Primary One Preparation - Mathematics

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• Primary One Preparation - Mathematics (Part 1)
  

New parentswill have to come to terms with the great changes to Primary School Mathematicssyllabus when their children enter Primary One. In fact, the older you are, the bigger the shock.

If you wereborn in the 60's or 70's, the early Primary math you were familiar with areprobably addition, subtraction, and the memorization of multiplicationtimes-tables up to 12.  You will be mostmistaken if you think your child is going to be graded on the same methods thathad you acing your math tests during your time. Unlike the rote learning you might be familiar with that focused on theapplication of specific techniques for solving math problems, the new PrimaryMath syllabus focuses on how much the child actually understands thefundamental concepts.

It is nolonger enough that the child knows that 7+3=10 or 9x6=54.  The child is expected to understand why, andhow the same results can be attained by a variety of other means.

Understanding the Challenge:

Again, thefirst thing we need to do is understand what we are up against.  Based on MOE's 2007 Primary Math curriculum,the Primary 1 syllabus covers:

WHOLENUMBERS1.   Numbersup to 100.
Includes:

• Counting to tell the number of objects in a given set,
• Comparing the number of objects in two or more sets,
• Use of ordinal numbers (first, second, up to tenth) and symbols (1st, 2nd, 3rd, etc.),
• number notation and place values (tens, ones),
  This can get quite hairyat later stages when the child goes to Primary 2 and above and deals withhundreds and thousands, eg. How many tens make up 87 (answer=8) and how manyones make up 87 (answer=87) and how many tens and ones make up 87 (answer= 8tens and 7 ones).
  A variation could be: Howmany ones are there in the digits from 1 to 20? (This refers to the numbers 1,10, 11, 12, 13, 14, 15, 16, 17, 18, 19, so the answer is 12)
• Readingand writing numbers in numerals and in words,
• Comparing and ordering numbers,
• Numberpatterns. Students are normally requested to fill in missing numbers in a givensequence.  They will need to infer thepattern from the given numbers.  Thesesequences can have really complex relations, depending on the school.
  Excludes:
• Useof the terms ‘cardinal number’ and ‘ordinal number’,
• Use of the symbols > and <.
  
  

2.   Additionand subtraction
Includes:

• Conceptsof addition and subtraction, useof the addition symbol (+) or subtraction symbol (−) to write a mathematicalstatement for a given situation,
  
  

• Thegoal here is to make students understand the concept by seeing the problem fromvarious angles.
  
  

• Comparingtwo numbers within 20 to tell how much one number is greater (or smaller) thanthe other,
• Recognisingthe relationship between addition and subtraction,
• Buildingup the addition bonds up to 9 + 9 and committing to memory,
  
  

• Thisis a key Primary One activity, and one which children can be taught to masterduring pre-schools.  It facilitates themental arithmetic process.
  
  

• Solving 1-step word problems involving addition and subtraction within 20. This demonstrates the application of the addition and subtraction process.  As shown in the following example, this couldbe quite tricky for the uninitiated. "There were 51 passengers in a bus. Some passengers alighted at thefirst bus stop. How many passengers alighted at the first bus stop if 39passengers were left in the bus?" (Answer: 51 - 39 = 12)
  
  

• Additionof more than two 1-digit numbers. Additionand subtraction within 100 involving: a2-digit number and ones; a2-digit number and tens; two2-digit numbers,
  
  

• Addition and subtraction using formalalgorithms. Yes,this is where students will be taught concepts of carry-overs and borrowingwhich could be extended indefinitely beyond 2 digit problem sums.
  
  

3.   Mentalcalculation
Includes

• Addition and subtraction within 20. Here,students are expected to be able to compute the sums in their head withoutshowing any working.
  
  

• Additionand subtraction involving. A2-digit number and ones without renaming; A2-digit number and tens.
  
  

4.   Multiplicationand division
Includes

• Multiplication as repeated addition (within 40). Useof the multiplication symbol (×) to write a mathematical statement for a givensituation;
• Divisionof a quantity (not greater than 20) into equal sets: giventhe number of objects in each set; giventhe number of sets.
  
