Planning backward, teaching forward Backward Planning Planning backward, teaching forward We plan backwards (from the end point back to the beginning point) We must know what we want students to do We must know what we want them to achieve (this is what we are measuring – why else would you waste their time or yours fluffing around) We must plan the task for them to do first (what is the verb, what is the skill, what is the knowledge they must have) We must teach them together with lots of practice together We must model for them initially so that they know how to do the task (Draw them in, model, do it together We teach forwards – we are very used to this, uni taught us to teach forward, they also taught us to lead students to the answer through the questioning method – for example when I do observations of people I will often hear them say… What can you tell me about… or Today we are learning about….who know about this…. What do you know. If you know your class well enough (and have done the learning design exercise plus have conducted some diagnostic assessments so you know where they are at, here’s my two cents and me standing on my soap box, we’re here to teach them, we’re not here to waste their time in the carpet while we fluff around. Turn off the “uni teacher voices” cause its killing the kids, talk to them as if they are the most interesting people in the world and you are happy to download new information to them.

Backward Planning Planning backwards Teaching forwards Be clear on the learning intention – write down what they must achieve Work out how you are going to measure (assess and record method, checklist, tasksheet, photo) Design tomorrow’s review questions Design today’s task Design some more of today’s tasks to practice with together Design a today’s task that you are going to demonstrate Design an engaging story that links them into the concept or find a video clip or something from real life that links to what they are learning Tell them what they are learning (learning intention) Tell them how you are going to measure them (assessment) Draw them in with something that engages (see Learning Design & Mu Model or TL Cycle) Demonstrate, model, explain the task, knowledge, skills (they shut up and listen – you lend them your thinking) Do the task together, practice until most everyone has it mastered Student’s individually demonstrate the task, teacher measures proficiency and provides feedback (tick off on checklist or take photo or collect task sheet?) Review together at the end of the lesson Put into tomorrow’s review to continue to consolidate the concept (target those who didn’t get it

Pick the learning intention Recognise and represent multiplication as repeated addition, groups and arrays (ACMNA031) Recognise multiplication as repeated addition Recognise multiplication as groups of Recognise multiplication in arrays Represent multiplication as repeated addition Represent multiplication as groups Represent multiplication as arrays Recognise multiplication as repeated addition Multiplication in arrays Multiplication in groups Multiplication written numerically Represent multiplication as repeated addition Pick the learning intention I picked one which was Recognise and represent multiplication as repeated addition, groups and arrays (ACMNA031) When I broke the content down I realised that you must teach groups before you teach arrays and then you can teach repeated addition (along a number line works nicely!!) They must first learn to recognise this (recognise means to identify something as previously seen or known or to perceive as existing or true, then recognise as a verb has synonyms like acknowledge, appreciate, understand, grant, concede) How do I measure their recognition? I must present them with something where they can say “ooh that’s multiplication in arrays, in groups, as repeated addition) Represent – to present again or anew – to exemplify or portray. How do I measure this, simply get them to redo something I just taught them.

Recognise and represent multiplication as repeated addition, groups and arrays (ACMNA031) Recognise multiplication as repeated addition Recognise multiplication as groups of Recognise multiplication in arrays Represent multiplication as repeated addition Represent multiplication as groups Represent multiplication as arrays How am I going to be measuring, assessing or recording their attainment? Recognise multiplication as groups, arrays, repeated addition Say and point… this is a group of Say and point… this is an array… an array is things organised in a row or column Say and point… this is repeated addition of…. repeated addition can be written as multiplication Use my checklist to tick off their recognition Represent multiplication as groups, arrays, repeated addition Record groups of tasks presented to them Record arrays of tasks presented to them Record multiplication as repeated addition when presented to them Take a picture of their work for a portfolio task Pick the learning intention I picked one which was Recognise and represent multiplication as repeated addition, groups and arrays (ACMNA031) When I broke the content down I realised that you must teach arrays before you teach groups and then you can teach repeated addition (along a number line works nicely!!) They must first learn to recognise this (recognise means to identify something as previously seen or known or to perceive as existing or true, then recognise as a verb has synonyms like acknowledge, appreciate, understand, grant, concede) How do I measure their recognition? I must present them with something where they can say “ooh that’s multiplication in arrays, in groups, as repeated addition) Represent – to present again or anew – to exemplify or portray. How do I measure this, simply get them to redo something I just taught them.

