In the Primary Four Mathematics Syllabus (2007), students need to understand the number notations and place values of (ten thousands, thousands, hundreds, tens and ones.) Based on this requirement, there are many questions that came out from it to test students on this point.
One questions is to ask students to re-arrange five digits to get either the largest/smallest number. The solution process to teach your children would be,
1) Ask the student to arrange the digits from largest to smallest or smallest to largest depending on the question asked.
2) Check for the digit "0" (zero) if the question is requesting for Smallest Number. Otherwise, students can just put down the 5-digits number in the order they have arranged in Step 1.
3) If there is the digit "0", ask students to read the instructions again to check if it is asking the student to form the largest 5-digit number.
4) If there is such instruction to form the smallest 5-digits number, student need to move the digit "0" from the first digit to the second digit (eg. From 0,1,2,7,8 to 1,0,2,7,8). Otherwise just put down the digit in the order arrange ignoring the digit zero. (i.e. 1278)
5) After the re-arrangement in Step 4, students can just write the digits in the order they have arranged to answer the question.
With the ongoing need to add critical thinking into questions, I have now seen questions where they have added in restrictions in forming the largest number. For example,
"Rearrange the digits 7,1,3,4,9 to form the largest digits that is more less than 50 000."
The solution process is as follows:
1) Rearrange the digits from biggest to the smallest, from left to right. (i.e. 9,7,4,3,1)
2) Looking from the biggest digit to the smallest, take out the digit that is smaller than the first digit of the restriction. (ie. The first digit of the restriction is 5 thus we choose the digit 4).
3) After taking out the digit from Step 2, strike it away from the list. (i.e 9,7,3,1).
4) Write the rest of the digits in the same order onto the right hand side of the digit selected from Step 2 and you should get the answer. (ie 49731).
In conclusion, the digit "0" would complicate questions that ask for the smallest number and restrictions posed could complicate questions that ask for the largest number. So parents please ask children to pay attention to these two aspect when answering questions that need to rearrange digits.
Sunday, July 25, 2010
Sunday, July 18, 2010
Primary Four: Writing Numerals into Words (Up to 100 000)
Primary Four Syllabus dictate that students need to write and read numbers in numerals and in words. In this entry, we will discuss how to help students write the numbers into words.
This process builds on the assumption that students have a strong foundation in writing any numbers up to 999 into words. And with this process helps students pave the way to writing numerals into words for numbers that are less than 10 Million, as required by the Primary Five Syllabus.
1) Ask the students to bundle the digits, with every three digits bundled into one unit, starting from the back.
For instance, if the digit given is 37890, ask them to bundle it into this way 890 as the first bundle follow by the second bundle which is 37. To help the student visualise it, maybe you can ask them to circle the bundles out in the numerals or put a slash. Example is 37 / 890.
2) Next ask the student to write in words for the bundle on the most left. So in this case would be 37. Once the students has written into words for the bundle, you can tell the student that the second bundle from the right is always for the thousands, as such, asking him to put in then word "thousands" right after he has written into words for the second bundle.
So in this case after the student have written "Thirty-seven" ask him/her to write down thousands after it, forming the words "Thirty-seven thousands".
3) After that write in words for the next bundle which is "890".
4) Put all those words that the students have written in the order of the bundle of digits and the students should get the correct answer.
5) To double check whether the answers are correct, ask students to cover the numerals and convert what he has written in words into numerals. After the conversion, students need to check with what they have written is similar to the question. This form of checking would also strengthen students ability to write words into numerals.
Some of the common mistakes arise when they are zeroes in the numerals so parents are remind to ask students to take care of these zeroes when writing into words.
Another common mistakes would be spelling, so parents do encourage your children to check the spelling as well.
This process builds on the assumption that students have a strong foundation in writing any numbers up to 999 into words. And with this process helps students pave the way to writing numerals into words for numbers that are less than 10 Million, as required by the Primary Five Syllabus.
1) Ask the students to bundle the digits, with every three digits bundled into one unit, starting from the back.
For instance, if the digit given is 37890, ask them to bundle it into this way 890 as the first bundle follow by the second bundle which is 37. To help the student visualise it, maybe you can ask them to circle the bundles out in the numerals or put a slash. Example is 37 / 890.
