# Fractions

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Fractions

## 1. Operations with fractions

1.1.1. concretely

1.1.1.1. fraction blocks

1.1.2. pictorially

1.1.2.1. fraction circles

1.1.2.2. fraction strips

1.1.2.3. number lines

1.1.3. symbolically

1.1.3.1. find LCM

1.1.3.2. eg.

### 1.2. subtracting

1.2.1. concretely

1.2.1.1. fraction blocks

1.2.2. pictorially

1.2.2.1. fraction circles

1.2.2.2. fraction strips

1.2.2.3. number lines

1.2.3. symbolically

1.2.3.1. find LCM

1.2.3.2. eg.

### 1.3. multiplying

1.3.1. concretely

1.3.1.1. fraction blocks

1.3.2. pictorially

1.3.2.1. number lines

1.3.2.2. area model

1.3.3. symbolically

1.3.3.1. eg.

### 1.4. dividing

1.4.1. concretely

1.4.1.1. fraction blocks

1.4.2. symbolically

1.4.2.1. eg.

1.4.3. pictorially

1.4.3.1. fraction strips

1.4.3.2. number lines

2.1.1. eg. 1/4

2.2.1. eg. 5/4

2.3.1. eg. 2 1/4

## 3. representing

### 3.1. modeling

3.1.1. concretely

3.1.1.1. fraction blocks

3.1.2. pictorially

3.1.2.1. fraction circles

3.1.2.2. fraction strips

3.1.3. symbolically

### 3.2. relationships between fractions

3.2.1. comparing

3.2.1.1. concretely

3.2.1.1.1. fraction blocks

3.2.1.2. pictorially

3.2.1.2.1. fractions circles

3.2.1.2.2. fraction strips

3.2.1.3. symbolically

3.2.1.3.1. eg. 1/2<3/4

3.2.2. ordering

3.2.2.1. concretely

3.2.2.1.1. fraction blocks

3.2.2.2. pictorially

3.2.2.2.1. fraction circles

3.2.2.2.2. fraction strips

3.2.2.3. symbolically

3.2.2.3.1. eg. 1/8< 1/5< 1/4<1/2

3.2.3. equivalent fractions

3.2.3.1. concretely

3.2.3.1.1. fraction blocks

3.2.3.2. pictorially

3.2.3.2.1. fraction circles

3.2.3.2.2. fraction strips

3.2.3.3. symbolically

3.2.3.3.1. eg. 3/4 = 6/8

3.2.4. simplifying

## 4. Using fractions

### 4.1. authentic tools used to work with fractions

4.1.1. clocks

4.1.2. cooking

4.1.3. measuring tapes

4.1.4. measuring spoons/cups

### 4.2. experts using fractions

4.2.1. carpenters

4.2.2. chefs

4.2.3. pharmacists

4.2.4. hairdressers

4.2.5. investors

4.2.6. STEM (science, technology, engineering, and mathematics)

### 4.3. future advantages in learning with an understanding of fractions

4.3.1. fractions are related to ratios, rates, percent, proportion

4.3.2. fractions are used in other math concepts: solving equations, finding volume and surface area, graphing equations, etc.

4.3.3. fractions are used in other subjects: biology, chemistry, physics, economics, cooking, business, etc.

4.3.4. fractional understanding builds on larger mathematics cognitive processes including proportional reasoning, spatial reasoning, probability, and algebraic reasoning (Bruce, Chang, Flynn, Yearly, 2013)

### 4.4. Real -life uses/Authentic Scenerios where fraction knowledge would be important

4.4.1. construction

4.4.2. telling time

4.4.3. money/sales/investments

## 6. Constructivist MultiMedia Teaching Ideas

### 6.1. Constructivist critical criteria for interactive multimedia (Herrington and Standen, 2000 )

6.1.1. 1. authentic context that reflects use in real-life

6.1.2. 2. ill defined authentic activities

6.1.2.1. Solve a problem, fix something that isn't working, develop a creative solution

6.1.2.1.1. choose a site that does a poor job of teacher a particular math concept - students analyze the site and provide creative solutions to improve the site. Site should teach the specific concept better. Concept was used in this paper http://www.ascilite.org.au/ajet/ajet17/neo.html