This is multiplication in groups Multiplication can be shown as groups of things 3 x 4 = 12 Learning Intention: Multiplication as groups Specify: Multiplication as a times table represented with numbers & symbols Multiplication as repeated addition Multiplication as arrays Multiplication as groups of This is multiplication in groups Now to planning backwards – I want them to recognise groups – tomorrows review task This will also be blown up into an a3 coloured poster and laminated (without the descriptor on the side)

This is multiplication in an array Multiplication can be shown in arrays – Arrays are organised into rows and columns 3 x 4 = 12 llll lll lll Learning Intention: Multiplication as arrays Specify: Multiplication as a times table represented with numbers & symbols Multiplication as repeated addition Multiplication as groups of This is multiplication in an array Now to planning backwards – I want them to recognise arrays– tomorrows review task This will also be blown up into an a3 coloured poster and laminated (without the descriptor on the side)

This is multiplication as repeated addition Multiplication can be shown as repeated addition 3 x 4 = 12 4 + 4 + 4 = 12 3 + 3 + 3 + 3 = 12 Learning Intention: Multiplication as repeated addition Specify: Multiplication as a times table represented with numbers & symbols Multiplication as arrays Multiplication as groups of This is multiplication as repeated addition Now to planning backwards – I want them to recognise repeated addition– tomorrows review task This will also be blown up into an a3 coloured poster and laminated (without the descriptor on the side)

This is: Groups – Arrays – Repeated addition llll lll lll 4 + 4 + 4 = 12 3 + 3 + 3 + 3 = 12 Now to planning backwards – I want them to recognise groups, arrays and repeated addition and tell me each one when I point to it – I might make up some flashcards of these for the future – this is tomorrows review task

Tell me: Groups – Arrays – Repeated addition 4 + 4 + 4 = 12 3 + 3 + 3 + 3 = 12 Today’s task – tell me is this arrays, groups or repeated addition

Tell me: Groups – Arrays – Repeated addition llll lll lll Today’s task – tell me is this arrays, groups or repeated addition

Tell me: Groups – Arrays – Repeated addition Today’s task – tell me is this arrays, groups or repeated addition

Multiplication as groups Lesson Multiplication as groups

Groups – this is groups – there are 2 groups of 4 Shut Up I’m teaching you this is groups of

Groups – this is groups – there are 5 groups of 4 Shut Up I’m teaching you this is groups of

Groups – this is groups – there are 3 groups of 4 Shut Up I’m teaching you this is groups of

Groups – can you draw – 2 groups of 3 Lets do this one together, I’ll use the big whiteboard, you use your little whiteboards, draw me circles like mine for our groups, how may groups do I have? Great and how many do I need to put into my groups? Great – draw it then show me with a smile

Groups – can you draw – 3 groups of 2 Lets do this one together, I’ll use the big whiteboard, you use your little whiteboards, draw me circles like mine for our groups, how may groups do I have? Great and how many do I need to put into my groups? Great – draw it then show me with a smile

Groups – can you draw – 2 groups of 5 Lets do this one together, I’ll use the big whiteboard, you use your little whiteboards, draw me circles like mine for our groups, how may groups do I have? Great and how many do I need to put into my groups? Great – draw it then show me with a smile

Worksheet task

Multiplication as arrays Lesson Multiplication as arrays

Arrays– arrays are things organised into rows and columns. An array of 6 eggs 2 rows of 3 = 6 2 x 3 = 6 An array of 6 eggs 3 columns of 2 = 6 3 x 2 = 6 Shut up I’m teaching you this watch me and learn Arrays are things organised into rows and columns – I want you to remember this always because I’m going to ask you to tell me this tomorrow, you could tell your mum and dad this tonight, arrays are things organised into rows and columns See I have an array of 6 eggs here – this is two rows of three eggs, see a row here and a row here, there are three in each row, I’ll count them – it equals 6. I can write this as a multiplication sum, I’ll give you an extra happy smile today if you can remember to write your arrays like this when we do them together later. See this one is the same, its an array of 6 eggs as well – this is in columns though, its 3 columns of 2 eggs, see a column here, a column here and a column here. There are 6 eggs and I’ve written it as a multiplication sum here!!

Arrays – things organised into rows and columns An array of 12 Grannies 3 rows of 4 grannies = 12 grannies or 4 columns of 3 grannies = 12 grannies 3 x 4 = 12 4 x 3 = 12 Shut up I’m teaching you this watch me and learn Arrays are things organised into rows and columns Here I have an array of 12 grannies– this is 3 rows of 4 grannies which is 12 grannies, I can count them but it takes a long time which is why it is quicker to learn our multiplication or times tables and do it this way. I can also show my array of 12 grannies as 4 columns of 3 grannies, it’s the same 3x4 or 4x3

Arrays – things organised into rows and columns An array of 15 Gummi Bears 5 rows of 3 bears = 15 bears or 3 columns of 5 bears = 15 bears 5 x 3 = 15 3 x 5 = 15 Shut up I’m teaching you this watch me and learn Arrays are things organised into rows and columns Yum an array of 15 gummi bears– this is 5 rows of 3 bears which is 15 bears, I can count them but it takes a long time which is why it is quicker to learn our multiplication or times tables and do it this way. I can also show my array of 15 gummi bears as 3 columns of 5 bears, it’s the same 5x3 or 3x5 They are all 15 yummy bears no matter which way I put them in an array

Arrays – can you draw – 2 rows of 3 balls (extra points if you give me the multiplication sum) Arrays are things organised into rows and columns Say it with me Arrays are things organised into rows and columns Tell me what is an array Arrays are things organised into rows and columns Lets make some arrays, I’ll use the big whiteboard, you use your little whiteboards, draw me 2 rows of 3 balls? Great and how rows do I need to put in my array? Great – can you draw it another way as 2 rows of 3 - show me with a grin Can you write the multiplication sum? Do you remember how? I can show you, you can copy.

