Must-Practise Problem Sum Questions from Top Primary Schools --- GET NOW! The current approach to learning math in Singapore primary schools is through the math model method. Under this approach, students are required to draw math models that illustrate the questions. For lower primary students, modeling might seem unnecessary but the skills being mastered will come in handy at upper primary level where problem sums becoming more challenging. To give your lower primary child a head start, this article will show you some techniques for math modeling. 1. Background on math model method This methodology was created by a Singaporean teacher called Hector Chee. Due to its practicality, the method was soon taught in all schools, starting from Primary One. This new method presented a challenge to parents who might have been taught using algebra or other math methods. As a result, many could not help their children to develop the right math model techniques for the different kinds of math problem sums. 2. Main concepts in Singapore math model method In the math model method, there are basically 2 concepts that form the foundation for all further iterations. 2.1 The part whole concept In this concept, the child starts with understanding the relationship between parts. Once understood, they can represent these relationships using rectangular blocks to model math questions. Let’s look at one example to better understand how the part whole concept works. In the image below, the child starts off learning how to add the individual balls to understand a simple addition question of 3 +2 =5. At this stage, it is important to use real images such as the balls to let the child connect the dots. Once the child has understood the above, we can take out the balls and uses blocks as representations. Below is how the image can be drawn. Once the kid accepts the blocks as representations, he or she will be in a good position to understand further abstraction. After the above, we can go one step further to visualize the question in even more abstract terms. Here, we don’t need the individual blocks. Instead, just a visual distinction between 3 and 2 is enough to represent the relationship between the blocks. In summary, this technique uses the relationship of the parts to let children learn about the whole. 2.2 The change concept The change concept helps children to understand the concepts of adding and subtracting. Let’s take a look at an example of subtraction. In the example below, we are teaching a child how to subtract 1 from 3 i.e. 3-1=2. Again, we start off the math model by using realistic objects. Once the child is similar with subtracting, we can proceed to using a more abstract representation. In this step, we replace the objects with blocks. In the final step, replace the individual blocks with larger blocks. This sets the foundation of all future problems where a child can just use the bigger blocks to present items that can be added or subtracted. This will help your child to see what is the change answer to the problem sum questions. 3. Applying math models to learning fractions, ratios and decimals Now that you are familiar with the basic math models, I will show you how you can use them in solving different types of math problems. 3.1 Fractions Fractions can be represented using the part whole concept. F0r the purpose of illustration, let’s solve the following problem sum on fractions. “Peter is selling pencils. He sold 3/5 of them in the morning and 1/4 of the remainder in the afternoon. If Peter sold 200 more pencils in the morning than in the afternoon, how many pencils did Peter have in the beginning?” To solve this problem sum, we will use the part whole concept to draw the following math model. First, draw 5 equal blocks and shade 3 of them to represent 3/5. Step 1: Peter sold 3/5 of his pencils on Monday Next, divide the unshaded portion into 4 parts and shade one of them in a different color to show 1/4 of the remainder Step 2: Peter sold 1/4 of the remainder in the afternoon The third step is to make all boxes equal by cutting 1 red shaded box into 2 as shown below. Step 3: Make all boxes equal size The fourth step is to calculate how many pencils does each box represents. The question says that there are 200 more pencils being sold in the morning. In this case, 200 is equal to 5 red boxes since there are 5 more shaded boxes in the morning. So, each box = 200/5 = 40. Step 4: calculate the number of pencils represented by each box The final step is to calculate the total number of pencils. Since there are 10 boxes in total, the answer to the question is 40 * 10 = 400 pencils. The final math model will look like the below: Step 5: calculate total number of pencils 3.2 Ratios For learning ratios, you can use either the part whole concept or the change concept. In the example here, we will use the change concept. “The ratio of Amy and Karen’s money is 5:3. After Amy spent half of her money, she had $15 less than Karen. What was the total amount of money that both girls had in the beginning?” The first step is to draw out the ratio. Step 1: Ratio of Amy and Karen’s money is 5:3 The next step is to draw out the diagram after Amy has spent half of her money. Step 2: Ratio of Amy and Karen’s money after Amy spent 1/2 of her money The third step is to shade out the block that represents the difference between Amy and Karen’s money. Step 3: Shade the block that represent the difference in money between the 2 girls The question tells us that the black shaded block = difference between 2 girls’ money = $15. In other words, we know now that 1/2 block = $15. Therefore, 1 block = $30. This can be seen from the image below. Step 4: Find the value of each block The final step is to calculate the total amount of money that both girls had in the beginning. From step one, we know there are 8 blocks in total. So the answer is 8 * $30 = $240. 