Clements and Sarama. (2000). The earliest geometry Teaching Children Mathematics, 7 (October), 82-86.
Papic, M. (2007). Promoting repeating patterns with young children - More than just alternating colours! Australian Primary Mathematics Classroom, 12 (3), 8-13.
Warren, E., and Cooper, T. (2006). Using repeating pattern to explore functional thinking. Australian Primary Mathematics Classroom, 11 (1), 9-14.
Origo (2008). The Origo handbook of mathematics education. QLD : Origo Education. Parker, A. ( 2008). Mental maths strategies : year 1 : Glebe Pascal Press : Database
Monday, October 24, 2011
Sunday, October 23, 2011
Week 4: Geometry and measurement
VISUALIZING
-In relation to the topic of visualizing, teachers need to ensure that by the end of the lesson, children should be able to form mental images of geometric shapes by using spatial memory and spatial visualization. Apart from that, children also were required to recognize and represent objects from various points of view.
- As to help the students to achieve those objectives mentioned above, activities for instance visualizing the shape could be carried out in the class ( Clement & Sarama (2000)). Children are told to close their eyes and think of a shape namely a triangle. Then, they will be asked to open their eyes and look around the classroom to find the shape that they they were thinking about. As to make the activities more changeling, the teacher can prompt questions like " I have a shape in my mind, it has six faces which are rectangle, and 8 corners. What is the shape that I am thinking?
- Apart from that, Clement and Sarama ( 2000) also suggested another class activities which helps in developing children's sense of visualization, which is game of quick image. This activity requires the teacher to show the image and quickly hide the image. Then, the children need to guess the shape and describe the properties of the image. In describing the properties of the shape, the children will need to use terms like number of faces, edges, and corners. By putting the terms into practice of conversation, children will engage in a more meaningful learning experience.
- In addressing the issue of visualizing to the students, teacher needs to put forward the notion of representing and recognizing objects from different point of view. Taking shape of a pyramid as an example, if it is viewed from the bottom, then it is in the shape of a square. If a pyramid is viewed from the side view, then it is in the shape of a triangle. By addressing these, it eventually helps the children to see how different shapes are put together to form another shape.
From the side view, a pyramid looks like a triangle, while on the bottom view, it is in the shape of a square.
LOCATION AND SPATIAL RELATIONSHIP ( Unit blocks, maps and spatial relation)
Young children should be able to specify locations and describe spatial relationships using coordinate geometry and other representational systems. In engaging the students in this topic, the engagement of map is highly recommended. Clement and Sarama (2000) suggests that map as a tool in teaching location and direction to the children. For instance, preschoolers children will be able to learn quickly if they have examined a map beforehand. Young learners need to learn about location, thus engaging the students with the use of maps is a good strategy.Clement and Sarama ( 2000) suggest that the children could mark a path from a table to the rubish bin with masking tape. Then, the teacher can draw a map alongside the path. The table which appears alongside the path might become something else, for instance shops or bus stop.
Suggested class activities : Students can work this in a group of five in which they need to create a village or city out of cardboard. Using the cardboard, they will create various shape blocks representing different buildings. As to develop the student's spatial ability, the cardboard is represented open as they can manipulated flat surface as to create a village. With the help of a small bee b
ot ( a simple programmed robot for the children), the teacher can instructed the children to move the robot from point A to point B. In explaining to the others what path needs the robot take from A to B, their spatial language is develop.
The village created by the students using the cardboard which serves as a map in explaining how to get from one point to one point.
The bee bot robot serves as a 'car' in which the students need to move it from point A to point B. In getting the robot to reach the destination, students need to describe the journey taken by the robot. In describing the journey taken by the robot, spatial language will be further explored and used by the children.
* Clement & Sarama ( 2000) also states that computer assisted activities helps in facilitating children's learning of navigation and map skills. It is perceived that young children can abstract and generalize the directions and measurement which eventually required them to move a thing from a point to another, for instance a racing car game.
