The National Council of Teachers of Mathematics has been transformative and influential in the c

The National Council of Teachers of Mathematics has been...

Key Concepts

Professional Organizations in Mathematics Education

These organizations, such as the National Council of Teachers of Mathematics, play a key role in shaping the teaching and learning of mathematics through setting guidelines, developing resources, and advocating for best practices in the field. They serve as a forum for collaboration among educators and help drive systemic changes in mathematics education at various levels.

Curriculum Standards

Curriculum standards provide a structured set of goals and outcomes for what students should know and be able to do in mathematics. These standards guide educators in lesson planning, assessment design, and resource development, ensuring consistency in the educational experience across different regions and schools.

Assessment Standards

Assessment standards establish benchmarks for evaluating student understanding and skills in mathematics. They inform the development of both formative and summative assessments, helping educators measure student progress and identify areas that need improvement, thereby supporting effective instructional strategies.

Instructional Resources

Instructional resources refer to the teaching materials and tools developed to support the implementation of curriculum standards. These resources can include digital content, textbooks, interactive software, and other supports that aid teachers in delivering effective, engaging, and conceptually-sound instruction.

International Assessments

International assessments, such as those conducted by global agencies, provide comparative data on student performance in mathematics and science across different countries. They help educators and policymakers understand global trends, set benchmarks, and learn from international best practices to enhance domestic education systems.

Transcript

00:02 In this problem, we're asked to figure out which of the following conjectures is false.

00:08 Okay? so we're going to look at each conjecture, try out a few examples, and see if we can determine whether or not the statement is true or false.

00:16 So the first one, if x is odd, then x plus one is even.

00:21 So let's just try out a few of them.

00:24 So let's pick an odd number.

00:25 So we can start with three for an odd number.

00:29 We'll let x equal three so then three plus one is four okay so far so good uh let's try another odd number let's try x equals five well then five plus one is six all right this is looking promising what if i did a negative number like x equals negative seven well then negative seven plus 1 is negative 6.

01:08 That's still an even number.

01:10 I just noticed a typo here.

01:12 This should be 5 plus 1.

01:16 So it looks like when you have an odd number and you add one to it, it just takes you to whatever the next number is, which we know that odd and even numbers go back and forth between each other.

01:28 So if we start with an odd and add one to it, the next one's going to be even.

01:32 So this guy looks like it's true.

01:35 Let's go to the next one.

01:36 The sum of two odd numbers is even.

01:39 Okay, so once again, let's start with some odd numbers, add them together, and see what we get.

01:44 So let's start with two odd numbers, but have them both be positive.

01:49 So one plus three are both odd.

01:53 Okay? so one plus three gives us four.

01:56 That's even.

01:58 Let's try two negative.

02:00 So let's go negative five plus...