Peter Jelinek - Unit Code CUR4203 Lecturer: Jennifer Moyle · PDF filePeter Jelinek - Unit Code CUR4203 © Peter Jelinek 2011 ... 4-week mathematics lesson overview (Year 5 ... English

Peter Jelinek - Unit Code CUR4203 Lecturer: Jennifer Moyle

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Peter Jelinek - Unit Code CUR4203 © Peter Jelinek 2011

Table of Contents Part A – My Philosophy of Teaching and Learning in the Mathematics Learning Area _______________________________________________ 3 Part B – School and Classroom Context __________________________________________________________________________________ 8 Part C – Class Timetable ______________________________________________________________________________________________ 12

Part C – 4-week mathematics lesson overview (Year 5 – Number fractions & decimals) ____________________________________________ 13

Part D – Daily Work Pads

- Lesson 1 ____________________________________________________________________________________________________ 25 - Lesson 2 ____________________________________________________________________________________________________ 28 - Lesson 3 ____________________________________________________________________________________________________ 31 - Lesson 4 ____________________________________________________________________________________________________ 33 - Lesson 5 _______________________________________________________________________________________________+____35 - Lesson 6 ____________________________________________________________________________________________________ 37 - Lesson 7 ____________________________________________________________________________________________________ 40

Part E – Assessment Rubric for Lesson 20 ________________________________________________________________________________ 42

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Part A - My philosophy of teaching and learning in the Mathematics learning area

“I hear and I forget; I see and I remember; I do and I understand”. The principle behind this often-used proverb is essentially the one

that underpins my philosophy of teaching and learning in the mathematics learning area. There is much evidence in the literature that a

hands-on approach to numeracy instruction is a powerful one when teaching this area of the curriculum. According to Booker, Bond, Sparrow,

and Swan (2004), the use of physical materials and manipulatives is fundamental to, and should be on-going in, the teaching and learning of

mathematics. This is because many of the mathematical concepts and ideas that need to be learned by individuals are not intrinsically

obvious. Physical materials introduced early in a mathematics curriculum readily reveal patterns that need to be applied later on to larger

numbers, fraction ideas and complex ideas in geometry and measurement when materials are no longer useful in the modelling of situations

directly. Booker, Bond, Sparrow, and Swan (2004) believe that in order to promote numeracy in students, it is necessary to engage them in

authentic mathematical tasks, games and investigations that require critical thinking and understanding rather than simply the memorisation

of facts, procedures and techniques. They go on to cite a useful definition of numeracy given by the National Council of Teachers of

Mathematics (2000); “the ability to explore, conjecture and reason logically and to use a variety of mathematical methods to solve problems”.

Although they are fundamental to the development of mathematical understanding, materials and manipulatives by themselves do not

literally carry any meaning. Usiskin (1996) makes the crucial point that it is language that communicates ideas, not only describing concepts

but also by helping them to take shape in every learner‟s mind. According to Booker, Bond, Sparrow, and Swan (2004), language is the key to

all aspects of mathematical learning and this is not confined to the specialised vocabulary of mathematics. It is vastly more complex than that;

discussion amongst students is needed to bring out the explicit construction of links between understood actions on the objects and related

processes involving symbols. Schoenfeld (2001) expresses the view that in building problem-solving abilities, students need a range of literacy

skills, including the ability to report, display, explain and argue for their own solutions to see that getting the right answer is the beginning

rather than the end. The ability to communicate thinking convincingly is equally important. So the principles described by important Australian

language acquisition theorists like Halliday and Cambourne are equally relevant to teaching and learning in the mathematics learning area as

they are to teaching and learning in the English learning area (I described these in some detail in the personal philosophy section of my

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English forward plan). Also, the Australian Curriculum Assessment and Reporting Authority (ACARA) emphasises “an appreciation of the

elegance and power of mathematical reasoning”, stressing that teachers need to be encouraged to help students become self-motivated,

confident learners through inquiry and active participation in challenging and engaging experiences (“Mathematics Rationale”, [n.d.]). It goes

on to say that “students must become numerate as they develop the capacity to recognise and understand the role of mathematics in the

world around them and the confidence, willingness and ability to apply mathematics to their lives in ways that are constructive and

meaningful”.

This overarching perspective that mathematics is learned by individuals constructing ideas, processes and understandings for

themselves rather than through the transmission of preformed knowledge from teacher to learner, now dominates conceptions of

mathematics learning (Lambdin & Walcott, 2007). This is essentially a constructivist view of knowledge acquisition. This constructivist

perspective focuses on the learner, and sets out to guide the individual in the construction of mathematical ways of knowing and operating

based on existing knowledge, a focus that requires 3 phases according to Herscovics and Bergeron (1984): a determination of the form or

knowledge that may be used as a foundation for building the intended concepts or processes; an understanding of whether such a basis is

present for the learner; and, an assurance that each step in the proposed construction is accessible to each individual (targeting the

individual‟s zone of proximal development as Lev Vygotsky might have said). According to Booker, Bond, Sparrow, and Swan (2004), “when

children construct their own mathematics, that knowledge is both personal and owned; something over which they have control so that their

learning experiences empower them rather than leave them relying on procedures that have been developed by someone unknown, in

response to problems that are no longer remembered for a time and situation no one can recall” (p. 13).

So once again the literature points to social constructivism as a key philosophy of effective teaching and learning, in this instance in the

learning area of mathematics. And once again, my personal philosophy has been informed by the work of the early behaviourist and

constructivist theorists, the work of both Halliday and Cambourne, and ACARA‟s view that students need be encouraged to develop and apply

numeracy skills through the strands of Number and Algebra, Measurement and Geometry, and Statistics and Probability. I firmly believe that

knowledge is actively created not passively received, and I support the view that new ways of knowing are built through reflection on both

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physical and mental actions, and that learning is a social process requiring engagement in dialogue, discussion and negotiation to finally

extract meaning. I also support the „gradual release of responsibility‟ model of teaching and learning documented in the First Steps literature

(Annandale, Bindon, Handley, Johnston, Lockett, & Lynch, 2004), a model I supported in the English learning area. This includes modelling

(teacher demonstrations), sharing (students contribute with teacher direction), guiding (students work with teacher scaffolding, support and

feedback) and applying (students work independently). In addition, I believe that effective programming for numeracy learning must first

begin with assessment of the current learning achievements of students, a view expressed for the programming for English literacy learning

by Winch, Johnston, March, Ljungdahl, and Holliday (2010). These authors stress that once it has been determined what students already

know and can do, it is essential to implement a thorough program that builds on this prior knowledge, and that uses diverse teaching and

learning strategies that can deliver authentic, challenging curriculum content in a scaffolded learning environment.

In the Mathematics program that I have formulated for my Year 5 class at XXX Primary, I have used a range of on-line, oral and

written resources to integrate the Number and Algebra strand of ACARA‟s mathematics curriculum with elements of both Measurement and

Geometry, and Statistics and Probability (the Curriculum Framework areas of Working Mathematically, Measurement, Chance and Data, and

Space), and elements of The Arts and Health and Physical Education learning statements in the Curriculum Framework (1998). I have

included whole-class, small-group and individual speaking and listening activities, and modelled and shared reading, in conjunction with

explicit mathematics instruction that generally follows a gradual release of responsibility philosophy. Small group instruction and cooperative

learning to help scaffold the education of students at educational risk in my classroom will be a big part of this teaching program (Kagan

groupings that include high, medium-high, medium-low and low ability students in each group). During my 5-week block practice, my use of

whole-class discussions and brainstorming, and Kagan strategies like Think-Pair-Share and Rally Robin, will help facilitate whole-class, small-

group and paired student learning. My assessments will include text-specific checklists, anecdotal observations during whole-class and

individual activities, rubrics for more complex and rich tasks, and a summative assessment to be determined as the 5-week program unfolds. I

will also ensure that I foster a happy, open, creative and social learning environment that supports and tolerates error in the classroom, that I

model the best human values and virtues, and that I give timely feedback that is honest, constructive, explicit, personalised and kind.

