Tutorials (Pictures)
Posted on: October 13, 2010
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EAB 023 : Pictures from tutorials
The whole semester memories
Probability (Activity)
Posted on: October 13, 2010
Probability (Activity)
Activity 1 : Probabilities with cards (Hatfield, p. 445, 2005)
Directions:
- Place five cards with the numbers o through 4 on them in a cardboard box.
- What is the probability of drawing a card with a number less than 5 on it? There are five possible outcomes and none of them are favorable; therefore, the probability of drawing a card with a number less than 5 on it is 5/5 = 1.
- What is the probability of drawing a card with a number greater than on it? There are five possible outcomes and none of them are favorable- the probability of this occurring is 0/5 or 0.
- If an event is sure to happen, the probability is 1. If there is no favorable outcome and an event is sure not to happen, the probability is 0.
Activity 2 : Probability Path(Hatfield, p. 446, 2005)
Directions
Follow the possibility path. Tossing a die five times will get you from the start position to one of the lettered boxes.
- Toss the die. If the number on the die is odd, follow the odd path. If the number is even, follow the event path.
- Follow the path twenty five times. Keep a tally mark record of the box in which you finish each time. Which boxes do you end in most often? Least often?
- What percent of the twenty five tosses lands in each box?
probability path
this picture was taken during probability tutorial
Statistics & Probability
Posted on: October 13, 2010
Statistics and Probability
From my understanding, probability is examining the chance of any events will happen. Probability is to predict the chance of something occurring. For example:
- The probability of shark attack in Malaysia is 0 in 100
- She has 50-50 chance of passing the exam
- The chance of snow today is 70%
According to Hatfield (2005), the basic purpose of probability theory is “to attempt to predict the likelihood that something will or will not occur”.
Probability of an event = Number of actual outcomes/ Total number of possible outcomes
“Chance deals with the concepts and randomness and the use of probability as a measure of how likely it is that particular events will occur” (Australian Education Council, 1991, p.27)
Classroom Activities for Children
These activities are taken from Early Mathematical Exploration book by Nicola Yelland, Deborah Butler and Carmel Diezmann (p.115-127, 1999)
Activity 1 : Train Tracks (Length)
Estimating and comparing length in non standard units
Materials : plasticine, paper clips and newspapers
Activity: Have the children roll their pieces of plasticine into a long train. Discuss how many paper clips long they think their train is and how they could find out using only one paper clip. Remind the children that they must make the first imprint so that the end of the paper clip is at the end of the train and that each imprint must ouch the one before it.
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Activity 2 : Mini-Olympics (Length)
Hold a mini-Olympics in the playground. Have the children measure how far they can throw a beanbag or jump from a standing position. The distance can be measured in footsteps, handsteps, handspans, body lengths, or metres.
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Activity 3 : How Many Squares? (Area)
Measuring and comparing area
Materials: geoboards and elastic bands
Activity: Using elastic bands and a geoboard, the children explore the different shapes they can make using six whole squares. Change the number of squares that can be used.
Variation: In pairs, one child makes a shape without showing it to his partner. this is then described to the partner giving enough information for the partner to copy it.
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Activity 4 : Which Holds More ? (Volume)
Materials : 3 different sized containers, water, rice or sand
Activity: provide each pair of children with 3 containers. Label the container with different symbol. Have them estimate which container holds the most and which container hold the least. Encourage the children to use the materials to measure and compare the volume of the containers. Ask questions to initiate discussion.
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Activity 5 : Guess and Measure (Mass)
Estimating and measuring mass in non-standard units
Materials : balance scales, identical containers filled with foam, shells, cotton wool, sand, blocks, salt, flour, counters or nails
Activity: Prepare four containers and label them so that the children know the contents. Invite the children to estimate which container they think will be lightest or heaviest and to explain why. Ask the children for ways to check their estimates and encourage them to try out their suggestions. Ask them to order the containers from lightest to heaviest. Children discuss their results.
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Measurement (1)
Posted on: October 10, 2010
Measurement
Measurement involved in our daily life. Measurement is everywhere.
Most of our typical activities need measurement. Measure the distance of a journey. Measure the amount of ingredients when we are cooking. Measure our height and weight.
According to Yelland et al,(1999), measurement is “finding out ‘how much’ of a particular attribute” and also involves “understanding of the attribute to be measured, knowledge of how to measure the attribute, and good number understanding”.
