Grade 3 program - Home - Back-to-Front Maths



Grade 3 programContents TOC \o "1-3" \h \z \u Assessment strategy: PAGEREF _Toc306719370 \h 2Regular consolidation and practice activities: PAGEREF _Toc306719371 \h 2Term 1: PAGEREF _Toc306719372 \h 4Term 2: PAGEREF _Toc306719375 \h 10Term 3: PAGEREF _Toc306719378 \h 14Term 4: PAGEREF _Toc306719382 \h 19Grade 3 programThis program has been created for use by a single teacher with students working from grade 3 in a single class. It is designed to maximise the effectiveness of teaching and make use of the connections between related concepts. Only three direct teaching activities have been planned for each group for each week. This leaves two lessons free for direct teaching, revision and regular weekly routines (see below).Instructions for Back-to-Front Maths Activities:JP means journal problem. Blast activities have a letter and then a number. E.g. JP.5 means Journal Problem number 5, but activity A3 means blast activity A3.Investigations are optional, but provide a valuable learning experience to use in rotational group time and help tie the different activities together. Most should take around 1 lesson to get started and then can be used at other times as well, such as during follow up and practice activities.Regular weekly routines:Play number sense games, match representations, make and partition numbers, create arrays and fill in blank number charts. Also organise shapes into groups, play shops and look regularly at times on the clock, the class timetable and calendar, and talk about directions to known locations. Make halves and quarters of various 2D shapes, 3D objects, lengths and groups and play chance and data sorting games. Use non-standard measurements and order lengths, volumes, masses and areas and talk about “how big” attributes are.Assessment strategy:Throughout the year you should assess on numerous occasions. Please find below a suggested schedule for your assessment tasks from Back-to-Front Maths. Remember that you will need to include your own assessment for Fluency, and also for mental mathematics. A content test would be an appropriate assessment for these.Semester 1:Early in semester 1 complete the first moderation task. This will give you baseline measurements for students’ proficiencies in problem-solving, reasoning and understanding. It will also help explain the standards to you in a more meaningful manner. This should be formative only, not summative.During semester 1 try to examine 3-5 students per lesson during Journal problems in order to gauge their improvements. These should be formative only.Towards the end of semester 1, mark the last 3-4 Journal problems for each student using the tick-and-flick box. Use these marks in combination with the Blasts book to mark the criteria sheet in this document. In your content test you will also need to include some application questions for students who are in the C/D/E category, which may be selected from those suggested in the lesson plans.Towards the end of semester 1 complete the second moderation task. Final grade for reporting: Compare the results from your criteria sheet and the second moderation tasks to check that they align. If there is a discrepancy, then you will need to use your judgement to grade the student appropriately. Be aware that the moderation tasks only exist to help illustrate the criteria. You may find that you have been marking too easily or too hard, so adjust your marking accordingly.Semester 2:Consider using an investigation throughout the semester and using this as an additional assessment piece. If using these, never use the first investigation as a summative piece as both students and teachers need time to get used to the requirements.Continue marking 5 students per lesson on Journal problems as formative tasks.Towards the end of semester 1, mark the last 3-4 Journal problems for each student using the tick-and-flick box. Use these marks in combination with the Blasts book to mark the criteria sheet. You will also need to include some application questions for students who are in the C/D/E category, which may be selected from those suggested in the lesson plans.Towards the end of semester 2 complete the third moderation task. Final grade for reporting: Compare the results from your investigations, criteria sheets and the third moderation tasks to check that they align. If there is a discrepancy, then you will need to use your judgement to grade the student appropriately. Term 1: Focus concepts: Number names and concepts, counting, decimal numbers, negative numbers, ordering, addition and subtraction including partitioning, joining and separating, 2D and 3D shapesCurriculum Statements covered this term:Term 1: Australian Curriculum statements to achieve by