EDUC4721: Assignment 1 Suzanne NimmoTiered Lesson 2094959

Tiered Lesson (Differentiated by Readiness)

Name & Student Number: Suzanne Nimmo: 2094959Lesson Topic: Fractions Curriculum Area: Mathematics Year Level: 6-7

Links to the Australian curriculumYear 6: Solve problems involving addition and subtraction of fractions with the same or related denominators (ACMNA126)Year 7: Solve problems involving addition and subtraction of fractions, including those with unrelated denominators (ACMNA153)

Brief descriptionClass description The class I’m currently teaching is a composite year 6/7 class which hosts 22 year 7’s and 8 year 6’s. The high prevalence of year 7’s inevitably means that I will be structuring the content at a higher level but still utilize appropriate differentiation to cater for the Year 6 curricular needs. The class itself struggles at times with curriculum content and numerous students within the class have learning difficulties, ranging from slight to severe. The classroom is fairly small and hosts 30 students, resulting in limited movement potential for future activities. The class itself is respectful and willing to learn but often highly inattentive and in constant need of encouragement. I have observed that the students lack dedication and do not demonstrate a sense of pride in their work. In this lesson, I hope to encourage and engage students with the content, whilst sparking curiosity and interest in lifelong learning that will develop far beyond the classroom walls.What will be covered in the lessonThis lesson will be the second lesson of the Fractions and decimals unit. The lesson will introduce fractions in a simplistic manner by both adding and subtracting fractions. Fractions of both related denominator and unrelated denominator will be discussed. The first lesson in the unit will cover concepts such as the components of fractions and the correct terminology when discussing fractions, in addition to the pre-test.

Learning Objectives: As a result of engaging with the lesson, students will:Understand that

- Fractions are utilized in the real world- Solving fraction problems can involve addition and subtraction with related

denominators- Solving fraction problems can involve addition and subtraction with

unrelated denominators

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EDUC4721: Assignment 1 Suzanne NimmoTiered Lesson 2094959

Know (e.g. facts, vocabulary, dates, information)

Pre-existing knowledgeThe components of a fraction are

numeratordenominator

A fraction with a denominator of 1 is a whole number

When the numerator is greater than the denominator it is an improper fraction

An improper fraction is usually expressed as a mixed number?

To simplify a fraction, the numerator and denominator are divided by their highest common factor. This process is called cancelling

New knowledge

When adding and subtracting fractions whose denominators are the same, just add or subtract the numerator

When adding or subtracting denominators that are different: First find the equivalent fractions using the lowest common denominator. Then secondly add or subtract the numerators.

Be able to (do) (Skills, processes)

For example 3=3/1

For example 15/ 4

For example 134

=3 14

For example 2440

=8 x38 x5

=35

2440

∧3

5are equivalent fractions

For example: 25+ 1

5=3 /5

And 1−58=8

8−5

8=3 /8

For Example 9

10−3

4=18−15

20= 3

20

Essential Questions

What is a fraction?How are fractions relevant in the real world? List examplesWhat is a related denominator?What is an unrelated denominator?In what situations would we need to add or subtract fractions?

Lesson Title: Adding and Subtracting FractionsPreassessment of Students’ Readiness

Students will be given a pre-test (Appendix 1) in order to gauge their current readiness

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EDUC4721: Assignment 1 Suzanne NimmoTiered Lesson 2094959

levels. This test will predominantly incorporate the addition and subtraction of fractions. This test will inevitably cover some concepts too advanced for the year 6 students but will allow the teacher to effectively gauge where the class and individual students are at and can therefore alter subsequent lessons accordingly.

This test will begin with simplistic concepts and advance rapidly, in order to distinguish which concepts need to be further reinforced throughout the unit. The test will be conducted in a non-threatening manner with students being reassured that it is merely a necessity which assists the teacher in knowing precisely what needs to be taught.

Lesson PlanLesson Sequence

Introduction: 10 minutesDiscuss the concepts learnt last lesson and their relevance in the real world. What do we already know about fractions?

Introduce today’s topic: Addition and Subtraction of fractions with related and unrelated denominators.