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References

Annandale, K., Bindon, R., Handley, K., Johnston, A., Lockett, L., & Lynch, P. (2005). First Steps Assessing Current Literacy Challenges:

Linking Assessment, teaching and learning (2nd ed.). Port Melbourne: Reed International.

Booker, G., Bond, D., Sparrow, L., & Swan, P. (2004). Teaching primary mathematics (3rd ed.). Melbourne: Pearson Education.

Curriculum Framework for Kindergarten to Year 12 Education in Western Australia (1998). Osborne Park, WA: Curriculum Council.

Herscovics, N., & Bergeron, J. (1984). A constructivist vs a formalist approach in the teaching of mathematics. Proceedings of the Eighth

International Conference on the Psychology of Mathematics Education, Sydney, Australia.

Lambdin, D., & Walcott, C. (2007). Changes through the years: Connections between psychological learning theories and the School

Mathematics Curriculum. In G. Maring, M. Strutchens & C. Porting (Eds.), National Council of Teachers of Mathematics, Reston Virginia.

Mathematics Rationale. [n.d.]. Retrieved from the ACARA website:

http://www.australiancurriculum.edu.au/Mathematics/Rationale

National Council of Teachers of Mathematics (2000). Principles and Standards fro School Mathematics. National Council of Teachers of

Mathematics, Reston, Virginia.

Schoenfield, A. (2001). Reflections on an impoverished education. In L. Steen (Eds.), Mathematics and Democracy, National Council on

Education and the Disciplines, Washington, DC.

http://www.australiancurriculum.edu.au/Mathematics/Rationale

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Usiskin, Z. (1996). Mathematics as a language. In Communication in Mathematics, K-12 and Beyond, 1996 NCTM Yearbook, National Council

of Teachers of Mathematics, Reston, Virginia.

Winch, G., Johnston, R.R., March, P., Ljungdahl, L., & Holliday, M. (2010). Literacy (4th ed.). South Melbourne, Victoria: Oxford University

Press.

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Part B - School and classroom context

___________________________ _____ XXX Primary School

XXX Primary School is a rural school located about 20 km South-East of XXX. The school first opened in 1972, representing an

amalgamation of smaller schools. Most students who attend XXX Primary go on to secondary education at XXX High school. The school

grounds are dominated by gum trees and grassed playing areas fringed by grazing land on three sides. A modern administration block and

Library were added to the school in 1999, as was a purpose-built pre-primary transportable. In 2000, a covered assembly area, canteen,

gardener‟s shed and sports storage area were also added and by 2003, a P&C air conditioning program had been fully implemented. In 2010,

funding became available from the Federal Government‟s Building Education Revolution program to replace the original pre-primary

transportable building with a 2-classroom, arts block, and 3-classroom Early Childhood Centre.

XXX Primary school has five Level 3 classroom teachers and five Senior Teachers that that provide outstanding pastoral care, ensuring

that all students are motivated not only to attend school (96% attendance rate) but to achieve to the best of their abilities in all areas. The

teaching staff ranges in experience form 11 years to 35 years, with the average length of service per teacher of 10 years. The Principal is

supported by a Deputy Principal and administration staff. Every staff member is actively involved in financial decision-making at the school,

and each teacher has the responsibility for at least one learning area. Currently, the school comprises 195 students that are mostly from

second or third generation European origin. Most are either living in the town of XXX or farming areas nearby. Buses transport about 56% of

the students to and from school. There is 1 pre-primary class and 7 classes representing each year level from Year 1 to 7. The school has

recently adopted the „bumping‟ model (CMS) of behaviour management (Barrie Bennett and Peter Smilanich) throughout the school, and this

year the school has been trialling the Australian Curriculum and expects to continue down this path in the foreseeable future. One curricular

priority at the school is in English spelling, with the Diana Rigg program a key priority. Students in each class are divided into 3 spelling-ability

groups, with specific testing given 4 days each week in each class. The school also has a strong physical education, music, dance and drama

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focus, and this is geared to performance at the local festival held in the streets of XXX in October each year. One of the highlights of the

school‟s involvement in this festival is a May Pole dance performed by some of the upper primary students. This has recently become the

outstanding feature of XXX Primary‟s school logo.

The Year 5 class at XXX Primary School is my teaching practicum placement (the classroom timetable is shown in Part C). The physical

layout of the classroom changes weekly, but usually has a „U‟ shape as its most general configuration. The method of instruction is

predominantly whole-class, although my Mentor teacher is amenable to group work and this has already commenced. Students are allocated

to new seating positions as much as once daily. The class comprises 9 female students and 14 males (see Figure 1). One has mild dyslexia

(„HH‟), another has ADHD („HN‟) and one is of indigenous origin („PL‟).

Explicit instruction to the whole class is the predominant method of mathematics instruction in this classroom, and the progress of

students appears to be largely worksheet-driven. Students also regularly participate in individual on-line instruction (Accelerated Maths;

published by Renaissance Learning) and many appear to thoroughly enjoy it. According to the most recent round of NAPLAN testing, the class

average for numeracy is just a couple of percentage points short of the Australian classroom average, with 4 students considered to be at

educational risk; apart from the SAER students, most of the students are at Year 5 level. There are 3 students who can be considered talented

and gifted with respect to their mathematics ability and can be confidently given the role of peer mathematics tutor. My Mentor teacher is a

Level 3 teacher with almost 30 years teaching experience. I am looking forward to my 5-week block practice – there is a good sense of fun,

spirit and adventure in the classroom. This should provide a good foundation for my instruction during Term 4.

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Figure 1 – XXX Primary School class profile (Year 5).

No. Name M/F Background

Information

Typical or non-

typical Learner

Interests Learning

style

Multiple

intelligence preference

Other factors Implications for

Teaching

1 Typical Scooter riding Enjoys Phys Ed;

Excellent maths; weak English

2 Typical Four-square; loves her friends

Enjoys art

3 Typical Listening to music

(mp3 player & boom)

Enjoys Phys Ed and art SAER student

4 Typical Swimming and

bike riding

Swimming and bike

riding

TAG student

6 Typical Motor bike riding Sport

7 Restless; Typical Sport; Computer

games

SAER student; Needs

one-on-one attention

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9 Mild dyslexia Good work ethic; average ability

Kayaking; Music; Fishing

Enjoys art Take dyslexia into account during

assessments

10 Twin Typical Kayaking; Music; Cycling; Motor bike

Enjoys art

11 ADHD (medicated

twice daily)

Very weak academically

Needs intensive one-on-one instruction

12 New in Term 3

Typical Motor bike riding Enjoys sport and art

13 Typical Chess Excellent English writing skills; enjoys

science

TAG student

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14 Single child Very bright;

exceptional writer (poetry); Typical

Sport; Animal

person

Excellent English

writing skills; enjoys art

15 Restless; Typical Sport; computer games; her pet

rabbit

Enjoys maths and art SAER

Typical Fishing Enjoys maths

16 Indigenous Restless

17 Missed 5-6 weeks

of school; Typical

Painting;

motorbike riding

18 Average ability;

Typical

Sport; scooters;

music; dance; camping; games

19 Typical Pet dog; Singing

and playing music

Enjoys maths and art TAG student

20 Typical Sport; hockey;

climbing

Enjoys English writing

and art

21 Restless

22 Restless Runner‟s Club Enjoys science SAER student; Needs one-on-one attention

23 Very weak academically;

Typical

Sport; Watching movies

Enjoys art SAER student; Needs one-on-one attention

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Part C – Class timetable (XXX Primary School - Year 5)