  
  • Solving 1-step word problems with pictorialrepresentation.
    
    

Excludes  

• Use of multiplication tables,
• Use of the division symbol (÷).
  
  

MEASUREMENT 1.   Lengthand mass
Includes

• Measurement and comparison of the lengths/ masses of two or more objects in non-standard units,
• 
  
  
  
  • The trickiest of this class of problems would be the logic-based transitiverelations: If A is heavier than B and B is heavier than C, then A must beheavier than C.  Such questions normallymanifest themselves as balancing beams with objects A, B and C.
    
    

• Useof the following terms: long, longer, longest; short, shorter, shortest; tall,taller, tallest; high, higher, highest; heavy, heavier, heaviest; light,lighter, lightest.
  
  

Excludes

• Findingthe difference in length/ mass.
  
  

2.   Time
Includes

• Telling and writing time to the hour/ half hour.
  
  

• Children should be trained to read time off an analog clock when they are in K2 orearlier to have an easier time when they have to cover this subject in P1.
  
  

Excludes  

• 24-hour clock.
  
  

3.   Money
Includes

• Identifying coins and notes of different denomination, Matchinga coin/ note of one denomination to an equivalent set of coins/ notes ofanother denomination, Eg.  $2 note is equal to 3 x 50 cent coins, 2 x 20cent coins, and 1 x 10 cent coin.
  
  

• telling the amount of money. Incents up to $1; Indollars up to $100.
  
  

• Useof the symbols $ and ¢. Solvingword problems involving addition and subtraction of money in dollars only (orin cents only).
  
  

Excludes

• Combinations of dollars and cents.
  
  

GEOMETRY 1.   Basicshapes (rectangle, square, circle, triangle)
Includes

• Identifying and naming the 4 basic shapes from 2-D and 3-D objects,
• Describing and classifying shapes.
  
  

2.   Patterns
Includes

• Making/completingpatterns with 2-D cut-outs according to one or two of the following attributes: shape, size, colour
  
  

• Making/completingpatterns with 3-D models: cube, cuboid(rectangular block), cone, cylinder. Eg.  How many squares are there in a cube? (Answer= 6)  How many circles are there in acylinder? (Answer = 2)
  
  

DATAANALYSIS1.   Picture  graphs
Includes

• Collectingand organising data. Makingpicture graphs; Useof a symbol/picture to represent one object; Readingand interpreting picture graphs in both horizontal and vertical forms.
  
  

Excludes

• Picturegraphs with scales.
  
  

Primary One Preparation - Mathematics (Part 2)

Now thatyou know what your child will be required to do in Primary One forMathematics, the question is how you can help prepare your child so that he/shecan cope with the subject.

With properguidance, it should not be too difficult for the average child toundergo the following progress schedule.  Please note that this should NOTbe taken as a definitive guide to gauge the ability of children!

1.   1-2years old

• Recognize and say the 10 numeral digitsfrom 0 - 9 in the correct sequence
• Recognize shapes (circle, triangle, rectangle,square)
• Count objects up to 10
  
  

2.   3-4years old

• Write the 10 numeral digits
• Finger math (show 0 to 9 using fingers)
• Count objects up to 100
• Count down from 20
• Differentiate between ordinal, cardinal andnominal numbers
  • Ordinal: Thenumber is used to indicate the order of things in a set, ie. 1 comesbefore 2, 3 comes after 2.  They show the rank or position, eg. First(1st), Second (2nd), Third (3rd), etc.
  • Cardinal:The number is used to indicate quantity.  It answers the question of"how many?".  This is normally the result of counting, eg. 3apples, 10 rabbits, 1 me.
  • Ordinal:The number is used as an identity.  Eg.  My home block number is27.  My birthday is on 5 Feb.  My telephone number is . My favorite bus is No. 197.
  • Compare:
    • Quantity:More, equal, less
    • Size:Bigger, same size, smaller
    • Length:Taller (longer), same height (length), shorter
    • Weight:Heavier, same weight, lighter
    • Speed:Faster, same speed, slower
      
