Picture Graphs

A graph is a pictorial representation of data. In Primary 1, pupils have learnt picture graphs based on one-to-one representation (i.e. using a symbol to represent 1 object).

In Primary 2, pupils learn to read, interpret and draw picture graphs with scales, with each symbol could represent more than 2 objects.

Pupils are lead  to see the need for using a scale when the numbers are large. Pupils are also exposed in both horizontal and vertical forms of picture graphs.

The data presented in the graphs should be related to students‟ experiences and interests, e.g. their favourite flavor of ice cream, favourite sport etc.

There will not be any use of incomplete symbol / picture at their level.

LEARNING OUTCOMES

 *Make picture graphs with scales

*Read and interpret picture graphs with scales

 *Solve problems using information presented in picture graphs

Volume

What is volume?

Volume  of an object refers to the amount of space it occupies.  In Primary 2,

students learn that the volume of water/liquid refers to the amount of water/liquid occupying the

space in the container.

The capacity of a container, the amount of substance it can hold, will be introduced in Primary 3.

Students also learn to measure and compare volumes or amounts of liquid using one of the

following methods:

*By pouring the amounts into identical containers and comparing their heights,

 *By pouring each amount into small and identical containers and counting the number

of units (the amount in each small container is a non-standard unit),

*By measuring the amount of liquid using a standard unit such as the Litre.

Notes:

*Students have not learnt decimals therefore use the terms more than or less than 1 litre when explaining or comparing volumes of liquid to students.

*Volume of solid will be taught in Primary 5.

That's all for now. :)

Time

Notes

 

1.   Hour hand -shorter hand

      Minute hand - longer hand

  

2.   Reading the hour hand can be a problem for students   especially when it is pointing between two numbers. It is a good habit for them to draw a line, extending the hour hand. This enables them to see clearly.

In addition, they can take also take note of the minute hand. As long as the minute hand hasn't point to the number 12, the hour hand refers to the earlier of the two numbers.

For example, in this case the arrow is pointing between 2 and 3. From the red line, it is clear that the hour hand hasn't reached 3. Therefore, it cannot be 3 O' clock but 2.55 in this case.

3. It is important for students to know where to draw the hour hand. It depends heavily on where the minute hand is pointing to. Therefore, where one draws the hour hand,  is important as it represents the movement of a clock.

(Observe the hour hand in each picture)

 

 

 

 

If the minute hand is between 1 - 4 ( 5- 20 minutes), then the hour hand should be drawn slightly after 11.

 

 

 

If the minute hand is between 4 - 8 (25-40 minutes), then the hour hand can be approximately in the middle, between 11.00 and 12.00.

 

 

 

 

If the minute hand is between 9-11 (45-55 minutes), then the hour hand should be drawn nearer to 12.00.

 

 

4.  A.M and P.M stand for Ante Meridian and Post Meridian respectively. They are latin words which mean "before midday" and "after midday".

The terms 12 a.m and 12 p.m may cause confusion and should not be used. Therefore, it is advisable to use the terms 12 noon and 12 midnight.

Learning Outcomes
-tell and write time to 5 minutes ( in terms of the minute hand, every 5 minutes)

-Use a.m and p.m to differentiate between morning, afternoon and evening

-Use abbreviations h and min

-Draw hands on the clock face to show time

-derive the duration of one hour/half hour from an o'clock face.


That's all! Thank you :)

 

 

Feedback on Fractions

1) Identifying whether a fraction or a part is required.

Some students have difficulty identifying what the question wants, whether a part or a fraction. For example, if the question has a statement like" ____________of the figure is shaded." , this requires pupils to write a fraction; meaning there should be a numerator and denominator.

However, for questions which require a number for an answer, the questions will have the word pieces/parts in them for example
" ________ parts of the figure is shaded?"
(Refer to examples below)

Pupils wrote the numbers instead of fractions.











 














2) Unit Fractions

Unit fractions are fractions with 1 as their numerators. For example one- fifth, one quarter, one - half.