-In relation to the topic of visualizing, teachers need to ensure that by the end of the lesson, children should be able to form mental images of geometric shapes by using spatial memory and spatial visualization. Apart from that, children also were required to recognize and represent objects from various points of view.
- As to help the students to achieve those objectives mentioned above, activities for instance visualizing the shape could be carried out in the class ( Clement & Sarama (2000)). Children are told to close their eyes and think of a shape namely a triangle. Then, they will be asked to open their eyes and look around the classroom to find the shape that they they were thinking about. As to make the activities more changeling, the teacher can prompt questions like " I have a shape in my mind, it has six faces which are rectangle, and 8 corners. What is the shape that I am thinking?
- Apart from that, Clement and Sarama ( 2000) also suggested another class activities which helps in developing children's sense of visualization, which is game of quick image. This activity requires the teacher to show the image and quickly hide the image. Then, the children need to guess the shape and describe the properties of the image. In describing the properties of the shape, the children will need to use terms like number of faces, edges, and corners. By putting the terms into practice of conversation, children will engage in a more meaningful learning experience.
- In addressing the issue of visualizing to the students, teacher needs to put forward the notion of representing and recognizing objects from different point of view. Taking shape of a pyramid as an example, if it is viewed from the bottom, then it is in the shape of a square. If a pyramid is viewed from the side view, then it is in the shape of a triangle. By addressing these, it eventually helps the children to see how different shapes are put together to form another shape.
From the side view, a pyramid looks like a triangle, while on the bottom view, it is in the shape of a square.Young children should be able to specify locations and describe spatial relationships using coordinate geometry and other representational systems. In engaging the students in this topic, the engagement of map is highly recommended. Clement and Sarama (2000) suggests that map as a tool in teaching location and direction to the children. For instance, preschoolers children will be able to learn quickly if they have examined a map beforehand. Young learners need to learn about location, thus engaging the students with the use of maps is a good strategy.Clement and Sarama ( 2000) suggest that the children could mark a path from a table to the rubish bin with masking tape. Then, the teacher can draw a map alongside the path. The table which appears alongside the path might become something else, for instance shops or bus stop.
Suggested class activities : Students can work this in a group of five in which they need to create a village or city out of cardboard. Using the cardboard, they will create various shape blocks representing different buildings. As to develop the student's spatial ability, the cardboard is represented open as they can manipulated flat surface as to create a village. With the help of a small bee b
ot ( a simple programmed robot for the children), the teacher can instructed the children to move the robot from point A to point B. In explaining to the others what path needs the robot take from A to B, their spatial language is develop.
The village created by the students using the cardboard which serves as a map in explaining how to get from one point to one point.
The bee bot robot serves as a 'car' in which the students need to move it from point A to point B. In getting the robot to reach the destination, students need to describe the journey taken by the robot. In describing the journey taken by the robot, spatial language will be further explored and used by the children.
* Clement & Sarama ( 2000) also states that computer assisted activities helps in facilitating children's learning of navigation and map skills. It is perceived that young children can abstract and generalize the directions and measurement which eventually required them to move a thing from a point to another, for instance a racing car game.
Racing car game
Monday, October 17, 2011
Workshop 4 : Geometry and shape
MEASUREMENT ( Selecting appropriate units and indirect comparison)
- In this entry, topic on measurement will be further explored, aiming in establishing a learning experience which introduce and extends the student's understanding the aspect of indirect comparison. In teaching the concept of measurement, teacher needs to address the difference between standard units and non standard units.Origo ( 2008) defines standard units as a set amount which is used to measure a quantity in which it is uniform and have been approved and acknowledged by a regulatory body. The examples are meter, centimeter or seconds.