      
    
    
• Time:
  • 7o'clock in the Morning, 12 o'clock in the Afternoon, 7 o'clockat Night
    
    
  
  

3.   5-6years old :

• Perform simple addition and subtraction oftotals up to 10
• Understand addition bonds:
  • 10= 1+9 = 2+8 = 3+7 = 4+6 = 5+5 = 6+4 = 7+3 = 8+2 = 9+1
  • 9= 1+8 = 2+7 = 3+6 = 4+5 = 5+4 = 6+3 = 7+2 = 8+1
  • 8= 1+7 = 2+6 = 3+5 = 4+4 = 5+3 = 6+2 = 7+1
  • ...
    
    
• Simple number series
  • eg.1, 3, 5, 7, ... (odd numbers)
  • eg.5, 10, 15, 20, ... (5's)
    
    
• Up to 5 times table in terms of groups of 1's,2's, 3's, 4's and 5's.
• Recognise and write the English equivalentsof the numerals
• Read the 12 hours of the analog clock, and applyAM and PM
• Identify Singapore coins and notes ofdifferent denominations, up to S$10.
• Tell the value of money by summing up coins, upto S$1. (No decimal point)
• Identify 3D shapes: cube, box, cone, sphere,cylinder and the number of 2D faces they present
  
  

In general, ifthe child possesses the above skills by the time they complete K2, he/sheshould be well prepared for Mathematics in Primary One.  There is NOneed for the child to master the entire P1 syllabus by K2 in order to do wellin Primary One!

Enlisting external help

A number ofparents believe that children could be effectively enriched in Math as early as3 months old!

• In programmes such as those offered by Shichida,babies are trained to look at dot charts, which are essentially flashcards withsimilar sized dots, and be able to quantify and differentiate the number ofdots on each card if they are trained on a regular basis.
• As early as 3 years old, some programmes (eg.Shichida and Little Neuro Tree), attempt to teach concepts such asmultiplication.
• Programmes that have stronger academic basisinclude those from Kumon,Enopi Math,SakamotoMethod, and E&PLearning Place.  These programmes are generally worksheet-oriented.  Children would be taught a method during the lesson,and are expected to bring home and complete a set of work sheets on adaily basis.  Each work sheet generally takes about 15 minutes tocomplete.  Most of these programmes are own-time-own-target, ie. thechild's progress is entirely dependent on his/her own capability.  Somechildren can even finish up to so-called "Primary 6 - equivalent"levels by the end of K2!
• Abacus courses are also very popular amongstparents.  A popular franchise is CMA MentalArithmetic, which uses a unique 2-handed method to train children asyoung as 3 years old to do quite complex arithmetic sums.  The apparentmental computation ability of some of their graduates is simply astounding -check out the video recording of a Mediacorp programme which featured the CMAprogramme.
• It is noteworthy, however, that the abacusmethod is quite different from the number bonding method that students areexpected to learn and master in Primary One.  There is a possibility thatchildren who learnt abacus may get confused when it comes to numberbonds.  Just be cognizant of this potential problem if you decide to tryout abacus training.
• It should also be noted that anumber of the pre-school math enrichment programmes may not be usefulbeyond Primary 2, where students will start encountering more problem sumswhich require higher ordered thinking than the mechanics of computation. Being able to do speedy computation involvingaddition/subtration/multiplication/division will NOT guarantee a good grade forstudents when they are promoted to Primary 3 and beyond.  Suchskills will not give the student any substantial edge in the GEPqualification examinations in Primary 3 either.  In fact, students will beallowed to use calculators for some papers in the Mathematics PSLE examinationwhen they reach Primary 5 and 6.
  
  

Do check out the following Kiasu Forum threads for more ideas:

• All About Pre-School Math Enrichment
• All About Primary School Math Enrichment
• P1 - Math
• CMA Mental Arithmetic