Grade 5 Program

Grade 5 program

Contents

© Kennedy Press Written by Tierney Kennedy www.backtofrontmaths.com.au Grade 5 program This 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: A. 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.

B. 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 class

 Discuss geometric properties of lines, angles, shapes and objects using correct terminology

 Compare 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 portrayed

 Look for patterns in: numbers, geometric repetitions, dances or songs, games, prices (e.g. 2 for the price of 1) and measurement formulae

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.

© Kennedy Press Written by Tierney Kennedy www.backtofrontmaths.com.au  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.

Focus concepts: Number names and concepts, counting, decimal numbers, negative numbers, ordering, addition and subtraction including partitioning, joining and separating, 2D and 3D shapes

Term 1: Australian Curriculum statements (to achieve by the end of the year)

ACMNA104 - Recognise that the place value system can be extended beyond hundredths ACMNA105 - Compare, order and represent decimals

ACMNA099 - Use estimation and rounding to check the reasonableness of answers to calculations

ACMNA291 - Use efficient mental and written strategies and apply appropriate digital technologies to solve Problems

ACMMG111 - Connect three-dimensional objects with their nets and other two-dimensional representations ACMMG112 - Estimate, measure and compare angles using degrees. Construct angles using a protractor

This is what your term focus looks like: Week 1 – Diagnostic Testing Weeks 2-3 – Place Value with whole numbers Week 4 – Relative size, Number Lines and Ordering Weeks 5-6 – Decimal Numbers Weeks 7-9 – Addition and Subtraction Week 10 – 2D & 3D Shapes

© Kennedy Press Written by Tierney Kennedy www.backtofrontmaths.com.au 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 in Years 5-7: Relative size then Proportional Reasoning

1. T ape 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.

2. 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.

3. 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).

4. 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.

5. 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.

6. Ask students to make the following fractions all using an A4 piece of paper to be the whole: ½, ¼, 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 numbers to 100 000 Focus Resources Regular Tasks or Indirect Teaching Homework Suggestions Place Value with whole numbers to one JP.2 Building large numbers hundred thousand. A2. Number names for ten thousands

Make sure that kids understand: A3. Partition ten thousands There are 100 ones in a hundreds block and 10 ones in a tens block (Yep this is A4. More than 99 999 serious! Hold up a ten block and ask A5. Visualise numbers to 100 000 the kids if we chopped it up into the ones how many there would be) © Kennedy Press Written by Tierney Kennedy www.backtofrontmaths.com.au A thousands block has 10 hundreds not 6.

Base ten pattern continues for numbers of any size

© Kennedy Press Written by Tierney Kennedy www.backtofrontmaths.com.au Week 4: Number lines and ordering with relative size Focus Resources Regular Tasks or Indirect Teaching Homework Suggestions Number lines and ordering to 100 000, JP 3 – Ordering numbers in the base 10 with a focus on the relative size of system numbers in the base 10 system. Watch A6. Order numbers to 100 000 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 1000

Relative 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.

Week 5: Addition and Subtraction of large numbers Focus Resources Regular Tasks or Indirect Teaching Homework Suggestions Adding and Subtracting large numbers D1. Add numbers to 999 999 with regrouping. Check out the grade 3 D2. Subtract numbers to 999 999 program for these same weeks for kids

Make sure that kids understand: 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)

© Kennedy Press Written by Tierney Kennedy www.backtofrontmaths.com.au Weeks: 6-8: Decimal Numbers Focus Resources Regular Tasks or Indirect Teaching Homework Suggestions Consolidating tenths and introducing  JP 4 – Visualising tenths. This will hundredths take a long time, so make sure that K1: Classify 2D shapes into you do it properly. families Make sure that kids understand:  A12. Identify and describe decimal K10. Classify 3D shapes Tenths (like all fractions) have to be the fractions: first place into families same size as each other. The shape doesn’t matter but the size really does.  A13. Identify and describe decimal fractions: second place Tenths are smaller than ones.  J.5 - Ordering decimal numbers Hundredths are smaller than tenths.  A15. Compare and order decimal Tenths and hundredths are not negative numbers numbers.  A18. Interpreting representations Decimal numbers follow the same base- of numbers ten system as we use for whole numbers.  A19. Adjusting decimal 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.

