New parents will have to come to terms with the great changes to Primary School Mathematics syllabus when their children enter Primary One. In fact, the older you are, the bigger the shock.
If you were born in the 60’s or 70’s, the early Primary math you were familiar with are probably addition, subtraction, and the memorization of multiplication times-tables up to 12. You will be most mistaken if you think your child is going to be graded on the same methods that had you aceing your math tests during your time. Unlike the rote learning you might be familiar with that focused on the application of specific techniques for solving math problems, the new Primary Math syllabus focuses on how much the child actually understands the fundamental concepts.
It is no longer enough that the child knows that 7+3=10 or 9×6=54. The child is expected to understand why, and how the same results can be attained by a variety of other means.
Understanding the Challenge:
Again, the first 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:
- Numbers up to 100
- 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 hairy at later stages when the child goes to Primary 2 and above and deals with hundreds and thousands, eg. how many tens make up 87 (answer=8) and how many ones make up 87 (answer=87) and how many tens and ones make up 87 (answer= 8 tens and 7 ones).
- A variation could be: How many 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)
- reading and writing numbers in numerals and in words,
- comparing and ordering numbers,
- number patterns.
- Students are normally requested to fill in missing numbers in a given sequence. They will need to infer the pattern from the given numbers. These sequences can have really complex relations, depending on the school.
- use of the terms ‘cardinal number’ and ‘ordinal number’,
- use of the symbols > and <.
- Addition and subtraction
- concepts of addition and subtraction,
- use of the addition symbol (+) or subtraction symbol (−) to write a mathematical statement for a given situation,
- The goal here is to make students understand the concept by seeing the problem from various angles.
- comparing two numbers within 20 to tell how much one number is greater (or smaller) than the other,
- recognising the relationship between addition and subtraction,
- building up the addition bonds up to 9 + 9 and committing to memory,
- This is a key Primary One activity, and one which children can be taught to master during pre-schools. It facilitates the mental 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 could be quite tricky for the uninitiated. “There were 51 passengers in a bus. Some passengers alighted at the first bus stop. How many passengers alighted at the first bus stop if 39 passengers were left in the bus?” (Answer: 51 – 39 = 12)
- addition of more than two 1-digit numbers,
- addition and subtraction within 100 involving
∗ a 2-digit number and ones,
∗ a 2-digit number and tens,
∗ two 2-digit numbers,
- addition and subtraction using formal algorithms.
- Yes, this is where students will be taught concepts of carry-overs and borrowing which could be extended indefinitely beyond 2 digit problem sums.
- Mental calculation
- addition and subtraction within 20,
- Here, students are expected to be able to compute the sums in their head without showing any working.
- addition and subtraction involving
∗ a 2-digit number and ones without renaming,
∗ a 2-digit number and tens.
- Multiplication and division
- multiplication as repeated addition (within 40),
- use of the multiplication symbol (×) to write a mathematical statement for a given situation,
- division of a quantity (not greater than 20) into equal sets:
∗ given the number of objects in each set,
∗ given the number of sets,
- solving 1-step word problems with pictorial representation.
- use of multiplication tables,
- use of the division symbol (÷).
- Length and mass
- measurement and comparison of the lengths/ masses of two or more objects in non-standard units,
- The most tricky of this class of problems would be the logic-based transitive relations: If A is heavier than B and B is heavier than C, then A must be heavier than C. Such questions normally manifest themselves as balancing beams with objects A, B and C.
- use of the following terms:
long, longer, longest
short, shorter, shortest
tall, taller, tallest
high, higher, highest
heavy, heavier, heaviest
light, lighter, lightest
- finding the difference in length/ mass.
- 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 or earlier to have an easier time when they have to cover this subject in P1.
- identifying coins and notes of different denomination,
- matching a coin/ note of one denomination to an equivalent set of coins/ notes of another denomination,
- Eg. $2 note is equal to 3 x 50 cent coins, 2 x 20 cent coins, and 1 x 10 cent coin.
- telling the amount of money
∗ in cents up to $1,
∗ in dollars up to $100.
- use of the symbols $ and ¢,
- solving word problems involving addition and subtraction of money in dollars only (or in cents only).
- combinations of dollars and cents.
- Basic shapes (rectangle, square, circle, triangle)
- identifying and naming the 4 basic shapes from 2-D and 3-D objects,
- describing and classifying shapes.
- making/ completing patterns with 2-D cut-outs according to one or two of the following attributes
- making / completing patterns with 3-D models:
∗ cuboid (rectangular block)
- Eg. How many squares are there in a cube? (Answer = 6) How many circles are there in a cylinder? (Answer = 2)
- DATA ANALYSIS
- Picture graphs
- collecting and organising data,
- making picture graphs,
- use of a symbol/picture to represent one object,
- reading and interpreting picture graphs in both horizontal and vertical forms.
- picture graphs with scales.
Next: Part 2