare- Bigger Unknown(fewer) Erin found 9 fewer shells than Katie. If Erin found 6 shells, how many shells did Katie find?

Compare- Smaller Unknown(fewer) Large dogs live 4 fewer years, on average, than small dogs. If small dogs live to be 16 years old, how long do large dogs live?

Add to- Missing 2nd Addend Forty-two birds were in a tree. Some more birds flew over and landed. Then there were sixty-three birds all together. How many birds flew over and landed in the tree?

Add to- Missing 1st Addend Marie had some beads on a string. She added eighteen more to the string. Then there were thirty-one beads all together. How many beads were first on the string?

Take From- Missing Minuend Some cans were on a supermarket shelf. A customer bought nineteen cans so there were thirty-five cans left. How many cans were originally on the shelf?

Compare- Difference Unknown(more) The Seahawks scored forty-three points and the Broncos scored eight points. How many more points did the Seahawks score than the Broncos?

Compare- Smaller Unknown(more) In Dallas, it rains seventy-nine days a year. That’s forty-three more days a year than it rains in Phoenix. How many days a year does it rain in Phoenix?

Compare- Bigger Unknown(fewer) Erin found fifteen fewer shells than Katie. If Erin found seventeen shells, how many shells did Katie find?

Fractions- Find the Whole A group of students watched basketball practice. When the bell rang, ¾ of them went back to class and the other 12 stayed to watch. How many students were there in all?

Fractions- Find the Whole(multi-step) In a recent survey, 1/6 of the respondents said they did not like their job. Of those who said they liked their jobs, ¾ or 15 people said they also liked their spouse. How many people took part in the survey?

Reflection Teachers need to work the problems out before teaching them- we are learning too. This is just 1 problem solving strategy, you still need to teach the others. Lower grades need to introduce this strategy and practice, because the upper grades need this strategy in place for students to be successful with Common Core. This strategy is mentioned in DPI and is part of Foundations of math training. It will work if taught properly and used weekly just like every other problem solving strategy. We have to be strategic in selecting the problems that we use with our students so they will be practicing strategies that they can use in the future. We can’t tell them what strategies to use on these tests. These strategies need to seem like part of them, just like the reading strategies that they use.