When comparing unit fractions, students can use this statement to guide them. "The larger the denominator,the smaller the unit fraction." Another translation will be "the more people sharing a cake, the smaller the portion each person will receive."

(taken from http://www.freewebs.com/workstattion/MATH/fractions/activities.htm)

From the figure above, one can see that the larger the denominator,

the smaller the portion of one unit is

3) Fractions that make a whole

From the example given (refer to picture below), the student is unable to see that 1 whole is actually the full fraction, in this case, 4/4. In order to get the fraction for the whole, one can retrieve the information by looking at the denominator of the other fraction given.

Therefore, the answer should be 1/4 and 3/4 make 1 whole (4/4).

 That's all!

Fractions

Dear Parents,

For your reference.

The concept of fractions provide the children with opportunities to make sense and relate to the language and notation of fractions using everyday examples such as pizzas or birthday cakes that are round and chocolate bars that are rectangular.

Similarly, fractions doesn’t apply on round/ rectangular objects only, they apply generally to various types of shapes, including triangles.

Fractions are numbers; which tell us how much of a whole it represents.

For example; when a whole is divided into 2 equal parts, 1 out of 2 equal parts is represented as 1/2.

The total number of equal parts is called a whole and known as a denominator as for the number of the items cut/shaded/taken is known as a numerator.

Learning Outcomes:

·         Interpret a fraction in terms of equal parts of a whole

·         Read and write fractions

·         Compare and order

-unit fractions (same numerator eg 1/2, 1/3)

-like fractions ( same denominator eg 2/5, 4/5)

·         Add and subtract like fractions within one whole

*Students are not required to learn fraction as part of a set of objects (eg  of 20) as this will be dealt with in Primary 4.

Thank you

Money

Dear Parents

For your reference.

Learning objectives:

• counting the amount of money in a given set of notes and coins
• reading and writing money in decimal notation
• comparing 2 or 3 amounts of money
• converting an amount of money in decimal notation to cents only and vice versa
• solving word problems involving money in dollars only (or in cents only)

Preparation for this topic goes back to the early part of the year. Click HERE to read more about it.

Some Important Notes

1) We read $15 as 'fifteen dollars' but some children may write it as '15$'. Children need to be mindful of the difference in speech and writing.

2) When counting money, we count from the highest to the lowest denominations.

3) Some pupils have the misconceptions that the set with more  coins has a greater amount of money. Some students may relate the size of a coin with its value, thus perceiving, for example, a 50-cent coin as having a higher value than a 1-dollar coin.

4) Students have not learnt the concept of decimals, so the decimal point is

regarded as a point separating the cents from the dollars, and the two digits after the decimal point denote the number of cents.

5) Point out that to change dollars to cents, just remove the “$” sign and

the dot. Remind students to put a dot after the dollars to separate the

dollars from the cents. Point out that they are not to use both “$” and “¢” together.

More on Mass & feedback on homework

Learning objectives: 

• read the scale on a weighing machine where the indicator does not point exactly to the numbers on the scale
• Use a weighing machine to determine the order of the masses of two or three items
• use the unit, gram (g), for measuring mass
• read a scale which shows masses less than 500g
• measure and compare masses in g
• solve two-step word problems involving addition and subtraction
• solve one-step word problems involving multiplication/ division concept
• Using models to solve word problems

Feedback on pupils' homework

1. Inversion of numbers

There are many children who inverted the numbers in the tens and ones place (see picture). To prevent this, encourage them to read aloud their answers. For example:

one hundred, one hundred and ten, one hundred and twenty, one hundred and thirty... 

103 is read as one hundred and three.

130 is read as one hundred and thirty.

Otherwise, they can do the vertical working to prevent error: 

100 + 10 = 110

110 + 10 = 120

120 + 10 = 130 

2. Good Practice

Some scales in the workbook may seem too much for the children. Encourage them to extend a line from the indicator and between the intervals (the shorter lines).

Hope this helps!

More on Measurement

Not drawn to scale

Notice the parts on the weighing balance in my previous post? Now, when we are given any scale, we can see it being applicable to any standard units (e.g. m, cm, kg, g) as long as we understand how to find the parts within the scale.

