::References::

Papic, M. (2007). Promoting repeating patterns with young children - More that just alternating colours. Australian Primary Mathematics Classroom, 12(3), 8-13.

Warren, E., & Cooper, T. (2006).  Using repeating patterns to explore functional thinking. Australian Primary Mathematics Classroom, 11(1), 9-14.

Images

[Photograph of a cute shy girl wearing a pink dress and pig tails]. Retrieved October 29, 2011, from: http://www.pamsclipart.com/clipart_images/cute_shy_little_girl_wearing_a_pink_dress_and_pig_tails_0515-0910-2919-0941.html

[Photograph of 3-D shapes]. Retrieved October 29, 2011,from: http://www.google.com/imgres?q=3d+shapes&hl=en&biw=1280&bih=642&gbv=2&tbm=isch&tbnid=cuBLSMAGLMHUbM:&imgrefurl=http://janelanguagelearning.blogspot.com/2010/05/langauge-of-3d-shapes.html&docid=ABl4-G7fJgoxNM&imgurl=http://1.bp.blogspot.com/_q1VAgiM7ILY/S-y-p8dzYkI/AAAAAAAAAWE/tEBpHg39fBQ/s320/3d_shapes_2dr3.jpg&w=242&h=187&ei=nleuTr3nJ-jEmQWEj-XuDg&zoom=1&iact=hc&vpx=893&vpy=344&dur=1792&hovh=149&hovw=193&tx=128&ty=65&sig=104975189844656493803&page=1&tbnh=123&tbnw=159&start=0&ndsp=21&ved=1t:429,r:12,s:0

[Photograph of ‘feel box’]. Retrieved October 29, 2011, from: http://www.google.com/imgres?q=feel+box&num=10&hl=en&gbv=2&biw=1280&bih=642&tbm=isch&tbnid=5thiZVhCwR4c4M:&imgrefurl=http://www.pattersonmedical.com/app.aspx%3Fcmd%3Dget_product%26id%3D81644&docid=DMCXVVMdf8e2TM&imgurl=http://www.pattersonmedical.com/content/images/SPRProductImages/Regular/8343.JPG&w=260&h=235&ei=sFiuTofXJOqviQfTmYjwDw&zoom=1&iact=hc&vpx=747&vpy=153&dur=2167&hovh=188&hovw=208&tx=127&ty=93&sig=104975189844656493803&sqi=2&page=1&tbnh=135&tbnw=141&start=0&ndsp=18&ved=1t:429,r:3,s:0

[Photograph of 2-D shapes]. Retrieved October 29, 2011, from: http://www.google.com/imgres?q=2d+shapes&start=21&num=10&hl=en&gbv=2&biw=1280&bih=642&tbm=isch&tbnid=46zevg8cD6g8pM:&imgrefurl=http://www.tts-group.co.uk/shops/tts/Products/PD1723468/2D-Shape-Set/&docid=Hdd7VPOjS4LfoM&imgurl=http://www.tts-group.co.uk/_rmvirtual/media/tts/images/legacy/M2DS.jpg&w=552&h=398&ei=v1muToeBDIbGmAWby4XHAg&zoom=1&iact=hc&vpx=822&vpy=334&dur=796&hovh=191&hovw=264&tx=164&ty=88&sig=104975189844656493803&sqi=2&page=2&tbnh=127&tbnw=184&ndsp=18&ved=1t:429,r:10,s:21

[Untitled photograph of Mathematics for children]. Retrieved October 29, 2011, from: http://www.google.com/imgres?q=2d+shapes&start=179&num=10&hl=en&gbv=2&biw=1280&bih=642&tbm=isch&tbnid=Z4034x8v6MWmhM:&imgrefurl=http://whatsthebuzz.edublogs.org/2011/03/19/2d-shapes/&docid=zxDlkR4NrhqblM&imgurl=http://whatsthebuzz.edublogs.org/files/2011/03/IMG_0265-1htydk7.JPG&w=2592&h=1936&ei=HVuuTpvVLebJmQXwjsnADg&zoom=1&iact=hc&vpx=213&vpy=315&dur=3271&hovh=139&hovw=187&tx=65&ty=72&sig=104975189844656493803&sqi=2&page=10&tbnh=125&tbnw=172&ndsp=19&ved=1t:429,r:13,s:179

