Team Teaching for Numeracy

www.pdst.ie

1 Table of Contents

Reflection 3

Mathematical Skills 4

Assessment 6

Using Cuisenaire Rods 8

Using a Hundredth Wheel 9

Dotted Paper 11

Reflections on Classroom Practice (Video) 12

Planning for team teaching 13

Long Term planning template 14

Short term planning template 16

Appendix 1: Nrich Problems 19

Appendix 2: Journal Prompts 20

Hundredth Wheel Templates 22

Reflection:

Reflection: Beginning of Workshop

What is your experience of team teaching?

Key recommendation from the group:

Reflection: End of Workshop

What will you take from today to inform team teaching in your school?

2 Mathematical Skills Junior and Senior Infants 1st and 2nd Class Understanding and Recalling  Recall and understand terminology  Recall and understand terminology and facts Implementing  Devise and use mental strategies and  Devise and use mental strategies and procedures for carrying out mathematical procedures for carrying out mathematical tasks tasks  Use appropriate manipulatives to carry out  Use appropriate manipulatives to carry mathematical tasks and procedures out mathematical tasks and procedures  Execute procedures efficiently Reasoning  Classify objects into logical categories  Classify objects into logical categories  Make guesses and carry out experiments to  Recognise and create sensory patterns test them  Recognise and create mathematical patterns  Justify the processes or results of activities and relationships  Justify the processes and results of mathematical activities Integrating and Connecting  Connect informally acquired mathematical  Connect informally acquired mathematical ideas with formal mathematical ideas ideas with formal mathematical ideas  Recognise mathematics in the  Recognise mathematics in the environment environment  Recognise the relationship between verbal,  Recognise the relationship between concrete, pictorial and symbolic modes of verbal, concrete, pictorial and symbolic representing numbers modes of representing numbers  Carry out mathematical activities that involve  Carry out mathematical activities that other areas of the curriculum involve other areas of the curriculum  Understand the mathematical ideas behind the procedures he/she uses Communicating and Expressing  Discuss and explain mathematical  Discuss and explain mathematical activities activities  Listen to and discuss other children’s  Record the results of mathematical mathematical descriptions and explanations activities concretely and using diagrams,  Discuss and record the results of pictures and numbers mathematical activities using diagrams, pictures  Discuss problems presented concretely, and symbols pictorially or orally  Discuss problems presented pictorially or orally Applying and Problem Solving  Select appropriate materials and  Select appropriate materials and processes processes for mathematical tasks for mathematical tasks and applications Select and apply appropriate strategies for  Select and apply appropriate strategies for completing a task or solving a problem completing a task or solving a problem  Recognise solutions to problems  Recognise solutions to problems  Apply concepts and processes in a variety of contexts

3rd and 4th Class 5th and 6th Class Understanding and Recalling  Recall and understand terminology, facts and  Recall and understand facts, definitions and definitions formulae Implementing  Devise and use mental strategies and  Devise and use mental strategies and procedures for carrying out mathematical tasks procedures for carrying out mathematical  Use appropriate manipulatives to carry out tasks mathematical procedures  Use appropriate manipulatives to carry out  Execute standard procedures efficiently with a mathematical procedures variety of tools  Execute standard procedures efficiently with a variety of tools Reasoning  Make hypotheses and carry out experiments  Make hypotheses and carry out experiments to test them to test them  Make informal deductions involving a small  Make informal deductions number of steps  Search for and investigate mathematical  Explore and investigate mathematical patterns patterns and relationships and relationships  Reason systematically in a mathematical  Reason systematically in a mathematical context context  Justify processes and results of mathematical  Justify processes and results of mathematical activities, problems and projects activities, problems and projects Integrating and Connecting  Connect informally acquired mathematical  Connect informally acquired mathematical ideas and processes with formal mathematical ideas and processes with formal mathematical ideas and processes ideas and processes  Understand the connections between  Recognise mathematics in the environment mathematical procedures and the concepts used  Represent mathematical ideas and  Recognise mathematics in the environment processes in different modes: verbal, pictorial,  Represent mathematical ideas and processes diagrammatic and symbolic in different modes: verbal, pictorial,  Understand the connections between diagrammatic, and symbolic mathematical procedures and the concepts  Recognise and apply mathematical ideas and used processes in other areas of the curriculum  Recognise and apply mathematical ideas and processes in other areas of the curriculum Communicating and Expressing  Discuss and explain the processes used and  Discuss and explain the processes used and the results of mathematical activities, problems, the results of mathematical activities, and projects problems and projects in an organised way  Listen to and discuss other children's  Listen to and discuss other children's mathematical descriptions and explanations mathematical descriptions and explanations  Discuss and record the processes and results  Discuss and record the processes and of work using a variety of methods results of work using a variety of methods  Discuss problems presented verbally or  Discuss problems and carry out analyses diagrammatically and carry out analyses Applying and Problem Solving