Time Monday Tuesday Wednesday Thursday Friday

8.50am 10.20am

4-minute mile (maths)

Daily Fitness

Physical Education whole-school teaching

Daily Fitness

Daily Fitness

Maths Maths Maths Maths

Recess 10.40am 12.10pm

English English

Physical Education whole-school teaching

English English

Lunch Break 12.50pm 1.55pm

Library

Resiliency & Mapping

DOTT

Science Sport Ed

Crunch ‘n Sip 2.00pm 3.05pm

Health Art

DOTT

LOTE – Madam Scott Homework

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Part C – FOUR-week* mathematics lesson overview (Year 5 –Fractions & decimals)

N

16 Working

Mathematically 4

(Decimals)

MM/Space

E N

17 Time Concepts 2

(Sequence &

Passage)

MM/Number

E N

18 Decimals (Place

Value)

MM/Work Math

E N

19 Ordering Decimals on Number Lines

MM/Number

E N

20 EXIT

Working

Mathematically 5 (Decimals)

MM/Chance/Data

E

WM SE WM SE WM SE WM SE WM SE

CD S CD S CD S CD S CD S

M HP M HP M HP M HP M HP

S TE S TE S TE S TE S TE

A TA A TA A TA A TA A TA

N

11 Introduction to

Decimals

MM/Number

E N

12 Working

Mathematically 3 (Fractions)

MM/Measurement

E N

13 Time Concepts 1

(Analogue and Digital)

MM/Number

E N

14 Fractions as

Divisions and Decimals

MM/Algebra

E N

15 Fractions as

Decimals, Ratios and Percentages

MM/Chance/Data

E






N 6

Fractions are

Numbers

Too!

MM/Space

E N 7

Adding &

Subtracting

Fractions

MM/Number

E N 8

Working

Mathematically 2

(Fractions)

MM/Work Math

E N 9

Ordering Fractions

& Number Lines 2

Complex Fractions

MM/Number

E N 10

Equivalent

Fractions

(Jellybean Activity)

MM/Chance/Data

E






N

1

ENTRY Language of

Mathematics

(Fractions Focus)

MM/Number

E N

2 Introduction to Unit Fractions

MM/Chance/Data

E N

3 Ordering Fractions on Number Lines 1

Simple Fractions

MM/Number

E N

4 Working

Mathematically 1

(Introduction)

MM/Algebra

E N

5 Understanding

Equivalent

Fractions

MM/Chance/Data

E






* Note that there is no Maths instruction in my practicum class on Wednesdays. As a result, the lessons described in this overview will be taught over the entire practicum period of FIVE weeks. Note also that numbers in RED have corresponding Daily Work Pad entries.

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Mathematics Program Overview

Lesson

Week

Time

Mathematics concept

Activities

Integration (maths clusters)

Integration (other areas)

CD N WM S M A

1 1 20min Mental mathematics (number)

„Multiplication Tic-Tac-Toe‟ activity (multiplication) ability-level worksheet games

√

1 1 60min The language of maths (number)

Read Mr. J‟s Pancakes Recipe and identify maths language

Rally Robin maths language (SIX groups of FOUR)

Pair-share difference between fractions and other maths language

De Bono‟s reflection (YELLOW & GREEN hats) Maths Journal – document the language of

fractions (teacher assessment)

√ √ English S, L, R & W

2 1 20min Mental mathematics (Chance/data)

„Dice Bingo‟ addition (chance & data; probability). Which numbers are turning up most often and why?

√ √

2 1 60min Introducing fractions Read Apple Fractions and pair-share thoughts about the text, before completing worksheet (peer assessment)

Outdoor whole-class activity – halves, thirds, quarters, fifths & eighths student groupings

Maths Journal – document understanding of fractions (teacher assessment)

√ English S, L, R & W HP&E

3 1 20min Mental mathematics (Number)

„Discard‟ game (addition/subtraction) – can you be the first player to discard ALL your cards?

√

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3 1 60min Comparing and ordering fractions (number line)

Revise previous lesson concepts (including numerator and denominator) – short on-line tutorial:

http://www.sheppardsoftware.com/mathgames/

fractions/fracTut1.htm

Video „Comparing & ordering fractions‟: http://www.youtube.com/watch?v=6i0iYJbOggE

Pair-share thoughts (De Bono‟s YELLOW and BLACK hats); complete worksheet (self assessment)

Fractions „Clothesline‟ – students in SIX groups of FOUR order laminated cards containing simple fractions on a class clothesline

„Human‟ fractions – students in SIX groups of FOUR (more complex fractions) place themselves in order of their fraction cards

Maths Journal – document mathematical thinking (teacher assessment)

√ √ √ English S, L & W

4 1 20min Mental mathematics (Algebra)

„Maths Cloze‟ worksheet (addition) – can you identify the missing numbers?

√

4 1 60min Working mathematically (problem solving number/fraction sentences)

Introduce problem solving concepts and number sentences

Rally Robin known problem solving strategies

Explain „See, Plan, Do, Check‟ method and different problem solving techniques

In-class role-play – SIX volunteer students investigate strategies to successfully negotiate the „Cross the River‟ activity

Complete ability-level worksheets (self assessment)

De Bono‟s reflection (GREEN hat)

√ √ √ English S & L

http://www.sheppardsoftware.com/mathgames/%20fractions/fracTut1.htm


http://www.youtube.com/watch?v=6i0iYJbOggE

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5 2 20min Mental mathematics (Chance/Data)

„PIG!‟ (chance) – can you be the first player to reach 50 without busting?

√ √

5 2 60min Equivalent fractions You Tube video „Let‟s Play Math – Lesson 6 Equivalent fractions‟:

http://www.youtube.com/watch?v=2-_eRsg1a7k

Pair-share thoughts (De Bono‟s thinking hats)

Outdoor „Human Fractions‟ activity in TWO groups „Numerators‟ and „Denominators‟

On-line „Matching Equivalent Fractions‟ interactive game (Sheppard Software):

http://sheppardsoftware.com/mathgames/fractions/me

mory_equivalent1.htm

Complete PMI chart and glue into Maths Journal (teacher assessment)

√ English S, L & W HP&E

6 2 20min Mental mathematics (Space)

„Three Hexagon‟ game (space) – can you fit 3 counters onto a straight line on the hexagon?

√ √

6 2 60min Understanding that fractions are discrete numbers

Cut strips of paper 50cm long and fold at intervals to gauge understanding that fractions are numbers

Pair-share thoughts about fractional intervals Reinforce concept - fractions are parts of a

number sequence

Create board games to demonstrate understanding of the fractional number concept (teacher assessment)

√ √ √ √ English S & L The Arts


„Number Climber‟ activity (addition) – Help the mountaineer ADD his way to the top of the mountain.

