Grade 6 program - Kennedy PressBack-to-Front Maths



Grade 6 programContents TOC \o "1-3" \h \z \u Grade 6 program PAGEREF _Toc410128572 \h 1Grade 6 program PAGEREF _Toc410128573 \h 2Regular weekly routines: PAGEREF _Toc410128574 \h 2Assessment strategy: PAGEREF _Toc410128575 \h 2Term 1: PAGEREF _Toc410128576 \h 4Term 2: PAGEREF _Toc410128577 \h 9Term 3: PAGEREF _Toc410128579 \h 13Term 4: PAGEREF _Toc410128580 \h 17Grade 6 programThis program has been created for use by a single teacher with students working from grade 5 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: Focus concepts: Place value and relative size of whole and decimal numbers, negative numbers, addition and subtraction, 2D and 3D shapesTerm 1: Australian Curriculum Statements to achieve by end of the yearACMNA124 Investigate everyday situations that use integers. Locate and represent these numbers on a number line ACMNA123 Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers ACMNA122 Identify and describe properties of prime, composite, square and triangular numbers ACMNA128 Add and subtract decimals, with and without digital technologies, and use estimation and rounding to check the reasonableness of answers ACMMG140 Construct simple prisms and pyramids Your focus this term is on:Week 1: Diagnostic testingWeeks 2 and 3: Place value and whole numberWeek 4: Relative size, Number Lines and OrderingWeeks 5 - 7: Decimal numbersWeek 8: Addition and subtraction of Decimal Numbers Week 9: Negative Numbers Week 10: 2D & 3D Shapes All material identified by is material subject to copyright under the Copyright Act 1968 (Cth) and is owned by the Australian Curriculum, Assessment and Reporting Authority (2013).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 inRelative size then Proportional Reasoning 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 number line task, with 0 or 1 at one end, and 1 million at the other.Ask the students to make 23.7 using MAB. Watch for students who think that it can be made by using 23 blocks, then leaving a space or putting a dot, and then making another 7. If they do this, push the blocks back together and ask what it is now (they may say 30 once the space or “dot” is no longer showing, but think that the 30 turns into 23.7 as soon as a space is visible). These students may also think that 23.7 becomes 24.6 if one of the “point seven” blocks moves across the point to the other side, or that 23.7 becomes 7.23 if you rotate it.Ask students to make as many different halves as they can using an A4 sheet of paper as the whole. Test each guess to make sure that each really is a half. Label each half with a different letter and stick to the board. Ask students which half they think is the biggest (they are allowed to vote for more than one, but do NOT lead them by saying “or are they all the same” – you are diagnosing if they realise this or if they think that shape changes size and if you say something like this they will all vote for that answer).Fold a piece of paper into thirds (evenly – there are no such things as uneven thirds) and ask the kids what they think you have made. If they say “three quarters”, fold the paper in half so that you make sixths and ask again so that you can double check.Draw a circle on the board. Draw a line to cut the circle into halves. On one half, draw a line to cut that half into two quarters, but leave the other half as it is. Colour one of the quarters. Ask the students what you have made. If they say thirds, cut the other half into two quarters and ask again. If they say “now it’s a quarter”, then continue cutting any of the pieces that are not coloured (leave the one quarter as it is) and ask again. This is a very persistent misconception.Ask students to make the following fractions all using an A4 piece of paper to be the whole: ?, ?, 1/3, 1/5, 1/6, 1/7, 1/8 (repeat with two of everything, three of everything etc. but making sure that the answers are not bigger than one). Then taking your unit fractions, place them on an open number line between 0 and 1. Check that they have an understanding of the relative size of fractions as well as proportion size.Weeks 2 and 3: Place value with whole numberTargeted teaching: Place Value with whole number. Building large numbers and getting used to how big they really are.Resources:Yr 5 JP JP 2: Building large numbers (online) Yr 6 - JP 2: How big is one billionA1. Naming millionsA2. Naming hundred millionsInvestigation idea:Could we make 1 million marks on the basketball courts in 20 minutes? Draw a circle around every 100 to keep track.Regular tasks or indirect learning:Homework suggestions:Week 4: Relative size of whole numbersFocus Number lines and ordering to 100 000, with a focus on the relative size of numbers in the base 10 system. Watch out for kids who do not have a solid understanding of relative size to 1000. Go back and do this during this week instead of large numbers if needed as it is a critically important concept. See grade 3 program of this same week.