 Select appropriate materials, concepts and  Select appropriate materials, concepts and processes for mathematical tasks and processes for particular tasks and applications applications  Apply concepts and processes in a variety of  Apply concepts & processes in a variety of contexts context  Analyse problems and plan an approach to  Analyse problems & plan an approach to solving them solving them  Select and apply a variety of strategies to  Select and apply a variety of strategies to complete tasks and projects or solve problems complete tasks and projects or to solve problems  Reflect upon and evaluate solutions to  Evaluate solutions to problems problems Consider a range of assessment opportunities when implementing team teaching (Primary School Mathematics Curriculum Teacher Guidelines p.35)

Task Assessment Opportunities Pupil Voice 1 Represent fractions and solve problems using Cuisenaire Rods (Level B.1: See Fractions Manual p.42)

Task Assessment Opportunities Pupil Voice Represent fractions 2 using paper strips (Level B.1: See

Fractions Manual p.41)

Task Assessment Opportunities Pupil Voice Represent fractions 3 using Geoboards (Level B.7: See Fractions Manual p.43

Task Assessment Opportunity Pupil Voice Represent fractions 4 using a Set Model (Level B.1: See Fractions Manual p.45 - 46)

Task Assessment Opportunity Pupil Voice 5 Represent fractions using a hundredth wheel (Level B.1 and B.6: See Fractions Manual p. 42 and Place

Value Manual p. 99

Cuisenaire Cuisenaire is a collection of coloured rods ranging in length from 1cm to 10cm. Each rod represents a number from 1 to 10. The rods can be used to foster understanding of a wide variety of ideas in number. The structure of the rods means that children come to recognise each number in terms of its length rather than as a collection of discrete objects. The use of Cuisenaire rods will support the development of mathematical concepts throughout the primary school years. From infant classes, pupils will build on earlier work with a variety of concrete resources and continue to develop their understanding of the components of number and addition and subtraction through the use of Cuisenaire rods. Furthermore, the rods can help to support the linear and area models for representing fractions, decimals, percentages and also multiplication and division problems (adapted from Pitt, 2001, p, 87).

Image sourced at:http://upload.wikimedia.org/wikipedia/commons/5/5c/Cuisenaire-Rods-2.png ICT: http://www.cuisenaire.co.uk/index.php/home/videos/cuisenaire-rods-in-the-classroom/video/ https://nrich.maths.org/4348 8

The Hundredth or Decimal Wheel Provide pupils with two different coloured hundredths wheels (or decimal wheels) as shown below. This is a good example of the area model for tenths and hundredths. A hundredths wheel is divided into 10 sections, each divided further into 10 equal intervals. When a slit is cut along one radius and two wheels of different colours are placed together, the model can be used to show decimals and fractions of less than one. This model will be familiar to pupils, as many have seen “pies” divided into thirds, fourths, tenths, and so on. Ignoring the smaller gradations, the hundredths wheel is simply a tenths wheel. (Place Value Manual, pg. 81)

3 Dot Paper (1 cm)

Reflections on Classroom Practice:

What are the elements of good practice relating to team teaching?

What good practice in relation to numeracy are teachers highlighting?

What skills are the pupils demonstrating?

Planning for Numeracy

What areas need to be considered in your plan for numeracy?

Long-term Plan for Numeracy team teaching - 4 weeks Teachers: Number of Groups: Strands and Strand Units:

Concepts and Learning Experiences:

Skills Development:

Assessment Findings:

IEP/IPLP Targets:

Pupil Groupings based on Initial Assessment and Learning Trajectory Levels (Flexible):

Methodologies:

Maths Resources and ICT:

Maths Language:

Short Term Plan for Numeracy: 1 week Pupil Groupings: Assessment options: Methodologies Maths Resources and Maths Language and ICT Vocabulary

Class Level:

Teachers:

Strand:

Strand Unit:

Monday Tuesday Wednesday Thursday Friday Group : Teacher led Teacher led Teacher led Teacher led Teacher led

