Activity 1
The initial introduction to the Singapore bar models will involve simple straightforward addition and subtraction problems. An example of each kind follows and both of the problems come from the Primary Mathematics 3A Workbook (1992).
(a) 9+7=
The sum of 9 and 7 is ____.
(b) 9-7=
The difference between 9 and 7 is ____.
Using a basic fact less than 20 will introduce the students to how the models work. I will give the students several examples using basic facts less than 20 until they grasp the concept. Then I will introduce them to the slightly more abstract diagram where the units are no longer represented individually. For example:
Find the sum of 65 and 89.
65+89=
The sum of 65 and 89 is ______.
This model above is representative of the way the models appear once the students have been introduced to them. The end-to-end model is preferable since it is linear and makes a connection to measurement. I will have the students solve several problems that are just numerical, using the end-to end model. Then the students will use construction paper cut-outs to create models on their paper. This will provide a hands-on way to create the models. Once the students have made some with pre-cut models, they will draw their own representations. In making all models, one requirement will be that the related equation should also be written.
Following the work with straightforward equations, the next step will be to move the students into using the models to represent word problems. Initially we will work with addition and subtraction. The same model can often represent several word problems related by the commutative property or the inverse relationship shared by addition and subtraction. Developing these concepts through problem solving will help to make these connections more meaningful for the students and will lead to greater motivation.
Ryan's sister is 15 years old. How old is Ryan if he is 4 years older than his sister?
The equation that goes with this problem is 15+4=19 years or 4+15=19 years. A few other problems that could be asked using this same model, but changing where the unknown is, are as follows:
Ryan is 19 years old. His sister is 15 years old. How many years older is Ryan?
The equation for this problem is: 15+4=19 years.
Ryan is 19 years old. He is 4 years older than his sister. How old is his sister?
The equation for this problem is: 19 - 4 = 15 years old
Once the students are solving word problems, they will be required to write the equation and also to label the answers. The focus will be on being able to solve the problem with a bar model while also showing a corresponding equation. The numbers within the word problem will get more challenging. Similar problems with three digit numbers would be the next step to take with the students. The students will work with the same model for several related scenarios where each time the unknown is different. These related problems will continue to show inverse relationships and the commutative property. Once the students are comfortable with the models and with writing related problems, I will be able to move quickly to more difficult numbers since addition and subtraction through the millions has already been covered.
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