the end of the year. In this term we will be looking at numbers to 1000 rather than to 10 000.Grade 3:ACMNA052 - Recognise, model, represent and order numbers to at least 10000 ACMNA053 - Apply place value to partition, rearrange and regroup numbers to at least 10000 to assist calculations and solve problems ACMNA054 - Recognise and explain the connection between addition and subtraction ACMNA055 - Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation ACMMG063 - Make models of three-dimensional objects and describe key features ACMMG064 - Identify angles as measures of turn and compare angle sizes in everyday situations This is what your term focus looks like:Week 1:Diagnostic testingWeek 2-3: Place value with whole numbers: build numbers with three digits (if appropriate – if not, follow the years 1 or 2 plans as appropriate). Note – we will be making larger numbers later in the year.Week 4:Number lines and ordering: ordering numbers to 100 and then to 1000 with relative sizeWeek 5:Count in 2s, 3s, 5s and 10sWeeks 6 – 9:Addition and Subtraction Weeks 10:2D and 3D shapes - classificationTeaching Sequence:Week 1: Diagnostic testing Choose from these tasks to see what your kids really understand and help you to identify what to do from here on inNumber conservation, simple Partitioning then Relative sizeAsk the students to make 23 using MAB. Move the blocks around and see if they need to count them again or if they know that there is still 23. Ask them to make 23 in multiple different ways (e.g.23 ones, 1 ten and 13 ones). Move all of these around. Ask the students which is the biggest. Hopefully they will say that they are all the same, but watch for students who need to check.Try pretending to make 23, but change the ones for tens and tens for ones (actually making 32 not 23). Count out loud as you pick up 2 x ones blocks, “ten, twenty” then pick up 3 x tens blocks and count “twenty-one, twenty-two, twenty-three”. Watch for students who don’t have any problems with this.Give students a three digit number (e.g. 325) and write it on a HTO chart. Ask students to make it in as many different ways that they can using hundreds, tens and ones (e.g. 2 H, 12 T and 5 Ones). Watch for students who just move the digits to different positions (e.g. 235 = 325)Tape one straight line of masking tape most of the way across your classroom. Place 1 MAB cube at one end, and 1000 MAB cube at the other end.? Ask each child to draw the number line on their A3 piece of paper with the 1 and one end and the 1000 at the other. Tell them to write where 10 and 100 should go. Get them to write their names on the paper.Repeat the above, but with 200 at one end and 1300 at the other end. Ask them to work out the midway point.Weeks 2 and 3: Place value with whole numbers, Targeted teaching:Build numbers past 100 (if appropriate – if not, follow the years 1 or 2 plans as appropriate)Make sure that kids understand:There are 100 ones in a hundreds block and 10 ones in a tens block (Yep this is serious! Hold up a ten block and ask the kids if we chopped it up into the ones how many there would be)If you make 23 using 2 tens blocks and 3 ones blocks and then switch the position so that the ones are on the right it is not now 32. Moving the blocks doesn’t change the size. Same with 3 digit numbers.Resources:Back to Front Maths:JP.1 Numbers bigger than 100 JP.2 Number Names to 999Blast A3: More than 100Blast A4: Multiple hundredsOther:Regular tasks or indirect learning:K1 or K2: Shape families (this can be done as part of rotation group activities)Look regularly at the clock and work out how long until something happens.Homework suggestions:List 2-3 examples from home of:SquaresTrianglesRectanglesCircles or ovalsWeek 4: Number lines and orderingDiagnostic task for 2 digit place value:Make a number of squares joined together into rows and columns, all blank. Then write a number into one square and have the students fill in all the rest as if the squares were part of a hundreds chart (like for the jigsaw, but with blank squares). Corner squares are great for extending higher 2s and 3s before doing relative size with number lines. See below:394335723905740405334016163937008834101289685876301112520101178Targeted teaching:Ordering numbers to 100 and then to 1000 with relative sizeMake sure that kids understand:For the hundreds chart: watch for students who count in ones regardless of where the squares are in relation to each other (or tens). Watch for students who cannot do two-step questions (corner squares)For the number line to 1000 watch for these misconceptions: equally spacing the 10 and the 100, placing 100 in the middle, placing 100 at about one quarter of the line’s length (closer to the one), and placing the 100 up near the 1000Resources:Back