of rectangles. They convert between 12 and 24 hour time. Students use a grid reference system to landmarks. They and different angles. Students outcomes of chance experiments with equally likely outcomes and assign probabilities between 0 and 1. Students pose questions to gather data, and data displays appropriate for the data. MAG Planning Semester 1 Year 5 TOPIC CONTENT DESCRIPTOR KEY IDEA Pre-ASSESS ASSESSMENT INVESTIGATION STUDENT JOURNAL RESOURCES 5.1.1 Going Fishing Applicable to all content descriptors Helping students construct a deep understanding of mathematical ideas and processes by engaging them in doing mathematics: creating, conjecturing, exploring, testing, and verifying' Fish Problem Solving Introduce the FISH problem solving strategy to the students by starting a discussion on real life fishing. (5 W’s & H) Option 1 What time is it now? What will the time be in a thousand seconds? Using the green FISH to explain how reasonable is your answer. Option 2 How high would a stack of a 1000 cubes be? Using the green FISH to explain how reasonable is your answer. Making your first Million FISH Problem Solving kit Maths learning journal CONTENT DESCRIPTOR KEY IDEA Pre-ASSESS ASSESSMENT INVESTIGATION STUDENT JOURNAL RESOURCES 5.1.2 ACMNA098 Identify and describe factors and multiples of whole numbers and use them to solve problems Each counting number is divisible by one and itself, and some counting numbers are also divisible by other numbers Multiplication which has an inverse relationship with with division, is helpful in finding factors Introduce a revision finding a factor and using multiples Option 1 A furniture shop sells chairs in sets of four. Which of the following numbers of chairs would make complete sets. 10, 12, 15, 20, 22, 28, 35? Justify You have been to create a display of field trip photos for a class webpage. Create a diagram of your various layout options for arranging them on the screen. Select one and justify why it would best fit suit the screen? your answer using a green fish example Option 2 A gardener has 12 flowering plants that he wants to plant in equal rows at the front FISH Problem Solving kit Closing the Gap – Ladybirds Cubes / MAB units/Games ) cardboard squares multiplication table (for differentiated learners) poster size sticky notes (for living charts) or alternatively use cardboard IWB - Promethean Planet - sample flipchart images displayed below for further clarification. Google images (some attached below) - this is and individual learning.
entrance to the garden. What are all the ways he can arrange the flowers in equal rows? Justify your answer using a green fish example Option 3 A concert organiser has 200 seats he needs to arrange in rows with access aisles on the sides and one in the middle. What are his possible options for moving concert attendees quickly and safely in and out of their seats. Justify your choice of most efficient seating arrangement you would recommend he use. Justify your answer using a green fish example TOPIC CONTENT DESCRIPTOR KEY IDEA Pre-ASSESS ASSESSMENT INVESTIGATION STUDENT JOURNAL RESOURCES 5.1.3 ACMNA291 Use Efficient mental and written strategies and apply appropriate digital technologies to solve problems Students are able to addition and subtraction problems, selecting the most efficient method from a bank of known mental and written strategies Review strategies that students should have learnt in lower grades (accessing prior knowledge) Before completing this MAG, it is suggested that two diagnostic are completed to check students prior This way, a better picture of what the students already know and can do is established. This will assist in choosing the strategies to be taught in individual classrooms (either for revision and consolidation or extension). Students list outcomes of chance experiments with equally likely outcomes and assign probabilities between 0 and 1. Students pose questions to gather data, and construct data displays appropriate for the data. FISH Problem Solving kit A3 for poster, coloured pencils or felt pens Mental Computation using Natural Maths Strategies by Ann and Johnny Baker Student Learning Journal