Using the scales above to measure an eraser, the children can give me a more precise answer when it comes to its length. We started with 'about 4 cm' using the scale right on top. Then we move down to the one below and measured 'between 3.5 cm and 4 cm' and finally we had '3.8 cm' as the answer. Therefore, we can conclude that the scale at the bottom can give us the most accurate reading here.


Do note that the topic decimal is not in P2 syllabus.


However, the children will need to know to how to read the scale on a weighing balance where the indicator does not point exactly to the numbers on the scale. Each shorter line stands for a value.

Note the red dots marked on the weighing scale. We take interest in the shorter lines between 30 kg and 40 kg. Now, when the indicator does not stop at the number, the children have to find out the value of each part.

Think 'number patterns' when we do this. A guess & check can be done to find out the answer.


An example of thinking aloud:

First, let's see where the indicator points to. (between 30 kg and 40 kg)


Then, let's do 'counting on' based on the guess and check method.


30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40






Let's take a look at another example:

The heaviest item that this weighing scale can measure is 100 g. When the children are given questions like this where the indicator is not pointed to a given number, they have to figure out themselves.


Let's try the 'counting on' using the guess and check method.
I pay attention to the shorter lines. (There are 9.)
So, I can count on from 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30.
Therefore, when I reached the 30 g mark, I am sure that each shorter line represented 1 g.

Math workbook Part 2 pg 82

There are 2 things to note in this pupil's work. First, I can conclude that this child is ready to handle some concepts of decimals. I can use language like '0.5 kg' in my explanation. I will be able to ask this child to solve this addition number sentence 6.5 + 0.5 = ? Second, I am sure this child did not check the numbers given after 6. He/ She wrote 6.5 kg because it happens to be a halfway mark.


It will be confusing to the children if we introduce them to a new concept (decimals) just to explain another new concept. Therefore, build on their prior knowledge of 'counting on'.The shorter lines have numbers which are missing just like in a number pattern. As usual, we do a guess and check.


6, __, __, __, 8


6, 7, __, __, 8 (wrong)


6, __, 7, __, 8 (correct)


6, 6.5, 7, 7.5, 8 (correct but the topic decimals is not in P2 syllabus)






Topics involving measurements include 'length', 'mass' and 'volume'.



That's all!

Mass

Tip of the day: If you want to lose weight, go to the moon.

Mass is a measure of the amount of matter in an object, whereas weight is the force of gravity acting on that mass. When astronauts orbit the earth in the space shuttle, their weight is less than it is on earth but their mass does not change. Hence, it is accurate to refer to mass instead of weight.


In Primary One, the children were introduced to the concept of mass with 2 objects as an example:


Say, I hold a brick in one hand and a basketball in the other and ask "Which is heavier?" From their experience, children will likely know that although the ball is larger in size, the brick is heavier. Then, I will proceed to ask the class to name some things that are heavier and light. These ideas were further developed as the children hold objects and feel the pull of gravity. In most cases, the masses of two objects cannot be compared by sight, they must be held to determine which is heavier. Simply, I do not randomly choose the objects. Otherwise, some choices are quite obvious e.g. a piece of paper and a basketball.


This week, we will cover the standard units for measuring mass - kilogram (kg) and gram (g). At home, children should look for products that are packaged or sold by mass. (e.g. a cake mix, a box of cereal, a candy bar or a bag of apples.)


Avoid measuring bottled drinks or canned beverages as they are more closely related to the topic volume.


Avoid saying kg as 'k-g'. Pronounce kg as kilogram because we don't pronounce g as 'g', we say gram.




Learning objectives: (there are some more!)

• read a scale which shows '1 kg', 'less than 1 kg' or 'more than 1 kg'
• find the mass of an object in kg using the balance with 1-kg masses
• compare the masses of objects and tell which is heavier or lighter

Note the smaller parts within the scale? I will have a separate post about it.




Thank you.

Commonly-made mistake for Length

Look at the pictures above, which one of the following is the correct way to measure the green rectangle?


That's right! It is the picture below. Any object to be measured must be placed an the '0' cm mark.