to Front Maths:Blast A1: Order numbers to 99 JP.3 Number lines adjust numbers down to 1-100 if your kids get stuck on 1-1000 Blast A6: Order numbers to 999Other:Regular tasks or indirect learning:K4: Classify 3D shapes into families (can be done in rotation group time or independently) Look regularly at the clock and work out how long until something happens.Homework suggestions:List 2-3 examples from home of:CubesPyramids or conesRectangular prisms (boxes)Spheres (balls)Week 5: Counting and counting patternsTargeted teaching:Count in 2s, 3s, 5s and 10s. Make numbers bigger or smaller by tens and hundreds and see the patterns.Make sure that kids understand:Counting does not always need to start at 1Counting can go forwards or backwardsCounting is about how many objects there are, not about saying numbers in orderWhen we count in tens it is because the number is ten bigger (e.g. If I start at 16 and I end at 26, how much did I put with 16 to turn it into 26?)Resources:Back to Front Maths:JP.12 Counting PatternsBlast A2: Count in 2s, 5s and 10s to 99Blast A5: Make numbers bigger or smaller by ones, tens and hundreds Other:Regular tasks or indirect learning:K7: 2D shapes within 3D shapes (can be done in rotation group time or independently)Look regularly at the clock and work out how long until something happens.Look at the calendar and work out how long until events happen (e.g. how many weeks until the holidays, how many weeks until the season changes, when Easter is…)Homework suggestions:Find and draw different 3D objects with at least one of the following faces. You can have different objects for each dot point or find one object that meets multiple dot pointsSquare or rectangular facesTriangular faces (at least one face)Circular facesWeeks 6-9: Addition and Subtraction to 99 with regroupingTargeted teaching:Addition and Subtraction to 99 with regrouping. We will be building this concept slowly over 4 weeks so that kids really understand the purpose. You also have weeks 5-6 of term 3 to catch up on whatever you don’t get done from this.Make sure that kids understand:Kids need to be able to partition numbers to 20 in lots of different ways before we get them to add two digit numbers (e.g. 12 is 6 and 6 but it’s also 5 and 7 and also 9 and 3)Regrouping across the tens and ones is important to do before adding and taking away that needs this (e.g. make 57 in lots of different ways using tens and ones blocks – 5 tens and 7 ones, 4 tens and 17 ones…)Resources:Back to Front Maths:Regrouping numbers:JP.4 Regrouping numbers to 999 (adjust this to a two-digit numbers first)Addition:D3: Add numbers to 99 with no regroupingD4: Extending strategies to add numbers to 99 with regroupingJP8: Adding with regroupingD5: Add numbers to 99 with regrouping D6: Add numbers to 99 using partitioningSubtraction:D10: Subtract numbers to 99 with no regrouping JP9: Subtracting with regrouping D11. Extending strategies for subtracting to 99 with regroupingD12. Subtract numbers to 99 mentally with aid of MABD13. Subtract numbers to 99 using regroupingPossibly:Use D1-D2 and D8-D9 with kids who have problems adding and subtracting Other:Regular tasks or indirect learning:Make as many different shapes as you can with 4 multilinks cubes and try to draw them.Look regularly at the clock and work out how long until something happens.Look at the calendar and work out how long until events happen (e.g. how many weeks until the holidays, how many weeks until the season changes, when Easter is…)Homework suggestions:Practice adding and subtracting small numbers (e.g. D1 and D2 from the Blast books)There is an addition grid in section D of the Teaching Resource Book for regular addition and subtraction practice that would be good here.Week 10: 2D and 3D shapes - classificationTargeted teaching:Classifying 2D and 3D shapesMake sure that kids understand:Triangles do not have to have the point facing up. Squares can still be squares when they are on funny angles.Triangles, hexagons, etc do not have to be regular – they can have different length sides and still be trianglesResources:Back to Front Maths:2D shapes:JP31: 2D shapesK5: Construct 2D shapesJP32: 3D shapes and K6: Construct 3D shapes Other:Regular tasks or indirect learning:Homework suggestions:Term 2: Focus concepts: Counting patterns, Money, Fractions, Multiplication and Division including arrays and sharing, Time, Length and VolumeCurriculum Statements covered this term:Term 2: Australian Curriculum statements to achieve by the end of the yearGrade 3:ACMNA059 Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents ACMNA058 Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole ACMNA056 Recall multiplication facts of two, three, five and ten and related division facts ACMNA057 Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies ACMMG061 Measure, order and compare objects using familiar metric units of length, mass and capacity ACMMG062 Tell time to the minute and investigate the relationship between units of time This is what your term focus looks like:Week 1-2 – FractionsWeek 3 - MoneyWeek 4 - 5 - NAPLANWeek 6 - Time Week 7 - 8 - Measurement – Length and VolumeWeeks 9 - 10 – MultiplicationTeaching Sequence:Weeks 1-2: FractionsInvestigation ideas:Take an A4 piece of paper and ask students to fold a half. Discuss how they know it is a half (have to be the same). Cut down the fold so that you have two halves. Stick one on the board. Repeat this process making as many differently shaped halves as possible, always testing that each really is one half by placing the halves on top of each other. Once you have at least 4 differently shaped halves ask students which half they think is the biggest. Spend the rest of the session overlaying, cutting and reorganising the pieces to show that all of the halves are actually the same.Targeted teaching:Common Fractions, Ordering fractionsMore than one (focus on unit fractions, but in weird looking ways)Make sure that kids understand:You can’t have a big half and a small half, and likewise you can’t have a big quarter and a small quarterFraction names refer to the size of the portion rather than what it looks like. The two halves may look different even though they are equal in size.Halves and quarters do not need to be symmetricalWatch for students who think that cutting paper makes more paper (not just more pieces – the two pieces of paper stuck back together would be bigger than the original)Watch out for kids who think that a vertical orientation is bigger than a horizontal orientation for an identical rectangle (rotating a shape makes it bigger or smaller apparently!)Resources:Back to Front Maths:JP8: One half is always one halfC2: Fractions are equal parts of a groupC3: Fractions can be written in symbols JP5: Ordering fractions C8: Identify equivalent fractions C11: Represent whole numbers and fractionsFor kids who are stuck:C1: Fractions are equal parts of a whole Regular tasks or indirect learning:Make lots of arrays from counters and draw them on grid paper. Give kids 24 counters. Show them one array (e.g. 4x6) and something that isn’t an array (e.g. try arranging 24 into rows of 5 and they won’t work). Challenge the kids to find as many arrays as possible with their counters. Repeat with different numbers, including odd numbers that are composite (e.g. 15) and also prime numbers that won’t work to make multiple arrays (e.g. 11).Homework suggestions:Give kids afternoon tea to share out between multiple people, but don’t give them an amount that can be shared without cutting things up (e.g. give 13 biscuits to share between 3 people so that there will be left overs).When giving kids toast or fruit, cut the pieces up into halves or quarters and put them all on the same plate. Ask kids how many pieces of bread or fruit you started with before cutting them up.Week 3: MoneyTargeted teaching:Notes and coins can be put together in different ways to make the same amounts of money.Make sure that kids understand:An amount of money can be made in different ways using collections of coins. One coin can be used to be the same amount as several other coins (e.g. 10 lots of 10c coins is the same amount as $1, not more)Having lots of coins doesn’t mean that there is lots of money – it depends on the value of the coinJust because a question says “more”, “and” or “total” doesn’t mean you have to add. Use a part-part-whole model to figure out what the question is asking first.Resources:Back to Front Maths:JP.6: Multistep with moneyBlast B1: Interpret and use moneyBlast B2: Calculate costOther:Regular tasks or indirect learning:Use rulers to measure things in your classroom (e.g. your desk, your pencil, the length of the board, the width of the doorway, the length of the room)Homework suggestions:Find objects at home that have particular lengths. E.g. Find 3 things that are about 30cm long. Find 3 things that are about 1m long. How high is the door to your bedroom? How high is your table?Weeks 4-5 NAPLANDo whatever you want during this timeWeek 6: TimeTargeted teaching:Elapsed Time, half hours and quarter hours and 5 minute intervals.Make sure that kids understand:One minute is always exactly the same lengthYou can tell the time just using the hour hand (see the link in the resources column)An hour has 60 minutes. Half an hour has 30 minutes. Quarter of an hour has 15 minutes.The time of the day is not dependent on what you are doing – just because you have a sleep during the day doesn’t mean that it is morning when you wake upResources:Back to Front Maths:JP.25: Elapsed timeBlast F1: Read and record 12 hour time Blast F2: Half hours and quarter hours Blast F3: Record sequences of time Blast F4: CalendarsOther:Regular tasks or indirect learning:Homework suggestions:Weeks 7-8: Measurement: length and volume Targeted teaching:Whole class investigations on length and volume using standard unitsMake sure that kids understand:Use the same unit of measurement when comparing objects (e.g. the same sized block)You have to fit in as many units as possible when measuring, ensuring that there are no gaps or overlaps.Parts of units are used where a whole unit cannot fit. We use fractional language to describe these parts.A fat container will hold heaps more than a skinny container. The closer you get to a sphere, the more volume it holds.Resources:Back to Front Maths:Blast E5: Measure and estimate length in centimetres JP.20: LengthJP.22: Volume Blast E7: Measure and estimate volumesOther:Regular tasks or indirect learning:Homework suggestions:Weeks 9-10: Multiplication, arrays and sharingTargeted teaching:Multiplication, arrays and sharingMake sure that kids understand:Multiplying means “lots of”, “groups of”, “rows of” or “columns of”Division means “how many” (groups, lots, rows or columns)Kids really, really need to get the concept of arrays (e.g. 3 x 5 = three rows of five OR five rows of three)If you turn an array around by 90o then you can show why multiplication works both ways (why 3x5=5x3)Resources:Back to Front Maths:JP10: Multiplication and arraysBlast D16: Arrays and skip countingBlast D17: Symbol for multiplicationBlast D18: Multiplying and addingBlast D19: TurnaroundsJP11: Division and sharingOther:Regular tasks or indirect learning:Homework suggestions:Term 3: Focus concepts: Larger numbers, regrouping, formal operations, fractions, chance and data, position and directionAustralian Curriculum statements to achieve by the end of the yearACMNA052 Recognise, model, represent and order numbers to at least 10000 ACMNA053 Apply place value to partition, rearrange and regroup numbers to at least 10000 to assist calculations and solve problems ACMNA058 Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole ACMNA054 Recognise and explain the connection between addition and subtraction ACMNA055 Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation ACMNA056 Recall multiplication facts of two, three, five and ten and related division facts ACMNA057 Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies ACMSP067 Conduct chance experiments, identify and describe possible outcomes and recognise variation in results ACMSP068 Identify questions or issues for categorical variables. Identify data sources and plan methods of data collection and recording ACMSP069 Collect data, organise into categories and create displays using lists, tables, picture graphs and simple column graphs, with and without the use of digital technologies ACMSP070 Interpret and compare data displays ACMMG065 Create and interpret simple grid maps to show position and pathways This is what your term focus looks like:Week 1-2 – Large numbers and regrouping to 10 000Week 3-4 - extending and connecting fractions – halves and quartersWeek 5 - NAPLANWeek 6 - Time Week 7 - 8 - Measurement – Length and areaWeeks 9 - 10 – MultiplicationTeaching Sequence: Weeks 1-2: Larger numbers and regroupingInvestigation ideas:Create number expanders up to thousands Create posters with images of large numbersUse the place value charts from the year 3 Journal and Blast book to create visual representations of various large numbers – these have pictures of MAB for numbers up to 10 thousandsOrdinal numbers: Set up a race between students where they have to come in a particular position (e.g. give the fastest person 4th). The winners are the students who come in the correct position, not the person who is the fastest.Targeted teaching:Large numbers and regrouping to 10 000Make sure that kids understand:There are 100 ones in a hundreds block and 10 ones in a tens block (Hold up a ten block and ask the kids if we chopped it up into the ones how many there would be)If you make 23 using 2 tens blocks and 3 ones blocks and then switch the position so that the ones are on the right it is not now 32. Moving the blocks doesn’t change the size. Same with 3 digit numbers.Resources:Back to Front Maths:Blast A6: Order numbers to 999Blast A7: Regrouping Blast A8: Introducing the thousands placeBlast A9: Order numbers to 9 999Other:Regular tasks or indirect learning:Homework suggestions:Weeks 3-4: Extending and connecting fractionsInvestigation ideas:Use 3 JP.5 as a whole class to create representations for various fractions and place them on a number line. Each of the fractions should be accompanied by a visual representation, the