√


http://sheppardsoftware.com/mathgames/fractions/memory_equivalent1.htm

http://sheppardsoftware.com/mathgames/fractions/memory_equivalent1.htm

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7 2 60min Addition and subtraction of fractions with the same denominator

Prior content revision (part-part-whole) You Tube video „Adding and subtracting

fractions‟: http://www.youtube.com/watch?v=52ZlXsFJULI

Pair-share thoughts about video (De Bono‟s YELLOW & BLACK hats)

Complete ability-level worksheets (peer assessment)

Students in TWO groups – „Fruit Shoot‟ fraction addition and subtraction games (students swap after 15 min)


fractions/FruitShootFractions.htm

Maths Journal – key understandings about the addition and multiplication of fractions

√ English S, L, R & W

8 2 20min Mental mathematics (Work math)

Interactive Working Mathematically game: http://www.studyladder.com.au/learn/mathematics/

activity/

√ √

8 2 60min Working mathematically (number/fraction sentences)

Review problem solving strategies („See, Plan, Do, Check‟, working backwards, guess & check, etc)

Rally Robin known problem solving strategies

Complete ability-level „Word FRACTION Sums‟ worksheets („Whales‟, „Cockatoos‟ & „Woylies‟ groups)

De Bono‟s GREEN hat reflection within group



„Discard‟ game (addition/subtraction) – can you be the first player to discard ALL your cards?

√

http://www.youtube.com/watch?v=52ZlXsFJULI

http://www.studyladder.com.au/learn/mathematics/%20activity/

http://www.studyladder.com.au/learn/mathematics/%20activity/

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9 3 60min Comparing and ordering fractions (number line continued)

Review comparing and ordering fractions: You Tube video „Comparing and ordering fractions‟:


„Human fractions‟ – students in SIX groups of FOUR given laminated cards containing complex fractions (eg. 3¼) and after group discussion, line up in fractional order (students can see the laminated cards but cannot speak)

Students exchange cards and repeat exercise on TWO more occasions

Interactive on-line resource: „Escape from Fraction Manor‟ (reasoning with fractions):

http://www.thinkingblocks.com/HauntedFractions/HF

GameLoader.html

Pair-share De Bono‟s YELLOW hat reflection



„Dice Bingo‟ addition (chance & data; probability; 10-sided dice). Which numbers are turning up most often and why?

√ √

10 3 60min Unit & Equivalent Fractions

Revise equivalent fractions (on-line You Tube video „Let‟s Play Math – Equivalent fractions‟:


Students in 3 similar-ability groups. ONE jar of jellybeans per group (jars contain FIVE colours each but represent different equivalent fractions of unit fractions eg. „Whales‟ halves and quarters; „Cockatoos‟ halves, quarters and fifths; „Woylies‟ thirds, fifths and eighths)

Individuals guess number of jellybeans Groups sort colours, determine fractions, and

graph results. Compare fractions and graphs to other groups



http://www.thinkingblocks.com/HauntedFractions/HFGameLoader.html

http://www.thinkingblocks.com/HauntedFractions/HFGameLoader.html


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„Multiplication Tic-Tac-Toe‟ activity (multiplication) ability-level worksheet games

√

11 3 60min Introducing decimals Introduction „Converting Fractions to Decimals‟ You Tube video clip (1.06min):

http://www.youtube.com/watch?v=BaXlDbX4Zr4&fea

ture=related

Rally Robin De Bono‟s WHITE hat reflection before whole-class discussion

Direct instruction: the equivalence of „tenths‟ and 0.1s (base ten blocks grid paper number line)

Students in pairs play „Frecimals‟. Each pair has a pack of 10 smiley-face cards (one card = one tenth = 0.1 of the pack), one deals the other any number of the cards, the other writes down the fraction and decimal equivalents. Pair-share thinking behind each choice, then swap roles.

Line up 10 students each holding a „tenth‟ card (one tenth, two tenths, etc) and 10 students each holding a „decimal‟ card (0.1, 0.2, etc). Students with decimal cards to find and pair up with their matching fraction card student

Complete fraction-decimal conversion worksheet

Maths Journal – how are decimals similar to fractions? How are they different?

√ English S, L & W

12 3 20min Mental mathematics (Measurement)

„Coordinate Bingo‟ game (measurement) – first person to circle all 15 coordinates wins!

√ √

http://www.youtube.com/watch?v=BaXlDbX4Zr4&feature=related


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12 3 60min Working mathematically (number/fraction sentences)


Rally Robin (in pairs) known problem solving strategies

Complete ability-level „Word FRACTION Sums‟ worksheets using a DIFFERENT problem-solving strategy than Lesson 8

De Bono‟s GREEN hat reflection within group Maths Journal – Update and reflect upon the

new problem solving strategy used

√ √ √ English S, L, R & W


„Number Climber‟ activity (subtraction) – Help the mountaineer SUBTRACT his way to the top of the mountain.

√

13 4 60min Telling time (analogue and digital)

Grab students‟ attention by viewing You Tube video „Dave Allen – Telling the Time‟ (bleep out 3.38 to 3.40 min!):

http://www.youtube.com/watch?v=MS5P6GcUC4s

Rally Robin known relationship between days, hours, minutes and seconds (groups of FOUR)

Complete „Time Conversion‟ worksheet - includes fractions of hours and minutes (self assessment)

Interactive „Time-for-Time‟ website (students find out how long they have been alive how long til their next birthday)

http://www.time-for-time.com/howold.htm

Students draw and decorate their own individual analogue and digital clocks

Maths Journal – students reflect on which is their favourite way of telling time and why

√ √ English S, L & W The Arts

http://www.youtube.com/watch?v=MS5P6GcUC4s

http://www.time-for-time.com/howold.htm

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14 4 20min Mental mathematics (Algebra)

„Maths Cloze‟ worksheet (subtraction) – can you identify the missing numbers?

√ √

14 4 60min Fractions as divisions and decimals

On-line interactive resource - Gamequarium‟s „Death to Decimals‟ on-line (warm-up):

http://www.mrnussbaum.com/death_decimals/index

Direct instruction – the equivalence of fractions, written divisions and decimals (eg. ½ = 1 ÷ 2 = 0.5)

One decimal place - Bureau of Meteorology website (convert temperature decimals for the month of September to equivalent fractions):

http://www.weatherzone.com.au/station.jsp?lt=site&lc

=9965&list=ds

Plot daily temperatures on a line graph to show weather trend for the month

Add data and graph to Maths Journal



„Cross the Bridge‟ dice game (probability) – what are the best numbers to place your counters on?

√ √

15 4 60min Decimals as ratios and percentages

Direct instruction – equivalence of decimals, ratios and percentages (eg. 0.5 = 1:2 = 50%)

„Peanut butter & jam sandwich‟ experiment. Students in 6 groups of 4 given FOUR different ratios (measured in spoonfuls) of each of peanut butter and jam to MIX and spread on bread slices cut into quarters

Group then whole-class discussion to determine most popular recipe (expressed both as percentages and ratios)

Maths Journal – Describe experimental procedure and record results


http://www.mrnussbaum.com/death_decimals/index

http://www.weatherzone.com.au/station.jsp?lt=site&lc=9965&list=ds

http://www.weatherzone.com.au/station.jsp?lt=site&lc=9965&list=ds

22


16 4 20min Mental mathematics (Space)

„Three Dodecagon game (space) – can you fit 3 counters onto a straight line on the dodecagon?

√ √

16 4 60min Working mathematically (decimal sentences)


Complete ability-level „Word DECIMAL Sums‟ worksheets using a DIFFERENT problem-solving strategy than Lesson 12

De Bono‟s GREEN hat reflection within group

Maths Journal – Reflect on the differences between solving decimal and fraction problems

√ √ √ English S, L, R & W


„Maths Grid Bingo‟ game (subtraction) – can you circle THREE called-out numbers in a row?

√

17 5 60min Sequence and passage of time

Brainstorm months of students‟ birthdays (which are before, after or equal to the current month?)

Student given identities of important historical figures, lining up outside alongside a 30m rope (marked at 100-year intervals) in ascending order of birth date of the characters.

