Mathematical properties and multiplication:
The big ideas:
Source: Splash Maths (2020). Retrieved from https://www.splashlearn.com/math-vocabulary/multiplication/multiplication-chart
Models of multiplication:
The set model:
The array model:
The length of the rectangle is 6cm and the width is 4cm. What is the area?
The measurement or length model:
The combinations or cross product model:
Reys et al. (2020) suggest these strategies for teaching multiplication: commutativity, skip counting, patterns for squares and nines.
Mathematical properties
Youtube. (2015). Properties of multiplication. Retrieved from https://youtu.be/jG9E2pev3bQ
Children’s language
Materials language
Mathematics language
Symbolic language
Language
How many altogether?
How many altogether?
4 times 3 equals 12
4 x 3 = 12
Materials
Familiar objects, toys etc
Substituted objects, graphics, counters, MAB blocks, place value mats, number lines
Substituted objects, diagrams, graphics
Symbols
Recording
Draw pictures
Draw pictures
4 times 3 equals 12
4 x 3 = 12
Personal reflection:
Concept. skill or strategy:
The Hindu strategy of multiplication, also called Lattice multiplication is an excellent visual way to develop the concept.
A possible misconception:
ACARA:
Resources:
Word Count: 267
The big ideas:
Multiplication is repetitive addition where all parts are equal to each other. There is only 1 type of multiplication, but 4 different ways to picture or model multiplication. Consider Egyptian and Hindu strategies when teaching in the classroom.
Source: Splash Maths (2020). Retrieved from https://www.splashlearn.com/math-vocabulary/multiplication/multiplication-chart
Models of multiplication:
The set model:
There are 5 biscuits on two plates. How many biscuits all together?
|
The array model:
The length of the rectangle is 6cm and the width is 4cm. What is the area?
|
The measurement or length model:
I have two ropes that are 4 metres long. How many metres are they all together?
|
The combinations or cross product model:
Amanda has 6 friends who want to go to the movies, but only 2 tickets. How many different groups can she bring?
|
Reys et al. (2020) suggest these strategies for teaching multiplication: commutativity, skip counting, patterns for squares and nines.
Important elements of multiplication:
· Prime factorisation
· Null factor property
· Identity property (a concept)
· Factors and multiples
· Lowest common multiples
· Greatest common factor
Mathematical properties
Youtube. (2015). Properties of multiplication. Retrieved from https://youtu.be/jG9E2pev3bQ
Children’s language
|
Materials language
|
Mathematics language
|
Symbolic language
| |
Language
|
How many altogether?
|
How many altogether?
|
4 times 3 equals 12
|
4 x 3 = 12
|
Materials
|
Familiar objects, toys etc
|
Substituted objects, graphics, counters, MAB blocks, place value mats, number lines
|
Substituted objects, diagrams, graphics
|
Symbols
|
Recording
|
Draw pictures
|
Draw pictures
|
4 times 3 equals 12
|
4 x 3 = 12
|
Personal reflection:
When I was learning multiplication, hands-on activities supported me best. This aligns with Columba’s (2013) statement students should be engaged in manipulating materials that model the concept of multiplication.
The Hindu strategy of multiplication, also called Lattice multiplication is an excellent visual way to develop the concept.
A possible misconception:
Students learn that multiplication is repeated addition, therefore can sometimes believe that that the product of the two values will always be greater than the values themselves. This is not the case when working with fractions or decimals. The use of a number line will support in remedying this misconception.
ACARA:
Multiplication: Year two / Number and algebra / Number and place value / ACMNA031
Elaboration:
- Representing array problems with available materials and explaining reasoning
- Visualising a group of objects as a unit and using this to calculate the number of objects in several identical groups
Scootle resource: The array: go figure http://www.scootle.edu.au/ec/viewing/L108/index.html This game outlines strategies for solving multiplication using arrays and breaking them into columns and rows.
Resources:
Operation maths requires the student to complete maths activities to progress through the levels. https://apps.apple.com/us/app/operation-math/id487387270
Word Count: 267