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.

Model Drawing with Fractions Marissa spent 2/3 of her money at the mall and had $10 left. How much money did she spend at the mall? (Anna) Have teachers work the problem. Discuss how you really can’t start with these problems but these are the problems students must do by 4th grade. P. 49 Now we are going to play are you smarter than a 5th grader. Using Model Drawing we are going to solve some 4th and 5th grade problems. Have teachers discuss why this strategy works well with fractions

Fractions Jia earned money babysitting. She spent ¼ of the money on lunch. She spent ½ the money on a DVD, and she saved $4. How much money did Jia spend on the DVD.

Change the Whole 30 second graders had a choice of 3 different instruments to play in music class. Half chose the drums and of the remaining kids, two-thirds chose the guitar and the rest chose the recorder. How many students chose the recorder? (Anna) Teach how to do a drop down bar when the denominator changed. You will have to model this for the teachers and then practice with the next problem. Remind the students that this is a 2nd or 3rd grade problem in Singapore. Note the rigor. Most textbook word problems aren’t rigorous enough.

Fractions Angela baked cookies. She gave 1/3 of them to her sister, and she put 5/8 of the remaining cookies in the freezer. If she had 1 dozen cookies left, how many cookies did she bake?

Division of Fractions by Whole Number https://www.youtube.com/watch?v=_11SEY-P_h0 There is ½ of a candy bar that needs to be divided evenly among 3 children. What fraction of the total candy bar will each child receive? (Becky) P 58 Have teachers work this problem and discuss. This is 5th grade curriculum

Bridge to Algebra with Comparison Problems Maria rented 2 video games and 3 DVDs for a total of $23. Each video game cost $1.50 more to rent than each DVD. What was the cost of renting DVDs? (Becky) Have teachers solve and then discuss.

Comparison Alma and Elmo sold a total of 96 raffle tickets for a school fundraiser. Alma sold 14 more tickets than Elmo. How many tickets did each student sell?

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.