Grade 4 program - Back-to-Front Maths



Grade 4 programContents TOC \o "1-3" \h \z \u Grade 4 program PAGEREF _Toc403641249 \h 2Regular weekly routines: PAGEREF _Toc403641250 \h 2Assessment strategy: PAGEREF _Toc403641251 \h 2Term 1: PAGEREF _Toc403641252 \h 4Term 2: PAGEREF _Toc403641254 \h 8Term 3: PAGEREF _Toc403641256 \h 14Term 4: PAGEREF _Toc403641258 \h 18Grade 4 programThis program has been created for use by a single teacher with students working from grade 4 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:Complete mental maths calculation (including asking non-standard questions such as “I start at 8 and end at 56, what happened?” and multi-step questions such as “I ended up with 7, but I had divided by 2 and done something else to get there from my starting number 20 - what could I have done?”) Practice procedures such as: regular operations, writing numbers in words, digits and expanded notation, ordering numbers and finding factors or multiples of starting numbers Discuss unit fractions, including finding unit fractions of numbers, areas, lines, 3D objects and groups (e.g. half of 14, one third of the distance between here and the oval)Read and interpret time, itineraries and calendars as used in classDiscuss geometric properties of lines, angles, shapes and objects using correct terminologyCompare relative size using various attributes (length, area, mass, volume)Discuss relative likelihood using language of chance for current events, and giving the chance a numerical value where appropriate and considering the reliability of the data (e.g. the weather bureau has predicted an 80% chance of rain today – what does that mean?)Examine the use of data and statistics in popular media and discuss whether the data is biased, how reliable it is and whether it has been accurately portrayedLook for patterns in: numbers, geometric repetitions, dances or songs, games, prices (e.g. 2 for the price of 1) and measurement formulaeAssessment 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: Australian Curriculum statements to achieve by the end of the yearACMNA072 - Recognise, represent and order numbers to at least tens of thousands ACMNA073 - Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems ACMNA079 - Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation ACMNA074 - Investigate number sequences involving multiples of 3, 4, 6, 7, 8, and 9 ACMMG088 - Compare and describe two dimensional shapes that result from combining and splitting common shapes, with and without the use of digital technologies ACMMG089 - Compare angles and classify them as equal to, greater than or less than a right angleThis is what your term focus looks like:Week 1 – Diagnostic testingWeeks 2-3 – Place value with whole numbersWeek 4 – Number lines and orderingWeeks 5 – Addition and subtraction of large numbersWeek 6 - 8 - Decimal numbersWeek 9 – Adding and subtracting of decimal numbersWeek 10 – classification of 2D and 3D shapesTeaching 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 numbersTargeted teaching:Regrouping large numbers. Consider adjusting this to do 3 digit numbers first and then working with larger numbers in term 2.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.A thousands block has 10 hundreds not 6.Base ten pattern continues for numbers of any size.Resources:Back to Front Maths:To introduce: use Blast A1 and A2 to revise 3 digit numbers. JP.1: Regrouping in large numbersBlast A6: Number names for ten thousandsBlast A8: Multiple hundredsBlast A9: More than 99 999Blast A10: Visualise numbers to 100 000Other:Regular tasks or indirect learning:Homework suggestions:Week 4: Number lines and orderingTargeted teaching:Relative size of numbers past 1000 (if appropriate – if not, follow the years 2-3 plans as appropriate)Make sure that kids understand:Relative size of numbers to 1000 first (grade 3 JP 3)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 1000Relative size is very different to absolute size. We need to look at “about” how big one number is compared to another rather than always using 1cm to represent one.There are hundreds between each thousand, not just at the start.Resources:Back to Front Maths:JP.3: Ordering large numbers (adjust this to 1-1000 if needed)Blast A5: Order numbers to 10 000Blast A11: Order numbers to 100 000Other:Regular tasks or indirect learning:Homework suggestions:Week 5-6: Addition and Subtraction of large numbersTargeted teaching:Adding and Subtracting numbers with regrouping. Check out the grade 3 program for these same weeks for kids who are stuck.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…)We can make numbers using different combinations of hundreds, tens and ones and it can still be the same number (e.g. 324 can be 3 hundreds + 2 tens + 4 ones, but it can also be 2 hundreds + 12 tens + 4 ones)Resources:Back to Front Maths:Blast D1: Add numbers to 99 using regrouping Blast D2: Add numbers to 9 999Blast D3: Subtract numbers to 99 using partitioning or trading Blast D4: Subtract numbers to 9 999Other:Consider using D5 and D6 if you get timeRegular tasks or indirect learning:Homework suggestions:Weeks 7-9: Decimal NumbersTargeted teaching:Investigating tenths, Identifying and describing tenths, Regrouping tenths, Comparing and ordering decimal numbersMake sure that kids understand:Tenths (like all fractions) have to be the same size as each other. The shape doesn’t matter but the size really does.Decimal numbers follow the same base-ten system as we use for whole numbers. Decimal numbers, fractions and division are really the same thing – they are just different ways of representing the same amount.The denominator in fractions does not relate to decimal numbers. 