National Council of Teachers of Mathematics

National Council of Teachers of Mathematics (NCTM) Standards: Website Lesson Plans Edwina Schweitzer Grand Canyon University: EED 364 November 25, 2012 The National Council of Teachers of Mathematics (NCTM) is a council that has set in place standards that are to be followed and adhered to when creating mathematical lesson plans. These standards are national and require a lot of the teachers as far as what and how they teach math. While there are many choices of lesson plans that support the standards set by the NCTM regarding number sense and operations, only four will be used to fulfill the following criteria. . Four lesson plans were chosen to illustrate the support of the NCTM standards: A. Problem-solving: Math, episode 1, (Discovery Education, n. d. ) is a lesson plan that helps students understand the importance of numbers. In this lesson the objectives are to show the students the importance of numbers in math, and show examples of how they are used in everyday life. The stud ents start out by watching the video, Problem-solving: Math, episode 1, and then talking about all of the numbers that they see in the classroom, such as the numbers on a clock or how many paint brushes or windows there are.The students are then asked to imagine a world without numbers and give ideas of how things would be different. They are then asked to write down examples of how they have used numbers, such as dividing candy among friends, being first in line, or being measured at the doctor. They are then asked to share these examples with the class and post them as a reminder of the importance of numbers in their everyday lives. B.Activity 3: Exploring the effect of operations on decimals, (Illuminations, 2000-2012) is a lesson plan that gives students the opportunity to â€Å"explore the effects of addition, subtraction, multiplication, and division on decimal numbers. † This lesson provides a Maze Playing Board sheet that allows students to play a game while making th eir way through the maze. The object of the maze is to finish the maze with the highest decimal number. Examples of addition, subtraction, multiplication, and division of decimal numbers are shown on an overhead projector for the students to see as a visual aid.This activity requires the use of the calculator, which provides practice using a calculator while having fun with a maze. The students are then put into groups of three to discuss their results. C. I’ll halve s’more please!! (Jackson, n. d. ) is a lesson plan that uses fractions to solve riddles provided in a PBS episode of Cyberchase, entitled Zeus on the Loose. The students watch the episode and then use fractions to solve the riddles while learning the parts of the fractions and their importance in everyday life.There is a handout that is included with the lesson plan and a list of materials, including s’mores ingredients, large numbers and a bar of paper cut out for fractional use. D. Life is Full of Problems, (Young, n. d. ) is a lesson plan that helps students learn how to read, interpret, and devise a solution to math problems. This lesson requires the use of mental solving, paper and pencil, and calculator usage. The students learn to double check their answers for correct procedures and solutions. There are several ideas listed in this lesson plan that may fit into any diverse classroom.This is a lesson plan that is particularly good for encouraging mental solving of mathematic equations. While the mental solving is attempted first, they may check their mental answers by working the problem out on paper, then double checking themselves with the calculator. This incorporates three different means of problem solving, and not only teaches the importance of mental capabilities, it enables the students to finish with the use of calculators. 2. The methodology of number sense is used in each of the lesson plans in various ways. Problem-solving: Math, episode 1, (Discovery Educat ion, n. . ) includes a vocabulary list that the others do not. â€Å"Vocabulary is an integral part of developing the skills and concepts necessary to explain solutions to problems,† (Camelot Learning, n. d. ). All of the lessons use number importance and provide activities to enhance this importance. Even though some of these activities may not have vocabulary words to accompany the lesson, they could be incorporated into them. If the higher grades already know the vocabulary words for the lessons being taught, they could be a refresher so that the students did not forget them. 3.The activities that were included in these lesson plans include mathematical operations such as addition, subtraction, multiplication and division of decimals and fractions. Calculators are used in two of the activities, and the importance of the use of numbers is emphasized in all activities. Problem solving techniques are given as examples and the students are encouraged to improve on them through the completion of the activities. One lesson plan even includes a S’mores snack in the activity. Students would not only get to work with S’mores, but eat them afterwards! 4.These websites are appropriate for K-5th grade students, depending upon the lesson being taught and the extent to which the teacher would like to instruct it. All of the lesson plans are adaptable for students, but grades 3-6 seemed to be the best to benefit from them as they are listed. A couple of the lesson plans included variations that could be made simpler or more difficult, depending upon the grade and needed difficulty level. This variation in difficulty is also good for the differentiation of the students. 5. The lesson plans all provided ideas for differentiated instruction.These were also ideas that could be used for different grade levels, depending upon how in-depth the teacher wanted to go. Small groups were assigned to discuss the results of some of the activities. This could be hel pful with those students that have greater challenges and may struggle with their activities. Some of these activities could be made partner activities to help ELL students or those that may tend to be slower academically. 6. These lesson plans are important to the student’s understanding of mathematics because all of the lesson plans contained vital knowledge of the importance of numbers in everyday life.The students need to learn the components of these lessons to be successful at anything in life, as they are basic but important components. All of these lessons show the students how numbers surround them and that without numbers their world would not be the same at all. They constantly use numbers on a daily basis, right down to their phone number, address, age, size of clothes, and how tall they are. By providing the examples of this and then providing the opportunity for hands on activities to illustrate this importance, the students may be less likely to make the commen ts, â€Å"Why do I have to learn this? I will never use this! 7. The activities within the lesson plans could improve student achievement by providing the visual, hands on activities necessary for student understanding and growth. By allowing the students to participate in the activities and have fun, they will remember the concept being taught better because they have witnessed how important it is and have learned by the fun activities provided. The success of the students can be far greater when they are allowed to participate in hands on activities as opposed to simply being lectured on a particular concept. It is always easier to remember something when you had fun doing it.This principle is the same with lessons. The more opportunities for the students to do activities or games that pertain to the lesson, the better chance the students have to remember the concept being taught. This is only a success builder in academics. 8. Manipulatives were used in all of these lessons to s ome extent. The Problem-solving: Math, Episode 1 lesson plan could use a few more ideas for manipulative use. Where the students were asked to look around the classroom and find things that contained numbers, they could choose items from the classroom to total one to ten items.This could be done by counting out one book, two sheets of paper, three markers, four crayons, etc. Manipulatives may be changed or increased in any of the lesson plans, depending upon the teacher and how he/she chooses to provide them. The four lesson plans that were chosen and described all adhere to the standards set in place by the National Council of Teachers of Mathematics (NCTM). Each lesson plan had the NCTM link or listed standards included in the body of the lesson plans. These standards are important for teachers to be aware of and use when creating lesson plans for mathematic instruction.By having these standards set in place and using them, all of the students will have the same emphasis and impor tance put on number sense and operations, regardless of grade level or school. Reference Camelot Learning. (n. d. ). Camelot learning math intervention curriculum. Retrieved November 25, 2012 from http://www. camelotlearning. com/why-camelot/methodology. Discovery Education. (n. d. ). Problem-solving: Math, episode 1. Discovery education. Retrieved November 25, 2012 from http://www. discoveryeducation. com/teachers/free-lesson-plans/problem-solving-math-episode-1. cfmIlluminations. (2000-2012). Activity 3: Exploring the effect of operations on decimals. Illuminations. Retrieved November 24, 2012 from http://illuminations. nctm. org/LessonDetail. aspx? id=L252. Jackson, C. (n. d. ). I’ll halve s’more please!! National teacher training institute. Retrieved November 25, 2012 from http://www. thirteen. org/edonline/ntti/resources/lessons/m_half/index. html Young, K. (n. d. ). Life is full of problems. Retrieved November 25, 2012 from http://www. learningpt. org/pdfs/mscLes sonPlans/young. pdf ———————– National Council of Teachers Page 2