Week 9: Addition and Subtraction of decimal numbers Focus: Resources: Regular Tasks or Indirect Teaching Homework Suggestions: Adding and subtracting decimal D4. Adding decimal numbers JP 29: Five Blocks Challenge numbers D5. Subtracting decimal numbers

Make sure that kids understand: See above

Week 10: 2D and 3D shapes - classification

© Kennedy Press Written by Tierney Kennedy www.backtofrontmaths.com.au Focus Resources Regular Tasks and Indirect Teaching Homework Suggestions Classifying shapes, building and K6. Subfamilies of quadrilaterals analysing 3D objects, nets K7. Subfamilies of triangles

K8. Construct a range of 2D shapes

K9. Properties of 3D shapes

Term 2: Australian Curriculum statements (to achieve by the end of the year)

ACMNA106 Create simple financial plans

ACMNA102 Compare and order common unit fractions and locate and represent them on a number line

ACMNA103 Investigate strategies to solve problems involving addition and subtraction of fractions with the same denominator

ACMNA098 Identify and describe factors and multiples of whole numbers and use them to solve Problems

ACMNA099 Use estimation and rounding to check the reasonableness of answers to calculations ACMNA100 Solve Problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental, written strategies and appropriate digital technologies

ACMNA291 Use efficient mental and written strategies and apply appropriate digital technologies to solve Problems

ACMMG108 Choose appropriate units of measurement for length, area, volume, capacity and mass

ACMMG109 Calculate the perimeter and area of rectangles using familiar metric units

ACMMG110 Compare 12- and 24-hour time systems and convert between them

This is what your term focus looks like: Week 1 & 2 - Fractions Weeks 3 – Money Week 4 & 5 – Free for NAPLAN prep Week 6 – Time Weeks 7-8 – Multiplication Weeks 9-10 – Length and Area

Weeks 1-2: Fractions Investigation ideas: Take an A5 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. Focus Resources Regular Tasks and Homework Tasks Common fractions, ordering, tenths, equivalence, more than one C3. Revising comparing and ordering common Indirect Teaching fractions Make sure that kids understand: C4. Different formats for tenths 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 C5. More than 10 tenths: or smaller). C6. Represent whole numbers and fractions Watch for students who think that cutting paper makes more paper (not just more pieces – the two pieces of paper stuck back together C8. Identify equivalent common fractions 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.

© Kennedy Press Written by Tierney Kennedy www.backtofrontmaths.com.au 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.

© Kennedy Press Written by Tierney Kennedy www.backtofrontmaths.com.au Weeks 3: Money Focus Resources Regular Tasks and Homework Tasks Money, saving, borrowing and multistep questions B1. Working with dollars and cents Indirect Teaching

JP 6: Multistep with Money Make sure that kids understand: An amount of money can be made in different ways using JP 7: Saving and Borrowing Money collections of notes coins.

Having lots of coins doesn’t mean that there is lots of money – it depends on the value of the coin

Just 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.

Weeks 4-5 Do what you want during NAPLAN time Weeks 6: Time Focus Resources Regular Tasks and Homework Tasks Time, elapsed time, duration of events and planning an event 5 JP.23 - Making a quick trip Indirect Teaching

F1. Read and record 24 hour time Make sure that kids know: An hour has 60 minutes. Half an hour has 30 minutes. Quarter of an F2. Calculate time: hours and minutes hour has 15 minutes. F3. Recording days and dates 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