written fraction, a decimal representation, and a percentage (if possible depending on the students).Targeted teaching:Fractions: half and quarter of a whole, writing fractions with symbols. Go into other unit fractions if you can, but make sure that halves and quarters are really solid before you try. If you don’t get to things other than halves and quarters that’s ok as we can do it in grade 4.Make sure that kids understand:You can’t have a big half and a small half, and likewise you can’t have a big quarter and a small quarterFraction names refer to the size of the portion rather than what it looks like. The two halves may look different even though they are equal in size.Halves and quarters do not need to be symmetricalWatch for students who think that cutting paper makes more paper (not just more pieces – the two pieces of paper stuck back together would be bigger than the original)Watch out for kids who think that a vertical orientation is bigger than a horizontal orientation for an identical rectangle (rotating a shape makes it bigger or smaller apparently!)Resources:Back to Front Maths:Blast C5: A quarterBlast C6: One quarter of a groupBlast C7: Symbol for a quarterBlast C8: Fraction namesOther: Lots of practice at making halves, quarters (and eighths) of 3D objects, 2D shapes, groups and lines.Regular tasks or indirect learning:Homework suggestions:Weeks 5-6: Formal operations and inverse operations Targeted teaching:Inverse operations. Use the rest of this time to catch up on the addition and subtraction stuff that you didn’t get done from term 1. If you have spare time, start the chance and data content that is next in the program early as it is a bit tricky to fit everything in.Resources:Back to Front Maths:JP14: Inverse operationsBlast D15: Relationship between adding and subtractingOther:Regular tasks or indirect learning:Homework suggestions:Weeks 7-8: Chance and Data Investigation ideas:3 JP.27 Collecting Data investigation Targeted teaching:Chance and Data: Graphing – grouping, using data, displaying data and simple chance experiments. All of the activities in the data section here are based on doing an investigation on collecting data.Make sure that kids understand:All events have some kind of likelihood but very few things are absolutely certain.Some things are more likely than others. Having two options doesn’t make them both the same (e.g. It could rain or not rain, but that doesn’t make them both 50/50 – the chance of rain depends on the season)Data can be collected or found for the purpose of answering questions Data needs to be classified or organised in a way that best fits the question to be answered. Data can be organised in different ways for different purposes. Resources:Back to Front Maths:DataJP.27 Collecting Data investigationJP29: Graphing data investigationBlast J6: Symbol for multiplicationBlast J8: Making picture graphs with one-to-many correspondenceBlast J10: Making bar graphs with one-to-many correspondence ChanceJP24: (couldn’t find) JP26: Simple chance experimentsOther: For kids who are strugglingBlast J4: Making picture graphs with one-to-one correspondenceRegular tasks or indirect learning:Homework suggestions:Weeks 9-10: Position and Direction Investigation ideas:Create a map of the classroom or part of the school (such as the playground). Use a grid and grid references. Use accurate measurements. Put on a north point or orient the map towards north. Give directions to different locations as a “treasure hunt”. Targeted teaching:Describing and finding locations on a simple map, giving basic directions using a direction (half turn, quarter turn etc.) and distance (how many metres or steps).Make sure that kids understand:Directions are described using position (forwards, backwards, left, right) and distance (how many steps, describing an object in the distance)Resources:Back to Front Maths:JP36: Maps and Directions Blast M1: Locate points of interest on maps Blast M2: Use simple scale to create mapsOther:Regular tasks or indirect learning:Homework suggestions:Term 4: Focus concepts: Number concepts, Transformations, Area, Mass, Patterns and Functions, GeometryCurriculum Statements covered this term:Term 4: Australian Curriculum statements to achieve by the end of the yearGrade 3:ACMNA060 Describe, continue, and create number patterns resulting from performing addition or subtraction ACMMG061 Measure, order and compare objects using familiar metric units of length, mass and capacity ACMMG066 Identify symmetry in the environment ACMMG064 Identify angles as measures of turn and compare angle sizes in everyday situations This is what your term focus looks like:Week 1-3 – Geometry and Angles, Flip, slide and turn,Week 4-5 – Area and massWeek 6-10 – Patterns and function Teaching