This a digital story book created by me focusing on aspect of time. It is about a child visiting a local annual hot air ballon festival. the setting is Malaysia which is familiar for my students. It can also be used by other teachers since hot air balloon is a common topic for most children. this is originally done using Power Point Presentation. Teachers will also need a paper analog clock or a real clock to highlight the time to the students during the shared reading. example of analog clock:
The story~
Hot air balloon pictures references:
Samlee860407 (2010). The royal Kedah international hot air balloon festival @ alor setar, Kedah. Retrieved October 25 from
Teachers can make a big tree trunk and beanstalk on the class floor using cardboards for the trunk and green paper for the beanstalk. The teacher will be the Giant . Then, students will need a small note book to jot down their answers.
For indirect comparison ,the teachers asks students to compare the height of the big tree with the height of the classroom tables, windows, chairs and the Giant. Students will have to stand or even lie down near the tree to make comparison. They will then need to write which object is taller or shorter than the big tree in their note book.
The teacher can also teach measurement by using non standard units. First, students will be asked to select a large unit such as their hands, feet, books and etc. Next they will use their selected units and measure the height of the big tree. eg:
big tree = 10 hands
After that, the teacher will ask students to choose a smaller unit such as eraser, coin and etc. Next, they will measure the big tree with the smaller units. eg:
big tree = ....coins
The teacher would then highlights on the different of the units by asking
T: which unit you use less when measuring the big tree?
S: the large unit~
T: which unit you need more to measure the big tree?
S: the small unit
T: So, the larger the unit, the fewer you need to measure an object. But, sometimes, you need a smaller unit to measure small objects. Can you give me some examples small objects that need to be measured using small units?
S: a book, a bottle and a pencil case.
Making measuring devise for the Giant
Students will work in groups and the teacher, as the giant will tell the students that they need to give back the magic beans and it will be 4 cups of beans in a container. Then, the teacher will give each group a cup, a container, a jar of green beans and a marker. Students will then will have to put one cup a time into the container and label the container with the marker at the level of each cup. After they finish labeling the 4 cups of beans, the teacher then ask questions such as "are you sure that you have put 4 cups of beans, the giant will be really angry if it's not correct. why don't you check it by putting the beans from the container into the cup". these would scaffold their comprehension on the fact that each level that that they had label is equal to one cup and vice versa. Finally, each group will present the container with magic beans to the giant. It's so easy~^^
Teachers can ask students to visualise a the table from the top and how it looks like. Then students are required to look for other object in the classroom that they can visualise into a shape. They could write the objects into a table. for example
In order to extend their understanding on shape attributes, teachers can teach students by using cooked or uncooked spaghetti:
Spaghetti is a good resources to teach kids in focusing to shape attributes. First, teachers can ask students to make the shape that they had visualised and wrote in the table. Then, teachers can highlight on the shape by asking questions such as"how many sides is there in the triangle?" "what do you think about the size of the sides in the triangle?are they the same?". These could be done with different shapes and the cooked spaghetti can be used for shapes for instance, oval or circle.
Location & Direction
Firstly, teachers need to introduce to students the concept of right, left, forward and back. This video would be use to introduce the concepts before moving on to the next game:
Tourist map
This is a big map of a tourist spots in a small town located in Malaysia. It was made highly suitable for my Malaysian students since they would be familiar with the name of places, and road's names. Other teachers can just change these to be used in own respective class. The map is big for teachers to put it in front of class. Teachers could also make the map for each group.
What do you need to play this game:
1.the tourist map
2. a counter for each group to move
how to play this game:
1. students will be divided into groups of four. then, they will choose a counter.
2. The teacher will demonstrates how the game will be played where each group will be a tourist guide and receive a mission to show direction to tourists in order to go to certain tourists spots. for eg:
"show the tourists how to go from Shangri-la Hotel to the garden."
Then, the group will discuss the direction and show to the whole class how they go to the location using their counter.
3. The teacher starts the game and facilitates the game by scaffolding them using questions such as "where will you turn after that?left or right?"
Teaching repeating patterns to children can be done by using music.