TOPIC CONTENT DESCRIPTOR KEY IDEA Pre-ASSESS ASSESSMENT INVESTIGATION STUDENT JOURNAL RESOURCES 5.1.4 ACMNA099 Use estimation and rounding to the reasonableness of answers to calculations In our everyday lives we constantly use estimation and rounding. We don’t always need the exact or correct answer. Learners use fish thinking, with estimation and rounding strategies, to check the of answers. FISH problem solving kit (especially green fish) Maths learning journals Various items for estimation eg paperclips Large jar filled with jelly beans ( or similar) ‘Great Estimations’ by Bruce Goldstone Cards The learning journal is used throughout this MAG to get students to think about and reinforce what is being taught. It is hoped that the concept will be better understood, when students describe their understanding in their own language rather than formal ‘teacher talk’. How many jelly beans? 1. Show students a large jar filled with jelly beans. 2. Get students to examine the jar and determine about how many jelly beans are inside. 3. Students are to record estimations and working out on sticky notes. Sticky notes are then stuck onto a large poster so that all answers can be viewed. 4. Students share what they answered, noting the range of answers. 5. Discuss how students decided on answers. 6. Distinguish between estimating and guessing. (Estimates involve strategies.) Key Question: Is it okay to make an estimate? Discuss - Are we looking at an estimate or an exact answer? Is it important? Students write responses to question in their Maths’ Learning Journal using examples to support there response FISH problem solving kit (especially green fish) Maths learning journals Various items for estimation eg paperclips Large jar filled with jelly beans ( or similar) Estimations’ by Bruce Goldstone Flash Cards TOPIC CONTENT DESCRIPTOR KEY IDEA Pre-ASSESS ASSESSMENT INVESTIGATION STUDENT JOURNAL RESOURCES 5.1.5 ACMNA101 Solve problems Interpreting and Whole class game: TAG Teacher Observation checklist Dividing by Ten FISH problem solving kit Counters
involving division by a one digit number, including those that result in a remainder representing the remainder in division calculations sensibly for the context. Explore the inverse relationship between multiplication and division Dice Calculators Worksheets TOPIC CONTENT DESCRIPTOR KEY IDEA Pre-ASSESS ASSESSMENT INVESTIGATION STUDENT JOURNAL RESOURCES 5.1.6 ACMNA102 Compare and order common unit fractions and locate and represent them on a numberline Fractions represent numbers that have their own properties and their own position on a number line. Each fraction can be associated with a unique point on the number line, but not all of the points between integers can be named by fractions. Recognising the connection between the of unit fractions and their denominators What do we know Frayer Model: Using the Frayer model (template attached) have students work in learning teams to explore their knowledge about ‘Fractions’. Have each team share their model and discuss findings as a class. Clarify any Correctly define any required terms. Option 1 A 1500 go-kart race is 13.5 laps around a short track. Show 13.5 on a number line Option 2 What is bigger 3/8 or 3/4? Draw a model to show your reasoning Option 3 Where would 1 ⅖ and 2 ¾ go on the number line Ordering and Comparing Fractions: Ask students to use a half, a third, a quarter and three quarters as reference points to determine the size of a fraction, or to order and compare fraction numbers. For example, ask: Is ⅝ smaller or bigger than a half? Does knowing that 4/8 is a half help? Use what you know to say whether 8 ¼ is more or less than ⅝ . . Have students use these strategies to order sets of fractions with unlike numerators and unlike denominators; for example: 23, 45, 56, 9 10. FISH problem solving kit number lines Desk mats Ropes IWB number Fraction cards - Fraction Umbrella’s Fraction - monkeys Fraction cards - rectangular Templates provided in resource folder
TOPIC CONTENT DESCRIPTOR KEY IDEA Pre-ASSESS ASSESSMENT INVESTIGATION STUDENT JOURNAL RESOURCES 5.1.7 ACMNA103 Investigate strategies to problems involving addition and subtraction of fractions with the same denominator. The effects of operations for addition and subtraction with fractions and decimals are the same as those with whole numbers. Fractions are parts of a whole Number lines can be used to add or subtract fractions Fractions can be or subtracted horizontally or vertically. You only add or subtract the numerator You change the fraction to a fraction if the numerator is larger than the denominator. Review equivalent fractions to ensure this concept is understood as fractions may need to be renamed as equivalent fractions with like denominators to add and subtract. Checklist Are students able to: - Addition and subtraction of fractions using the jump strategy on a number line. - Addition and subtraction of fractions using a pictorial representation. - Addition and subtraction of fractions in a horizontal and vertical format. - Addition and subtraction of fractions based on a word problem. Teacher models the idea of a fraction tree and reminds students that a tree is a that can be divided. It is a repeated pattern. FISH problem solving kit Fraction Frames -cards/ strips Double sided counters Counters Fraction shapes / circles TOPIC CONTENT DESCRIPTOR KEY IDEA Pre-ASSESS ASSESSMENT INVESTIGATION STUDENT JOURNAL RESOURCES 5.1.8 ACMNA100 Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental, written strategies Use a range of multiplicative strategies when operating on whole numbers. Use a loop card game ‘I have.. Who has..’ Self Assessment I can down how I solved a problem, showing every step I know my tables to 10. I can use them to multiply multiples of 10 and 100 Patterns Students investigate patterns in the multiplication grid. Students discuss these patterns and record observations. For example, students compare FISH problem solving kit Loop card games Variety of manipulatives Multiplication worksheet X two by one digit and by two digit