-Heirdsfield ( 2011) comes out with a series of teaching sequence in which it serves as a guideline to a more effective teaching of measurement. Firstly, the teacher needs to get the students to identify the attribute to be measured, for instance getting the students to compare the perimeter of their class table with non standard measuring devices such as ice cream sticks, pins or paper tape.
The pictures above shows the non standard measurement devices namely paper tape, ice cream sticks and pins.
These two pictures demonstrates indirect comparison of the perimeter of the table with ice cream sticks and pins. In order to get the most accurate measurement of the comparison, pins is a better option compared to ice cream sticks.
* Tips : teacher can get the students to talk about the comparisons, for instance asking the students to describe what they did and what are the measuring devices that they used in this indirect comparison.
MAKING A MEASURING DEVICE
- Measuring device is an important element in this topic. Previously, we have been talking about factors to be consider in selecting the most appropriate units and indirect comparison in relation to standard and non standard. Thus, in this section, a further exploration on creating a meaningful learning experience addressing the topic of making our own measuring device will takes place.
- In establishing a learning experience to address this topic, firstly, teacher needs to provide the students with the materials. In this activities, several materials such as popcorn, cups and container ( see picture below) is needed.
The cups containing popcorn will dole out as 'measuring devices' in measuring the volume of other containers.
In measuring the volume of containers ( picture below), cups of popcorn is one of the ways that can be used. Firstly, teacher needs to set up the students in group of three. The teacher explains to the students what they should do. The students need to fill the cups with popcorn and then pour it to the container as to see how many cups of popcorn will occupy the container. Thus, the number of cups = the volume of the container.
The picture shows the process of occupying the containers with the popcorn using the cup provided.
*Teacher should note the students that when they finish pouring the first cup of popcorn into the container, they need to mark the level of the popcorn using a marker pen. This is to track down how many cups have the students pour. That marks will helps the students not to get confuse.
The marks put indicates that the container is able to occupy four cups of popcorn, which means that the volume of the container is approximately equals to four cups of popcorn. The cups of popcorn acts as a measuring device which manages to measure the capacity of the container. Thus, this activity does engage the students in making measuring device.
As presented above, that container, let's name it container A. Container A manages to occupy four cups of popcorn. Then, teacher gives the students a bigger container, container B. As to make the challenge more changeling, the students needs to measure the capacity of the container B ( how many cups can the container hold), without using the cups. The students will use container A as to get the volume of the container B.
Container A has become a new measuring device in which it can be used to measure the volume of container A. Asking the students to justify their measuring device and how it works in measuring container B is a good activities as it stimulus the students reasoning and critical thinking skills. The dialogue between the teacher and students may seem to appeared as below.
- In this entry, topic on measurement will be further explored, aiming in establishing a learning experience which introduce and extends the student's understanding the aspect of indirect comparison. In teaching the concept of measurement, teacher needs to address the difference between standard units and non standard units.Origo ( 2008) defines standard units as a set amount which is used to measure a quantity in which it is uniform and have been approved and acknowledged by a regulatory body. The examples are meter, centimeter or seconds.
-Heirdsfield ( 2011) comes out with a series of teaching sequence in which it serves as a guideline to a more effective teaching of measurement. Firstly, the teacher needs to get the students to identify the attribute to be measured, for instance getting the students to compare the perimeter of their class table with non standard measuring devices such as ice cream sticks, pins or paper tape.
The pictures above shows the non standard measurement devices namely paper tape, ice cream sticks and pins.- Then, in doing the comparison, the students need to identify the most appropriate units in which they would used as to measure the perimeter of the table. Teacher should let the students to choose which measuring device would they use ( pins, ice cream stick or paper tape). However, the teacher should address that the smaller a measuring device holds, the measurement is more accurate. Let's say that if the teacher demands the most accurate measurement, then the students need to use the pins as it is the smallest amongst the others measuring devices.
- Schwartz (1995) claims that the children measure things based on individual purpose. Thus, in making learning experience more meaningful, teacher can come out with activities of making a portfolio, compiling the comparisons that they did so that they can show it to the families and friends later.
