Science- Kindergarten
... o Take 3 add 2 each time, 2n + 1, and 1 more than twice a number all describe the pattern 3, 5, 7, … o graphing data on Aboriginal language loss, effects of language intervention one-step equations: o preservation of equality (e.g., using a balance, algebra tiles) o 3x = 12, x + 5 = 11 perimeter o A ...
... o Take 3 add 2 each time, 2n + 1, and 1 more than twice a number all describe the pattern 3, 5, 7, … o graphing data on Aboriginal language loss, effects of language intervention one-step equations: o preservation of equality (e.g., using a balance, algebra tiles) o 3x = 12, x + 5 = 11 perimeter o A ...
Mathematical Investigation: Paper Size
... preceding terms, does that mean we have to start with the first two terms or why must the second term be ‘1’? Ans: Since there is nothing in the zero-th term (T0), then T0 = 0 and so T2 = T0 + T1 = 0 + 1 = 1. So we just need the first term. But there are also other sequences that are similar to the ...
... preceding terms, does that mean we have to start with the first two terms or why must the second term be ‘1’? Ans: Since there is nothing in the zero-th term (T0), then T0 = 0 and so T2 = T0 + T1 = 0 + 1 = 1. So we just need the first term. But there are also other sequences that are similar to the ...
Year 5 Week 7 - Pearson Schools and FE Colleges
... with 1-wave pattern across 1 quadrant. Chn copy and complete [Y5] Complete wave pattern on rest with 2 lines of symmetrical patterns symmetry at right angles. Show with two lines of reflective symmetry. Draw triangles symmetry at right and reflect in mirror line. angles ...
... with 1-wave pattern across 1 quadrant. Chn copy and complete [Y5] Complete wave pattern on rest with 2 lines of symmetrical patterns symmetry at right angles. Show with two lines of reflective symmetry. Draw triangles symmetry at right and reflect in mirror line. angles ...
Full text
... In summary, (2.13) is an equation that is homogeneous of degree 6 in n, and homogeneous of degree 12 in k. To complete the proof, it suffices to verify that (2.13) is true for seven distinct values of n, say 1 ≤ n ≤ 7. To verify that (2.13) is true for n = 1, say, one simply substitutes n = 1 and ve ...
... In summary, (2.13) is an equation that is homogeneous of degree 6 in n, and homogeneous of degree 12 in k. To complete the proof, it suffices to verify that (2.13) is true for seven distinct values of n, say 1 ≤ n ≤ 7. To verify that (2.13) is true for n = 1, say, one simply substitutes n = 1 and ve ...
slides04
... multiple loops to match intuition on how control structures are used to program a solution to the problem, but data is stored sequentially, e.g., in an array or file. Programming based on control leads to more problems than programming based on structure. Therefore, use the structure of the data to ...
... multiple loops to match intuition on how control structures are used to program a solution to the problem, but data is stored sequentially, e.g., in an array or file. Programming based on control leads to more problems than programming based on structure. Therefore, use the structure of the data to ...
Dropping Glass Balls Glass balls revisited (more balls)
... multiple loops to match intuition on how control structures are used to program a solution to the problem, but data is stored sequentially, e.g., in an array or file. Programming based on control leads to more problems than programming based on structure. Therefore, use the structure of the data to ...
... multiple loops to match intuition on how control structures are used to program a solution to the problem, but data is stored sequentially, e.g., in an array or file. Programming based on control leads to more problems than programming based on structure. Therefore, use the structure of the data to ...
1.1 Patterns and Inductive Reasoning
... 2 can be written as the sum of two primes. This is called Goldbach’s Conjecture. No one has ever proven this conjecture is true or found a counterexample to show that it is false. As of the writing of this text, it is unknown if this conjecture is true or false. It is known; however, that all even n ...
... 2 can be written as the sum of two primes. This is called Goldbach’s Conjecture. No one has ever proven this conjecture is true or found a counterexample to show that it is false. As of the writing of this text, it is unknown if this conjecture is true or false. It is known; however, that all even n ...