Brainstorm favourite TV shows (which are before or after the 6.00pm news?)

Students create their own weekly TV guides, showing start times and durations of programs

De Bono‟s GREEN hat reflection

Maths journals – Update with reflection


18 5 20min Mental Mathematics (Work math)

Interactive Working Mathematically games: http://www.studyladder.com.au/learn/mathematics/acti

vity/

√ √

http://www.studyladder.com.au/learn/mathematics/activity/

http://www.studyladder.com.au/learn/mathematics/activity/

23


18 5 60min Decimals and place value

Revise „Converting Fractions to Decimals‟ You Tube video clip (1.06min):

http://www.youtube.com/watch?v=BaXlDbX4Zr4&fea

ture=related

Direct instruction: the equivalence of „hundredths‟ and 0.01s (base ten blocks grid paper number line)

Whole-class discussion Place value cards to 0.1 (tens, units, and tenth

decimals) – model place value of temperatures in Lesson 14

Place value cards to 0.01 (tens, units, tenth & hundredth decimals) – model place value for a range of decimal currencies

Ability-level worksheets (ordering numbers with 1 and/or 2 decimal places)

√


„Number Climber‟ activity (multiplication) – Help Mr Mountaineer MULTIPLY his way to the top of a mountain

√



24


19 5 60min Comparing and ordering decimals (number line)

Interactive ordering game – Decimals and Fractions (choose ability level):

http://www.mathsisfun.com/numbers/ordering-

game.php

Pair-share thoughts (De Bono‟s YELLOW and BLACK hats); complete worksheets at ability level (peer assessment)

„Decimal Clothesline‟ – student peg laminated cards containing numbers (includes both one and two decimal place numbers) in a number line on the classroom „clothesline‟

Formal whole-class assessment of 5-week maths block (content and assessment methodology to be decided after Lesson 18)



„PIG!‟ game (chance) – can you be the first player to reach 50 without busting?

√ √

20 5 60min Working mathematically (fraction and decimal sentences)

Short revision – working mathematically

Complete ability-level „word FRACTION and DECIMAL Sums‟ worksheets („Whales‟, „Cockatoos‟ & „Woylies‟ groups). Formal assessment task - students required to demonstrate the use and understanding of one or more problem solving strategies, to clearly show an understanding of maths concepts, to clearly show all working, and to take care with their use of maths terminology). Formal assessment rubric*

De Bono‟s reflection within group (GREEN hat) Update Maths Journal

√ √ √ English S, L, R & W * See Assessment Rubric for this activity (Part E)

http://www.mathsisfun.com/numbers/ordering-game.php

http://www.mathsisfun.com/numbers/ordering-game.php

25


Part D - Daily Work Pad Week 1 – Lesson 1 Curriculum Framework Core Values Time Learning Experience Preparation/Resources Assessment/Recording

1.1 1.2 1.3 1.4 1.5 1.6 1.7

9.00am (20 min)

9.20am

(45 min)

In Brief: Determining students‟ understanding of

mathematics language, specifically the language of fractions.

Mathematics – The language of mathematics

Reading, Speaking & Listening – Mr. J’s Pancake Recipe; participation in mixed-ability group activity

Writing – Maths Journals

In Detail:

Warm up:

Mental Maths (Number) – Students complete

„Multiplication Tic-Tac-Toe‟ worksheets focusing on mental multiplication

______________________________________

Introduction:

Teacher introduces focus maths areas (fractions

and decimals) for the forthcoming 5 weeks, and specifically the language of maths for this lesson.

Teacher allocates students to groups of 4, with

students assigning themselves a number

between 1 and 4 (Kagan Numbered Heads). Teacher reminds students that this is a

cooperative learning exercise and that in group work like this, students need to focus on their

social skills, including listening to their peers, and

respecting other students‟ points of view. Students also need to be individually accountable

(ie. ALL students need to contribute). Student #2 in each group collects enough

photocopies of Mr J’s Pancake Recipe for each

member of his/her group.

Body:

Teacher models reading of text, emphasising

text-specific language (eg. whisk, bicarbonate,

„Whales‟, „Cockatoos‟ and

„Woylies‟ groups complete worksheets at

each group‟s ability level.

‘Mr J’s Pancake Recipe’ PowerPoint

One SAER student allocated to each group

24 x photocopies of „Mr J‟s Pancake Recipe‟

To what extent were the students working towards being able to:

1. Identify mathematics language in a non-

fiction text

2. Classify mathematics

language as „fractions‟ language or other

3. Document conclusions

about maths language

by writing entires into a maths journal

Student work sample –

teacher assessment (checklist)

2.1 2.2 2.3 2.4 2.5

3.1 3.2 3.3 3.4 3.5 3.6 3.7

4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8

5.1 5.2 5.3 5.4

ACARA Mathematics Content Descriptors

Pose questions and collect categorical or

numerical data by observation or survey

(ACMSP118)

Specific Learning Objectives

At the end of the lesson, the students will be working towards being able to:

1. Identify mathematics language in a non-

fiction text

2. Classify mathematics language as

„fractions‟ or „other‟ mathematics language

3. Document findings about mathematics language in their Maths Journals

http://www.australiancurriculum.edu.au/Glossary?a=M&t=numerical+data

http://www.australiancurriculum.edu.au/Elements/ACMSP118

26


10.10am (15 min)

curdled, spatula).

Teacher allows students 2 min to Rally Robin any

MATHS language they have identified in the text with their FACE partner, before giving each

group 5 minutes to discuss their findings and highlight their words on their photocopies.

Teacher and students brainstorm words and

phrases that the students have identified as maths language, before teacher goes through

PowerPoint text word-by-word, identifying the

language of mathematics where appropriate (eg. medium-sized, minutes, large, cup of, etc)

Teacher gives students 2 minutes to Rally Robin

FRACTIONS language they have identified in the text with their SHOULDER partner, before giving

each group 5 minutes to discuss their findings

and highlight their words on their photocopies. Teacher and students brainstorm words and

phrases that the students have identified as

fractions language, before teacher goes through PowerPoint text word-by-word, identifying

fraction terms where appropriate (eg. spoonful, ½, quarter, part).

Conclusion: Share results of groups work in a whole-class

discussion

Students record their words in 2 columns of their

Maths Journals, one column for Fraction words and phrases, another for Other mathematical

language.

View Edward De Bono introducing the Six

Thinking Hats concept (2.55min)

http://www.youtube.com/watch?v=o3ew6h5nHcc

Peers to read and give De Bono‟s YELLOW (good

points) and GREEN (creativity) hat feedback

Students‟ Maths Journals

Teacher collects students‟ Maths

Journals

http://www.youtube.com/watch?v=o3ew6h5nHcc

27


28



1.1 1.2 1.3 1.4 1.5 1.6 1.7

9.00am

(20 min)

9.20am

(50 min)

In Brief: Understanding the relationship between

different unit fractions (up to sixteenths) to a whole.

Mathematics – The relative size of fractions

Reading - Apple Fractions by Jerry Pallotta and Rob Bolster

Speaking & Listening – Participation in whole class discussion and outdoor group activities


In Detail:

Warm up:

Mental Maths (Chance/data) – Students play

„Dice Bingo‟ game. More details in the adjacent column

______________________________________

Introduction:

Teacher introduces the terminology numerator,

denominator and fraction bar (the line between

the numerator and denominator in a fraction). Teacher introduces focus of the maths lesson

(fractions up to sixteenths) and the class text

Apple Fractions by Jerry Pallotta/Rob Bolster.

Body:

Students seated at their desks.

Teacher completes modelled reading of the

selected text emphasising text-specific language and including focus questions.