1. The teacher can show these simple musical instruments and then do a demonstration in order to show repeating patterns for eg:
drum, chime bell; drum, chime bell; drum, chime, bell
2. After that the teacher can ask students "what is the sounds that I have made?what instruments have i used?what were the patterns of the sounds?"
3. Students then can try making their own repeating sounds patterns using objects in the classroom or body movements for eg:
clap hands, knock on the door, sounds of pencil case and etc.
This activity would make students understand the concept of repeating patterns better since children could relate to sounds and it will enable them to use their creativity in creating patterns. Teachers could extend this activity by making it more fun by recording the sounds made by students and present them to the whole class.
Function machine: qualitative change
Firstly, teachers can show video on Dr. Seuss Star Belly Sneetch machine to introduce the function machine and how it works(Jack cough on software, 2009):
starting from 4.45, students could clearly see how a function machine works.
In order to enhance their understanding on the function machine, teachers can ask questions such as
T: how do the sneetches look like before they went through the Star Belly machine?
S: they do not have any star on their belly
T: how about after they went through the machine?
S: they have a star on their belly!!
Then teachers can relate to the state before the sneetches have stars as the 'input' and after they got stars as the 'output'. Besides, teachers can also explain to students that the Star Belly machine is a function machine that will change something that went through it. After that, teachers can show pictures of objects so that students can use their prior knowledge about Star Belly machine to understand qualitative change in function machine.
Teachers can ask question such as: "what was the colour of the square before it went through the function machine?", "what about the star?". Then, students will guess what would happen to the rocket. This activity is fun and students will definitely understand the function machine by using Cartoon as they could relate to it better.
1·For the second workshop, I have broaden a little bit my "mathematical horizon" as I explored on subitising, counting, number sequences, addition/subtraction, multiplication, number facts strategies and mental computation. So, I would explain on some of the strategies that adults particularly teachers can practice in order to support the development of these skills which are important for students in order to move to the next stage in growing up with math. 1. Subitising
Children acquire sight recognition of a quantity in subtising where they can automatically know the numbers of objects when they see them (Clements, 1999). Children may develop this ability through mathematical knowledge such as the domino pattern or without them (Clements, 1999). In classroom, teachers can use subitising flash cards (picture below)to teach this skill where numbers are represented via the dots on the cards.
Besides, the koala race game is also suitable to teach children subitising where they can play in groups. Each student will have 1 koala as a counter, then, they will take turn in throwing the dice and the counter can move forward if their chosen number appears on the dice. The winner is the first person who reaches the final.
The fly swatter game is also challenging and enjoyable where it is also played in groups. One person will place the cards and the others will have a fly swatter each person. They have to snap numbered cards that appear twice. Thus, children’s automaticity in subitising can be enhanced through this activity.
·
2. Counting
There are many ways to teach children how to count. Teachers or parent can use story books which are interested for the children. In illustration, My big book: Winnie the Pooh is suitable for children to learn counting through shared reading whereby the characters introduce the numbers in a sequence and there are also colourful pictures which appeal to them. Teachers can ask guiding questions such as:
what number do you think come after number 2?
can you count how many bags of carrot rabbit has in this story?
These questions will be able to support students to count in meaningful context.
Additionally, technology is also a great choice in teaching children counting skills since they love using technology in learning. For example, in babyfirsttv.com, there are many fascinating videos for children in supporting their learning including counting. The picture beside is on counting one until five where there are 5 chicks and children can follow the video in counting the chicks. Children can also play games which are available in this website.
3. Forward number word sequence/number word after/backward number word sequence/number word before
For these skills, teachers can give children big numbered cards and ask them to arrange them on a cloth line using cloth pegs. For example, for number word sequence, they would arrange from 1,2,3,4,5,6 and etc. They can also comprehend the ideas of number word after, before and backward as they move the cards according to teachers instructions and questions such as:
where do you think number 5 should be?, beside which number?
what is the number before number 11?
lets read aloud the numbers backward starting from number 12
This activity is also appeal for children as it involve active participation and movement in classroom. Teachers can also ask children to hold the cards and arrange themselves in order to enhance these skills.