2) Next ask the student to write in words for the bundle on the most left. So in this case would be 37. Once the students has written into words for the bundle, you can tell the student that the second bundle from the right is always for the thousands, as such, asking him to put in then word "thousands" right after he has written into words for the second bundle.
So in this case after the student have written "Thirty-seven" ask him/her to write down thousands after it, forming the words "Thirty-seven thousands".
3) After that write in words for the next bundle which is "890".
4) Put all those words that the students have written in the order of the bundle of digits and the students should get the correct answer.
5) To double check whether the answers are correct, ask students to cover the numerals and convert what he has written in words into numerals. After the conversion, students need to check with what they have written is similar to the question. This form of checking would also strengthen students ability to write words into numerals.
Some of the common mistakes arise when they are zeroes in the numerals so parents are remind to ask students to take care of these zeroes when writing into words.
Another common mistakes would be spelling, so parents do encourage your children to check the spelling as well.
Sunday, July 11, 2010
Primary Four: Round to Nearest Tens or Hundreds
In Primary Four Mathematics Syllabus (2007), students need to learn how to round off numbers to the nearest ten/hundreds. In this case, the schools are teaching students to
1) draw a number line
2) write two nearest tens/hundreds where the number lies in between.
3) Find out which nearest ten/hundred is the number closest to, then choose it as the answer.
The common confusion comes in getting the two nearest ten, especially if they have the digit '9' in the tens or hundreds place. Students usually will be confused on how to get the higher nearest ten/hundred.
What parents can do is to teach them this method.
1) Write the lower ten/hundred where the number will fall above. If it is a 5 digit number, take the first four digits (for rounding to the nearest ten) or the first three digits (for rounding to the nearest hundred). After taking the first four digits, add another zero behind (for rounding to the nearest ten) to get the lower ten. Or for rounding to the nearest hundred, add another two zeroes to the first three digits to get the lower hundred.
2) Add ten/hundred to the lower number that is derived in Step 1 to get the higher ten/hundred. In this case, there will be less confusion as to which number is chosen.
3) Looking at the digit in the ones place, for rounding to the nearest ten or looking at the digit in the tens place, for rounding to the nearest hundred. If the digit is 1,2,3,4 then take the lower ten/hundred. If the digit is 5,6,7,8,9 then take the higher ten/hundred.
Now some parents might be thinking why not ask the student to immediately look at the digit after Step1 to get the answer, but my opinion is that it would be better to teach students the more complete and easier to master method, which is teaching all the three steps.
The common mistakes that students might make while carrying out the recommended three steps are during the addition, students make careless mistakes, thus it is recommended that parents encourage students to check their answer after completing Step 2 to make sure that the addition is done correctly.
1) draw a number line
2) write two nearest tens/hundreds where the number lies in between.
3) Find out which nearest ten/hundred is the number closest to, then choose it as the answer.
The common confusion comes in getting the two nearest ten, especially if they have the digit '9' in the tens or hundreds place. Students usually will be confused on how to get the higher nearest ten/hundred.
What parents can do is to teach them this method.
1) Write the lower ten/hundred where the number will fall above. If it is a 5 digit number, take the first four digits (for rounding to the nearest ten) or the first three digits (for rounding to the nearest hundred). After taking the first four digits, add another zero behind (for rounding to the nearest ten) to get the lower ten. Or for rounding to the nearest hundred, add another two zeroes to the first three digits to get the lower hundred.
2) Add ten/hundred to the lower number that is derived in Step 1 to get the higher ten/hundred. In this case, there will be less confusion as to which number is chosen.
3) Looking at the digit in the ones place, for rounding to the nearest ten or looking at the digit in the tens place, for rounding to the nearest hundred. If the digit is 1,2,3,4 then take the lower ten/hundred. If the digit is 5,6,7,8,9 then take the higher ten/hundred.
Now some parents might be thinking why not ask the student to immediately look at the digit after Step1 to get the answer, but my opinion is that it would be better to teach students the more complete and easier to master method, which is teaching all the three steps.
The common mistakes that students might make while carrying out the recommended three steps are during the addition, students make careless mistakes, thus it is recommended that parents encourage students to check their answer after completing Step 2 to make sure that the addition is done correctly.
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