- Schwartz (1995) claims that the children measure things based on individual purpose. Thus, in making learning experience more meaningful, teacher can come out with activities of making a portfolio, compiling the comparisons that they did so that they can show it to the families and friends later.
These two pictures demonstrates indirect comparison of the perimeter of the table with ice cream sticks and pins. In order to get the most accurate measurement of the comparison, pins is a better option compared to ice cream sticks.* Tips : teacher can get the students to talk about the comparisons, for instance asking the students to describe what they did and what are the measuring devices that they used in this indirect comparison.
MAKING A MEASURING DEVICE
- Measuring device is an important element in this topic. Previously, we have been talking about factors to be consider in selecting the most appropriate units and indirect comparison in relation to standard and non standard. Thus, in this section, a further exploration on creating a meaningful learning experience addressing the topic of making our own measuring device will takes place.
- In establishing a learning experience to address this topic, firstly, teacher needs to provide the students with the materials. In this activities, several materials such as popcorn, cups and container ( see picture below) is needed.
The cups containing popcorn will dole out as 'measuring devices' in measuring the volume of other containers.In measuring the volume of containers ( picture below), cups of popcorn is one of the ways that can be used. Firstly, teacher needs to set up the students in group of three. The teacher explains to the students what they should do. The students need to fill the cups with popcorn and then pour it to the container as to see how many cups of popcorn will occupy the container. Thus, the number of cups = the volume of the container.
The picture shows the process of occupying the containers with the popcorn using the cup provided.
*Teacher should note the students that when they finish pouring the first cup of popcorn into the container, they need to mark the level of the popcorn using a marker pen. This is to track down how many cups have the students pour. That marks will helps the students not to get confuse.
The marks put indicates that the container is able to occupy four cups of popcorn, which means that the volume of the container is approximately equals to four cups of popcorn. The cups of popcorn acts as a measuring device which manages to measure the capacity of the container. Thus, this activity does engage the students in making measuring device.
As presented above, that container, let's name it container A. Container A manages to occupy four cups of popcorn. Then, teacher gives the students a bigger container, container B. As to make the challenge more changeling, the students needs to measure the capacity of the container B ( how many cups can the container hold), without using the cups. The students will use container A as to get the volume of the container B.
Container A has become a new measuring device in which it can be used to measure the volume of container A. Asking the students to justify their measuring device and how it works in measuring container B is a good activities as it stimulus the students reasoning and critical thinking skills. The dialogue between the teacher and students may seem to appeared as below.
Teacher : can we use container A as to measure container B?
Student : Yes, we can do that. ( Pour the popcorn in container A to B). Two containers A equals to one container B.
Teacher : What about the quantity of cups? How many cups fits into container B?
Student : Container A equals to 4 cups of popcorn. Meanwhile, container B equals to 2 times container A. Thus, container B equals to 8 cups of popcorn.
Student : Yes, we can do that. ( Pour the popcorn in container A to B). Two containers A equals to one container B.
Teacher : What about the quantity of cups? How many cups fits into container B?
Student : Container A equals to 4 cups of popcorn. Meanwhile, container B equals to 2 times container A. Thus, container B equals to 8 cups of popcorn.
The container A in this situation serves as a new measuring device that the students had created from the early process in which it equals to 4 cups of popcorn. Thus, this container can be used as to measure the volume of other big container namely container B.
Sunday, October 16, 2011
Workshop 3 ( Function)
FUNCTION
-Function generally describes the relationship between two set of numbers in which it is associated with one quantity, which is referred as the input with another quantity which is known as output.
- In teaching and learning function, one of the important notions that shouldn't be taken for granted is the integration of function machine. In producing a function machine, Wiloushby (1997) gives out an example on a function machine which is made up of a large box. The game started as a student comes in the box, in which an object is passed through him via input hole and he needs to push something via the output hole. The input could be a cocoa powder and the output is a bar of chocolate.
