Paying Attention to Fractions-002 Group 3

6. Fractions Across Strands and Grades + Ministry Resources (Emma C.)

Strands & Grades

Instructing fractions in a punctuated fashion (chucked), allows students to better comprehend fractions as a unit. While also allowing teachers to be responsive to students when planning additional activities. Students are then able to connect their understanding of fractions to other math units and concepts.

Resources

To aid in leaning and understanding fractions there are many wide ranging resources listed by the ministry. These resources vary from research articles, webcasts, educational documents and digital games.

Key Concepts - Section 4 by Sarah C.

Unit Fractions

In part-whole fractions, the denominator indicates the fractional unit, or the number of equi-partitions of the whole being considered. Students develop flexibility in representing unit fractions by using physical models, pictures, and numbers.

The Whole

The denominator provides information
about how the whole has been divided

Example: When considering 3/2 as a
quotient, the 3 is the whole and the 2 shows the number of partitions

Equivalency

When determining equivalent
fractions, students are
identifying different fractional
units that can be used to
describe a quantity

Example: 1/3 = 5/15 = 7/21

Comparing and Ordering

Deciding which of the
relations is equal to, is
than, or is greater than

Students can use models,
benchmarks, common
numerators, equivalent
fractions and/or unit
fractions to compare and
order fractions

Operations

Students need a conceptual
understanding of equivalency,
estimating, unit fractions, and
part-whole relationships to
understand operations

When these concepts are
explored meaningfully,
students develop an implicit
understanding. For example,
students may realize that
3/4 = 1/4 + 1/4 + 1/4

3 Models that should be used (Eduardo)

Area Model

one shape represents the whole. The whole is divided into fractional regions.

Set Model

a collection of items represents the whole amount. Subsets of the whole make up thefractional parts.

Volume Model

a three-dimensional figure represents the whole. The whole is divided into fractionalregions that are occupied by space within the figure.

2. Why is Understanding Fractions Importans (Ashley S.)

Daily Life

Understanding fractions supports individuals in everyday activities (e.g., cooking, carpentry, sewing, etc.)Not understanding fractions can cause difficulties in adulthood (e.g., failure to understand medication regiments)

Building a Foundation

Understanding fractions allows students to build a foundation to develop an understanding for more complex mathematical concepts (e.g., proportionality and ratio, linear relationships, trigonometry, and radial measure)

3. Models that should be used (Jasmine)

Different types of Models

Area Model: a shape that represents the whole. With the fractional regions being equal in area they may not all be congruent.Set Model: A bunch of items that represents the whole amount. Subsets of the whole make up fractional parts.Volume Model: when a three-dimensional figure represents the whole. This whole would be divided into fractional regions that are occupied by space within the figure.

Area Model

Set Model

Number Line Model

Part-Part Relationships

Using Models

When students using models it will help them test and develop predictions about the relationships within the fractions.When using models the students have to make sure the whole remains unchanged. Which means the selection of model is important that the whole will not be spilt. Number lines are a good example to make sure that the whole is preserved.Using models to compare fractions like a rectangle or a number line.Allow students to use models to determine equivalent fractions.

How Can We Promote Fractions Thinking? (Olivia Sieczkowski)

Unit Fractions

-Counting from 0-1, in each individual unit which helps students understand the relationship between parts and wholes -Introduce mixed and proper fractions at the same time -use precise language

Representations

- Introduce pictures and notational representations at the same time - Provide familiar representations to new fraction concepts - Provide similar representation throughout multiple grade levels (number lines, volume)- Avoid introducing circles in P/J grades

Equivelence and Comparing

-Help students understand the difference between parts and wholes and to consider both the numerator and denominator when comparing fractions -Help students connect to other number systems besides division

Operations

-Create a strong base for using operations throughout P/J grades( i.e introduction of dollars and cents)-Ensure prior essential knowledge of operations is in place before introducing fractions

Main topic

4 Constructs: Lexia Simmons

Part-Whole Relationships

Denominator indicates the fractional unit being used
Numerator indicates the number of fractional units being counted

Part-Part Relationships

The Denominator indicates the number of items that are in one part of the set
The Numerator indicates the number of items that are in the other part of the set
Adding the numerator and the denominator together determines the fraction unit being used to partition, or divide, the set.

Quotient

Dividing the numerator by the denominator
Equal Sharing
Result is the decimal equivalent for the fraction››

Operator

Use of a fraction to enlarge or shrink a quantity by a factor
Fraction reduces or increases a quantity

Introducing Fractions-Section 1 by Loe G.B. 1. 5 TYPES OF FRACTIONS (note: numerator and denominator could also be negative.)

Simple Fractions

Definition: Digits in both the numerator and the denominator are integers; the denominator ≠ 0.

Examples

Proper Fractions

Definition:
Digits in both the numerator and the denominator are integers; the numerator < the denominator.

Examples

Unit Frations

Definition:
Digits in both the numerator and the denominator are integers; the numerator = 1.

Examples

Mixed Fractions

Definition:
A quantity represented by an integer and a proper fraction

Examples

Improper Fractions

Definition:
Digits in both the numerator and the denominator are integers; the numerator > the denominator.

Examples

Complex* Fractions

Definition:
Either or both the numerator and the denominator are fractions.

Examples