Grade 3 IMO papers
Let’s talk about what division really is — it is repeated subtraction; much the way multiplication is repeated addition.
Let’s say I have the basic problem 16 ÷ 4. I could start with 16 and then subtract 4, subtract another 4, another 4, and another 4 until I run out and reach zero. I would have to do this 4 times. If I had 16 cookies that I wanted to share equally among 4 friends, I could do the “one for you, one for you, one for you, and one for you” process and still end up with 4 cookies for each.
But what about 375 ÷ 50? If I don’t know how to divide by double digit numbers, the repeated subtraction process might actually be a good choice . . . at least showing some number sense to know that 375 divided by 50 means “How many 50’s in 375?” I know if I subtract 50 six times, I still have 75 left. I can subtract another 50 and I have 25 left over. So 375 ÷ 50 = 7 with a remainder of 25.
Dividing using the distributive law
|69 ÷ 3||60 + 9||(60 ÷ 3) = 20
(9 ÷ 3) = 3
|20 + 3 = 23|
|391 ÷ 3||390 + 1|| (390 ÷ 3) = 130
(1 ÷ 3) = cannot be divided
|130 with Remainder 1|
Before a child is ready to learn long division, he/she has to know: Continue reading
Place value and Face value
Face value of a digit is the digit itself whereas Place value can be termed as the location of the digit in the numeral.
The value of a place in the place value chart is 10 times the value of the place just to its right.
A quick look at the grade 2 lesson on introduction to multiplication
While multiplying always remember :
An even number x an even number = an even number
An odd number x an even number = an even number
An odd number x an odd number = an odd number
Distributive property of multiplication
Listing down some methods to simplyfy addition.
- Doubles (such as 6 + 6)
- Near doubles: Try adding a double and the remainder. Solve 7 + 6, (6 + 6+ 1) or (7 + 7 – 1).
- Making a ten or a multiple of 10: To add 7 + 6, I can take 3 from the 6 and put it with the 7 to make 10 and 3. This holds good even with multiples of 10 like 20, 30 40, etc
- 1 more, 1 less: Show problems such as: 8 + 1, 51 + 1, and 6 – 1, 22-1
- Place value Decomposition: 35 + 22 can be decomposed into tens and ones 30+20 added to 5+2. Or 35 – 22 can be decomposed to 30-20 plus 5-2.
Pictorial representation of the strategies above :
Some tips and tricks to start multiplication which will help you in knowing your times tables. I followed this approach with my daughter (she is in grade 1 rt now) and am very happy with the results. She does not have any apprehensions of which table is asked and does a quick mental maths if she does not know the answer.
Tips to approach the concept of multiplication :
I explained these concepts using lego pieces . You can use anything small and handy.
- Now that the kids know 2 digit addition the best approach to start multiplication is by asking them to do repeated addition. Ask them to count the objects in groups of 2 then 3 and so on.
- Once they are thorough with repeated addition you can ask them to do skip counting.
- Ask them to divide the total number of objects into equal groups.
- Arrange the total number of objects in an array of row and column.
Below is a figure to illustrate how multiplication can be introduced to kids.
Reasoning tips and tricks
Finding the odd one out
Step 1 : Look out for common things
Step 2 : Find a pattern in the similarities
Step 3 : Which one is different and why ? Cross out the similar ones.
Step 4 : Mark the answer .
What comes next
Step 1 : Look at the changes / similarities between each diagram
Step 2 : Look for a pattern in the changes
Step 3 : Do the different changes one at a time.
Step 4 : Look out for the right option