Reproduce the follow shape with cubes Photograph the shape from a different angle to the one shown here. Describe it attributes and create a net for it. CONTENT DESCRIPTOR KEY IDEA Pre-ASSESS ASSESSMENT INVESTIGATION STUDENT JOURNAL RESOURCES 5.1.10 translations, reflections and rotations of shapes. Identify line and rotational symmetries. Line and rotational symmetry are investigated through the physical manipulation of regular and irregular polygons. Shapes may have have one line of symmetry, vertically, horizontally or diagonally (symmetrical) or no line of symmetry or have more than one line of symmetry, including vertically, horizontally and diagonally. A circle has infinite lines of symmetry. Option 1 Choose a then use it to draw a pattern showing reflections and rotations. Option 2 The rectangular entrance to my new has 24 one metre square tiles. They have been placed in a symmetrical pattern. Three different colours of tiles have been used. The tiles around the border are the same colour. What does my entrance look like? And how can you be sure your pattern has symmetry? Option 3 Equilateral, isosceles and scalene triangles all have 3 sides, 3 corners and 3 angles. Do they also have 3 lines of symmetry? Use models or diagrams to demonstrate your answer. -Symmetry in the environment The objective of this activity is to investigate symmetry in the world around them Where in the environment can you find symmetry? Students venture into the world around them and document evidence of symmetry. Photographs, drawings and sketches can be used to support their findings. FISH problem solving kit paper squares, dot, grid, graph, plain paper pencils, scissors mirrors Google images, Magazines CONTENT DESCRIPTOR KEY IDEA Pre-ASSESS ASSESSMENT INVESTIGATION STUDENT JOURNAL RESOURCES 5.1.11 ACMMG109 - Calculate the perimeter and area of rectangles using familiar metric units. Exploring efficient ways of calculating the perimeters of rectangles such as adding the Option 1 Using 1 cm grid paper draw two different rectangles with perimeters of 32 cm. What is the difference in their areas. Find a rectanfle where the perimeter and area have the same numerical value FISH problem solving kit Grid 1cm2 Ruler Rectangular shapes of different sizes Geoboards
length and width together and doubling the result. Exploring efficient ways of finding the areas of rectangles Option 2 You have a room that 3 m long and 5 m wide. What would be the area that you would need to carpet? The room has skirting boards that will need painting. Can you work out the perimeter? Option 3 This shape is formed by 5 squares. If the perimeter of the shape is 48 cm, what is its area? TOPIC CONTENT DESCRIPTOR KEY IDEA Pre-ASSESS ASSESSMENT INVESTIGATION STUDENT JOURNAL RESOURCES 5.1.12 ACMMG115 Apply the enlargement transformation to familiar two dimensional shapes and explore the properties of the resulting image compared with the original Make enlargements and reductions of shapes, pictures and maps Introduce the concept of scale and enlargement change the size of an object, but not the shape. Can students enlarge a shape using: a grid system a scale factor Can students identify how a shape was enlarged - eg. doubled, 4 times? Enlarge the picture using one of the methods shown (grid enlargement or scale factor) When complete, write a statement about which method was used (eg. grid system or scale factor) and why and what happens to the perimeter and area of shapes when they are enlarged. TOPIC CONTENT DESCRIPTOR KEY IDEA Pre-ASSESS ASSESSMENT INVESTIGATION STUDENT JOURNAL RESOURCES 5.1.13 ACMMG108 Choose appropriate units of measurement for length, area, volume, capacity and mass recognising that some units of measurement are better suited for some tasks than others, for example kilometres rather than metres to measure the distance Milligrams, Grams, Kilograms, Tonnes: Sort objects according to the appropriate unit used to record their mass? Convert units of measurement (grams, kilograms, tonnes)? Use equipment to measure the mass of an object? Don’t sink the Boat! Students are to imagine that they are boarding a ship to travel to a mystery island for a 3 day stay. FISH problem solving kit Scootle IWB