3.3 Decimals Let’s go through one last problem sum to see how to use the math model for decimals. “Mary has $15 before shopping. After buying 5 identical pencil cases, she was left with $9. How much does each pencil case cost?” The question has a before and after effect, thus making it suitable to use the change concept. Step 1: Mary has $15 before shopping and $9 after shopping The next step is to show that the difference between the before and after can be represented by 5 blocks (to illustrate 5 pencil cases) Step 2: Represent the pencil cases as 5 blocks The question tells us that the 5 pencil cases are identical. Hence, to find the price of 1 pencil case, we simply have to take the difference between the before and after i.e. $15-$9 =$6 and divide that by the 5 blocks. This gives us $6/5=$1.2. This can be represented by the final math model below. Step 3: Calculate the cost of 1 pencil case We hope this tutorial has been helpful in showing you the techniques for using the Singapore math model method. If you have further questions, please leave them in the comments. Source: www.teach-kids-math-by-model-method.com var dd_offset_from_content = 40;var dd_top_offset_from_content = 0;var dd_override_start_anchor_id = "";var dd_override_top_offset = ""; How To Gain Entry to TOP Secondary Schools?Try Official Maths Olympiad Today Tags: Lower Primary (7-10), mathematics, Singapore, Upper Primary (10-12)
The Singapore Math Method in Action Imagine you walk into a third-grade classroom just in time for math class. The teacher says, “Today we’re going to learn about long division.” Students are directed to watch while the teacher demonstrates the steps and actions necessary to solve a long division problem. Imagine the next day you walk into another third grade classroom. The teacher says, “Amanda has some pennies she wants to put in some jars.” She hands out baggies of pennies and places jars on the desks. She then clarifies, “Amanda has 17 pennies she wants to share equally in 5 jars.” Students are directed to try to figure out how that might work and then come together to share their ideas about what sharing equally means and how they approached the problem. The first classroom is using a more typical approach to math, while the second is using Singapore Math. Both classrooms are located in the United States and neither has any affiliation with the country of Singapore. That’s not a riddle, the second class has simply started using a different approach to teach math--the Singapore Math method. What is Singapore Math? What is referred to as Singapore Math in other countries is, for Singapore, simply math. The program was developed under the supervision of the Singaporean Minister of Education and introduced as the Primary Mathematics Series in 1982. For close to twenty years, this program remained the only series used in Singaporean classrooms. In 1998, Jeff and Dawn Thomas realized that the math program they brought back from Singapore and used to supplement their own child’s schoolwork could be useful to schools and home-schooling families across the nation. As the program began garnering attention, the couple incorporated under the name Singaporemath.com Inc and their books began being marketed under the name Singapore Math TM books. The program has a unique framework with a focus on building problem-solving skills and an in-depth understanding of essential math skills. It is closely aligned with curriculum focal points recommended by the National Council of Teachers of Mathematics and the Common Core State Standards. Who’s Using Singapore Math? Singapore Math first gained popularity amongst homeschoolers and small private schools. When the 2003 Trends in International Mathematics and Science Study scores revealed Singapore’s 4th and 8th graders were the top math performers in the world, public education started taking a closer look at the method. With so much interest in the method, U.S. educational publisher Houghton-Mifflin Harcourt teamed up with the leading educational publisher in Singapore to publish and distribute a math series called Math in Focus: The Singapore Approach. This series and the Thomas’ Primary Mathematics are the only curriculum packages available to United States educators for teaching the Singapore Math method. As reported in a 2010 article in the New York Times (and the program’s website), Primary Mathematics is now being used in upwards of 1500 schools, has been adopted for use by the California State Board of Education and is on the Oregon State Board of Education’s supplemental materials list. Math in Focus is being used by nearly two hundred school districts and private and charter schools. The Singapore Math Philosophy It’s not the content that makes Singapore Math different than other methods, it’s the philosophy of what’s important and how it should be taught. Singapore Math focuses on building fundamental math skills based on the understanding that without a strong foundational base, students won’t be able to have anything to draw on when it comes to increasingly complicated math learning. This doesn’t mean, however, that the skills elementary students learn are simplistic. The view is that when teaching a concept or a skill it’s important to spend as much time as needed for students to master the skill. That way you’re not moving on to the next concept with the thought that earlier skills can always be retaught if necessary. They can simply be revisited instead, opening up more instructional time. The method uses a three-step learning model, which consistently introduces concepts in a progression. It moves from the concrete to visual representation and then on to the more abstract (questioning and solving written equations). Students are taught not only to know how to do something, but also why it works.