Teacher gives students 2 minutes to pair-share

their thoughts about the text with a partner, before handing out Pie-Chart worksheets (2) for

students to complete. Students are required to show the fraction (eg. ⅛) and written English

(eg. one eighth) versions of the shaded areas on

Dice Bingo Students randomly

allocate any number between 2 and 12 to

each square on a 25-square grid worksheet.

Teacher rolls 2 x Smart

Board dice and if the total of the 2 dice

matches a number on a student‟s grid, that

number is circled (only one number per dice

roll). The first student

to circle all numbers shouts out „Bingo!‟

Repeat game as required.

Digital copy of ‘Apple Fractions’ loaded onto

Smart Board computer

24 x Pie Chart worksheets


1. Understand that unit fractions are all parts

of one whole


peer assessment

2. Document findings in

their Maths Journals



2.1 2.2 2.3 2.4 2.5

3.1 3.2 3.3 3.4 3.5 3.6 3.7

4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8

5.1 5.2 5.3 5.4


Model and represent unit fractions

including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete

whole (ACMNA058)



1. Understand that unit fractions are all

parts of one whole

2. Document findings in their Maths Journals

http://www.australiancurriculum.edu.au/Elements/ACMNA058

29


10.10am (10 min)

each pie chart. The second worksheet is an

extension exercise. Students exchange their completed worksheets

with a partner for peer assessment (answers

provided on Smart Board). Teacher asks students to come outside and form

ONE tightly-bunched group.

Teacher asks students to form 2 equal groups. If

not possible (23 students in the class for example), teacher asks students why this can‟t

be done before standing aside one student so

that only an even number of students remain. Teacher asks students focus questions (eg. “How are these new groups related to our original group”, etc).

Teacher repeats this exercise, this time dividing

the students into quarters and eighths before

discussing the fractional parts formed. Teacher asks focus questions to determine students‟

understanding of the fractional „part-part-whole‟ concept, and how each student is related to the

different groups. Teacher repeats this exercise, this time dividing

the students into thirds and fifths, before teacher

and students return inside.

Conclusion:

Teacher and students reflect on the activity,

discussing the differences between the part (part of one; part of a group) and the whole (a whole

one; a whole group). Which fractions are larger

than others? (halves, thirds, etc) Students record their conclusions in their Maths

Journals

Worksheet answers

loaded on Smart Board computer


Teacher collects

students‟ Maths Journals

30


31



1.1 1.2 1.3 1.4 1.5 1.6 1.7

9.00am

(20 min)

9.20am

(50 min)

In Brief: Comparing and ordering unit fractions on a

number line.

Mathematics – Fractional number lines

Viewing – On-line video Speaking & Listening – Participation in whole class

discussion and in-class and outdoor group activities


In Detail:

Warm up: Mental Maths (Number) – Students play „Discard‟

game. More details in the adjacent column

______________________________________

Introduction:

Teacher revises the terminology numerator and

denominator, and what students learned in the

previous lesson. Teacher reinforces prior content (fractions as

part of a whole) with a short, on-line tutorial

about fractions (Sheppard Software – „Fractions‟ tutorial):



Teacher introduces focus of the maths lesson

(fractional number lines) which will involve students viewing the You Tube video (9.06 min)

„How to compare and order fractions‟. Body:


Students view You Tube video (first 3.37 min

ONLY).


Discard Players in groups of 2 to 4 are dealt 5 cards

each. One card from the pack is turned face up,

and players who can make any number of

their cards equal the

number on the face card (using any

operations) can discard those cards. First player

to discard all cards is

the winner.

On-line tutorial loaded on Smart Board

computer

You Tube video ready to

go on Smart Board


1. Compare and order unit fractions on a

fraction number line

Student work sample – self

assessment

2. Document findings in




2.1 2.2 2.3 2.4 2.5

3.1 3.2 3.3 3.4 3.5 3.6 3.7

4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8

5.1 5.2 5.3 5.4


Describe, continue and create patterns

with fractions, decimals and whole numbers resulting from addition and

subtraction (ACMNA107)



1. Compare and order unit fractions on a fraction number line

2. Document findings in their Maths Journals





32


10.10am (10 min)


their thoughts using De Bono‟s YELLOW (good

points) and BLACK (bad points) hats. Students given Ordering Fractions worksheets

and 5 minutes to complete them.

Students mark their own worksheets using

answers displayed on the Smart Board. Teacher instructs students to form groups of 4

(teacher-determined). Teacher then gives each

group the 4 different laminated fraction cards (each with the same denominator) and 2 min to

determine the ascending order of the cards.

Teacher then asks groups (one at a time) to pin

the cards up in ascending order on a classroom „Clothesline‟ and explain the group‟s reasoning

behind its decision. Teacher then gives each group another 4

laminated fraction cards (not necessarily the

same denominator) and 2 minutes to determine

the ascending order of the cards. Teacher asks students to go outside and to form

a line in ascending order of each fraction card.

Students allowed to see the other fractions cards, but are asked to remain silent during the

ordering process. Students are asked (one at a time) to explain the

reasoning behind their choice of positions, before

moving back to the classroom and their desks.

Conclusion:

Teacher and students reflect on the morning‟s

activities, brainstorming the different strategies that students used to determine where their

fraction sat on a fraction number line.

Students document at least 2 different ways that

students to determine why their fraction was smaller of larger than fractions on either side of

them.

24 x Ordering Fractions worksheets (answers

loaded on Smart Board computer)

24 x Laminated cards

(4 simple fractions, same denominator)

Classroom Clothesline

already set up

24 x Laminated cards

(24 simple and complex fractions; not necessarily

the same denominator)


Teacher collects students‟ Maths Journals

33



1.1 1.2 1.3 1.4 1.5 1.6 1.7

9.00am (20 min)

9.20am

(10 min)

9.30am (45 min)

In Brief: Problem-solving mathematics fractions

sentences.

Mathematics – Number (fractions)

Speaking & Listening – Participation in whole class discussion and paired activities

Writing – Clear and neat written solutions

In Detail:

Warm up:

Mental Maths (Algebra) – Mathematic Cloze

exercise worksheets („Whales‟ “Cockatoos‟ & „Woylies‟ groups). More details

______________________________________

Introduction:

With students seated at their desks, teacher

introduces the concept of problem solving of

mathematical word sums. Students Rally Robin with face partner what they

know about problem solving strategies and how

they normally solve mathematical problems (prior knowledge). Social focus on taking turns and

listening carefully. Teacher uses „Question Cup‟ to randomly ask

students how they presently solve mathematical

problems.

Teacher introduces the concept that there are a

number of processes students can use to help them solve mathematical problems.

Body: Teacher answers the question “What is a

problem?” and introduces the example… “The area of a rectangle is 36cm². What could the perimeter be?”).

Eg. 15 - ____ = 8

(„Whales‟ groups

example)

Example processes Classifying, ordering,

comparing, estimating, predicting,

hypothesising, generalising,

representing, proving &

communicating.