Sequence: Weeks 1-4: Geometry, Angles and Flip, slide and turnInvestigation ideas:Create mosaics from tiling shapes. Preferably have the students attempt to replicate the shapes for tiling, and talk about flipping, sliding and turning as you complete the task.Targeted teaching:Angles and turns (right angles, straight angles, acute and obtuse)Flip, Slide and Turn to change the shape or make patterns.SymmetryMake sure that kids understand:Angles are an amount of turn. It doesn’t matter what direction they face (e.g. a right angle doesn’t have to be vertical and horizontal – it is the number of degrees that matters not the orientation)Changing one angle in a shape will alter the other angles and possibly change the shape altogether (e.g. if we start with a square but change one angle to be 45o, the other angles will change too and it definitely won’t be a square anymore, but if we change one angle in a triangle it will still be a triangle).2D shapes can be transformed with flips (reflections), slides (translations) and turns (rotations).2D shapes can be symmetrical or not. Symmetry is created by reflections.Resources:Back to Front Maths:JP35: Angles and TurnsBlast K9: Create anglesBlast K10: Angles and turnsJP33: Flip, slide and turn Blast L1: Flips, slides and turnsBlast L2: Patterns JP34: SymmetryBlast L3: Symmetry of 2D shapes K8: 2D shapes within 2D shapesOther:Regular tasks or indirect learning:Homework suggestions:Weeks 5-6: Area and Mass Targeted teaching:Estimating, measuring, comparing and ordering mass and area in standard unitsMake sure that kids understand:Mass is about how heavy something is, not how much space it takes up.Sometimes small objects can be very heavy – it depends on what they are made from.The same amount of mass can be differently shaped and take up significantly different amounts of space (e.g. a kg of metal vs a kg of feathers)Area is a measure of 2D flat space. It needs to have measurements in two dimensions, not just a length.Arrays is basically the same as area (multiplication expressed as rows and columns so that it is arranged into a grid)Resources:Back to Front Maths:Blast E4: Read measuring instruments (do the mass and area bits of this)JP23: MassBlast E6: Measure and estimate mass in grams Blast G1: Ordering objects (do the area and mass bits only)JP19: Identifies and distinguishes attributesBlast E9: Compare and order lengths, masses, volumes (do the mass and area bits)Other:Regular tasks or indirect learning:Homework suggestions:Weeks 7-10: Patterns and functionsInvestigation ideas:Create dance steps using repeating patterns and sequences. These can also include games where one action provokes a repetition (e.g. when the leader claps two times all the followers clap two times) or provokes a different action (e.g. 2 claps means the followers spin around).Create beading patterns using different shapes and patterns of beads.Play “what is missing”: The teacher creates a repeating or growing pattern using coloured counters. The students cover their eyes and the teacher removes part of the pattern (can be a whole repeating segment, or the end of one and start of another for added complexity). The students have to make what is missing.Targeted teaching:Patterns are about finding what stays the same each time and what is changing. When we find that bit we can describe it as a rule. Also, please help kids to understand that the “equals” sign doesn’t mean that the answer is coming next. It means “is the same as”. Make sure that you write some number sentences in the wrong order (e.g. 15 = 3x5) and also when there is no “answer” at all (e.g. 3 x 4 = 2 x 6)Make sure that kids understand:Patterns can be comprised of colour, shape, size, actions and numbers. How the pattern begins and how to get from one position in the pattern to the next (identify the pattern – whether it repeats or grows, and what is similar each time) is really important.Differences between items within a pattern and between patterns are also important.We can make generalisations about the rule that is used to make the pattern. In order to be a rule, it should be true for every step in the pattern. We can test a rule against subsequent steps in the pattern to check if it is right.Resources:Back to Front Maths:Blast H1: Growing and repeating patterns with matchsticks JP12: Counting patterns JP18: Growing and repeating patterns Blast H2: Growing patterns with numbers and skip-counting G5: Reversing a change G3: Making equivalent amounts JP15: Balance and equivalence Blast G4: Balancing equations JP16: Plant growthJP17: Sequence steps Possibly JP16: Plant growthJP17: Sequence steps Other:Regular tasks or indirect learning:Homework suggestions: ................
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