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.ResourcesYr 5 JP 3 – Ordering numbers in the base 10 system (online) OR Yr 3 JP 3 – Ordering numbers to 1000 as appropriateThe rest of this week is flexible as relative size of Base-ten numbers is a pivotally important concept to understand. Spend as much time as needed to build this concept well rather than moving on too quickly. Use extra weeks if needed.Please also note, week 10 which has 2D shapes is a big one, so consider taking some of those tasks to do now or to build in as homework tasks for the rest of this term.Regular tasks or indirect learning:Homework suggestions:Weeks 5-7: Decimal Numbers Targeted teaching: Revising tenths and hundredths, before introducing thousandthsMake 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.Tenths are smaller than ones (while this seems obvious it often isn’t at all)Hundredths are smaller than tenths. Thousandths are smaller again.Tenths and hundredths are not negative numbers.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:Week 5: Revise tenths and hundredthsGrade 5 journal problem 4 (get this online) to help students visualise tenths to start with. If needed, use the grade 5 blast activities on tenths to follow up. Allow 1.5 hours for this task as you might find a lot of students do not understand that tenths are smaller than ones. The Grade 5 lesson on the DVD shows this lesson in action and is worth watching.A5. Revising decimal fractions: hundredthsWeeks 6-7: Introduce thousandthsA6. Smaller than hundredths in decimal fractionsA7. Naming decimal placesJP.4 Regrouping with decimalsA8. Interpreting representations of numbersA10. Regroupings of the same numberA11. Adjusting decimal numbersRegular tasks or indirect learning:Homework suggestions:Week 8: Addition and Subtraction of decimal numbersTargeted teaching: Revise adding and subtracting whole numbers as appropriate.Adding and subtracting decimal numbers.See above for suggestions to watch out for.Resources:Consider revising addition and subtraction of whole numbers using: D1. Revise adding numbers to 999 999 and D2. Revise subtracting numbers to 999 999.D3. Adding decimal fractionsD4. Common problems with adding decimalsD5. Subtracting decimal numbersRegular tasks or indirect learning:Homework suggestions:Find 5 items in a catalogue that have prices involving dollars and cents, then show your working to add them all. What is the difference in price between the most expensive and least expensive?Week 9: Negative numbers Targeted teaching: Negative numbers and their relative size.Make sure that kids understand:Negative numbers are used for amounts less than zero, not between zero and one (decimal numbers). Lots of kids think decimal numbers are the same as negative numbers, so watch out for that.A number line is reflected around zero. So -17 is between -10 and -20, closer to -20. You can also have negative decimal numbers (e.g. if you owed the bank $2.50 your balance would be -2.5. This is between -2 and -3).Many students find it easier to conceptualise owing money than owing apples. Talk about loans from the bank and credit cards – the amount you need to pay back.Please don’t teach “short cut rules” with negative numbers as these tend to lead to difficulties in later years. Focus on relative position on a number line and where you would move rather than learning rules (e.g. “If I owed the bank $10 and I then spent $10, what would my bank balance be? Would I have paid off my loan and be back to zero or would I owe more money now?”)Resources:Investigation idea:Using the open number line idea from week 4, tape a long line across your class. In the middle, place 200. At the ? mark, place 500. Ask the kids to work out what numbers go at each end (one will be a negative).JP 3: Ordering positive and negative integersA15. Introducing negative integersA16. Using number lines with negativesRegular tasks or indirect learning:Homework suggestions:Week 10: 2D shapes - classificationTargeted teaching: Classifying shapes, constructing and analysing 2D shapes Please note: There is a lot in this week as we have allowed extra time earlier in the term to catch up on number concepts. Geometry will have a heavier focus in term 4.Resources:K3. Conventions for labelling shapes, angles and linesK4. Revising subfamilies of quadrilaterals and triangles7 Blasts K5 (get online) K5. Using compasses and rulers to make shapesRegular tasks or indirect learning: JP 31: Shapes GameHomework suggestions:K1. CongruentK2. ParallelTerm 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 end of the yearACMNA132 Investigate and calculate percentage discounts of 10%, 