Week 5 - Fractions

Question 1

What is a fraction?

Answer 1

A part of a whole that is smaller than 1.

Question 2

What are the different types of fractions?

Answer 2

Common

Proper

Mixed

Improper

Question 3

What are common fractions?

Answer 3

Foundation for fractions

Relates to division, decimals and %, computation,

Question 4

Initial fraction concepts

Answer 4

Partitioning into equal size parts - emphasis on the part whole relationship

Question 5

What do fractions represent?

Answer 5

It represents the relationship between the part and the whole. It typically does not indicate the size of the whole rather than symbolic representation.

Question 6

How to model fractions for understanding

Answer 6

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.

Question 7

What is an initial fraction concept when first introduced?

Answer 7

Sharing - prior knowledge.

Question 8

What are the various models of fractions?

Answer 8

Continuous model (region and area model)

Discrete model (sets model)

Division model (equal partition or sharing)

A linear (length) model (number line)

Question 9

What is the region or area model?

Answer 9

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.

Question 10

Using the region model to emphasise the language based process?

Answer 10

Practice drawing on a sheet of paper.

5/8 equal parts parts shaded

5 out of 8

5 eighths

5/8

Question 11

How to use the area/region model?

Answer 11

Use fraction mats for conceptualisation

Question 12

How to use length model?

Answer 12

1 metre of ribbon

1 metre of ribbon cut into two halves

Question 13

How to use sets model

Answer 13

Two circles with 3 stars in each

1/2 of 6 stars = 3 stars

Question 14

What are equivalent fractions?

Answer 14

Having the same value but different representation- can be simplified down

Question 15

How to work out equivalent fractions?

Answer 15

What you do to the bottom you must do to the top. Look at common denominators to work out what needs to be applied.

Question 16

What would you do for misconceptions of fractions?

2/3 = 8/9

Answer 16

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.

Question 17

What are rational numbers?

Answer 17

Any number that can be expressed or written as a fraction.

Question 18

What is the numerator?

Answer 18

A part of a given whole.

Question 19

What is a denominator?

Answer 19

The whole number of a fraction.

Question 20

Vinculum.

Answer 20

The line that represents the relationship between the part and whole.

Question 21

What are some different types of fractions?

Answer 21

Percentage

Decimals

Rate as ratio

Proportion

Question 22

What do equivalent fractions teach?

Answer 22

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.

Question 23

What do equivalent fractions relate to?

Answer 23

Rate, ratio, proportional reasoning and percentage.

Question 24

Strategy for generating equivalent fractions?

Answer 24

Most efficient to use multiplicative relationship - requires knowledge of factors and multiples

Question 25

Teaching sequence of equivalence?

Answer 25

1. Concept - a fractional amount can be represented in various ways
2. Record using student language
3. Record this representation symbolically
4. Practice with symbols, language and materials to demonstrate the relationship