Teacher:

Independent work: Independent work Independent work Independent work Independent work

IEP/IPLP targets:

Monday Tuesday Wednesday Thursday Friday Group: Independent Work: Independent Work: Independent Work: Independent Work: Independent Work:

Teacher:

IEP/IPLP targets: Teacher Led: Teacher Led: Teacher Led: Teacher Led: Teacher Led:

Monday Tuesday Wednesday Thursday Friday

Teacher led: Teacher led: Teacher led: Teacher led: Teacher Led: Group:

Teacher:

IEP/IPLP targets: Independent Work Independent Work Independent Work Independent Work Independent Work:

Monday Tuesday Wednesday Thursday Friday

Group: Independent Work: Independent Work: Independent Work: Independent Work: Independent Work:

Teacher: 16

Teacher Led: Teacher Led: Teacher Led: Teacher Led: Teacher Led:

IEP/IPLP targets:

17 Appendix 1: Nrich Problems

Number Detective: http://nrich.maths.org/204 Follow the clues to find the mystery number from the list below.

 The number has two digits.  Both of the digits are even.  The digit in the tens place is greater that the digit in the ones place.  The ones digit is not in the three times table.  The tens digit is not double the ones digit.  The sum of the two digits is a multiple of five.

Worms: https://nrich.maths.org/40

With a square in front of you, with the numbers 1 to 100 marked on as shown and the centre 16 squares marked in some special way, place your worm, perhaps made out of multilink, on the square. [Multilink are 2 cm long so get hold of some 2 cm squared paper; the backing paper for some "taky-back'' film is just the right size.] When you place your worm you have to make sure that the head is on one of the centre squares that are shaded differently. The head stays there, but while the worm is eating it wriggles and changes the shape of its body, in as many different ways as it can. Here are just three of the many ways in which the worm can be, and I've placed its head on the number 34. Find all the shapes and positions that the worm can be with its head fixed in the one place [in my example, on number 34, but you can choose any of those 16 squares]. Don't forget about the worm's body going North, South, East and West. Add up the numbers that the worm is on, that is the numbers that the head and the rest of the body are resting on. [In my first example 34 + 33 + 43 + 53 = 163; 2nd example gives 34 + 33 + 23 + 13 = 103; 3rd example gives 34 + 33 + 23 + 22 =112.] Find a good way of recording your results so that you can make sure you do not do the same one twice and so that you can compare the results easily.

Reach 100: http://nrich.maths.org/6753

18 Here is a grid of four "boxes":

You must choose four different digits from 1−9 and put one in each box. For example:

This gives four two-digit numbers: 52 (reading along the 1st row) 19 (reading along the 2nd row) 51 (reading down the left hand column) 29 (reading down the right hand column) In this case their sum is 151. You must choose four different digits from 1−9 and put one in each box. For example: Your challenge is to find four different digits that give four two-digit numbers which add to a total of 100. How many ways can you find of doing it?

The Deca Tree: http://nrich.maths.org/2006 In the forest there is a Deca Tree. A Deca Tree has 10 trunks, and on each trunk there are 10 branches, and on each branch there are 10 twigs, and on each twig there are 10 leaves. One day a woodcutter came along and cut down one trunk from the tree. Then he cut off one branch from another trunk of the tree. Then he cut off one twig from another branch. Finally he pulled one leaf from another twig. How many leaves were left on the tree then? Appendix 2: Journal Prompts

19 Prompts for the beginning of a topic or new term

 I want to become better at maths because…  My aim in maths this year is to…  I am improving at maths now because...  I would like to know how...

Prompts for the end of a topic or term

 The thing I’m proud of myself for learning is…

 The way I remember how to in my head is…

 I’m convinced that…

 I know I’m right because

 I’m surprised that…

 I figured this out by...

 A way I tried to solve this problem that didn’t work out was … I think it didn’t work out because...

 Something new I learned today was…

 I’m still confused by…  The thing I’m proud of myself for learning is…

 The way I remember how to in my head is…

 I’m convinced that…

 I know I’m right because

 I’m surprised that…

20 Prompts for pupil’s self-assessment and reflection

 I figured this out by...

 A way I tried to solve this problem that didn’t work out was … I think it didn’t work out because...

 Something new I learned today was…

Prompts to record and consolidate pupil’s mathematical thinking and understanding

 I saw a pattern…  I noticed….  This will also work for….  This will not work for…

21 22 23 24