Something with no OBVIOUS solution, that challenges students to think in novel ways…


1. Understand simple mental strategies

needed to solve

problems

2. Choose and apply an appropriate strategy to

successfully solve a mathematics word

fraction

3. Show their workings

clearly and neatly when solving a fraction

word sentence


teacher assessment

2.1 2.2 2.3 2.4 2.5

3.1 3.2 3.3 3.4 3.5 3.6 3.7

4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8

5.1 5.2 5.3 5.4


Use equivalent number sentences

involving multiplication and division to find unknown quantities (ACMNA121)



1. Understand simple mental strategies needed to solve problems

2. Choose and apply an appropriate strategy

to successfully solve a mathematics word

fraction

3. Show their workings clearly and neatly when solving a fraction sentence

problems

http://www.australiancurriculum.edu.au/Glossary?a=M&t=number

http://www.australiancurriculum.edu.au/Glossary?a=M&t=multiplication+


34


10.15am

(5 min)

Teacher explains „See, Plan, Do, Check‟ steps for

problem solving, and strategies that students can

use including simplifying the problem, acting out, listing all possibilities, constructing a table,

looking for a pattern, considering a similar problem, drawing, using materials, guessing and testing. Teacher introduces questions:

Teacher demonstrates mathematical thinking and

problem solving by encouraging students to act out a solution to the following problem: FOUR adults and TWO children want to cross a river in a boat that can only carry ONE teacher OR TWO students at any one time. How many trips will it take to cross the river? (trip = one-way journey) - Solution

Teacher introduces „Problem solving worksheet‟

to students on the Smart Board („My thinking‟,

„My working‟ and „My solution‟ sections), before handing worksheets out to students.

Teacher models the way the problem solving

worksheet can be used to solve problems by

working through a word sum problem with whole class on the board.

Teacher moves students into groups („Whales‟

“Cockatoos‟ & „Woylies‟) and hands out ability-appropriate word sum problems to each group.

Teacher stresses the importance of solving

problem INDIVIDUALLY using whatever

strategies students find useful. Students given 15 min to complete worksheets

(self-assessment using solutions provided).

Conclusion:

In their groups and using De Bono‟s GREEN

(creativity) thinking hat, students reflect on their answers, strategies and problem-solving methods

with their peers.

Teacher congratulates students on their group

working skills, and their attempts to solve their problems.

Questions - What do I need to find out? - What is the problem asking? - What do I know already? - How can I find this out? - Does my answer make sense, is it reasonable? Solution F – 2 adults cross B – 1 student returns F – 1 adult crosses B – 1 student returns (F = Forward; B = Back)

Template loaded on

Smart Board

24 x problem solving worksheets

Eg. („Whales‟ group)

I have some money in my wallet when I go shopping. I spend HALF at Bunnings and HALF what I have left at the Health Food shop. I now have $10 in my wallet. How much money did I have in my wallet to begin with?

35



1.1 1.2 1.3 1.4 1.5 1.6 1.7

9.00am

(20 min)

9.20am

(50 min)

In Brief: Understanding equivalent fractions.

Mathematics – All fractions can be represented in multiple ways

Viewing – On-line video and computer game Speaking & Listening – Participation in whole class

discussion and outdoor group activities


In Detail:

Warm up: Mental Maths (Chance/data) – Students play

„Pig!‟ More details in adjacent column…

______________________________________

Introduction:


(equivalent fractions) which will involve students

viewing the You Tube video (2.31 min) – Let‟s play math – Lesson 6 Equivalent Fractions.

Body:


Students view You Tube video:



their thoughts using De Bono‟s YELLOW (good points) and BLACK (bad points) hats.

Students then asked to move outside where

ropes have been laid out at intervals around the

school oval to represent fraction bars. Students divided into 2 groups… „Numerators‟ (8 students)

and Denominators (16 students)‟. Students reminded of focus social skills:

cooperating with peers, listening and taking

Pig! All students stand up at the start of the game.

Teacher rolls Smart Board dice and students

add the sum of the dice

to their totals. Students can sit down after any

throw of the dice (keep their score until the end

of the game). However, if a ONE appears on any

throw of the dice a

student is still standing, that student is excluded

from that round of the game. After 10 rolls of

the dice, the scores of

students who are sitting down are compared to

determine the winner.

Video loaded on the

Smart Board computer

16 x 2m ropes at

intervals around the school oval

Focus social skills


1. Recognise multiple ways of representing

equivalent fractions

2. Understand that all

equivalent unit fractions can be

simplified to that unit fraction

3. Document their reflections on

equivalent fraction activities on a PMI

chart



2.1 2.2 2.3 2.4 2.5

3.1 3.2 3.3 3.4 3.5 3.6 3.7

4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8

5.1 5.2 5.3 5.4


Investigate equivalent fractions used in

contexts (ACMNA077)



1. Recognise multiple ways of representing equivalent fractions

2. Understand that all equivalent unit

fractions can be simplified to that unit

fraction

3. Document their reflections on equivalent fraction activities on a PMI chart


http://www.australiancurriculum.edu.au/Glossary?a=M&t=equivalent+fractions


36


10.10am (10 min)

turns.

Teacher calls out the first fraction (eg. “One third!”), and students run to the first „fraction bar‟ and form the SIMPLEST fraction that represents

the one called out, with the appropriate number of students from the „Numerators‟ group stand

together ABOVE the fraction bar, with students from the „Denominators‟ group standing together

BELOW the bar.

Teacher confirms the correct fraction then blows

a whistle to signal students to run to the next fraction bar and to form an EQUIVALENT fraction

to the previous one. Teacher confirms the correct fraction, and either

asks students to from another equivalent fraction

at the next fraction bar, or calls out a new

fraction. Students return to their desks after 20 minutes of

this activity.

Teacher shows students Sheppard Software web

site, and where to find the website‟s „Matching Equivalent Fractions‟ game. Students spend 15

minutes on this activity.

http://sheppardsoftware.com/mathgames/fractions/

memory_equivalent1.htm

Conclusion:

Teacher and students reflect on the morning‟s

activities with the teacher introducing the concept of a PMI chart. Students reflect on their

lesson using De Bono‟s BLACK (negative), YELLOW (positive) and GREEN (possibilities)

hats. Session concludes with students filling out a

PMI chart to document their reflections. Students glue their completed PMI charts into


1 x whistle

PowerPoint with on-line

website loaded onto the Smart Board computer

24 x PMI charts


Teacher collects

students‟ Maths Journals

http://sheppardsoftware.com/mathgames/fractions/%20memory_equivalent1.htm

http://sheppardsoftware.com/mathgames/fractions/%20memory_equivalent1.htm

37



1.1 1.2 1.3 1.4 1.5 1.6 1.7

9.00am (20 min)

9.20am (50 min)

In Brief: Understanding that fractions are discrete

numbers.

Mathematics – Fractions as discrete numbers

Speaking & Listening – Participation in pair-share discussion


In Detail:

Warm up:

Mental Maths – Students play „Three Hexagon‟ game. More details in adjacent column

______________________________________

Introduction: Teacher introduces focus of the maths lesson

(fractions as numbers). Students will be asked to

cut identical strips of paper and imagine that they

represent a journey to the local tennis court.

Body: Students seated at their desks.

Teacher asks students to cut FOUR identical

strips of paper each.

Each student imagines that ONE strip represents

a journey to the local tennis court and that they will be allowed to rest exactly in the middle of

their journey. Students to draw a line on the

paper strip to represent the middle. Teacher drills the „halfway‟ point of their journey,

and students mark this point ½.

Teacher asks students how they would represent

the beginning and end of their trips, and encourages the responses 0/2 and 2/2.

Teacher asks students “How is this way of using a half different from when we have, for example,

Three Hexagon A game for two players. Each player has three

counters. The aim of the

game is to get all three Counters in a straight

line through the hexagon‟s midpoint.

The player going first places a counter on one

of the circles. The

second player places one Counter on another

circle. This continues until all the counters

have been placed.