As a whole class participate in the interactive activity utilizing the interactive white board.(See Appendix 4)

Tiered Activity: 30 minutes(See appendix 2 for relevant examples of

work)Dependent on students readiness levels (gauged by pre-test) the class will be divided into two groupsGroup A: Capable and possess a solid understanding of fraction principlesGroup B: Have some understanding of fractions but the concepts are not yet conceptualized and further explanation

Explanatory notes

This conversation aids as a simple refresher of what fractions are and how they are relevant beyond the walls of the classroom.This conversation builds on prior knowledge and introduces today’s concepts.

This whole class activity introduces the concepts of addition and subtraction in a fun, non-threatening manner whilst utilizing technology. These short slides sum up the concepts for today’s lesson perfectly whilst allowing the not so confident children to observe what needs to be done. This introduction activity immediately demonstrates what concepts need to be further reinforced

Two ability level based groups were chosen to allow the teacher to effectively support both groups of students without neglecting group time wise

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EDUC4721: Assignment 1 Suzanne NimmoTiered Lesson 2094959

is needed

Group A: (15 minutes) This group will initially begin the lesson by answering a group of questions regarding the addition and subtraction of fractions. It will begin fairly simplistically and increase in skill level rapidly.Students will be encouraged to work individually on problems but consult each other if they are stuck on a problematic exercise whilst the teacher is working with another group of students.When students have finished their work they can check their answer with the class set of calculators and mark their work accordingly

Group A: (15 minutes) For the second half of the lesson students will be assisted by the teacher in making a fractions colour by number worksheet for their partner to eventually complete in subsequent lessons. In this exercise students will create appropriate fraction problems for a partner to solve. This activity requires students to design problems that will have the same answer, allowing the answer to dictate a certain colour in the picture.

Group B: (15 minutes) The teacher will begin working with this group of students and go over concepts explicitly explaining each problem. These problems will begin simplistically to allow students to grasp the concepts and increase skill level sequentially

- To help students grasp the concept of fractions a number line will be utilized when working out

-Here students are expected to be independent learners and will be encouraged to work progressively on their problems.-They will understand that the problems are devised to be challenging but are definitively achievable- Students will be trusted to mark their own work with a calculator and will know that their marks will only form a small component of formative assessment

-This activity encompasses an element of fun whilst allowing the students to think outside the square and form their own complex problems- It encourages problem solving skills and allows students to be creative when devising their problems.- The answers given can be as simple or complex as the individual student deems, allowing them to work in their optimum zone of proximal development

-The teacher will begin working with this particular group of students first to ensure they grasp a solid understanding of the underlying concepts and predominant aims of the lesson.

-Students will be introduced to a number line because according to Siemon, Beswick, Brady, Clark, Faragher & Warran (2011) It can help students form mental imagery and conceptual

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simplistic real life problems

Group B: (15 minutes)For the second half of the lesson students will use the skill and number lines to answer a set of fraction problems.

Additional activityStudents who finish early can use one of the 6 class Ipads or 2 computers toutilize Scootle applications (Scootle, 2014) that will further consolidate their knowledge of fractions whist utilising technology in a fun and educationally appropriate manner.

understanding, key in developing a deeper understanding of addition and subtraction of fractions

-After modelling the activities students can then begin solving problems independently.-They will be expected to work individually during this time unless they are stuck on a problem, where they can consult the person sitting next to them- The first section of the lesson should have equipped them with the skills to be able to successfully answer the set of questions

- This activity is a mere back up just in case students work exceptionally well during the two tiered activities (See Appendix 3)

Lesson Closure/ Check for Understanding

Conclusion: 10 minutes- Each group will report what they did back to the wider class- Reconceptualise knowledge and allow students to discuss what was learnt

- What things in the lesson were challenging?- What was easy?- What can be improved?

Exit card- One thing I learnt today- One thing I thoroughly enjoyed- One thing that challenged me

This class discussion allows students to stop and reflect on what they have been working towards. The exit card is a form of summative assessment which allows the teacher, alongside the student’s work samples to accurately gauge what the students learnt from the lesson. It additionally forms a basis in which future lessons can be

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planned.