25% and 50% on sale items, with and without digital technologies ACMNA125 Compare fractions with related denominators and locate and represent them on a number line ACMNA127 Find a simple fraction of a quantity where the result is a whole number, with and without digital technologies ACMNA131 Make connections between equivalent fractions, decimals and percentages ACMNA122 Identify and describe properties of prime, composite, square and triangular numbers ACMNA123 Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers ACMNA129 Multiply decimals by whole numbers and perform divisions by non-zero whole numbers where the results are terminating decimals, with and without digital technologies ACMNA130 Multiply and divide decimals by powers of 10 ACMMG135 Connect decimal representations to the metric system ACMMG136 Convert between common metric units of length, mass and capacity ACMMG137 Solve problems involving the comparison of lengths and areas using appropriate units ACMMG139 Interpret and use timetables Your focus this term is on:Weeks 1-3: FractionsWeek 4: MoneyWeek 5: TimeWeeks 6-8: MultiplicationWeeks 9-10: Measurement: length and areaTeaching Sequence:Weeks 1-3: FractionsInvestigation idea: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.Target teaching:Common fractions ? decimal fractions ? percentages, equivalent fractions, Fractions that are more than oneMake sure that kids understand: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:Use the Investigation above to introduce this unit. Please note, if your students are a long way behind then this unit may take an extra week or two. Consider reading the book “Fixing Misconceptions in Fractions” by Tierney Kennedy as it has a great diagnostic test as well as a developmental sequence to catch kids up.Investigation above, then repeated for halves and thirds as needed.C1. Identify and describe equivalent common fractionsC8. Mixed numbers and improper fractionsA12. Vinculums in common fractionA13. Common and decimal fractionC9. Represent fractionsC10. Percentage as parts per 100C11. Percentage, fractions and decimalsC12. Percentage of and percentage offRegular tasks or indirect learning:Homework suggestions:Weeks 4: MoneyTarget teaching:Money, saving, borrowing and multistep questionsMake sure that kids understand:An amount of money can be made in different ways using collections of notes coins. 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:JP 6: Multistep with MoneyB1. Estimating with dollars and centsB2. Borrowing money costs youRegular tasks or indirect learning:Homework suggestions:Weeks 5: TimeTarget teaching:Read, interpret and use time tables and schedulesPlease note:This section is not in the Australian Curriculum other than as ACMMG139 Interpret and use time tables. If your students are already fluent with this then consider using this week to catch up on other concepts.Make sure that kids know:An hour has 60 minutes. Half an hour has 30 minutes. Quarter of an hour has 15 minutes. Note – for kids having trouble with Analogue clocks, take the minute hand off entirely and work on using only the hour hand and fractions knowledge to estimate the time. Then reintroduce the minute hand afterwards.Know 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.How to read and interpret clocks, calendars and schedules.Resources:F1. Read and record 24 hour timeF2. Calculate time: hours and minuteF4. Interpreting schedules and time tablesRegular tasks or indirect teaching:Homework strategies:Weeks 6-8: Multiplication (focus on arrays)Investigation ideas:Give each student 40 counters to arrange into as many different arrays as possible. Draw the arrays.Target teachingMultiplication to 2 digits by 2 digitsMultiplication of numbers involving decimalsExtending basic facts, developing and using mental strategies.Multiplying two digit by two digit and representing this as an array with four parts (e.g. 23 x 35 draw as a rectangle, then break into 20 and 3, and 30 and 5, producing 3x5, 20x5, 3x30 and 20x30 parts).Make sure that kids understand:Kids really, really need to get the concept of arrays (e.g. 3 x 5 = three rows of five OR five rows of three)Multiplying means “lots of”, “groups of”, “rows of” or “columns of”Division means “how many” (groups, lots, rows or columns)If you turn an array around by 90o then you can show why multiplication works both ways (why 3x5=5x3)Resources:Investigation above to introduce the concept of multiplication as an array6 JP.12 Multiply by double digitsD6. Extending multiplication and division factsD8. Distributive Law6 JP.9 Multiply by tenths and hundredthsD11. Multiply by tenths and hundredthsD12. Decimals in multiplyingD13. Decimals in multiplying 2Regular tasks or indirect learningHomework studentsWeeks 9-10: Measurement: length and area Target teaching:Length (including perimeter) and Area (including area of rectangles), extending area to triangles if appropriate.