Week 5 - Fractions Flashcards
What is a fraction?
A part of a whole that is smaller than 1.
What are the different types of fractions?
Common
Proper
Mixed
Improper
What are common fractions?
Foundation for fractions
Relates to division, decimals and %, computation,
Initial fraction concepts
Partitioning into equal size parts - emphasis on the part whole relationship
What do fractions represent?
It represents the relationship between the part and the whole. It typically does not indicate the size of the whole rather than symbolic representation.
How to model fractions for understanding
The use of pies and pizzas as concrete student materials assists with the initial development of fractions. The use of items that students can relate to is key.
What is an initial fraction concept when first introduced?
Sharing - prior knowledge.
What are the various models of fractions?
Continuous model (region and area model)
Discrete model (sets model)
Division model (equal partition or sharing)
A linear (length) model (number line)
What is the region or area model?
The use of a piece of paper cut or folded into equal sections and shaded helps represent this model. This helps with a hands on process and comparing two different fractions.
Eg. 6/12 represented as a clump or 6/12 as one row.
Using the region model to emphasise the language based process?
Practice drawing on a sheet of paper.
5/8 equal parts parts shaded
5 out of 8
5 eighths
5/8
How to use the area/region model?
Use fraction mats for conceptualisation
How to use length model?
1 metre of ribbon
1 metre of ribbon cut into two halves
How to use sets model
Two circles with 3 stars in each
1/2 of 6 stars = 3 stars
What are equivalent fractions?
Having the same value but different representation- can be simplified down
How to work out equivalent fractions?
What you do to the bottom you must do to the top. Look at common denominators to work out what needs to be applied.
What would you do for misconceptions of fractions?
2/3 = 8/9
They are adding 6 rather than using multiplicative relationship.
They are simply following the rule rather than looking at it as a whole representation of parts.
Use the set model to introduce how many are in each group.
What are rational numbers?
Any number that can be expressed or written as a fraction.
What is the numerator?
A part of a given whole.
What is a denominator?
The whole number of a fraction.
Vinculum.
The line that represents the relationship between the part and whole.
What are some different types of fractions?
Percentage
Decimals
Rate as ratio
Proportion
What do equivalent fractions teach?
Key conceptual understanding with fractions and extends basic fractional understanding.
Indicates fractions can be indicated in a number of ways.
Necessary for comparing, ordering and sequencing of fractions.
What do equivalent fractions relate to?
Rate, ratio, proportional reasoning and percentage.
Strategy for generating equivalent fractions?
Most efficient to use multiplicative relationship - requires knowledge of factors and multiples
Teaching sequence of equivalence?
- Concept - a fractional amount can be represented in various ways
- Record using student language
- Record this representation symbolically
- Practice with symbols, language and materials to demonstrate the relationship