[Untitled photograph of Mathematics for children]. Retrieved October 29, 2011, from: http://www.google.com/imgres?q=2d+shapes&start=179&num=10&hl=en&gbv=2&biw=1280&bih=642&tbm=isch&tbnid=8dOcrAxga7ELrM:&imgrefurl=http://whatsthebuzz.edublogs.org/2011/03/19/2d-shapes/&docid=zxDlkR4NrhqblM&imgurl=http://whatsthebuzz.edublogs.org/files/2011/03/IMG_0261-1lks1o7.JPG&w=2592&h=1936&ei=cluuTvrEG4z3mAXknMTbDg&zoom=1&iact=hc&vpx=370&vpy=296&dur=500&hovh=125&hovw=176&tx=150&ty=99&sig=104975189844656493803&sqi=2&page=10&tbnh=125&tbnw=176&ndsp=19&ved=1t:429,r:14,s:179

::Short Story about Time::

"Sorry, the time is running out!"

 

Today, Cassandra has three birthday party invitations at her friends house, Joshua, Liam and Erinne.  

Unfortunately, the time of the birthday party is the same! The party will start from 11 o’clock in the morning until 1 o’clock in the evening. So, she has 2 hours to go to the three houses.

What should Cassandra do to be able to go to the three houses?

Cassandra decides to go to Joshua’s house because his house is the nearest. After that, she will go to Liam’s house and finally, to Erinne’s house.  

From Joshua’s house, she has to ride her bicycle for about 15 minutes to go to Liam’s house. Then, from Liam’s house, it will take another 20 minutes to go to Erinne’s house. So, all together her journey will take 35 minutes.

  
Now, there is another 1 hour and 25 minutes left. She divides the time and she has 30 minutes to spend at Joshua's house, 30 minutes at Liam’s house while another 25 minutes to spend at Erinne’s house. 

At 11 o’clock in the morning, she arrives at Joshua’s house. After she gives the present to Joshua, she eats the food that Joshua’s mother prepared. 

At 11.30 o’clock in the morning, she thanks Joshua and tells him that she has to go somewhere. Joshua asks her to stay for a little while for cake time. But she says; “sorry, the time is running out!” and she goes to Liam’s house quickly.

After 15 minutes riding the bicycle, she arrives at Liam’s house. Luckily, Liam is about to cut the cake while everybody is singing. Cassandra gives the birthday present, joins the singing and eats the cake. 

After 30 minutes, at 12.15 o'clock in the afternoon, she thanks Liam and tells him that she has to go somewhere. Liam asks her to stay for a little while to join the games but she says; “sorry, the time is running out!” and goes to Erinne’s house quickly.

At 12.35 o’clock in the afternoon, she arrives at Erinne’s house. At Erinne’s house, Cassandra gives the birthday present and joins the games that they are playing. 

Finally, at 1 o’clock in the evening, the games finish and everybody is going home as well as Cassandra. She thanks Erinne and then going home happily. 

Cassandra is very happy today because she managed to go to all three birthday parties and spent a good time there.         
 

::Measurement::

Examples of activity that the teacher could do in the classroom to teach the children about measurement.

Activity 1: Selecting appropriate units

In pairs, ask the children to measure the length of the desk, whiteboard, notice board and the rectangle play mat by using their hands or steps in order to measure the objects. 

After that, ask them to measure the width of the objects.

Each pair should record the data in the table provided. 

Activity 2: Indirect comparison

After that, ask the children to move around the classroom and find another objects that have the same length and width with the objects that they have measure. Write the answer in a piece of paper.

