2016 Mathematics Contests – The Australian Scene Part 1
... (AMO) proved fairly demanding, with just three perfect scores. The International Mathematical Olympiad (IMO) also proved quite challenging for Australia, after three very strong years in a team led by Alex Gunning. Commendably, this year’s team all obtained medals (two Silver and four Bronze) but we ...
... (AMO) proved fairly demanding, with just three perfect scores. The International Mathematical Olympiad (IMO) also proved quite challenging for Australia, after three very strong years in a team led by Alex Gunning. Commendably, this year’s team all obtained medals (two Silver and four Bronze) but we ...
Mathematics MAT421A - Prince Edward Island
... The teacher should take advantage of the various opportunities available to integrate mathematics and other subjects. This integration not only serves to show students how mathematics is used in daily life, but it helps strengthen the understanding of mathematical concepts by students and provides t ...
... The teacher should take advantage of the various opportunities available to integrate mathematics and other subjects. This integration not only serves to show students how mathematics is used in daily life, but it helps strengthen the understanding of mathematical concepts by students and provides t ...
3. Mathematical Induction 3.1. First Principle of
... The second principle of induction differs from the first only in the form of the induction hypothesis. Here we assume not just P (n), but P (j) for all the integers j between k and n (inclusive). We use this assumption to show P (n + 1). This method of induction is also called strong mathematical in ...
... The second principle of induction differs from the first only in the form of the induction hypothesis. Here we assume not just P (n), but P (j) for all the integers j between k and n (inclusive). We use this assumption to show P (n + 1). This method of induction is also called strong mathematical in ...
MTH55A_Lec-10_sec_4
... Solving Linear InEqualities 1. Simplify both sides of the inequality as needed. a. Distribute to clear parentheses. b. Clear fractions or decimals by multiplying through by the LCD just as was done for equations. (This step is optional.) c. Combine like terms. ...
... Solving Linear InEqualities 1. Simplify both sides of the inequality as needed. a. Distribute to clear parentheses. b. Clear fractions or decimals by multiplying through by the LCD just as was done for equations. (This step is optional.) c. Combine like terms. ...
Pythagorean Triples Solution Commentary:
... the connection to the Greek idea of “applying areas.” As a first step, the square of side length c can be visualized as containing a square of side length a. Once the latter square is removed, is it possible to transform the remaining “area” into a square of side length b? You might want to have stu ...
... the connection to the Greek idea of “applying areas.” As a first step, the square of side length c can be visualized as containing a square of side length a. Once the latter square is removed, is it possible to transform the remaining “area” into a square of side length b? You might want to have stu ...
Unit B391/01 – Sample scheme of work and lesson plan
... produced sample schemes of work and lesson plans for Methods in Mathematics. These support materials are designed for guidance only and play a secondary role to the specification. Each scheme of work and lesson plan is provided in Word format – so that you can use it as a foundation to build upon an ...
... produced sample schemes of work and lesson plans for Methods in Mathematics. These support materials are designed for guidance only and play a secondary role to the specification. Each scheme of work and lesson plan is provided in Word format – so that you can use it as a foundation to build upon an ...
Content Area: Mathematics Standard: 4. Shape, Dimension, and Geometric Relationships
... When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. (CCSS: K.CC.4a) Understand that the last number name said tells the number of objects counted. The number of objects is the same ...
... When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. (CCSS: K.CC.4a) Understand that the last number name said tells the number of objects counted. The number of objects is the same ...
Standard/Benchmark/Indicator
... Student realizes that there are a variety of ways to represent expressions such as 2x is the same as x + x or $.50 can be represented with two quarters ($.25 = $.25) or five dimes ($.10 + $.10 + $.10 + $.10 + $.10). Use equivalent representations for fractional operations such as 2/4 + 2/4 which equ ...
... Student realizes that there are a variety of ways to represent expressions such as 2x is the same as x + x or $.50 can be represented with two quarters ($.25 = $.25) or five dimes ($.10 + $.10 + $.10 + $.10 + $.10). Use equivalent representations for fractional operations such as 2/4 + 2/4 which equ ...
Mathematics 20
... In Section 2.1, when grouping within a polynomial, pairs of terms were grouped together. It is also possible to group together three terms that form a special polynomial. This special polynomial will usually be a trinomial square. It is therefore necessary to be able to recognize a perfect trinomial ...
... In Section 2.1, when grouping within a polynomial, pairs of terms were grouped together. It is also possible to group together three terms that form a special polynomial. This special polynomial will usually be a trinomial square. It is therefore necessary to be able to recognize a perfect trinomial ...
Answers
... (d) True - a square is a special type of rectangle. However, the converse is false, not every rectangle is a square. (e) False (the circumference of a circle is only approximately 3 times the diameter) (f) True ...
... (d) True - a square is a special type of rectangle. However, the converse is false, not every rectangle is a square. (e) False (the circumference of a circle is only approximately 3 times the diameter) (f) True ...
open -ended questions for mathematics
... Now for the intentions for the use of these questions. The questions identified for grades 4, 5, and 8 should be used as classroom practice questions. Students can either work with them as members of cooperative groups or the teacher can use the questions for demonstration purposes to illustrate pro ...
... Now for the intentions for the use of these questions. The questions identified for grades 4, 5, and 8 should be used as classroom practice questions. Students can either work with them as members of cooperative groups or the teacher can use the questions for demonstration purposes to illustrate pro ...
