Week Three: Multiplication.

 Big Ideas:

There is one type of multiplication but there is four ways of picture or model multiplication, such as:  (1) The Set Model (2) The Array Model (3) The Measurement or Length Model (4) The Combinations (cross products) Model.

•          Multiplication is … repeated addition where all the parts that are added are equal to each other. Another way to say this is repeated addition of equal groups or sets.

The knowledge of Mathematical Properties, primary students need to know the operations and how to use before high school. The communitive, associative, distribution properties need to be understood, identified and efficient use of the properties in different situations is needed by all students.(Reys et al., 2012)

Concept Skills and Strategies

1.      Use Counting Strategy

2.      Multiplication is … repeated addition where all the parts that are added are equal to each other. Another way to say this is repeated addition of equal groups or sets.

3.      Use Doubles

4.      Build-up (x3 & x6) or Build-down (x9)

5.      The Turn-around 7’s

Null Factor Property (a concept) When a number is multiplied by 0, the product will be 0 e.g., 3 x 0 = 0 and 0 x 3 = 0. You can demonstrate this property using any of the models for multiplication such as the set model:

Identity Property (a concept) Any number multiplied by 1 remains the same eg., 3 x 1 = 3 and 1 x 3 = 3. You can demonstrate this property using any of the models for multiplication such as the set model.

•       Commutative Property Turnarounds 3 x 4=4 x 3

Associative Property 3 x (4 x 5)       =     (3 x 4) x 5

Distributive Property   

4 x 7  =  ?

= 4 x (5 + 2)

= (4 x 5) + (4 x 2)

=     20    +     8

=           28

•       A factor is a whole number that can be divided into another whole number to give a whole number quotient.

•       A multiple is the quantity achieved by multiplying 2 or more factors together.

Lowest Common Multiple (LCM) The LCM is the smallest number that all given numbers will divide into exactly e.g., “What is the LCM of 2, 3 and 5?”

Greatest Common Factor (GCF) The GCF is the largest number that will divide into all given numbers evenly e.g., “What is the GCF of 6, 12 & 18?”

Language Model 

	Children’s Language	Materials Language	Maths Language	Symbolic Language
Materials	Teddy bears, Lollies, Fruit etc.	Paddle pop sticks, MABS, counters,  graphs	MABS, graphs
Language	Plates of, sets of, cups of, packets of,  groups of, etc.	Multiplied by, by	Multiplied by, by, multiplication, equals	Multiplied by, by
Recording	NO symbols, chn. draw pictures only		Pictures of groups, taking of three by two with pictures	Symbols,

  Teaching Strategies

 The Times Tables Booklet is a cost effective as well as easy to make booklet that a teacher can use with small groups as well as individually.("How To Make A Times Tables Booklet | Top Notch Teaching", 2016)

 Following the below link teachers can use this with a whole class or students can use it by them selves as they work through the concept of multiplecation.

http://www.scootle.edu.au/ec/viewing/L2057/index.html

("Pobble arrays: find a factor - (TLF L2057 v6.0.0)", 2016)

Misconception

Multiplication and division problems differ from addition and subtraction as the elements in the problems represent different items. Such as 2x24=48

The first factor the number ‘2’ means how many groups. To make sure students don’t get confused by this layout work through the language model and only introduce the equation when each student is ready (Reys et al., 2012).

ACARA

Mathematics / Year 2 / Number and Algebra / Number and place value / ACMNA031

Resources and ideas 

("Egyptian Method of Multiplication", 2016)
https://www.youtube.com/watch?v=xTOHkuYwQYw 

 ("Play To Learn ~ Numbers & Counting", 2016)

https://au.pinterest.com/pin/276056652136764389/

("Grades K-8: Real World Arrays and Math", 2016)

Synthesis Textbook

There are four sorts of multiplication structures (1) equal groups (2) multiplication comparisons (3) combinations (4) areas of arrays. The first two students should become familiar with in primary school however this should then lead onto the last of the four.

- An understanding of the knowledge of mathematical properties that go with each operation is vital to students understanding of the operation and how to use it.

- Many students have difficulty with the idea of commutativity as they may subtract the smaller number from the larger number or divide the larger number by the smaller no what the order of the operation is. This is why it is so important teachers take great care for the order of operations and why the order matters. 
(Reys et al., 2012)

 References

          Egyptian Method of Multiplication. (2016). YouTube. Retrieved 3 April 2016, from https://www.youtube.com/watch?v=xTOHkuYwQYw
        Facts for life Multiplication (1st ed., p. 1). Retrieved from http://leo.acu.edu.au/pluginfile.php/1486741/mod_book/chapter/32713/Facts%20for%20Life%20X.pdf
        Grades K-8: Real World Arrays and Math. (2016). Pinterest. Retrieved 3 April 2016, from https://au.pinterest.com/pin/276056652136764389/
        How To Make A Times Tables Booklet | Top Notch Teaching. (2016). Pinterest. Retrieved 3 April 2016, from https://au.pinterest.com/pin/276056652136891386/ 
        Mathematics Foundation to Year 10 Curriculum by rows - The Australian Curriculum v8.1. (2016). Australiancurriculum.edu.au. Retrieved 3 April 2016, from http://www.australiancurriculum.edu.au/mathematics/curriculum/f-10?layout=1#levelF
        Play To Learn ~ Numbers & Counting. (2016). Pinterest. Retrieved 3 April 2016, from https://au.pinterest.com/pin/276056652136702161/ 
       Pobble arrays: find a factor - (TLF L2057 v6.0.0). (2016). Scootle.edu.au. Retrieved 3 April 2016, from http://www.scootle.edu.au/ec/viewing/L2057/index.html 
       Reys, R., Lindquist, M., Lambdin, D., Smith, N., Rogers, A., & Falle, J. et al. (2012). Helping Children Learn Mathematics. Milton Queensland: John Wiley & Sons Australia, Ltd.