Then, ask them to move around the classroom and find another objects that have different length and width of the objects that they have measure. This time, they have to write the answer in a piece of paper and give the reason why they think those objects have different area (e.g. The area of the desk is more than the area of the chair because the desk is bigger than the chair)

Activity 3: Making a measuring device

Let the children compare their answer with other pairs in the classroom. Develop their knowledge by asking why are the length and the width of the objects that they have measure are different with their friends? Tell the children that the answers are different as they are using their hands and steps which are different sizes with each other.

After that, teach the children to use measuring device to get a more accurate answer. Teach them the steps to make their own measuring device. For example:

•  Provides the children with a roll of paper streamers to make a measuring device.
• Choose one object to be the bigger unit such as the ice cream stick. Ask the children to make the measuring tape by using the ice cream stick as the bigger unit. Remind the children to label the measuring tape with numbers accordingly. 
• After that, repeat the same sequence by using paper clips as the smaller unit.

Finally, ask them to measure the objects that they have measure during the first activity by using their own measuring device and record the data in the table. 

For example, the length of the desk is 7 ice-cream sticks and 2 paper clips while the width of the desk is 5 ice-cream sticks and 3 paper clips. Every children will get the same answer as they are using the same measuring device that has the same units, which are; ice-cream sticks and paper clips.

A roll of paper streamers as the measuring device.

Measuring device by using paper clips as the unit.

::Geometry = Location and direction::

Example of activity that the teacher could do in a classroom to teach about location and direction:

Divides the children into pairs. One person in each pair will get a map and direction while the other person will be eyes closed. 

Basically, the person who have the map and direction have to give directions to their partners by using the map provided. Remind the children to give the direction verbally, without touching. 

This game could be conducted at the school field rather than in the classroom as the children will need more space to do the activity. In addition, each pair has to collect 6 stickers from the checkpoints in order to ensure that they are on the right track. 

The first pair who arrives the finish line will win the game. 

Example of map and direction (at the school field)

::Geometry = Focus on shape attributes::

Examples of activity that the teacher could to in a classroom to teach about shape attributes:

Provides the children with several 2-D shapes set.

A set of 2-D shapes.

Write the descriptions that focus on shape attributes on flash cards (e.g. riddles). Ask the children to guess and pick one shape that matched the descriptions given.

For example:

I have 4 equal sides. People always see me at the floor that made up from tiles. Who am I?

(Answer: Square)

Furthermore, the teacher could also ask the children to work in groups and form the 2-D shapes together. For example, if the teacher asks the children to form a circle, the children in each group have to hold their hands and form a circle. In addition, if the teacher asks the children to form a rectangle, the children might have to lay down and form a rectangle together. 

The children is forming a circle.

The children is trying to form a rectangular.

::Geometry = Visualizing::

Example of activity that the teacher could to in a classroom to teach visualizing:

Teach the children about 3-D shapes such as cube, cuboid, cone and pyramid.

 
Ask the children 'feel' the shape by imagine themselves inside that particular 3-D shape, and ask them to identify and show how many sides and faces do the shapes have.

The teacher could also encourage group competition where in groups; the children have to guess and identify what shape does the group representative or the teacher is trying to show in front of the classroom. The group that has the highest mark will win the game. 

After that, individually, give them a 'feel box' and let them guess and pick the correct shape according to the teacher's instruction. For example: " Pick me a shape that has 6 square faces and 12 equal sides". (the answer is cube)

The children is using the 'feel box'.

::Algebra = Functions::

Functions enables the children to:-

• Recognize and identify how things change in relation to each other.
• Describe the change in pictures or words,etc
• Describe the rules that show how things are related

Teachers can teach children about functions by using the 'Function Machine'. Let us see how this machine operates...

Input = small green circle / Output = big green triangle

  

Input = small yellow circle / Output = big yellow triangle

Can you identify the input in Figure 1.3 and the output in Figure 1.4?