·4. Early addition/subtraction
Children can practice these skills using concrete objects before they can do addition and subtraction abstractly in their mind (Smith, 2009). Teachers can use many concrete objects which are usually used for counting such as sticks, pebbles or beads. For instance, tens frames can be used to teach addition and subtraction as children can build a clear picture in their mind for computation before they can move on to mental computation.
addition
Eg: 3 + 2=
Children can use different coloured counters in order to understand the addition. So, 2 greens plus 3 purples equal to 5. The answer is 5
subtraction
Eg: 5 - 2 =
1.
There are 5 koalas on the coach, 3 reds and 2 greens.
2.
Take away 2 green koalas
3.
So, there are 3 red koalas left on the coach now.
It is easier for children if teachers associate colours in teaching addition and subtraction since they can easily see the idea of 'adding to' or 'take away'.
·5. Early multiplication/division multiplication- teachers can show the multiplication table for children to show that multiplication is by adding sets of equal numbers;for example the table below which explains that 2 multiply by 2 is 2 smiles + 2 smiles.so, the answer is 4. Besides, by using pictures to explain multiplications, children would understand the concept better.
division- teachers can use the idea of sorting; for example, 6 ÷ 2=, teachers can explain using the stars in picture below that 6 stars divided equally in 2 based on their colours would produce 3 groups of stars. The different colours can help children in comprehending that the stars has been divided equally according to their colours.
Teachers can also let children play this fun leap froggy division game as they become better in division. The game can be played in groups where each person would take turn in throwing two dices. For instance, the number on the dices are 4 and 6, so, the person can choose the number 46 or 64. Then this number need to be divided by 6 which the full number of a dice. For example, he/she chose 46, so, 46 ÷ 6 = 7 and the balance is 4. Then he/she can move the counter to number 4. The winner is the first person who reaches the final.This game is very exciting and can improve children division skill.
6. Number facts strategies for either addition and subtraction or multiplication and division
addition
6 + 9 = ?
6 red dots and 9 black dots.
one of the red dots will fill in the tens frame and the answer is 15.
children could clearly see this process as the card is folded under to show the changes of red dot.
multiplication
This card can show to children that 10 × 4 is the same with 4 × 10 which equal to 40.
Then, the card can be folded upward to hide the 10th row and show that 9 × 4 is the same with 4 × 9 . The answer is 36.
7. Mental computation strategies
Teachers can teach mental computation by using hundreds chart especially when solving bigger numbers. There are two types of hundreds chart which are zero hundreds chart and one hundreds chart. Children can use one counter to practice this skill; for example:
using one hundreds chart, 57 + 24 =
1. Firstly, put the counter on number 57
2. Then, move two row downward which also means add 20
3.Finally, move 4 box forward to number 81 which means add another 4. So, the answer is 81
Reflection
When I was in in primary school, I first learnt computation by using fingers and then using pebbles as counters. In learning addition and subtraction, my teacher used language such as add, minus or take away in order to understand the concepts. Then, I moved to using computation using numeral numbers; in illustration, to solve 3 + 2, we would have the standard pattern of,
3
+ 2
----------
5
------------
This pattern would be used in learning addition, subtraction as well as multiplication. For division, I usually use
The most interesting things is that I have just realise that there are many other ways in solving mathematical problems for children, after the second workshop. In my opinion, I was drilled to use these solutions during my primary school that I did not explore on other ways in solving addition, subtraction and etc. Besides, these are the standard answers required when answering exam questions in Malaysia as we need to show the computation for exam. I think teachers should let children to explore various ways in learning computation so that their mind would not be rigid to one way in computing numbers. Thus, in future, I would let my students to have their own creative thinking in solving mathematics in order for them to have a better comprehension on mathematical concepts. it is also due to the fact that mathematic is a 'maze' and I should let them use different path in order to get to their destination.
References:
Clements, D. H. (1999). Subitising: what is it? why teach it? Teaching children mathematics, 5 (7), 400 - 405. Retrieved from Queensland University of Technology Course Materials.
Milne, A. A., & Shepard, E. H. (2010). My big book: winnie the pooh. Bath: Disney Enterprises Inc.
Smith, S. S. (2009). Early childhood mathematics. Boston: Pearson.
Division [ Image]. Retrieved August 29, 2011, from coolmath4kids.com
