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Unit Title: The Number System

Specific Learning Disabilities (SLD): 2, Attention Deficit Hyperactivity Disorder (ADHD): 1,                             English Language Learners (ELL): 1

Interpret and compute quotients of fractions, and solve word problems involving division of fraction by fraction. For example, by using visual fraction models and equations to represent problems (Kendall, 2011).

Given visual instruction models and equations, students should be able to divide fraction by fraction. The students will then explain to the class why they consider their answer to be accurate.

After going through some tutorial with their teacher, students will compute the width of rectangular strip of land to the nearest meters given the area and the length. The students will then explain to their colleagues why their answer is 95% accurate.

Computer, worksheets and text books

• Motivation (Focus)

The teacher will commence the lesson by trying to get the attention of the students. As the teacher, I will get the students to count from 0 to 50 in steps of 5 and 0 to 20 in steps of 2.

I will ask the students questions such as:

Q. How many fours are in 20?

Q. How many fives are in 10?

• Teacher strategies and Guided instruction

Given the following fraction 4/9 ÷ 2/3, I will ask my students some questions while taking feedbacks from them.

Q. How could we solve the math?

Q. How could we use the relationship between multiplication and division to explain the math?

Say that I shall use the visual instructional model to show the quotient. Similarly, the relationship between division and multiplication will explain that 4/9 ÷ 2/3 = 2/3 because 2/3 of 2/3 = 4/9.

Also, I will my students to think of other questions that might be asked about the above information. I will take feedback and suggest the following question if the students do not.

Q. What other ways can we use to explain the above information?

Tell the students that the other way to explain the information is by using real life example. I will discuss with the students how to compute the width of a rectangular strip of land given that its area is 4/9 meters square and the length is 2/3 meters.

• Collaborative learning

The students will work in groups of 5 and accomplish certain activity. However, the students will be grouped according to their abilities to understand. The more able will work as one group while the less able will do the same. The group discussions will entail clarification on calculating the area of a rectangle. I will ask them the following questions.

Q. What is the formula for calculating the area of a rectangle?

Q. Is this a good way to present this information? Why?

I will give the students a period of 10 minutes to complete the activity and discus some of the questions they might have.

•  Closure and review

I will bring the whole class together and refer to individual student’s activity and take some feedback on the questions they have written. I will ask the following questions.

Q. what do you understand by the term number system?

Take feedback. Establish that it is a better way of representing certain types of numbers.

Q. What are some of the concepts tested under number system?

Take feedback. Establish that the concepts include composite numbers, divisibility, prime numbers and properties of perfect square.

• Activity or independent practice

Write a list of fractions on the board. For example 1/2, ¾, 8/9 and 3/7.

I will pose the following question to the students.

Q. What fraction will give ¼ if divided by 8/9?

Q. If there are 10 students, what fraction of chocolate will each get if they share ½ of the chocolate equally?

The students will use the above questions for their own practices.

• Evidence of students thinking

Given that the area of a rectangular piece of wood is ¾ meters square. Compute its length given that the width is a half the area?

The first level is recall and reproduction. For instance, the students will portray this level by computing the basic math of multiplication and division. The second level is working with skills and concepts (Taylor, Watson, & Nutta, 2014). For example, the students will have to explain why they think the question is about multiplication and division of fractions.

I will use the authentic formative assessment to assess the students’ group activity. The criteria       for their mastery are as follows.

• Three points: participated actively in class discussions, very attentive during discussions, applied the concept and solved the problem accurately and interestingly.
• Two points: showed moderate participation during class discussions, showed moderate attention during class discussion, applied the concept to write satisfactory problem
• One point:   showed little participation during class discussions, not attentive during class discussion, had difficulty in applying the concepts to solve the problems.

I will also provide the students with exams and use the results to determine their individual understanding level.

If the results from the assessment process are not appealing, then the teacher will reteach the lesson or will provide further instructions.

The students in my class have different needs; therefore, I will express different ways to ensure that they get the concepts. For a student with Attention Deficit Hyperactivity Disorder (ADHP), I will try and find out what he/she prefers as a learning style. Therefore, I will draw a table and the student will illustrate his/her preferred learning style. Some of them may prefer visual resources, auditory or kinesthetic. For the student with English Language Learners (ELL) problem, I will find an appropriate way to use his/her native language for illustration. Lastly, two students have Specific Learning Disabilities (SLD). For their case, I will allow them to use their fingers and scratch papers. Also, I will draw diagrams and math concepts.

Which concepts on division and multiplication of fraction should the students not miss?

Do brackets affect multiplication and division?

What are the real life examples of multiplication and division of fractions?