Published 29/10/2014 1. Study Smart, Not Study Hard Understanding root concepts is very important. For example, 7 x 6 is 7 groups of 6 objects within each group. It is not just about memorising the multiplication table. Understanding the root concepts enables your child to figure out his own answers even if they forget the multiplication table. Singapore Maths questions are usually non-routine and it challenges your child’s mind in different ways. Remember – the process is more important than the product. 2. Demonstrate Ideas With Concrete Examples Questions involving less than or more than in problem sums for example, can be quite confusing for some children. You can demonstrate these ideas more clearly by using objects such as little bears or counting cubes. For example, 3 more than 4 – place 4 bears on the table in a line, then add 3 more bears slowly to demonstrate ‘more than’. Instead of memorising the answer 7, your child can see for themselves what 3 more than 4 actually means. 3. Take Sufficient Time And Care To Read The Question Children often fail to understand what the question is asking because they tend to read the question incorrectly, which is different from not understanding the question. Singapore Maths is more than just about numbers as it requires a significant amount of language processing. It is important for children to build on their language skills in order to read questions correctly. 4. Learn In Small Incremental Steps Because Singapore Maths places great emphasis on conceptual understanding, practising in daily in bite size chunks of homework is better than cramming all work into a single torturous day. Let your child learn in small incremental steps or knowledge that they can build upon, day by day. Over time, a much stronger Mathematical foundation can be built this way. 5. Use Real World Examples As Stories If you think about it, mathematics is everywhere. For example, to illustrate what 1/4 means, you can tell a story about 4 children wanting to share a birthday cake. What do we do? What if there are 8 children who want to share the same cake? Will each child get more or less cake? Children learn better when they can see mathematics being applied in the real world. By Lau Chin Loong Co-founder of Seriously Addictive Mathematics (S.A.M), he is also the lead mathematics curriculum developer for S.A.M and the principal trainer for the franchise. He holds a Bachelor’s degree in psychology from Dalhousie University (Canada) and has an MBA from Leicester University (UK). He also holds a Post-Graduate Diploma in Education from NIE (NTU). Before co-founding S.A.M, he was a primary school teacher. He has taught at Swiss Cottage Primary School and Anglo-Chinese School (Barker). Chin Loong was in consumer banking at the United Overseas Bank prior to joining M.O.E. as a teacher. Seriously Addictive Mathematics In A Nutshell SAM is an award winning Maths program based on the Singapore Maths syllabus, suitable for children from 4 to 12 years of age. The program is delivered through a combination of Worksheets learning as well as Classroom learning. Students learn Singapore Maths at their own pace, according to their own ability. The unique program is rapidly gaining popularity with parents in Singapore as well as in other countries like Malaysia, Thailand, India and the United States. Website: www.seriouslyaddictivemaths.com.my Centre Locations: (Klang Valley) Bandar Utama, Aman Suria, Ara Damansara, Bandar Baru Klang, Bukit Jelutong, Cheras Bukit Segar, Kepong Sri Bintang, Kota Damansara, Kota Kemuning, Mahkota Cheras, Mont Kiara, Puchong Jaya, Setia Alam, SS2 PJ, Subang USJ (Negeri Sembilan) Seremban 2 (Perak) Ipoh, Teluk Intan (Penang) Bukit Mertajam, Bayan Lepas Tel: 03-7733 MATH (6284), 012-3833218 Email:email@example.com Facebook: www.facebook.com/SingaporeMaths.My