(Yes! The answer is: In Figure 1.3, the input is small blue circle while in Figure 1.4, the output is big red triangle.)   

Now, let's see how this 'Function Machine' operates using numbers....

Can you identify the missing numbers?

(Answer: The output for number 8 is 17 while the input for number 7 is 3) 

How can you get the answer?

Basically, the relation between the numbers is ( 'input' x 2) + 1. For example, if the input is 2; (2 x 2) + 1 = 5, so, the output is 5.

   

::Algebra = Repeating patterns::

“Repeating patterns are patterns where a group of elements repeat themselves as the pattern extends” (Warren & Cooper, 2006,p.10)  

This core is the smallest element of the repeating pattern. It should be repeated at least 3 times. For example, Ä O is a core or element of a pattern containing Ä O Ä O Ä O (Papic, 2007).

Sequence for exploring repeating patterns  

1.      Copying the pattern

a.       Draw the following patterns on a piece of drawing block and ask the children to copy the pattern using triangles and squares.

2.        Continuing the pattern

a.       Let the children guess the patterns that come next and before. Ensure that the children know that the patterns can be repeated in both directions.

3.      Identifying the repeating element

a.       Say the pattern out loud (e.g: triangle, square, triangle, square, triangle, square,..). Using a pencil, ask the children to circle the repeating parts.

4.      Completing the pattern

a.       Draw another repeating pattern, ask the children to continue the patterns and identify the repeating parts. With the children’s eyes close, remove some elements of the repeating patterns and ask the children to guess what the missing parts are.

5.      Creating a pattern

a.       Encourage the children to create their own repeating patterns. Enhance their learning by asking; why is it a repeating pattern? How can you continue this pattern? What is the repeating element?

6.      Translating a pattern to a different medium

a.       Develop their knowledge by encourage them to create repeating patterns by suing different medium such as ‘clap, step, clap, step, clap, step,…’ instead of ‘triangle, square, triangle, square, triangle, square,…’ 

Example of activity that the teacher could do in a classroom in order to introduces and extends understanding of repeating patterns to young children:-

1. Draw the pattern

 

·         2. Cover half of the pattern and only 1 set is visible

·         3. Ask the children; “How many green circles are there? How many blue circles are there?   How many circles all together?”

·         4. Ask them to record the data in a table (see Table 1)

·         5. Uncover the pattern and show two sets of pattern. Continue the sequence until there ar five sets visible.

·        6. Examine and analyse the table. 

Table 1

No. of set	No. of green circles	No. of blue circles	Total number of circles
1	1	2	3
2	2	4	6
3	3	6	9
4	4	8	12
5	5	10	15

Children might be able to examine the data recorded:-

"Green circles is increasing by 1"

"Blue circles is increasing by 2"

"The total is increasing by 3"

 

 

Furthermore, teachers might ask several questions to generalize children's thinking such as:-

If I had 10 green circles, how many blue circles would I have?

If I had 30 green circles, how many blue circles would I have?

If I had 40 blue circles, how many green circles would I have? How many sets of circles would I have?

If I had 100 sets, how many green circles would there be and how many blue circles would there be?

Finally, teachers also can make the lesson more challenging. This will help the children to develop their knowledge skills of early algebra. For examples:-

·         2, 4, 6, 8, 10, …. = What is the 12^th term? (Answer = 24)

o   Children can find the answer by continue the number sequence until 12^th term; 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24,…

o   Basically, the children will have know the answer by multiply the term with 2; 12 x 2 = 24. This is because if the 1^st term is 2, then the pattern will be the term multiply by 2.

·         1, 3, 5, 7, 9,… = What is the 10^th term? (Answer = 19)

o   This is quite challenging as it is odd numbers. Basically, the children will get the answer by continue the number sequence until 10^th term; 1, 3, 5, 7, 9, 11, 13, 15, 17, 19,…