“The journey has 2 equal part trips, and we have only travelled one part…” “Travelled ZERO halves and TWO halves…”


1. Understand that fractions represent not

only parts of a whole,

but are discrete numbers in their own

rights

Student work sample – teacher assessment

(checklist)

2. Create an interesting

and individual board game that shows an

understanding of the

size of fraction numbers


teacher assessment (rubric)

2.1 2.2 2.3 2.4 2.5

3.1 3.2 3.3 3.4 3.5 3.6 3.7

4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8

5.1 5.2 5.3 5.4


Compare and order common unit

fractions and locate and represent them on a number line (ACMNA102)



1. Understand that fractions represent not

only parts of a whole, but are discrete numbers in their own rights

2. Create an interesting and individual board game that shows an understanding of the

size of fraction numbers

http://www.australiancurriculum.edu.au/Glossary?a=M&t=number+line


38


10.10am (5 min)

half an apple?” Teacher invites students to label another

„journey‟ paper strip to show quarter journeys, then eighth journeys, and reinforces the concept

of a fractional number indicating a point on a line. Teacher invites students to count the

number of part journeys to help students accept the idea that fractions can be part of a number

sequence. Teacher repeats exercise with last paper strip,

this time inviting responses from students about the fractional number that would appear on a

paper strip folded in quarters with ZERO at one end, and TWO at the other. Teacher reinforces

the numbers 0, ½, 1, 1½ and 2. Students create any board game of their

choosing (using the template provided) that shows a 3km journey and that uses a pair of

dice. Students are required to show in each square, a fractional number that represents the

approximate position of the square on the board game journey.

Teacher gives students 5 minutes to Rally Robin

ideas for their proposed board games with a

partner. Teacher hands out board game templates and

allows students 30 minutes to complete the

activity.

Conclusion:

Students glue their completed board games into

their Maths Journals for collection and assessment by the teacher

Teacher asks focus questions to conclude the

activity.

Teacher encourages the

response that one „represents half a thing‟ and the other „indicates a point on a line‟ (compare

to number line).

24 x A3 board-game template photocopies


“What have you learned about fractions today?‟ “How is half and apple different from half a journey?” “How are they similar?”

39


40



1.1 1.2 1.3 1.4 1.5 1.6 1.7

9.00am

(20 min)

9.20am

(55 min)

In Brief: Adding and subtracting fractions with the

same denominator.

Mathematics – Fractions addition

Viewing – On-line videos Speaking & Listening – Participation in whole class

discussion and in-class and outdoor group activities


In Detail:

Warm up: Mental Maths (Number) – Students complete

„Number Climber‟ worksheet. See details

______________________________________

Introduction:

Teacher revises the terminology numerator and

denominator, and what students learned in the

previous lesson. Teacher reinforces prior content with a short, on-

line tutorial about fractions (Sheppard Software –

„Fractions‟ tutorial):




(adding and subtracting fractions) which will

involve students viewing the first 7.50 min of the You Tube video (9.49 min) „Adding and subtracting fractions‟.

Body:


Students view You Tube video (first 7.50 min).

http://www.youtube.com/watch?v=52ZlXsFJULI Teacher gives students 2 minutes to pair-share

Number Climber Help a mountain climber

scale a mountain by correctly adding 2

circled, single-digit numbers, and placing

the resulting value

(minus the „tens‟ digit if applicable) in the circle

above. Continue this addition to find the

number at the apex of

the mountain.

On-line tutorial loaded on Smart Board

computer

You Tube video ready to

go on Smart Board


1. Adding and subtracting fractions with the

same denominator

Peer-assessed worksheets

2. Document findings

about the relationship between fractions in




2.1 2.2 2.3 2.4 2.5

3.1 3.2 3.3 3.4 3.5 3.6 3.7

4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8

5.1 5.2 5.3 5.4


Investigate strategies to solve problems

involving addition and subtraction of fractions with the same denominator

(ACMNA103)



1. Adding and subtracting fractions with the same denominator

2. Document findings about the relationship

between fractions in their Maths Journals



http://www.youtube.com/watch?v=52ZlXsFJULI

http://www.australiancurriculum.edu.au/Glossary?a=M&t=denominator


41


10.15am

(5 min)

their thoughts using De Bono‟s YELLOW (good

points) and BLACK (bad points) hats. Students given Adding and Subtracting Fractions

worksheets („Whales‟, „Cockatoos‟ and „Woylies‟

groups have 10 minutes to complete worksheets at each group‟s ability level).

Students swap their completed worksheets with

a partner for marking – teacher hands out answer sheets.

Teacher divides student into 2 groups:

- the FIRST group plays “Fruit Shoot…

fraction addition” on-line game (students own choice of Levels 1, 2 and/or 3)


fractions/FruitShootFractionsAddition.htm - the SECOND group plays ““Fruit Shoot…

fraction addition” on-line game (students

own choice of Levels 1, 2 and/or 3)


fractions/FruitShootFractionsSubtraction.htm - after 15 minutes, groups change stations

Teacher reminds students to work quietly while

at the computer bank, and to respect the rights of those who work better in a noise-free

environment.

Conclusion:

Students record their conclusions in their Maths

Journals, comparing their observed similarities and differences between „whole number‟ number

lines and fraction lines.

8 x „Whales‟ worksheets 8 x „Cockatoos‟

worksheets 8 x „Woylies‟ worksheets

8 x „Whales‟ worksheet

answers

8 x „Cockatoos‟ worksheet answers

8 x „Woylies‟ worksheet answers

Book 30 minutes of time for Year 5 class on

computer bank

Focus social skills



http://www.sheppardsoftware.com/mathgames/%20fractions/FruitShootFractionsAddition.htm

http://www.sheppardsoftware.com/mathgames/%20fractions/FruitShootFractionsAddition.htm

http://www.sheppardsoftware.com/mathgames/%20fractions/FruitShootFractionsSubtraction.htm

http://www.sheppardsoftware.com/mathgames/%20fractions/FruitShootFractionsSubtraction.htm

42


Part E – Assessment Rubric* for Lesson 20 (see page 24)

Criteria

Assessment Skill 1 2 3 4 Score (1 - 4)

Understanding and use of problem-solving strategies

Little of no evidence of the understanding or use of problem solving strategies

Limited evidence of the understanding or use of problem solving strategies

Satisfactory evidence of the understanding or use of problem solving strategies

Clear evidence of the understanding or use of problem solving strategies

_______

Communication of problem-solving strategies

Inaccurately communicates concepts and solutions to problems

Limited communication of concepts and solutions to problems

Satisfactorily communicates concepts and solutions to problems

Accurately communicates concepts and solutions to problems

_______

Knowledge and application of mathematics content

Demonstrates little or no knowledge and/or application of maths content

Demonstrates limited knowledge and/or application of maths content

Demonstrates a general knowledge and/or application of maths content

Demonstrates a clear knowledge and/or application of maths content

_______

Use of mathematical terminology

Little or no mathematical terminology used or attempted

Some mathematical terminology presented, but incorrectly used

Mathematical terminology used and presented in a satisfactory manner

Mathematical terminology used and presented correctly and extensively

_______

Presentation of working The reader is unable to understand the steps taken in the problem‟s solution

The steps taken in the problem‟s solution are present but difficult to follow

The steps taken in the problem‟s solution are presented in a logical manner

The steps taken in the problem‟s solution are clear and easy to follow

_______

Total Score = / 20

* This rubric would be presented on an A4 page containing the title of the assessed activity (in this case, „Fraction and Decimal Word Sums‟), the date of the activity, the student‟s name and year level, and a final paragraph for the teacher‟s comments.

Documents

Peter Jelinek - Unit Code CUR4203 Lecturer: Jennifer Moyle · PDF filePeter Jelinek - Unit Code CUR4203 © Peter Jelinek 2011 ... 4-week mathematics lesson overview (Year 5 ... English