1 seventh is not the same as 0.7.Resources:Back to Front Maths:Year 5 JP.4 Visualising tenths (find online). Use this before you begin to introduce tenths as it is a great diagnostic task and gets kids thinking.C5: How many tenths make up one whole? C6: What different ways can I write tenths?A17: Identify and describe decimal fractionsA18: Regrouping tenthsA19: Compare and order decimal numbersC7: More than 10 tenths Other:Regular tasks or indirect learning:Homework suggestions:Week 10: 2D and 3D shapes - classificationTargeted teaching:Classifying shapes, building and analysing 3D objects and nets.Make 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:Blast K4: Classify shapes into familiesBlast K5: Properties of 3D shapesK8: Construct and experiment with shapes K9: 2D shapes within 3D shapes Other: if timeBlast K6: Classify 3D shapes into familiesRegular tasks or indirect learning:Homework suggestions:JP29: Four blocks challenge Term 2: Focus concepts: Counting patterns, Money, Fractions, Multiplication and Division including arrays and sharing, Time, Length and VolumeTerm 2: Australian Curriculum statements to achieve by the end of the yearGrade 4:ACMNA080 Solve problems involving purchases and the calculation of change to the nearest five cents with and without digital technologies ACMNA077 Investigate equivalent fractions used in contexts ACMNA078 Count by quarters halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line ACMNA075 Recall multiplication facts up to 10 × 10 and related division facts ACMNA076 Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder ACMNA074 Investigate number sequences involving multiples of 3, 4, 6, 7, 8, and 9 ACMMG084 Use scaled instruments to measure and compare lengths, masses, capacities and temperatures ACMMG290 Compare objects using familiar metric units of area and volumeACMMG087 Compare the areas of regular and irregular shapes by informal means ACMMG086 Use am and pm notation and solve simple time problems This is what your term focus looks like:Week 1-2: Fractions Weeks 3: MoneyWeek 4 -5: Adding and subtracting of decimal numbers (year 3/5 doing NAPLAN we missed this in term 1 so added in here- goes with money and fractions {I thought})Weeks 6: TimeWeek 7 – 8: Measurement – Length and AreaWeeks 9-10: Multiplication Teaching 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, equivalence, more than one Make sure that kids understand:Watch for kids who think that the shape of a half will change how big it is (triangular halves are much bigger than rectangular halves)Watch for kids who think that the orientation of a fraction changes its size (e.g. if you take a rectangle and turn it sideways it gets bigger or smaller).Watch 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 for students who think that halves must be symmetrical rather than the same size Watch for students who think that all fractions that are not halves are called quarters (they will call thirds “three quarters”, then “six quarters” if you fold it again).Watch for students who think that the name of a fraction relates solely to the number of pieces rather than the size of the pieces. Watch for students who think that even numbers also relate to evenly sized fraction bits – i.e. you can’t make even thirds because three is not an even number (therefore any three pieces are called thirds), so while halves and quarters have to be even it apparently doesn’t matter for the rest of them.Watch for students who think that all fractions start from a half, and therefore cannot fold fractions other than halves, quarters and eighths.Watch for students who think that the denominator is the same as a fraction – e.g. to make 0.7 you would cut a whole into seven pieces.Resources:Back to Front Maths:Check that kids really understand these:C1: Fractions are equal parts of a whole JP4: Equivalent fractions and making one halfC2: Fractions are equal parts of a groupC3: Fractions can be written in symbols Do:4 JP.8 Making halvesJP5: Ordering fractions C4: Compare and order common fractions C8: Identify equivalent fractions C11: Represent whole numbers and fractionsOther: Regular tasks or indirect learning:Homework suggestions:Weeks 3: MoneyTargeted teaching:Revision of money – total cost, money amounts and changeMultistep problems with moneyMake 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:JP6: Multistep with money Blast B5: Working with dollars and cents Other: think about which of these you need to useBlast B1: Interpret and use moneyBlast B2: Calculate total costBlast B3: Tender amounts of money to cover costs Blast B4: Estimate and calculate change Regular tasks or indirect learning:Homework suggestions:Weeks 4 - 5: Adding and Subtracting FractionsTargeted teaching:Adding and subtracting fractions with the same and related denominators by drawing pictures and visualising what is happeningMake sure that kids understand:See weeks 1-2Resources:Back to Front Maths:Blast C8: Identify equivalent fractions (this has been done previously, so just revise it)Blast C9: Counting common fractions Blast C10: Adding and subtracting fractionsOther: Regular tasks or indirect learning:Homework suggestions:Week 6: TimeSpend one day with all students on the following investigation: Grade 3 Blast F1 as inspiration (Available online)Targeted teaching:12 hour