Checklist of assignment components: Complete, step-by-step lesson description, with notes explaining how the lesson

represents an example of a tiered lesson to address various readiness levels Supplementary materials (e.g., copies of directions, handouts, etc. provided to

students) Copy and/or description of preassessment task used to assign individual students to

appropriate “tiers” Evaluation/ assessment criteria (e.g., rubric or checklist used to guide evaluation of

student work)

Bibliography

Jones, A. (2013). SmartStudy. Mathematics: Year 7. Pascal Press

Kaylees Educational Studio. (2014). Your Resource for Teacher Materials. Retrieved from http://www.kayedstudio.com/

KidsOLR. (2014.) Directory of Education for K-12 & College, Children, Teens, Kids, Parents, & Families. Retrieved from http://www.kidsolr.com/math/fractions.html

Scootle. (2014.) Australian Government Department of Education. Retrieved from http://www.scootle.edu.au/ec/p/home

Siemon, D., Beswick, k., Brady, K., Clark, J., Faragher, R., & Warran E (2011.)Teaching Mathematics: Foundation to Middle Years: Ways of working with addition and subtraction. Pg 525-528

The Australian Curriculum. (2014.) F- 10 Curriculum: Mathematics. Retrieved from http://www.australiancurriculum.edu.au/

Tomlinson, C. A. (2001). The ‘How To’s of planning lessons differentiated by readiness. In How to differentiate instruction in mixed ability classrooms (2nd ed., pp. 45-51). Upper Saddle River, NJ: Pearson.

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EDUC4721: Assignment 1 Suzanne NimmoTiered Lesson 2094959

Appendix 1

Fractions Pre-test

Name: ___________________________ Date: _____________________

a) Circle the picture below that shows about 1/2 of an apple.

b) If 4 people share a custard tart equally, how much of the tart will each person get?______________

c) Draw a picture of this situation.

d) 6 12+1 1

2+1 1

2=¿ ________

e) 7. Mr. Yates, Ms. Lee, and Mrs. Miller went to a pizza party. There was a pizza divided into 8 slices. They each had 1 piece of pizza. What is the fraction of the whole pizza that Mr. Yates, Mrs. Miller, and Ms. Lee ate in all? _______________________________

f) 25+ 3

10=¿

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g) . Mrs. Miller, Mr. Yates, and Ms. Lee spent all day Saturday baking cakes. They each made and decorated their own cake. All three cakes were the same size.

Mr. Yates cut his cake in half and ate 1 piece. What fraction of his cake did he eat?_______

Ms. Lee cut her cake into eight pieces and she ate three of them. What fraction of the cake did she eat?_______

Mrs. Miller cut her cake into 10 pieces and ate four of them. What fraction of the cake did she eat?________

Which teacher really pigged out?_________________

How much cake did all three teachers eat together? Show appropriate working out

h¿ 910

−34=¿

i) 4 12−2 1

4=¿

j ¿2 12+3 1

3=¿

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Appendix 2Group A: worksheet

Remember to show appropriate working out and check your answers with a calculator when finished

a)36+ 10

12=¿

b)5

10− 3

15=¿

c)158

+1 416

=¿

d) 1 832

−12=¿

e)245

+65=¿

f) 2−34=¿

g) 5 92+ 6

30+ 4

8=¿

h) Fill in the boxes to make the following equation correct. The same number goes in each box

1❑+ ❑

12= 7

12

i) If I ate ¾ of a pizza and my friend ate another ¾ of another pizza, how many pizzas did we eat altogether? How many whole pizzas did we need to buy?

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EDUC4721: Assignment 1 Suzanne NimmoTiered Lesson 2094959

Group A: Teacher Facilitated activityAn example of what students will be creating themselves but utilizing

addition and subtraction of fractions

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Colour by FractionsColour all fractions that are equivalent to 1/5 purple Colour all fractions that are equivalent to 2/5 greyColour all fractions that are equivalent to 3/5 blueColour all fractions that are

EDUC4721: Assignment 1 Suzanne NimmoTiered Lesson 2094959

Group B: worksheetRemember to show appropriate working out and check your answers will

a calculator when finished

a) 35+ 1

5=¿

b) 310

+ 710

=¿

c) 710

− 210

=¿

d) 34−3

8=¿

e) 910

−23=¿

f) 36+ 10

12=¿

g) 510

− 315

=¿

h) 158

+1 416

=¿

i) 832

−12

j) 245

+65=¿

k) 2−34=¿

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l) 5 92+ 6

30+ 4

8=¿

Group B: Teacher Facilitated activityAn example of a fraction wall the students will be creating themselves

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Appendix 3Additionally Activity for early finishers

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Appendix 4Introductory Interactive Activity

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