Highlight to children that some rulers have measurements of 'cm' and 'inches' on them so they have to identify and use the correct scale.

If the object (yellow rectangle) to be measured is not placed on the '0' cm mark, the children need to know how to find the difference in the length by subtracting the beginning mark from the end mark. For example, the yellow rectangle is 2cm - 1cm = 1cm long.








Referring to the Math Workbook 1A part 2 page 69, questions such as this:




          8cm                                           2cm
(i) The straw is _____ cm longer than the key.


Children are encouraged to write the measurement on top of the objects. A commonly-made mistake is children often write 8cm as the answer because they did not see that this question needs them to compare the lengths of 2 objects. The words in bold 'longer than' is a clue. Writing the measurements above the objects will help them to see this relationship. Finding the difference (how much more or less) means we do subtraction.

Labelling lines

Question: Draw a line BC that is 6cm.


The top picture shows the correct answer. Get your child to explain to you why the bottom 2 pictures show the wrong answers.


Drawing straight lines freehand is unacceptable.




Other learning objectives:

• Use a string to measure lengths of curves
• Solve one- and two-step word problems by relating them with addition and subtraction concepts such as 'part-whole', 'adding-on', 'taking-away' and 'comparing'
• Solve one- and two-step word problems by relating them with multiplication and division concepts such as 'group and item' and 'multiplying'
• draw models to solve the problems

Thank you for your attention!

Class activity: Length



We should use identical units for measuring an object. It is wrong to mix different units (tongue depressors and base-ten cubes.)

Please refer to my previous post about non-standard units.

Length

Dear Parents,

It has been a fun beginning to the topic where we got to compare the recumbent length and height of some children in 2 Thinker.

Nonstandard units: The children were given ice-cream sticks, paper clips and base-ten cubes as nonstandard units to measure some objects. They are encouraged to experiment with the appropriate unit that has the same attribute as that to be measured. For example, we would not want to measure the thickness of a page with an eraser or the length of a classroom with a paper clip.

Another important concept is the actual measurement using nonstandard units is always approximate. Look at the picture below, the length of the pen is closer to 4 paper clips than 5 paper clips long. We say that the length of the pen is about 4 paper clips long.

Below are some common mistakes to avoid when placing nonstandard units:

When two children accurately use the same unit to measure a particular object, both should get the same number. However, if they use different units, two different answers can be correct. Let's see...

It is helpful to discuss this idea when using body parts as arbitrary units. An example is the measuring of the width of the classroom in shoe lengths. Once the children understand what unit means, they can appreciate the problems associated with trying to communicate such measures outside their class or school. They will come to see that it is difficult to communicate measurements done with nonstandard units to other people. So, there comes standard units.

We read the book 'How Big is a Foot?' in class.

Your child needs to know:

• metre (m) - unit of measure for length
• estimate and measure 1m
• name objects that are more than 1m long and objects that are less than 1m long
• estimate and measure the lengths of objects in metres

Concepts in green were covered in Primary One.

Comparing two or more objects

Comparison of Height (Measuring from the top to the bottom) 

1. taller than (comparison of two items; with 2 letters 'e r' to remind us about this property)
2. tallest (comparison of three or more items; with 3 letters 'e s t' to remind us about this property)
3. shorter than
4. shortest
5. as short as
6. as tall as

For points 5 and 6, some children are still misled by the word 'short' or 'tall'. Please reinforce that these words wants us to identify the two items that have the same height.


 Comparison of Length (Measuring from the left to the right) 

1. longer than (comparison of two items; with 2 letters 'e r' to remind us about this property)
2. longest (comparison of three or more items; with 3 letters 'e s t' to remind us about this property)
3. shorter than
4. shortest
5. as short as
6. as long as

For terms 5 and 6, some children are still misled by the word 'short' or 'long'. Please reinforce that these terms wants us to identify the two items that have the same length.

More on Using Models: Multiplication & Division

To ensure that the children understand the different variables in a word problem, a checklist can be done as shown in this child's work. I used these 3 examples on page 53 of the workbook to explain to the children.

