Week 2 - Multiplication And Division Flashcards
What is multiplication?
Multiplication is repeated addition.
Where all the parts that are added are equal to each other - 4 + 4 + 4 = 4x3
What are the different types of multiplication?
There is only one type of multiplication
- sets model is the easiest
Different ways to picture multiplication?
Sets model
I have four bags of marbles. In each bag there are 14 marbles. How many marbles do I have altogether?
Measurement (linear/length) model
I have 4 lengths of rope. Each rope is 14m long. How long are the ropes altogether?
Array or area model
I have a rectangle which is 14cm long and 4cm wide. What is the area of the rectangle?
Cross multiplication
I have 14 shirts and 4 ties. How many different combinations of shirts and toes could I create? (Presuming I can only wear 1 shirt and 1 tie at a time)
What are the 5 properties of multiplication?
Null property - 0x0 = 0
Identity property - 1x2 = 2 (anything multiplied by 1 is itself)
Commutative property- turn arounds (axb = bxa)
Associative property - (a x b) x c = a x (b x c)
Distributive property - useful for 6x facts (5xa + 1xa)
3 x 13 = 3 x 3 x 10 - makes it easier (simplifying)
What are factors and multiples?
Factor is an integer or quantity that when multiplied by another integer or quantity results in a given number or expression.
A multiple is the quantity achieved my multiplying 2 or more numbers or quantities together.
2 x 3 (factors)
= 6 (multiple)
What is the highest common factor (HCF or GCF)?
The largest number that will divide into all given numbers evenly.
What are some multiplication difficulties?
When tables are learnt by reciting, children may count on
Children say they don’t know 7, 8 or 9 times tables
Confuse multiplication and addition
Only know the algorithm so have trouble with mental computation (break it down - distributive strategy and symbolic representation
What is division?
A sharing of a whole into equal parts.
Inverse relationship between multiplication and division is critical**
What are the types of division?
Partition
Sharing a large number into groups and seeing how many are in each group
“I have 10 pieces of sushi and 5 friends. How many can I give to each of my friends?”
Quotition
Repeated subtraction where a quantity is repeatedly subtracted from an amount to find the number of groups.
“I have 10 pieces of sushi and want to give 2 pieces to each of my friends. How many friends can I give sushi to?”
Division difficulties
Simply guessing
Difficulties with underlying multiplication facts
Division with 7, 8 and 9 too difficult