-Firstly, in integrating function machine, students should be encouraged to recognize how things change in relation to each other. Teacher should address the difference between qualitative and quantitative change. Qualitative change is quantity change, meanwhile qualitative change is the attribute change.
- The picture above shows an example of a function machine which can be used in the class. In getting the student understanding of the function machine concept, students should be encouraged to recognize the change in relation to each other. Get the students to describe the input and output by talking to the pairs regarding the differences of the input and the output, namely in terms of quantity or attribute change. Then, the students are asked to discuss about the rules that show how the input and output are related. In this example, the input/output change is quantitative change as the quantity changes, 1 at the input, and 2 and the output. The pattern shown in the function machine enable the students to draw a rule which best describes how the caterpillars change in quantity. Using the rule which best describe the relation between input and output, they need to fill the third column of the output. By leaving the third column of the output blank, this eventually helps in developing and enhancing multiplication skills of the students as to get the answer, they need to use their multiplication knowledge.
*useful tips : Function machine worksheet here give the students a choice of determining the rule, giving an input and the students need to determine the output. This serves as an exercise which enhance the student's skill of addition, subtraction, multiplication, and division.
Wednesday, October 12, 2011
Workshop 3 : Algebra ( Repeating pattern)
Hye, we meet again!! During my third workshop with Dr. Ann, we have been introduced to the concept of algebra. Algebra could be generally defined as a branch of mathematics dealing with relation, utilizing letters and and represent certain numbers or values. In relation to algebra topic, our attention was been drawn to the topic of ' pattern' and ' function'. These topics will be further explored in this entry in relation to provide a meaningful and hands on learning experience.
PATTERN
- Warren and Cooper (2006) classify two types of predominant pattern that a child explored in the early years, which is repeating pattern and growing pattern. Warren and Cooper (2006) put forward the notion that the learning of these patterns indirectly helps to children to develop their understanding of functional thinking, that is relationship between two data sets, at an early age.
- In teaching repeating patterns to the students, Papik ( 2007) recommended that children recognize and identify the repeating patterns better if they were immersed in meaningful experience.Those meaningful experience serves as a direction to the teaching and learning of patterns and algebra in the first years of schooling.
- Repeating patterns is a sequence or set which is repeated over and over. Liljedahl (2004) defines repeating pattern as a cyclic structure which is generated by repeated application of a smaller potion of the pattern itself. For example AB is a repeating unit of a pattern containing ABABABAB.
* Useful tips : In teaching repeating patterns to the children,teachers need to make sure that the children are able to recognize the core of the pattern.
In giving out a meaningful learning experience to the children which introduce and extends the understanding of repeating pattern, teacher can conduct the series of activities as below.
1) Recognize the pattern - at this stage, children needs to recognize the core of the pattern. Children needs to master this skill beforehand as the skill will be required in the next stage. The teacher can starts the lesson giving out an example of a repeating pattern.Taking example of repeating pattern of ABABABAB, this pattern will be displayed to the class ( see picture below). In getting the students to understand the concept of 'core', teachers can scaffold the learning process by giving out questions like
" What is being repeated in this pattern?"
" It is AB? Yes, AB is being repeated."
" Thus, what do we call AB? Yes, AB is the core of this pattern which eventually repeats itself, thus forming this pattern."
Warren and Copper advocates that patterns which is presented in a variety of different modes such as geometric shape appears to be more effective as it enhances the potential for generalizing the core of a pattern regardless of the mode. Taking that as a consideration, the teacher uses unfix cubes to represent ABABAB pattern horizontally. However, at the later stage where the students are required to copy and create the pattern, the students need to do it vertically in a tower pattern.
" It is AB? Yes, AB is being repeated."
" Thus, what do we call AB? Yes, AB is the core of this pattern which eventually repeats itself, thus forming this pattern."