time, fractions of hours, elapsed time, using calendars Make sure that kids understand:You 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.There are seven days in every week and these are in the same order every weekKnow the number of days in each month and that February is the only one that changes.Know that months don’t always start on Sundays and neither do years because the number of days in a month is not a multiple of 7.Resources:Back to Front Maths:You should be able to cut this down if you are regularly looking at clocks and calendarsBlast F1: Read and record 12 hour time and Blast F2: Fractions of hours JP23: Elapsed time Blast F3: Record sequences of time Blast F4: Calendars Blast F5: Locating days and dates on a calendar Other: Regular tasks or indirect learning:Homework suggestions:Weeks 7-8: Measurement: length and area Targeted teaching:Length and Area using standard units. Make sure that kids understand: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.Length is measured in a single dimensionArrays is basically the same as area (multiplication expressed as rows and columns so that it is arranged into a grid)Area is a measure of 2D flat space. It needs to have measurements in two dimensions, not just a length.The same area can have different shapes (e.g. 24cm2 can be a rectangle of 4x6 or 3x8 or 2x12 or a triangle with a base of 6 and a height of 8 and that is all the exact same area)Resources:Back to Front Maths:LengthBlast E2: (page 1 only) Estimating length, mass, area, volumeBlast E4: Measure and estimate length in m and cm - both during the one lessonArea – think about moving this to week 10 after you have done the multiplication stuff that comes nextRevise arrays before starting area. Make a lot of different arrays from the same number of squares so that kids understand that the same area can be made as different shapes.JP.21: Tiling a replica houseBlast E7: Measure area in square m and square cmOther: Regular tasks or indirect learning:Homework suggestions:Weeks 9-10: Multiplication Investigation ideas:Give each student 24 counters to arrange into as many different arrays as possible. Draw the arrays.Targeted teaching:Extending basic facts, developing and using mental strategies.Multiplying two digit by one digit and representing this as an array with two parts: the tens by the ones bit and the ones by the ones bit (e.g. see below the picture of 26 x 4 – you can see the 20x4 part and the 6x4 part)273650412573034798012573000Make 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:Blasts D7: Extend basic facts using x 10 and also Blast D8: Extend basic facts using mental strategies in the same lessonJP.9 (Multiplication with 2 digits), Blast D9: Multiply two digits by one digitOther: if timeRegular tasks or indirect learning:Homework suggestions:Term 3: Focus concepts: Larger numbers, regrouping, formal operations, fractions, chance and data, position and directionTerm 3: Australian Curriculum statements to achieve by the end of the yearGrade 4:ACMNA073 Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problemsACMNA079 Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation ACMNA077 Investigate equivalent fractions used in contexts ACMNA075 Recall multiplication facts up to 10 × 10 and related division facts ACMNA076 Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder ACMSP092 Describe possible everyday events and order their chances of occurring ACMSP095 Select and trial methods for data collection, including survey questions and recording sheets ACMSP096 Construct suitable data displays, with and without the use of digital technologies, from given or collected data. Include tables, column graphs and picture graphs where one picture can represent many data valuesACMMG090 Use simple scales, legends and directions to interpret information contained in basic maps This is what your term focus looks like:Week 1-2: Division, order or operations, distributive propertiesWeeks 3-4: Extending and connecting fractions, operations with fractions Week 5-8: Chance and DataWeeks 9-10: Position and Direction Teaching Sequence: Weeks 1-2: Division, multiples and factorsTargeted teaching:Division with larger numbers, remainders, associative and distributive properties of multiplication and divisionMake sure that kids understand:Division is the same thing as arraysDivision is the same thing as fractionsMultiples are just arrays made with a particular number as the row or columnFactors are the numbers that multiply together to give a totalResources:Back to Front Maths:JP10: Division with 2 digitsD11: Division with regrouping D12: Written methods for dividing D13: Dividing larger numbers D17: Subsets: multiples and factorsOther: Regular tasks or indirect learning:Homework suggestions:Weeks 3-4: Extending and connecting fractions, operations with fractionsTargeted teaching:Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete wholeMake sure that kids understand:See previous term’s work on fractionsResources:Back to Front Maths:This is deliberately a light fortnight to allow you time to make lots of different fractions and help kids to understand their sizeBlast C8: Fraction namesJP.5 Ordering fractions. 