Using the above checklist, the children can identify 2 out of the 3 variables. There will definitely be one unknown (box not checked). As stated in this post, the children have to know the following- using question (b) as an example:

• number of groups (4 plates)
• things (20 chicken wings)
• number of things in each group (unknown)

When the children translate these information into the bar models, they need to know that the number of groups mean the number of bars they need to draw. That is 4 bars in this example. Next, they need to state another information given- 20. They will draw the braces { } and write '20' under the whole bar model. Finally, the unknown is represented by a question mark (?).
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Math textbook page 136

We will replace bar models with dotted lines when:

1. the number of groups is not given (if that is what we need to find)
2. there are too many groups to be represented (e.g. 45 groups) 

Hope this helps!

Using Models: Multiplication & Division

This week, the children played a game to close the topic Multiplication Table of 4, 5 & 10. It is similar to a popular game Twister. For simplicity, the children only need to use their hands and/ or feet to touch the answer to the mathematical sentence. The shower curtains are bought from Daiso.

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Cuisenaire rods will be used to show the 'group and item' concept in multiplication for model drawing. Each coloured rod has a specific length. For example, the white rod stands for 1 unit and the red rod stands for 2 units and so on.

Let me use an example from the workbook to illustrate how we relate it to their work:



Page 49 of the Math workbook

First, we need to understand the question. Not all questions will always be telling you the 'groups' specifically. For example, there are 5 groups. Each group has 2 children. How many children are there altogether? We need to identify the 'number of groups' in this question as '3 baskets'.

We can use 1 white rod to represent 1 mango. Start by showing the 3 groups of 5 mangoes using only the white rods. Next, we look for another coloured rod that has the same length as the 5 white rods. We choose the light green one. How many light green rods do you think we will need for all the 15 white rods? Right, it is 3. So, we end up arranging 3 light green rods from end to end.

Finally, I showed the pupils how the model drawing will look if drew the conventional way (picture below). Most children are able to tell me the purpose of model drawing for Multiplication. Why drawing the conventional way for Multiplication is not recommended? Find out from your child.

Homework & feedback

Thank you parents for reading the class blog regularly. Your prompt response in acknowledging forms and other administrative task really helped Ms Nuzul and I to work more efficiently. There will be occasions when some parents experience irregular working hours and hardly interact with the child. Many children suggested that they can leave anything that requires your attention on the table first before they go to bed. Ashley even said that she will leave a pen with the document that requires acknowledgement for her parents' convenience!


Homework
Pupils would have received an A5-sized worksheet as an enrichment. There is no homework given today. The pupils can keep their Math files at home for revision until further notice.


Feedback on pupils' work
Please refer to Math workbook page 48, question 10(a) and (b).

Organising answers to a Math word problem is an important skill. Below are photographs of pupils' well-organised work.



Should be: There are 6 children.



Long division working is not necessary for P2.

Feedback on Math Performance Task 1

Dear Parents

The children were given the results of their performance task today. Many children made a mistake for Task 5. They need to differentiate between "10 groups" and "groups of 10". Click HERE to read about it in my previous post.

Please acknowledge the paper and return tomorrow.


Thank you!


Note: Pupils are assessed either through topical test or performance task for a topic. Since performance task was given for "Multiplication Tables of 2 and 3", there won't be a topical test for it.

More on Multiplication & Division

Refer to Math Workbook 2A Part 1 page 90. Working was presented wrongly in this example. They do not need to do the long division method. At their level,  they need to understand the division concept and show the division statement correctly.
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Number of groups & the number of items in each group

When we are solving word problems on Division, the question will either ask for the "number of groups" or "the number of items in each group". Let's take a look at an example of how the division statements for 15÷3=5 and 15÷5=3 will take on different word problems.

1) There are 15 peanuts.
      Max puts the peanuts equally onto 3 plates.
    How many peanuts are there on each plate? [Number of items in each group]

2) There are 15 peanuts.
    Max puts them equally onto some plates.
    There are 5 peanuts on each plate.
    How many plates are there? [Number of groups]