Warren and Copper advocates that patterns which is presented in a variety of different modes such as geometric shape appears to be more effective as it enhances the potential for generalizing the core of a pattern regardless of the mode. Taking that as a consideration, the teacher uses unfix cubes to represent ABABAB pattern horizontally. However, at the later stage where the students are required to copy and create the pattern, the students need to do it vertically in a tower pattern.
2) Copy a pattern - at this stage,teacher sets the students to re-create the patter. In doing so, teacher can sets the students in pairs, get the students to talk to each other regarding the pattern that has been shown to them at the beginning of the lesson. It is important for the children to verbalize and describing the pattern to each other. Then, the teacher explains that they need to create the exact pattern except that they will do it vertically, in a tower form, until the 4th term only.
3) Extend a pattern- students should be able to continue a pre- established rule, in this context would be the rule of copying and re create the pattern which have been shown to them at the beginning of the lesson.
4)Create a pattern- using the unfix cubes of different colours which each represent the unit A and B, students need to create the pattern instructed by the teacher. It is important for the teacher to put forward the notion of maintaining a consistent rule in creating the pattern.
5)Translate a pattern- at this stage, justification of the student's pattern will be evaluated. In order to assess whether the students understand the concept of repeating patter, students should be encouraged to justify their pattern and the strategy used to solve the task. For example, the teacher can post questions for instance
Student's task : copy ABABAB pattern using the unfix cubes, forming a vertical tower pattern until the 4th term
3) Extend a pattern- students should be able to continue a pre- established rule, in this context would be the rule of copying and re create the pattern which have been shown to them at the beginning of the lesson.
4)Create a pattern- using the unfix cubes of different colours which each represent the unit A and B, students need to create the pattern instructed by the teacher. It is important for the teacher to put forward the notion of maintaining a consistent rule in creating the pattern.
5)Translate a pattern- at this stage, justification of the student's pattern will be evaluated. In order to assess whether the students understand the concept of repeating patter, students should be encouraged to justify their pattern and the strategy used to solve the task. For example, the teacher can post questions for instance
Teacher : What is the unit being repeated in this pattern?
Student : AB is repeated in the pattern.
Teacher: How do you know when you stop? How do you know not to put the cube
together anymore? ( pointing at the student's tower pattern)
Student : Because we need to put the AB cube four times only. This is
the first,( pointing to the AB cube at the tower ), this is the second, third and the fourth. When it comes to fourth term, we need to stop building the tower.
Student : AB is repeated in the pattern.
Teacher: How do you know when you stop? How do you know not to put the cube
together anymore? ( pointing at the student's tower pattern)
Student : Because we need to put the AB cube four times only. This is
the first,( pointing to the AB cube at the tower ), this is the second, third and the fourth. When it comes to fourth term, we need to stop building the tower.
The questions posted eventually develops the student's higher order thinking and reasoning skills. In fact, it serves as a evident which clearly demonstrate the student's understanding of concept of repeating pattern and concept of number of repetition as well.
Monday, September 5, 2011
References
-Bobis, J.; Mulligan, J.; and Lowrie, T. (2008). Chapter 9: Promoting Number Sense: Beyond Computation in Bobis, J.; Mulligan, J.; and Lowrie, T, Mathematics for children : challenging children to think mathematically, Frenchs Forest, NSW: Pearson Education Australia, pp.215-242.
-Clements, Douglas H. (1999). Subitizing : what is it? why teach it? Teaching Children Mathematics, 5 (7), 400-405.
-Clements, Douglas H. (1999). Subitizing : what is it? why teach it? Teaching Children Mathematics, 5 (7), 400-405.