Full text
... originally referred to the vertically placed bar that cast the shadow on a sundial. The ancient Greeks also inherited a large body of algebra from the Babylonians, which they proceeded to recast into geometric terms. The gnomon became a recurrent figure in the Greek geometric algebra. There are seve ...
... originally referred to the vertically placed bar that cast the shadow on a sundial. The ancient Greeks also inherited a large body of algebra from the Babylonians, which they proceeded to recast into geometric terms. The gnomon became a recurrent figure in the Greek geometric algebra. There are seve ...
Unit 3: Algebraic Connections
... Use the rule “add 3” to write a sequence of numbers. Starting with a 0, students write 0, 3, 6, 9, 12, . . . Use the rule “add 6” to write a sequence of numbers. Starting with 0, students write 0, 6, 12, 18, 24, . . . After comparing these two sequences, the students notice that each term in the sec ...
... Use the rule “add 3” to write a sequence of numbers. Starting with a 0, students write 0, 3, 6, 9, 12, . . . Use the rule “add 6” to write a sequence of numbers. Starting with 0, students write 0, 6, 12, 18, 24, . . . After comparing these two sequences, the students notice that each term in the sec ...
GCD and LCM - UH - Department of Mathematics
... calculators to assist them in identifying patterns. ...
... calculators to assist them in identifying patterns. ...
Full text
... 1. The Fibonacci Composition Array To form the Fibonacci composition array, we use the difference of the subscripts of Fibonacci numbers to obtain a listing of the compositions of n in terms of ones and twos, by using Fn^1, in the rightmost column, and taking the Fibonacci numbers as placeholders. W ...
... 1. The Fibonacci Composition Array To form the Fibonacci composition array, we use the difference of the subscripts of Fibonacci numbers to obtain a listing of the compositions of n in terms of ones and twos, by using Fn^1, in the rightmost column, and taking the Fibonacci numbers as placeholders. W ...
Patterns and sequences
... Look at what is happening from 1 TERM to the next. See if that is what is happening for every TERM. ...
... Look at what is happening from 1 TERM to the next. See if that is what is happening for every TERM. ...
Detailed Lesson Plans
... T: Let's see how much we have remembered from our revision session. Try these tasks on your own: For each of the following sequences: - work out the difference - determine the next 3 terms using this rule - write down the formula of the sequence - check the formula using n = 1 and n = 4 - write down ...
... T: Let's see how much we have remembered from our revision session. Try these tasks on your own: For each of the following sequences: - work out the difference - determine the next 3 terms using this rule - write down the formula of the sequence - check the formula using n = 1 and n = 4 - write down ...
Patterns and Functions TABLE OF CONTENTS
... Students should be able to use a calculator throughout this activity. When the same calculation is performed repeatedly, it is helpful to use the constant function on the calculator. Some calculators have a constant key. In this case, you will key in the calculation, for example: [+] [1] [1] (plus 1 ...
... Students should be able to use a calculator throughout this activity. When the same calculation is performed repeatedly, it is helpful to use the constant function on the calculator. Some calculators have a constant key. In this case, you will key in the calculation, for example: [+] [1] [1] (plus 1 ...
Junior - CEMC - University of Waterloo
... side of the main stem. These leaves once again have groups of leaves branching off of a main stem. Even the smallest size leaves we can see on the fern have a bumpy shape that is similar to the entire fern. What are other examples of fractals in nature? blood vessels, broccoli, mountain ranges, naut ...
... side of the main stem. These leaves once again have groups of leaves branching off of a main stem. Even the smallest size leaves we can see on the fern have a bumpy shape that is similar to the entire fern. What are other examples of fractals in nature? blood vessels, broccoli, mountain ranges, naut ...