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:Length:E2. Find the perimeter and adding length measurementsE13. Converting between unitsIf appropriate: JP.18 Circumference of a circleArea: E4. Estimating and measuring area in cm2E5. Area of a rectangleIf appropriate: 6 JP.19 (calculating area – of triangles)Regular 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 end of the yearACMNA124 Investigate everyday situations that use integers. Locate and represent these numbers on a number line ACMNA131 Make connections between equivalent fractions, decimals and percentages ACMNA126 Solve problems involving addition and subtraction of fractions with the same or related denominators ACMNA123 Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers ACMNA122 Identify and describe properties of prime, composite, square and triangular numbersACMNA129 Multiply decimals by whole numbers and perform divisions by non-zero whole numbers where the results are terminating decimals, with and without digital technologies ACMNA130 Multiply and divide decimals by powers of 10 ACMSP144 Describe probabilities using fractions, decimals and percentages ACMSP145 Conduct chance experiments with both small and large numbers of trials using appropriate digital technologies ACMSP146 Compare observed frequencies across experiments with expected frequencies ACMSP147 Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables ACMSP148 Interpret secondary data presented in digital media and elsewhere ACMMG143 Introduce the Cartesian coordinate system using all four quadrants Your Focus this term is on:Week 1- 2: Division, order or operations, distributive propertiesWeek 3-4: Extending and connecting fractions, operations with fractionsWeek 5-9: Chance & Data Week 10: Position and Direction Term Plan:Weeks 1-2: Division, order or operations, distributive propertiesFocus:Remainders from division can be expressed as fractions, decimals and left overs.Division does have to be done in the right order as it is not associative, but you can use the distributive law.Make sure that kids understand:Division is the same thing as arraysDivision is the same thing as fractionsWhen we divide and have left overs we can write them as remainders, as fractions of the amount we are dividing by (e.g. if 3 left dividing by 5 then we would have 3/5) or as decimals (3/5 is 0.6)Multiples are just numbers that can be made into arrays other than all in one line. E.g. 15 can be made into an array of 3x5, not just 15x1.Factors are the numbers that multiply together to give a total. These are the numbers on the sides of an array (e.g. for an array of 15, 3 and 5 would be factors because 15 can be arranged into a 3x5 array).Resources:D14. Division remaindersD15. Expressing a remainderD16. Divide by tenths and hundredthsD17. Decimals in dividingD21. Introducing brackets and D22. Order of operationsD23. Interpreting equations with operations and D24. Applying order of operationsRegular Tasks or Indirect TeachingHomework SuggestionsWeeks 3-4: Extending and connecting fractions, operations with fractionsFocus:Adding and subtracting fractions with the same or related denominatorsExtend to adding and subtracting fractions with unrelated denominators if appropriate.Make sure that kids understand:See previous work on fractionsResources:C4. Estimating when adding fractionsC3. Adding fractions with related denominators.Note: the following activities extend student thinking to unrelated denominators, but this is not technically part of grade 6. Consider whether your students are ready for these first:JP.8 - Adding fractionsC5. Visually adding fractionsC6. Adding and subtracting fractionC7. Written method for adding fractionsRegular Tasks or Indirect TeachingHomework SuggestionsWeeks 5-9: Chance and Data See 4 week Chance and Data Unit below:Investigation ideas:Data investigation: takes 2-3 weeks including completing Blast and Journal problemsUse Journal problem 27 from grades 4-6 or Journal problem 26 from grade 7 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, Grade 6: J1-J4Target Teaching:Chance can be represented as fractions and decimal numbers between 0 and 1Data can be collected in different ways for different purposes. Data displays should be chosen based on what you want to show.