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).Blast C10: Adding and Subtracting FractionsOther: Regular tasks or indirect learning:Homework suggestions:Weeks 5-8: Chance and Data Investigation ideas:Data investigation: takes 2-3 weeks including completing Blast and Journal problemsUse Journal problem 27 as inspiration to design a survey, collect, group, classify, display and analyse data. Use blast activities as needed to help collect, group, display and analyse the results (J1-J8)Targeted teaching:Introduce data investigation with everyone. This will take 2 weeks. Learn about how useful data is for classification and discuss and decide whether more collection is needed. Discuss targeted samples, question formation and categories for answers.Graphing and interpreting 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)Chance is expressed as fractionsData 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 purposesData displays help us to see the patterns in large amounts of informationResources:Back to Front Maths:ChanceJP.24: Rolling a dieBlast I1: Language of chanceBlast I2: Difference between likely and certain Blast I3: Difference between unlikely and impossibleDataTwo-week data investigation explained above, which includes some of Blasts J1-J8.Blast J.10: Making bar graphs with one-to-many correspondenceBlast J.11: Making statements about dataJP30: Interpreting dataRegular tasks or indirect learning:Homework suggestions:Weeks 9-10: Position and Direction Investigation ideas:Create a map of the school 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”. (As per blast M2)Targeted teaching:Create and interpret simple grid maps to show position and pathwaysMake sure that kids understand:Directions are described using position (forwards, backwards, left, right) and distance (how many steps, describing an object in the distance)We give directions and distance in standard ways so that other people know automatically what we are talking about (N, S, E, W and distance in standard units of length)We create maps and plans using standard formats (e.g. North point, scale, grid refs, key)Resources:Back to Front Maths:Blasts M1: Locate points of interest on maps JP36: Maps and DirectionsBlast M2: Use simple scale to create mapsOther: if timeBlast M3: Giving directions gameRegular tasks or indirect learning:M1: Locate points of interest on maps M2: Use simple scale to create maps M3: Giving directions game Homework suggestions:Term 4: Focus concepts: Number concepts, Transformations, Area, Mass, Patterns and Functions, GeometryTerm 3: Australian Curriculum statements to achieve by the end of the yearGrade 4:ACMNA083 Use equivalent number sentences involving addition and subtraction to find unknown quantities ACMNA081 Explore and describe number patterns resulting from performing multiplication ACMMG084 Use scaled instruments to measure and compare lengths, masses, capacities and temperatures ACMMG290 Compare objects using familiar metric units of area and volumeACMMG091 Create symmetrical patterns, pictures and shapes with and without digital technologies ACMMG088 Compare and describe two dimensional shapes that result from combining and splitting common shapes, with and without the use of digital technologies ACMMG089 Compare angles and classify them as equal to, greater than or less than a right angleThis is what your term focus looks like:Week 1-4: Geometry, Angles and Flip, slide and turnWeek 5-8: Volume and MassWeeks 9-10: Patterns and functionsTeaching Sequence: Weeks 1-4: Geometry, Angles and Flip, slide and turnTargeted teaching:Nets for 3D shapes and looking at the 2D shapes that make up the faces.Angles and their types: Compare angles and classify them as equal to, greater than or less than a right angle.Transforming shapes by flips, slides and turns.Make 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.3D shapes are the same regardless of orientation (e.g. cylinders lying down rather than standing up)Resources:Back to Front Maths:3D shapes and nets:Blast K15: How many squares?Blast K11: 3D shapes have nets Blast K12: Predicting the shape from the net Blast K13: Identifying cube nets Angles:Blast K2: Create angles Blast K3: Properties of angles in 2D shapes Transformations:L1: Flips, slides and turns JP34: Tessellating trianglesL2: Classify and represent shapes that tessellateL3: Properties of tessellationsL4: Objects with size and orientation changesOther: if timeJP 35: Directions of turnRegular tasks or indirect learning:Homework suggestions:Weeks 5-6: Volume and Mass Targeted teaching:Compare objects using familiar metric units of Mass and VolumeMake 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)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.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:Volume:Blast E6: Measure and estimate volumesMass:JP.22: Postage costsBlast E5: Measure and estimate mass in g and kgOther: if timeRegular tasks or indirect learning:Investigation ideas:2 JP.24 and 2 JP.25 as an investigation for all studentsHomework suggestions:Weeks 7-10: Patterns and functionsTargeted teaching:Identifying and creating number patterns. Trading and equivalence.Introducing equations, inverse operations reverse 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 JP13: Trading counters Blast G1: Trading and equivalence Blast G2: What number am I thinking of?JP15: Ordering and sequencing dance steps Blast G3: Simple equations with double digit numbers Blast G4: Guess and check method JP16: Balance and equivalence Blast G5: All combinations of + and -Blast H2: Identify a rule for number patterns Blast H3: Create a number patterns based on a rule Blast H4: Continue number patterns Other: if timeRegular tasks or indirect learning:Homework suggestions: ................
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