This is a fascinating aspect of mathematics that two seemingly unconnected topics are in fact connected. In this case we have a connection between Algebraic expansions and selections. The number of ways of selecting r objects from a total of n is written as nCr So the above selections can be written mathematically as follows: Mathematically, the answer is8C6.
Ask the students to recall what a multiple is and to think of an example. Have a student share his example with the class.
Have the students also consider Pascal's Triangle. If your class has not studied it previously, ask, "Has anyone ever heard of Pascal's Triangle?
Ask students, "Did you know that multiples make a pattern in Pascal's Triangle?
Say something like this: Today, class, we will be talking about the patterns that multiples create in Pascal's Triangle. We are going to use the computers to learn about these patterns, but please do not turn your computers on or go to this page until I ask you to.
I want to show you a little about Pascal's Triangle and its patterns first. Teacher Input In this part of the lesson you will explain to the students how to do the assignment.
You should model or demonstrate it for the students, especially if they are not familiar with how to use our computer applets.
You may need to lead a discussion on Pascal's Triangle. Check to be sure that the students understand how to make Pascal's Triangle by having them create a portion on paper, or by drawing one on the board or overhead projector as they tell you what to write.
Open your browser but don't let the students open theirs yet to Coloring Multiples In Pascal's Triangle in order to demonstrate this activity to the students.
Ask students if the triangle that they created looks like the one displayed on the screen. You must now explain the applet to the students. This can best be done by setting your own number: Ask students to name multiples of 4 that they see in the triangle.
They will probably name numbers such as 4, 8, 12, 20, 28, and Click on these numbers to highlight them as the students call them out. You may have to give hints to help students determine the larger multiples of: Encourage the students to look for the pattern and make an educated guess about the larger multiples of 4.
Ask, "Can you guess, based on the pattern, what the large multiples are, without using a calulator? Ask a student to describe the pattern that she sees after all the multiples have been found. Ask the students what types of shapes are made by the multiples within the Pascal's Triangle.
Guided Practice Try another example, letting the students direct your moves. Or, you may simply ask, "Can anyone describe the steps you will take for this assignment? This time, choose a number such as 8 to try the example with.
Let the students call out multiples of 8 that they see in the triangle. The multiples of 8 include: You might want to ask students to compare this pattern to the one that was formed by the multiples of 4. Be sure to point out that all of the multiples of 8 are also multiples of 4 and yet the patterns are very different since the multiples of 4 are not necessarily multiples of 8.
Independent Practice Allow the students to work on their own to complete the rest of the worksheet. Monitor the room for questions and to be sure that the students are on the correct web site. Students may need help with finding the multiple of the harder numbers, such as 7.Extra Practice Worksheets with Answers; Video Tutorials; kaja-net.com1 - Exponents.
Balancing Equations. Class Notes and Online Resources; Extra Practice Worksheets with Answers; Video Tutorials; Writing and Graphing an Equation. Class Notes and Online Resources; Extra Practice Worksheets with Answers; Video Tutorials;. Solving Linear Equations One Variable 1 MULTIPLE CHOICE.
Choose the one alternative that best completes the statement or answers the question. Solve the equation. 1) y 10 = (- 9)2 - 23 + (- 3)2 1) Write the sentence as an equation.
25) The difference of - 40 and 7 is - 25). Patterns In Pascal's Triangle. Abstract. This lesson is designed to show students that patterns exist in the Pascal's Triangle, and to reinforce student's ability to identify patterns. How to efficiently calculate a row in pascal's triangle?
Ask Question. "How to efficiently calculate" - and you write a Python answer? – user Mar 22 '13 at 64 @H2CO3: The most efficient way to calculate a row in pascal's triangle is through convolution. First we chose the second row (1,1) to be a kernel and then in order.
Algebra 2 Honors The purpose of this course is to deepen your understanding of advanced algebra and statistics while preparing you for the SAT and higher level mathematics. You should be very comfortable with the concepts you learned in Algebra 1 since we will build upon them.
Linear Equations Questions - All Grades You can create printable tests and worksheets from these Linear Equations questions! Select one or more questions using the checkboxes above each question.