© Kennedy Press Written by Tierney Kennedy www.backtofrontmaths.com.au Weeks 7-8: Multiplication Investigation ideas: Give each student 40 counters to arrange into as many different arrays as possible. Draw the arrays. Focus Resources Regular Tasks and Homework Tasks Multiplication to 3 digits by 1 digit Week 7 Indirect Teaching Extending basic facts, developing and using mental strategies. D6. Multiply by 10 and 100 Multiplying two digit by one digit and representing this as an array D14. Subsets: multiples and factors 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 D15. Prime and composite numbers the 6x4 part) D16. Multiplication is associative

Week 8 Make sure that kids understand: 5 JP.9 Multiplication with 3 digits Multiplying means “lots of”, “groups of”, “rows of” or “columns of” D8. Solving multiplication problems Division means “how many” (groups, lots, rows or columns) D9. Solving multiplication problems 2 Kids really, really need to get the concept of arrays (e.g. 3 x 5 = three rows of five OR five rows of three) D18. Distributive Law

If you turn an array around by 90o then you can show why multiplication works both ways (why 3x5=5x3) Weeks 9-10: length and area Focus Resources Regular Tasks and Homework Tasks Length, standard units and perimeter; Area and rectangles Week 9 (Length) indirect Teaching 5 JP.18 Measuring Perimeter Make sure that kids understand: E2. Measure and estimate length in m and cm  You have to fit in as many units as possible when measuring, ensuring that there are no gaps or overlaps. E3. What is a standard unit for length?

 Parts of units are used where a whole unit cannot fit. We use E12. Converting between units for length fractional language to describe these parts.

 Length is measured in a single dimension Week 10 (Area) Year 4 JP.21 Tiling a replica house  Arrays is basically the same as area (multiplication expressed as rows and columns so that it is arranged into a grid)

© Kennedy Press Written by Tierney Kennedy www.backtofrontmaths.com.au  Area is a measure of 2D flat space. It needs to have E5. Measure area in square m and square cm measurements in two dimensions, not just a length. E6. Area of a rectangle  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)

Term 3: Focus concepts: Larger numbers, regrouping, formal operations, fractions, chance and data, position and direction

ACMNA104 Recognise that the place value system can be extended beyond hundredths

ACMNA105 Compare, order and represent decimals

ACMNA098 Identify and describe factors and multiples of whole numbers and use them to solve Problems

ACMNA101 Solve Problems involving division by a one digit number, including those that result in a remainder

ACMNA291 Use efficient mental and written strategies and apply appropriate digital technologies to solve Problems

ACMSP116 List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions

ACMSP117 Recognise that probabilities range from 0 to 1

ACMSP118 Pose questions and collect categorical or numerical data by observation or survey

ACMSP119 Construct displays, including column graphs, dot plots and tables, appropriate for data type, with and without the use of digital technologies

ACMSP120 Describe and interpret different data sets in context

Your term looks like this: Weeks 1-2: Division, order of operations, distributive properties Weeks 3-4: Fractions, Operations with Fractions, Weeks 5-8: Chance and Data Weeks 9-10: Position and Direction © Kennedy Press Written by Tierney Kennedy www.backtofrontmaths.com.au © Kennedy Press Written by Tierney Kennedy www.backtofrontmaths.com.au Term plan:

Weeks 1-2: Division, order or operations, distributive properties Focus Resources Regular Tasks and Indirect Teaching Homework Suggestions Remainders from division can be  Grade 4 JP.10 Division with 2 digits expressed as fractions, decimals and left (online) overs. D10. Division remainders Division does have to be done in the  D11. Expressing a remainder right order as it is not associative, but you can use the distributive law.  D17. Is division associative?