6.1.3. 3. access to expert performance andmodelling

6.1.4. 4. Multiple roles and perspectives

6.1.5. 5. Reflection

6.1.6. 6. Collaborative construction of Knowledge

6.1.6.1. Student created knowledge and sharing of fractions understnading

6.1.6.2. group project possibilities

6.1.7. 7. Articulation - learn to speak the language

6.1.8. 8. Coaching and Scaffolding

6.1.9. 9. Authentic Assessment

### 6.2. 10 critical elements for effective multimedia instructional design (Mayer, 2008)

6.2.1. Five principles for reducing extraneous processing

6.2.1.1. 1. Coherence

6.2.1.2. 2. Signaling

6.2.1.3. 3. Redundancy

6.2.1.4. 4. Spatial Contiguity

6.2.1.5. 5. Temporal Contiguity

6.2.2. Three principles for managing essential processing

6.2.2.1. 1. Segmenting

6.2.2.2. 2. Pretraining

6.2.2.3. 3. Modality

6.2.3. Two principles for fostering generative processing

6.2.3.1. 1. Multimedia

6.2.3.2. 2. Personalization

### 6.3. The math curriculum should: engage students in problems that require extended effort, allow for collaboration and discussion, make connections with other subjects, support the use of technologies for solving problems and exploring relationships (NCTM, 2014)

6.3.1. SCANS report identified collaborative activity, problem solving, communication, self-assessment, and competence and confidence with technology as critical to success in the 21st century (US Dept. of Labor, 1992)

### 6.4. Constructivist Learning Environments on the web (Jonassen, 1999)

6.4.1. 1. Question/Case/Problem/Project - learners solve or resolve (this is the goal)

6.4.1.1. Problem is represented in an appealing way (video/audio clip, narrative - this link has a great example of a math problem represented in a visual video format - coool way to lead off a lesson and engage students in the problem

6.4.1.2. students should be able to manipulate the problem in some way in order to engage with it.

6.4.2. 2. Related Cases -

6.4.2.1. similar problems and their solutions or non-solutions help scaffold memory

6.4.3. 3. information Resources

6.4.3.1. Information learners may need to solve the problem

6.4.4. 4. Cognitive (Knowledge Construction) Tools

6.4.4.1. eg. visualization tools

6.4.5. 5. conversation and collaboration tools

6.4.6. 6. social/Contextual Supports

6.4.6.1. eg coaching, scaffolding

## 9. Assessment and Evaluation

### 9.1. How are students assessed? How will they demonstrate a mastery of the curriculum expectations?

9.1.1. Assessment For Learning

9.1.1.1. frequent self-assessment opportunities

9.1.1.1.1. how will students be able to use this to improve?

9.1.2. Assessment As Learning

9.1.2.1. scaffolding opportunities built in to mm - preferably linked to the formative assessment results

9.1.3. Assessment of Learning

9.1.3.1. summative assessment - will this be a project, test or other?

## 10. Learners

### 10.1. Who are they? Grade level, age, etc.

10.1.1. Cultural background

### 10.2. What is the learning environment? Online? Bricks and Mortar? Blended environment?

10.2.1. I always like to consider students are in the online environment then we can be sure to include the instructional elements or "teacher voice" into the mm

10.2.2. or does the environment matter?

### 10.4. Previous experience with fractions?

10.4.1. Are we using this as a remedial piece - send a student to use this multimedia piece if they are having issues with this topic....or is this something where we introduce the topic for the first time. I think the later is easier to develop for plus can be multipurpose

### 10.5. Learning accommodations or special needs?

10.5.1. ensure audio component on each page of mm

10.5.2. videos contain captions and controls to stop/pause ect.

10.5.3. avoid flash if possible to increase accessiblility

## 11. The Lesson Plan

### 11.1. Three Part lesson

11.1.1. Minds-On

11.1.1.1. How will we activate students' prior knowledge?

11.1.2. Action

11.1.2.1. Engage students in active and authentic learning tasks

11.1.3. Consolidation

11.1.3.1. Student reflection on their learning

## 12. Multimedia Tools

### 12.1. How will we build and deliver this content?

12.1.1. Website?

12.1.1.1. Weebly, Google Sites?

12.1.2. Videos?

12.1.3. Learning Objects?

### 12.2. Assessment Tools

12.2.2. Moodle Quiz

12.2.3. Existing mm

12.2.4. Discussion Forums

12.2.4.2. Moodle

### 12.3. Collaboration Tools?

12.3.2. Wikis

12.3.3. MindMeister