Arrays – can you draw – 5 rows of 2 balls (extra points if you give me the multiplication sum) Arrays are things organised into rows and columns Sing it with me Arrays are things organised into rows and columns Tell me what is an array Arrays are things organised into rows and columns Lets make some arrays, I’ll use the big whiteboard, you use your little whiteboards, draw me 5 rows of 2 balls? Great and how rows do I need to put in my array? Great – can you draw it another way as 2 rows of 5 - show me with a grin Can you write the multiplication sum? Do you remember how? I can show you, you can copy.

Arrays – can you draw – 5 rows of 2 balls (extra points if you give me the multiplication sum) Arrays are things organised into rows and columns Whisper it to me Arrays are things organised into rows and columns Tell me what is an array Arrays are things organised into rows and columns Lets make some arrays, I’ll use the big whiteboard, you use your little whiteboards, draw me 5 rows of 2 balls? Great and how rows do I need to put in my array? Great – can you draw it another way as 2 rows of 5 - show me with a grin Can you write the multiplication sum? Do you remember how? I can show you, you can copy me on your little whiteboard

Worksheet Task

Multiplication as repeated addition Lesson Multiplication as repeated addition

Multiplication can be shown as repeated addition 3 rows of 3 birds 3 + 3 + 3 = __ birds 3 x 3 = __ birds Multiplication can be shown as repeated addition This means that instead of counting something that we see in groups or arrays we can write it as repeated addition and add it up See how I have some birds, I have 3 rows of 3 birds, I can count these or I can add them up quickly I can also show this as a multiplication sum – like we did with arrays before 3 x 3 = 9

Multiplication can be shown as repeated addition 2 groups of 3 cupcakes 3 + 3 = __ cupcakes 2 x 3 = __ cupcakes Multiplication can be shown as repeated addition This means that instead of counting something that we see in groups or arrays we can write it as repeated addition and add it up See how I have some cupcakes, I have 2 groups of 3 cupcakes, I can count these or I can add them up quickly I can also show this as a multiplication sum – like we did with arrays before 2 x 3 = 6

Multiplication can be shown as repeated addition 4 rows of 4 angry birds 4 + 4 + 4 + 4 = __ birds 4 x 4 = __ angry birds Multiplication can be shown as repeated addition This means that instead of counting something that we see in groups or arrays we can write it as repeated addition and add it up See how I have some birds, I have 4 rows of 4 birds, I can count these or I can add them up quickly I can also show this as a multiplication sum – like we did with arrays before 4 x 4 = 16

Multiplication as repeated addition 3 x 4 = 12 4 + 4 + 4 = 12 4 x 3 = 12 3 + 3 + 3 + 3 = 12 Multiplication can be shown as repeated addition Say it with me Multiplication can be shown as repeated addition Tell me what is repeated addition? Multiplication!!! Hooray!!! Lets do some of these, I’ll use the big whiteboard, you use your little whiteboards,

Multiplication can be shown as repeated addition _ rows of _ angry birds _ + _ = __ angry birds _ x _ = __ angry birds Multiplication can be shown as repeated addition Lets do some of these, I’ll use the big whiteboard, you use your little whiteboards,

Multiplication can be shown as repeated addition _ row of _ fish _ + _ = __ fish _ x _ = __ fish Multiplication can be shown as repeated addition Lets do some of these, I’ll use the big whiteboard, you use your little whiteboards,

Multiplication can be shown as repeated addition _ x _ = __ iceblocks _ + _ = __ iceblocks Multiplication can be shown as repeated addition Lets do some of these, I’ll use the big whiteboard, you use your little whiteboards, _ rows of _ iceblocks

Multiplication can be shown as repeated addition 2 x 3 = __ penguins Multiplication can be shown as repeated addition Lets do some of these, I’ll use the big whiteboard, you use your little whiteboards,

Multiplication as repeated addition 2 x 6 = + = 6 x 2 = + + + + + = Multiplication can be shown as repeated addition Say it with me Multiplication can be shown as repeated addition Tell me what is repeated addition? Multiplication!!! Hooray!!! Lets do some of these, I’ll use the big whiteboard, you use your little whiteboards,

Multiplication as repeated addition 2 x 4 = + = 4 x 2 = + + + = Multiplication can be shown as repeated addition Say it with me Multiplication can be shown as repeated addition Tell me what is repeated addition? Multiplication!!! Hooray!!! Lets do some of these, I’ll use the big whiteboard, you use your little whiteboards,