Task - Illustrative Mathematics
... These conjectures are likely best discussed in small groups and/or with the whole class, and so is best used in instructional, rather than assessment-based, settings. The discussions generated by student conjectures will likely yield productive insights into the nature of sums and products of real n ...
... These conjectures are likely best discussed in small groups and/or with the whole class, and so is best used in instructional, rather than assessment-based, settings. The discussions generated by student conjectures will likely yield productive insights into the nature of sums and products of real n ...
Section 3 - The Open University
... and proofs during your study of mathematics. In this section we examine these concepts more closely. This should help you to become more adept at reading and understanding mathematics, and should make you more familiar with the structures of various different types of mathematical proof. It should al ...
... and proofs during your study of mathematics. In this section we examine these concepts more closely. This should help you to become more adept at reading and understanding mathematics, and should make you more familiar with the structures of various different types of mathematical proof. It should al ...
1.5 Methods of Proof
... In this section rules of inference will be discussed. This will help clarify what makes up a correct proof. Some common forms of incorrect reasoning, called fallacies, will also be described. Then various methods commonly used to prove theorems will be introduced. The terms lemma and corollary are u ...
... In this section rules of inference will be discussed. This will help clarify what makes up a correct proof. Some common forms of incorrect reasoning, called fallacies, will also be described. Then various methods commonly used to prove theorems will be introduced. The terms lemma and corollary are u ...
CHAPTER 10 Mathematical Induction
... need to prove that they are all true. The method is really quite simple. To visualize it, think of the statements as dominoes, lined up in a row. Imagine you can prove the first statement S1 , and symbolize this as domino S1 being knocked down. Additionally, imagine that you can prove that any state ...
... need to prove that they are all true. The method is really quite simple. To visualize it, think of the statements as dominoes, lined up in a row. Imagine you can prove the first statement S1 , and symbolize this as domino S1 being knocked down. Additionally, imagine that you can prove that any state ...
Unit B392/02 – Sample scheme of work and lesson plan
... produced sample schemes of work and lesson plans for Methods in Mathematics. These support materials are designed for guidance only and play a secondary role to the specification. Each scheme of work and lesson plan is provided in Word format – so that you can use it as a foundation to build upon an ...
... produced sample schemes of work and lesson plans for Methods in Mathematics. These support materials are designed for guidance only and play a secondary role to the specification. Each scheme of work and lesson plan is provided in Word format – so that you can use it as a foundation to build upon an ...
syllabus - Cambridge International Examinations
... 4. apply mathematics in everyday situations and develop an understanding of the part that mathematics plays in the world around them; 5. solve problems, present the solutions clearly, check and interpret the results; 6. develop an understanding of mathematical principles; 7. recognize when and how a ...
... 4. apply mathematics in everyday situations and develop an understanding of the part that mathematics plays in the world around them; 5. solve problems, present the solutions clearly, check and interpret the results; 6. develop an understanding of mathematical principles; 7. recognize when and how a ...
Primes and Greatest Common Divisors
... the product of all the primes plus one. By hypothesis q cannot be prime because it is strictly larger than all the primes. Thus, by the lemma, it has a prime divisor, p. Because p1 , p2 , p3 , . . . , pk are all the primes, p must be equal to one of them, so p is a divisor of their product. So we ha ...
... the product of all the primes plus one. By hypothesis q cannot be prime because it is strictly larger than all the primes. Thus, by the lemma, it has a prime divisor, p. Because p1 , p2 , p3 , . . . , pk are all the primes, p must be equal to one of them, so p is a divisor of their product. So we ha ...
Roselle Park School District
... effectively. They need to use complex information and advanced tools. They need to know and understand how to use and apply mathematics. These high standards will benefit both our children and our society. The Roselle Park High School Mathematics Curriculum will develop students’ understanding of co ...
... effectively. They need to use complex information and advanced tools. They need to know and understand how to use and apply mathematics. These high standards will benefit both our children and our society. The Roselle Park High School Mathematics Curriculum will develop students’ understanding of co ...
Unit A502/01 - Sample scheme of work and lesson plan booklet (DOC, 4MB)
... In order to help you plan effectively for the implementation of the new specification we have produced sample schemes of work and lesson plans for Mathematics A. These support materials are designed for guidance only and play a secondary role to the specification. Each scheme of work and lesson plan ...
... In order to help you plan effectively for the implementation of the new specification we have produced sample schemes of work and lesson plans for Mathematics A. These support materials are designed for guidance only and play a secondary role to the specification. Each scheme of work and lesson plan ...
MCYA - Australian Mathematics Trust
... The AMOC Senior Problems Committee has been chaired for first time by Dr Norman Do, another former Olympian and Deputy Leader of the IMO team. Norm has done a terrific job in his first year in this position. The invitational program saw some outstanding results from Australian students, with a numb ...
... The AMOC Senior Problems Committee has been chaired for first time by Dr Norman Do, another former Olympian and Deputy Leader of the IMO team. Norm has done a terrific job in his first year in this position. The invitational program saw some outstanding results from Australian students, with a numb ...
1. Number Sense, Properties, and Operations
... whole numbers in problem situations including comparisons of savings rates at different financial institutions (PFL) vii. Express the comparison of two whole number quantities using differences, part-to-part ratios, and part-to-whole ratios in real contexts, including investing and saving (PFL) viii ...
... whole numbers in problem situations including comparisons of savings rates at different financial institutions (PFL) vii. Express the comparison of two whole number quantities using differences, part-to-part ratios, and part-to-whole ratios in real contexts, including investing and saving (PFL) viii ...