Math's Cool

EAB 023  : Pictures from tutorials


The whole semester memories

 

 

 

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 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


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)

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:

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