Measurement experiences
1. Length
Measure of something from one point to another point. Standard unit for length are the metre (m), the centimetre(cm) and the kilometre(km).
2. Area
Area is associated with coverage. Look for areas that are covered by objects that can be counted (Yelland et al, 1999).
3. Volume and capacity
Refers to three-dimensional space that is occupied by a substance, such as water and sand (Yelland et al, 1999). Standard units for volume are the litre(L) and mililitre(mL).
4. Mass
Mass are related to matter and heaviness of objects. The standard units for mass are the kilogram(kg) and gram(g)
5. Time
Understanding the sequence of events (eg: mathematics period is after geography period), duration of events (mathematics period is 1 hour) and the length of various units of time (eg: minutes, hours).
Reading an analogue clock requires an understanding of the role of each hand and the relationship between each hand and the number it is pointing (Yelland et al, 1999). For example, if the hour hand is pointing to 8, I say “Eight”. On the other hand, when the minute hand is pointing to the 8, I say “40 past”.
6. Temperature
Temperature is the state or degree of hot and cold in atmosphere, objects or body. The units for temperature is Kelvin (K), Celsius ( °C) and Fahrenheit ( °F).
Reference
Images taken from:
Geometry (Activity)
Posted on: October 10, 2010
Geometry (activity)
These activities are taken from Early Mathematical Exploration book by Nicola Yelland, Deborah Butler and Carmel Diezmann (p.115-127, 1999)
Activity 1 : Analyzing 3D shapes
Materials: fresh fruit or vegetables, coloured playdough, plastic knives, plates
Activity: A child models a piece of fruit or vegetable from the appropriately coloured playdough. The child cuts the item into a couple of pieces and puts them on plate. Another child identifies common 3D shapes on the plate and tries to recreate the piece of fruit or the vegetable. For example, a corrot would be made from orange playdough and when cut could have a cone and a cylinder
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Activity 2 : Spot the Shape
Identifying plane shapes in everyday objects
Materials: magazines
Activity: Children search for particular 2D shapes (eg; square) in a magazine and mark all shapes with a coloured spot
Variation: All items “spotted” for a particular shape could be cut out, put into a shape book and given a simple caption
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Activity 3 : Geoboard challenge
Challenge the children to make as many different triangles as they can using rubber bands on geoboards. Triangles can vary in their size, the relative lengths of the sides, the relative size of the angles and their position.
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Activity 4 : Forever Friends
Exploring symmetry
Materials: Paper, scissors, coloured wool
Activity: Children make a chain of paper dolls to represent themselves and their friends. They add facial features to each of the dolls to show how the individual characteristics of each person and add clothing. Wool can be added for hair.
Variation: Children could make a class chain. after each child has added their own features the chain is displayed on the wall and the class plays Guess Who?
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Reference
Images taken from:
Geometry (2)
Posted on: October 10, 2010
Developing Geometry Concepts
The van Hiele Levels
This concept has been introduced by two Dutch educators, Pierre van Hiele and Dina van Hiele. It refers to the study of children’s acquisition of geometric concepts and the development of geometric thought. There are five levels in this concepts discus by Clement, Fuys and Liebov (as cited in Hatfield et al., 2005)
Level 0 – Visualisation
- Students reason about basic geometric concepts
- React to geometric figures as wholes
- eg: a square is a square because it looks like one
Level 1 –Analysis
- Informal analysis of the parts and attributes and relationships among the parts of the figure
- eg: a square is a square because it has four equal sides and four right angles
Level 2 – Abstraction
- Logically orders the properties of concepts
- Form abstract definition
- eg: a square can be seen as both rectangular and paralelogram
Level 3 – Deduction (suits high school level)
- reasons formally within the context of a mathematical system
- complete with undefined terms, axioms and underlying logical system, definitions and theorems
Level 4 – Rigor
- compare systems based on different axioms and can study various geometries in the absence of concrete models.
Gsong that relates shapes to the real objects:
Video derived from:
video1-http://www.youtube.com/watch?v=o4zDyxxf8Gs
video2-http://www.youtube.com/watch?v=QpI7Ox17_fM
Geometry (1)
Posted on: October 10, 2010
Geometry
Geometry is all related to shapes and its properties.