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 fractions between 0 and 1Data 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:Chance (1 week)6 JP.24 – A pack of cardsI4. Probability as a measure between 0 and 1I5. Predict outcomes in similar situationsData (4 weeks)2 weeks – Data investigations and graphing resultsUse JP 27 Planning Data Collection as an investigation with the following Blast activities and journal problems:J2. Evaluate the usefulness of questions asked, J3. Categories for classifying data, J4. Variation in ResultsJ5. Creating circle graph approximations from fractionsJ8. Two way tablesJ9. Select a suitable display2 weeks – Central tendency and data interpretationJ10. Estimating an averageJ11. Calculating the meanJ12. Making inferences from the meanJ13. Describing what is average in two different waysJ14. Interpreting data: tablesJ15. Interpreting data: graphs J16. Interpreting circle graphsRegular Tasks or Indirect TeachingHomework Suggestions J1. Collect data (based on the class investigation)J6. Key percentages and circle graphs Week 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”. Focus:Position and Direction Create and interpret grid maps with conventions and using coordinates from a Cartesian plane (note, this will be built more heavily in term 4)Read and interpret compass directions and degrees of turnMake 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:Grade 6 Investigation: “Where do we live?” using the school location as point 0,0 on a Cartesian grid. (online)JP 35: Create a map (based on investigation above)M2. Read and interpret street map, globe, photo, atlas, and M3. Interpret plansM1. Latitude and LongitudeRegular Tasks or Indirect TeachingHomework Suggestions Term 4: Focus concepts: Number concepts, Transformations, Volume, Mass, Patterns and Functions, GeometryTerm 4: Australian Curriculum Statements to achieve by end of the yearACMNA133 Continue and create sequences involving whole numbers, fractions and decimals. Describe the rule used to create the sequence ACMNA134 Explore the use of brackets and order of operations to write number sentences ACMMG135 Connect decimal representations to the metric system ACMMG136 Convert between common metric units of length, mass and capacity ACMMG138 Connect volume and capacity and their units of measurement ACMMG142 Investigate combinations of translations, reflections and rotations, with and without the use of digital technologies ACMMG140 Construct simple prisms and pyramids ACMMG141 Investigate, with and without digital technologies, angles on a straight line, angles at a point and vertically opposite angles. Use results to find unknown angles Your focus this term is on:Week 1 – 4: Geometry, Angles and Flip, slide and turnWeek 5 – 6: Mass and VolumeWeek 7-10: Algebra, patterns and Functions Term Plan: Weeks 1-4: Geometry, Angle geometry and Flip, slide and turnFocus:Geometry, Angles, Flip, Slide and Turn 2D shapes and 3D objectsAngle properties (see investigation)Note: The next unit is smaller, so consider using more time in this unit and cutting out some from then.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:2 weeks: Geometry investigationInvestigate the angles in playground climbing frames and slides. See “slide safety” investigation for year 7 on Back-to-Front maths website. This investigation contains advanced angle geometry which is necessary for year 6 and is not contained in the Journals or Blast activities below.2 weeks: Activities belowRevise properties of triangles and quadrilaterals from term 1.E11. Using a protractorK8. 3D shapes have ‘nets’K9. Predicting the shape from the netJP.30 Triangles and quadrilateralsL1. Flips, slides and turns, L2. Lines of symmetryRegular Tasks or Indirect TeachingHomework SuggestionsWeeks 5-6: Volume and MassFocus:Volume and MassMake 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)Volume can be conceptualised as a 3D array – a bottom layer is the array and then you have a whole lot of layersResources:Volume:6 JP.17 – counting surface areaE8. Measuring volume in cubic centimetresE9. Volume of a rectangular prismMass:E6. Measure and estimate mass in grams and kilogramsRegular Tasks or Indirect TeachingHomework SuggestionsWeeks 7-10: Algebra, patterns and functionsFocus:Identifying and creating number patterns and functions. 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.A function describes when a rule is consistently applied.Resources:Spend roughly one week each on these topics:PatternsH1. Identify a rule for number patterns, H3. Identify pattern rulesH4. Create a number pattern based on a ruleH5. Identify the relationship between quantitiesH6. Identify the position of any termEquations JP 13. Writing + - equations with variablesConsider using: 7 Blasts H3 (online) and 7 Blasts H5 (online) writing equations and unknownsJP 16. Unbalanced scalesBalancing Equations G7. Solve problems: balancing equationsD25. Writing and evaluating expressions JP.14. Function machinesH5. Identify the relationship between quantitiesInverse: (this is the bit to skip if you are out of time)G4. Ordered PairsG5. Trends in tables and graphsJP 15: Equivalence statementsRegular Tasks or Indirect TeachingHomework Suggestions ................
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