 D18. Distributive Law Make sure that kids understand: Division is the same thing as arrays

Division is the same thing as fractions

When 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 arrays made with a particular number as the row or column

Factors are the numbers that multiply together to give a total

Weeks 3-4: Extending and connecting fractions, operations with fractions, link fractions, decimals and percent Focus Resources Regular Tasks and Indirect Teaching Homework Suggestions Building on the concept of division and what we do with remainders we will use Adding fractions: this to connect fractions to decimals and C8. Identify equivalent common introduce simple percent. fractions Add and subtract fractions with related denominators. C9. Adding and subtracting fractions

Make sure that kids understand: C10. Adding fractions with related © Kennedy Press Written by Tierney Kennedy www.backtofrontmaths.com.au See previous term’s work on fractions denominators Percent is the same as the number of hundredths as it represents fractions as C11. Percentage as parts per 100 out of one hundred. For example, 0.68 C12. Percentage, fractions and decimals is 68 hundredths which is 68/100 so that is also 68%) JP 8: Ordering Different Types of Fractions Percent can be more than one hundred, but only if the fraction is greater than one

© Kennedy Press Written by Tierney Kennedy www.backtofrontmaths.com.au Focus Resources Regular Tasks and Indirect Teaching Homework Suggestions Chance can be represented as fractions Data Investigation and decimal numbers between 0 and 1 JP - 27: Planning Data Collection Data can be collected in different ways Use blast activities from this list as for different purposes. Data displays needed for the investigation above. You should be chosen based on what you probably won’t need them all. want to show. J1. Choose data collection methods J2. Trial data collection methods and Make sure that kids understand: analyse  All events have some kind of J3. Evaluate the usefulness of questions likelihood but very few things are asked absolutely certain. J4. Categories for classifying data J5. Check the accuracy of data gathered  Some things are more likely than J6. Variation in Results others. J7. Select a suitable display J8. Create displays for data  Having two options doesn’t make them both the same (e.g. It could rain or not rain, but that Chance doesn’t make them both 50/50 – the 5 JP.24 JP 24: Rolling a Die chance of rain depends on the I1. Sample Space: all possible outcomes season) I2. Conduct experiments to collect data  Chance is expressed as fractions between 0 and 1 I3. Language of chance

 Data can be collected or found for I4. Probability as a fraction the purpose of answering questions I5. Are these outcomes equally likely?  Data needs to be classified or organised in a way that best fits the Data without needing the investigation question to be answered. J9. Creating circle graph approximations from fractions  Data can be organised in different ways for different purposes J10. Key percentages and circle graphs

 Data displays help us to see the J11. Describing what is typical in two patterns in large amounts of different ways information

© Kennedy Press Written by Tierney Kennedy www.backtofrontmaths.com.au © Kennedy Press Written by Tierney Kennedy www.backtofrontmaths.com.au 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”. Focus Resources Regular Tasks and Indirect Teaching Homework Suggestions Create and interpret simple grid maps M4. Use simple scale to create maps with conventions M1. Conventions for maps Read and interpret compass directions and degrees of turn M2. Compass points and degrees of turn

M3. Locate points of interest on maps Make sure that kids understand:  Directions are described using M5. Giving directions game 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)

Focus concepts: Number concepts, Transformations, Area, Mass, Patterns and Functions, Geometry

ACMNA107 Describe, continue and create patterns with fractions, decimals and whole numbers resulting from addition and subtraction

ACMNA121 Use equivalent number sentences involving multiplication and division to find unknown quantities

ACMMG108 Choose appropriate units of measurement for length, area, volume, capacity and mass

ACMMG114 Describe translations, reflections and rotations of two-dimensional shapes. Identify line and rotational symmetries

ACMMG115 Apply the enlargement transformation to familiar two dimensional shapes and explore the properties of the resulting image compared with the original

ACMMG111 Connect three-dimensional objects with their nets and other two-dimensional representations

ACMMG112 Estimate, measure and compare angles using degrees. Construct angles using a protractor

Week 1-4: Geometry, Angles and Flip, slide and turn Week 5-6: Volume and Mass Week 7-10: Patterns and Functions

