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The mean is the most commonly used measure of average close. To calculate the mean, add the values together and divide the total by the number of values.
A sequence a1, a2, a3, a4,... is an arithmetic sequence if there is a number c such that for each n, an + 1= an + c, that is an + 1 – an = c. Associative Property of Addition. For any numbers x, y , and z: (x + y) + z= x + (y + z). Attribute. A distinguishing characteristic of an object such as angles or sides of a triangle. Average. See: Mean.
From the Latin fac simile, meaning “made like,” the word facsimile refers to a process, system, or apparatus for reproducing graphic material at a distance. A drawing, page of text, or black-and-white picture is scanned by a light-sensitive device to produce an electric signal.
- Specialising
- Generalising
- Conjecturing
- Convincing
- Characterising
- Classifying
- Critiquing
- Improving
- Four Pairs of Thinking and Working Mathematics Characteristics
- Summary
Cambridge International’s definition: choosing an exampleand checking to see if it satisfies or does not satisfy specific mathematical criteria*. Specialising is often a good place to begin thinking about a mathematical question. It means considering a simpler or familiar example. The act of specialising is not to get to an answer as such, but rath...
Cambridge International’s definition: recognising an underlying pattern by identifying manyexamples that satisfy the same mathematical criteria. Generalising is the process of not focusing on one particular example, but rather trying to see a relationship among many. Example Let me use specialising again with another example: 5 + 7 = 12 Again, an o...
Cambridge International’s definition: forming mathematical questions or ideas. Conjectures are thoughtful ideas or guesses – they might turn out to be untrue. Once a conjecture has been made, learners should try to justify it mathematically. Example I conjecture that when you multiply an even number by an odd number the answer will be an even numbe...
Cambridge International’s definition: presenting evidence to justify or challenge a mathematical idea or solution. Developing mathematical reasoning involves trying to convince yourself and then someone else. It helps if the person you are trying to convince asks thoughtful questions. They should be convinced (or otherwise) through mathematical rea...
Cambridge International’s definition: identifying and describing the mathematical properties of an object. Learners often characterise mathematical shapes to find similarities and differences between them. Example Look for things that identify a kite: A kite is a 2D shape with four straight sides. It has two pairs of equal-length sides that are adj...
Cambridge International’s definition: organising objects into groups according to their mathematical properties. When we classify things, we sort them or group them based on similar characteristics. Example Sort these shapes by characteristics they have in common – square, kite, pentagon. A square is a 2D shape with four equal straight sides. It ha...
Cambridge International’s definition: comparing and evaluating mathematical ideas, representations or solutions to identify advantages and disadvantages. When we critique mathematical ideas or solutions, we are reflecting on what we can see. It also offers the opportunity to consider and discuss alternative viewpoints. Critiquing offers students th...
Cambridge International’s definition: refining mathematical ideas or representations to develop a more effective approach or solution. We can all improve and so it is an important characteristic to be able to reflect, refine and develop our mathematical ideas and solutions based on critiquing by ourselves or others to find more elegant solutions. E...
Specialising and GeneralisingConjecturing and ConvincingCharacterising and ClassifyingCritiquing and ImprovingThis blog gives you an insight into the TWM characteristics and hopefully you’re now feeling prepared and excited to bring them into your maths lessons. If you are looking for more support, the Cambridge University Press revised Primary and Lower Secondary mathematics seriessupports the 8 TWM characteristics, just look for the activities with the s...
A facsimile is a copy or reproduction of something. Many parents hope their children will be facsimiles of themselves; many children have other plans in mind. Facsimile comes from two Latin roots: facere, meaning "to make," and simile, meaning "like."
These symbols help to represent mathematical concepts and equations concisely. Math symbols turn a lengthy explanation into a quick, easy calculation, helping you easily find the answer. Example: Imagine you’re planning to find the area of a garden.
Mean, Median, and Mode Quick Quiz I. Answer the following questions. a) What is the mean of set A? A = {4, -2, 1/2, 7.5, 0} b) Amy's math grades are in the grid on the light. What is her 'homework' average? What is the mean of her 'quiz' grades? Amy's final grade is determined as follows: 20% homework 50% quizzes 30% final exam
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