Math Patterns and Functions K-8
... Describe situations in which the relationship between two quantities vary directly or inversely Extend, create, and generalize growing and shrinking numeric and geometric patterns (including multiplication patterns) Represent the relationship between quantities in a variety of forms (e.g., manipulat ...
... Describe situations in which the relationship between two quantities vary directly or inversely Extend, create, and generalize growing and shrinking numeric and geometric patterns (including multiplication patterns) Represent the relationship between quantities in a variety of forms (e.g., manipulat ...
Number Patterns - Standards Toolkit
... Number Patterns Grade Level: 1 Mathematics Domain and Cluster: Extend the counting sequence. Use place value understanding and properties of operations to add and subtract. Common Core standard(s) being assessed (if the task is intended to assess only one part of the standard, underline that par ...
... Number Patterns Grade Level: 1 Mathematics Domain and Cluster: Extend the counting sequence. Use place value understanding and properties of operations to add and subtract. Common Core standard(s) being assessed (if the task is intended to assess only one part of the standard, underline that par ...
Full text
... and copy out the visible letters, which are (serially, row by row) ITTIAOHTSOLOC. We then rotate the grid counterclockwise through 90° and again copy out the visible letters, which are IOLESIHIMLTAIM. Two more rotations gives us UMKAFGHGSYSODand NILHFLHNAIMFRE. Running these four groups together and ...
... and copy out the visible letters, which are (serially, row by row) ITTIAOHTSOLOC. We then rotate the grid counterclockwise through 90° and again copy out the visible letters, which are IOLESIHIMLTAIM. Two more rotations gives us UMKAFGHGSYSODand NILHFLHNAIMFRE. Running these four groups together and ...
Concatenation of Consecutive Fibonacci and Lucas Numbers: a
... Summary. Our look at two special sequences and the concatenation of consecutive terms in them has paid off in patterns of division and in providing the need for proofs by induction. Other special sequences can be looked at in this way. For instance the author has considered the sequence of triangula ...
... Summary. Our look at two special sequences and the concatenation of consecutive terms in them has paid off in patterns of division and in providing the need for proofs by induction. Other special sequences can be looked at in this way. For instance the author has considered the sequence of triangula ...
DOC
... Write the formula, without words for the number of white squares. Use b for the number of black squares and w for he white squares. Start with w = ...
... Write the formula, without words for the number of white squares. Use b for the number of black squares and w for he white squares. Start with w = ...
Year group - Bishopsworth
... sides, diagonals). Show a shape cut out of card and ask children to describe its properties, ensuring use of correct vocabulary. Could use virtual pinboard to create shapes ...
... sides, diagonals). Show a shape cut out of card and ask children to describe its properties, ensuring use of correct vocabulary. Could use virtual pinboard to create shapes ...
Patterns in nature
Patterns in nature are visible regularities of form found in the natural world. These patterns recur in different contexts and can sometimes be modelled mathematically. Natural patterns include symmetries, trees, spirals, meanders, waves, foams, tessellations, cracks and stripes. Early Greek philosophers studied pattern, with Plato, Pythagoras and Empedocles attempting to explain order in nature. The modern understanding of visible patterns developed gradually over time.In the 19th century, Belgian physicist Joseph Plateau examined soap films, leading him to formulate the concept of a minimal surface. German biologist and artist Ernst Haeckel painted hundreds of marine organisms to emphasise their symmetry. Scottish biologist D'Arcy Thompson pioneered the study of growth patterns in both plants and animals, showing that simple equations could explain spiral growth. In the 20th century, British mathematician Alan Turing predicted mechanisms of morphogenesis which give rise to patterns of spots and stripes. Hungarian biologist Aristid Lindenmayer and French American mathematician Benoît Mandelbrot showed how the mathematics of fractals could create plant growth patterns.Mathematics, physics and chemistry can explain patterns in nature at different levels. Patterns in living things are explained by the biological processes of natural selection and sexual selection. Studies of pattern formation make use of computer models to simulate a wide range of patterns.