Weeks 1-4: Geometry, Angles and Flip, slide and turn Investigate 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 years 6 and 7 and is not contained in the Journals or Blast activities below. For years 4 and 5 use problem 33 from year 6 or 7 journals and simply measure and replicate the angles as the investigation. Focus Resources Regular Tasks and Indirect Homework Teaching 3D shapes and their nets, Angles and Flip, Teaching slide and turn 3D shapes:  JP 31: 3D Shapes Challenge Make sure that kids understand:  K12. 3D shapes have ‘nets’  Angles are an amount of turn. It doesn’t matter what direction they  K13. Predicting the shape from the net face (e.g. a right angle doesn’t have to be vertical and horizontal – it is the Angles and transformations: number of degrees that matters not  K2. Properties of angles the orientation)  K3. Lines and angles in 2D shapes  Changing one angle in a shape will alter the other angles and  L1. Flips, slides and turns possibly change the shape altogether (e.g. if we start with a square but  L2. Objects with size and orientation changes change one angle to be 45o, the other  L3. Lines of symmetry angles will change too and it definitely won’t be a square anymore,  L4. Create patterns using orientation and size changes but if we change one angle in a triangle it will still be a triangle).  L5. Properties of tessellations

 2D shapes can be transformed  JP 34: Angles in Tessellating Patterns 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

Weeks 5-6: Volume and Mass Focus: Resources Regular Tasks and Indirect Homework Strategies Volume & Mass Volume Teaching  5 JP.20 – ordering volumes Make sure that kids understand:  E7. Measure and estimate volumes  Mass is about how heavy something is, not how much space it  E8. What is a standard unit for volume? takes up.  E9. Measuring volume in cubic centimetres  Sometimes small objects can be very heavy – it depends on what they  E10. Volume of a rectangular prism (if you get extra time only) are made from. Mass  The same amount of mass can be  E11. Measure and estimate mass in g and kg 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 layers

© Kennedy Press Written by Tierney Kennedy www.backtofrontmaths.com.au Weeks 7-10: Patterns and functions Focus Resources Regular Tasks and Indirect Homework Strategies Identifying and creating number patterns Teaching and functions. Trading and equivalence. Equivalent and Equations: Introducing equations, inverse JP 13: Trading Counters operations reverse a rule. G1. Simple equations G2. Guess and check method Also, please help kids to understand that JP 16: Unbalanced Scales the “equals” sign doesn’t mean that the G3. Use symbols for balanced equations answer is coming next. It means “is the G4. Greater than and less than same as”. Make sure that you write G5. Writing rules from number patterns some number sentences in the wrong G6. Inverse operations reverse a rule order (e.g. 15 = 3x5) and also when there G7. Use backtracking to solve problem is no “answer” at all (e.g. 3 x 4 = 2 x 6) Patterns and Functions: Make sure that kids understand: JP 17: Counter Patterns H1. Identify a rule for number patterns  Patterns can be comprised of H2. Create a number pattern based on a rule colour, shape, size, actions and JP 12: Growth Patterns in Plants numbers. H3. Display patterns with graphs  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.

© Kennedy Press Written by Tierney Kennedy www.backtofrontmaths.com.au © Kennedy Press Written by Tierney Kennedy www.backtofrontmaths.com.au SEMESTER 1- ASSESSMENT OUTLINE (BUILDING THE PORTFOLIO) What? When? Details? Term 1 B2F Maths Moderating Task 1 Week 1 Number (diagnostic to measure growth into term 2) (formative)

Week 2 Use B2FM Criteria Sheets JP 3 – Ordering numbers in the base 10 system Week 3/4 Number (selected by Yr level teams) Content Assessment - Whole Number Week 10 Number (selected by Yr level teams) Content Assessment – Decimals, + / - algorithms Week 10 Number (selected by Yr level teams) Content Assessment - Space Week 10 Bring along entire portfolio including any Moderating the Portfolio incidental tasks

Term 2 JP Multistep with money Week 3 Space

Content Money Week 3-5 Number

Content Time Week 6 Measurement (Compare growth with Term 1 task – summative B2F Maths Moderating Task 2 Week 5 assessment)

Content Assessment – Multiplication/ Week 10 To be used in Sem 2 Reporting Measurement