-NSW Department of Education and Training. (2009). Five little ducks. Retrieved September, 2, 2011 from http://www.curriculumsupport.education.nsw.gov.au/countmein/parents_five_little_ducks.html
-NSW Department of Education and Training. (2009). Ten Fat Sausages. Retrieved September, 2, 2011 from http://www.curriculumsupport.education.nsw.gov.au/countmein/parents_ten_fat_sausages.html
-The Origo Handbook of Mathematics Education. (2007). QLD: Origo Education
-Clements, Douglas H. (1999). Subitizing : what is it? why teach it? Teaching Children Mathematics, 5 (7), 400-405.
-Clements, Douglas H. (1999). Subitizing : what is it? why teach it? Teaching Children Mathematics, 5 (7), 400-405.
-NSW Department of Education and Training. (2009). Five little ducks. Retrieved September, 2, 2011 from http://www.curriculumsupport.education.nsw.gov.au/countmein/parents_five_little_ducks.html
-NSW Department of Education and Training. (2009). Ten Fat Sausages. Retrieved September, 2, 2011 from http://www.curriculumsupport.education.nsw.gov.au/countmein/parents_ten_fat_sausages.html
-The Origo Handbook of Mathematics Education. (2007). QLD: Origo Education
| -Perry, Bob and Dockett, Sue. (2002). Ch 5 : Young Children's Access to Powerful Mathematical Ideas in English, Lyn D (ed), Handbook of international research in mathematics education, Mahwah, NJ: Lawrence Erlbaum Associates, pp.81-111. |
Mental Computation Strategies
Mental computation Strategies
In solving the problem, 26 is split up to 20 and 6. Thus, 38 plus 20 equals to 58. We still have six remaining thus 58 plus 6 equals to 64. Beside, the students can as well split the 26 to 10, 10 and 6. By splitting a big number to a small one, it makes thing easier to the students. During the splitting process as well, it is important that the teacher prompt questions like
" why splitting 26 to 10, 10 and 6?",
"it is the still the same if 26 is split to 20 and 6?".
Those kind of questions eventually engages the student's reasoning and critical thinking skills as it gets them to think and viewing thing from different perspective.
Example of 100 chart
In promoting addition and subtraction skill in activities promoting mental computation, hundred chart can be used as well. In solving mathematical problem involving large numbers, hundred chart is effective compared to ten frames.
* Important note : In hundred charts and number line, there are several strategies involved. They are -splitting to tens backward, or forward,
-jumping to the nearest tens backward and forward
- add numbers if take away
- minus numbers if add on
It is crucial for teachers to address this in engaging the students with hundred charts and number line.
Bobis, Mulligan and Laurie ( 2008) defines mental computation as an ability to mentally calculate addition and subtraction based on knowledge of number facts. In this strategy, it is important for the students to be able to use another alternative to decompose two digit numbers for addition and subtraction. The integration of mental computation skills in early number frameworks enables the development of robust number fact knowledge based on number sense.
In solving the problem, 26 is split up to 20 and 6. Thus, 38 plus 20 equals to 58. We still have six remaining thus 58 plus 6 equals to 64. Beside, the students can as well split the 26 to 10, 10 and 6. By splitting a big number to a small one, it makes thing easier to the students. During the splitting process as well, it is important that the teacher prompt questions like
" why splitting 26 to 10, 10 and 6?",
"it is the still the same if 26 is split to 20 and 6?".
Those kind of questions eventually engages the student's reasoning and critical thinking skills as it gets them to think and viewing thing from different perspective.
Example of 100 chart
In solving problem like 72 - 25 = 47, the student can jump from 72 to 70. 25 is splitting up to 20 and 5, thus from 70, the students minus 20 and land at 50. From there, 50 minus 5, and lands at 45. As the 72 jumped to 70 and take away two, we need to plus two, thus it lands at 47.
* Important note : In hundred charts and number line, there are several strategies involved. They are -splitting to tens backward, or forward,
-jumping to the nearest tens backward and forward
- add numbers if take away
- minus numbers if add on
It is crucial for teachers to address this in engaging the students with hundred charts and number line.
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