Shape
Developing an understanding of shape involves “being able to identify, represent, visualize and analyze two-dimension and three-dimensional shapes” (Yelland, et.al, p.114, 1999).
In order to analyze shapes, children need to know the properties of the shapes and the relationships between shapes. Teachers should provide opportunities for students to build up practical knowledge about shape and its relationship to the physical world. For example:
- What is the shape of your pencil case?
- Can you name some shapes in this classroom?
- Can you name things that are square/ round, triangle?
Understanding of shapes are described under these categories: (Bobis, et al, 2009)
- Classifying shape and structure
- Transformation and symmetry
- Location and arrangement
Symmetry
There are two types of symmetry that commonly use to describe geometric shapes. (Bobis, et al, 2009)
- Line symmetry
~ associated with reflections
- Rotational symmetry
~ involves turning about a central point
Reference
Images taken from:
Algebra (Activity)
Posted on: October 9, 2010
Algebra (activity)
The activities are adapted from Elemantary and Middle School Mathematics, Teaching Developmentally by John A. Van De Walle (p.268, 2007)
Activity 1 : Pattern Strips
- Student can work group to extend patterns made from simple materials : coloured blocks, connecting cubes, buttons, geometric shapes.
- For each set of materials, draw two or three complete repetitions of a pattern on strips of tagboard about 5cm by 30cm.
- The students’ task is to use actual materials, copy the patterns for a variety of materials. Makes 10 to 15 different pattern strips for each set of materials.
- With six to eight sets, your entire class can work at the same time, in small groups working with different patterns and different materials.
Activity 2 : Same Pattern, Different Stuff
- Have students make a pattern with one set of materials given a pattern strip showing a different set.
- This activity can easily be set up by simply switching the pattern strips from one set of materials to another.
- A similar idea is to mix up the pattern strips for four or five different sets of materials and have students find strips that have the same pattern.
- To test if two patterns are the same, children can translate each of the strips into a third set of materials or can write down the A, B, C pattern for each.
Algebra (2)
Posted on: October 9, 2010
Algebra
Algebra is a study of patterns and relationships. Patterns and relationships are important in their own right, and studying them leads naturally into algebraic ideas.
Provides strategies for analyzing representataions, modeling situations, generalizing ideas and justifying statements. (Reys et al., 2007)
Pattern
? ? ?
Ask questions like:
- What is the tenth term?
- What shape is the twelfth term? Eighteenth term?
- How many of each shape are needed to extend the pattern to 30 terms?
Relations
Two types of relations: (Reys et al., p. 340-341, 2007)
1. properties of numbers
eg; the sum of an odd number and an odd number is even
o if a number is divisible by 2 and 3, then it is divisible by 6
2. functions
two sets of numbers are related in such a way that each number in the first set is related to one and only onenumber in the second set
Generalisation
Two ways of generalizations: (Reys et al., 2007)
- as a recursive expression
~ tells how to find the value of a term given the value of the previous term
- as a explicit equation
~calculate the value of one term given the number of the term.
Algebra
Posted on: October 9, 2010
Algebra
From my understanding, Algebra is a mathematical concept that is related to patterns, functions, relationships and changes.
Algebra is “a generalization of the ideas of arithmetic where unknown values and variables can be found to solve problems” (Taylor-Cox, 2003, p. 14).
Algebraic thinking
Algebraic thinking has been described as “the kinds of generalizing that precede or accompany the use of algebra” (Smith, 2003)
To think algebraically, you must (Hatfield et al., p.394, 2005):
- Have a conceptual understanding of patterns, relations, and functions
- Be able to represent and analyze mathematical situations and structures
- Be able to use mathematical models in representing quantitative relationships
- Be able to analyze change in a variety of contexts
Patterns
Mathematical patterns is any form of regularity or repetition.
Patterning involves “observing, representing and investigating patterns and relationships in social, and physical phenomena, and between mathematical objects themselves” (Australian Education Council, 1991, p. 4).
Repeating patterns
A set or sequence that is repeated over and over.
“repeating patterns must contain an identifiable unit of repeat where the pattern is produced by the continual use of a smaller segment or element” (Bobis et al., 2009, p.63)
Functions
Recognize and identify how ‘things’ change in relation to each other.
Describe the rules that show how the ‘things’ are related
“A function is a specific relation in which every element in one set is associated with one and only one element in another set” (Hatfieild, et,al., p.421, 2005)
Math's Cool 