between two towns Understand that not all countries use the metric system? TOPIC CONTENT DESCRIPTOR KEY IDEA Pre-ASSESS ASSESSMENT INVESTIGATION STUDENT JOURNAL RESOURCES 5.1.14 ACMNA106 Create simple financial Identify cashless transaction - you pay for goods without using actual money. identify and add GST to a product Know that goods refers to what can be bought, whether it is food, toys, clothes Develop a budget Measure keep within budgetary constraints. Explain and justify purchases made Provide each student with a ‘money wallet’ (small bag with a zipper or a zip lock bag with play money). Investigation Year 5 has been awarded $1000 to create a beautiful vegetable garden for their year level. You will be given a list of the materials, seeds and tools that you can buy. You must work out what you want to purchase and in what quantities. Remember your budget limit is $1000. You will complete your budget on a printed out table, which will be stuck on the back of an A3 piece of paper. You will have to specify the cost of each item, the GST included, the quantity, and the total cost of the garden. On the other side of the A3 piece of paper you will be able to design the vegetable garden from a bird’s eye view and include all the vegetables that you wish to grow. FISH problem solving kit junk mail calculators hardware catalogue grid paper Play money TOPIC CONTENT DESCRIPTOR KEY IDEA Pre-ASSESS ASSESSMENT INVESTIGATION STUDENT JOURNAL RESOURCES 5.1.15 ACMNA107 - Describe, continue and create patterns with fractions, decimals and numbers resulting Relationships can be described and generalisations made for mathematical situations that Exploring Numbers Give each student a copy of a filled in grid and a dice. Note it is Work out the rules that produced each of these patterns 512. 256, 128, 64, 32 11. 14, 17, 20, 23, 26 Choose 4 different numbers from 1 to 9 to put into 4 squares on a ring so the the difference between Joined squares is odd. FISH problem solving kit filled in 1-100 hundred-grid 1-6 numbered dice, one for each student Hundred-grid with removable numbers 1-30 number lines on A4 paper
from addition and subtraction have numbers or objects that repeat in predictable ways.. important to use zero as the starting point on the grid as fractions and decimals are of parts of a whole. Point out that there is a way to represent less than I whole. Add 5 and subtract 2 starting at the number 91 and ending at 103 What is the pattern of increase masking tape/chalk MAB cubes A4 paper Student learning journal TOPIC CONTENT DESCRIPTOR KEY IDEA Pre-ASSESS ASSESSMENT INVESTIGATION STUDENT JOURNAL RESOURCES 5.1.16 ACMSP120 - Describe and interpret different data sets in context. To introduce median and mode as strategies to solve problems. Ask the students if they know of any times/events functions/ or things where they have heard the word averages used? (determining student knowledge). Independently survey 20 students/people to find out how many siblings they have. Present your survey in a and provide the mean, median and mode information A class of year 5 students achieved the following scores on a 20 word spelling test 15, 20, 16, 17, 20, 19, 18, 17, 16, 19, 18, 17, 18, 19, 18 were displayed in a frequency table What were the highest and the lowest scores in the year 5 blocks/cubes addition charts division charts sticky notes/cardboard (for living charts) Promethean planet - teacher resource - You tube video TOPIC CONTENT DESCRIPTOR KEY IDEA Pre-ASSESS ASSESSMENT INVESTIGATION STUDENT JOURNAL RESOURCES 5.1.17 ACMMG114 Describe translations, reflections and rotations of shapes. Identify line symmetry and rotational symmetries. Objects in space can be transformed in an infinite number of ways and those transformations can be described and analysed mathematically. Looking at translations, reflections, and rotations of shapes Draw a shape, that has an infinite number of lines of symmetry that cannot be tiled without leaving gaps Create a NOTAN MASK to demonstrate a line of symmetry FISH problem solving kit writing/drawing materials magazines scissors, glue, rulers square and rectangular shaped paper (origami paper) geoboards or dot paper or i-pad app (for example Geoboard)
TOPIC CONTENT DESCRIPTOR KEY IDEA Pre-ASSESS ASSESSMENT INVESTIGATION STUDENT JOURNAL RESOURCES 5.1.18 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 Some questions can be answered by collecting and analyzing data, and the question to be answered determines the data that needs to be collected and how best to collect it. Silent Conversation Why do we ask questions? What do we do with the answers? Have you ever been surveyed? How have you been surveyed? Where have you seen surveys? What was it about? Review comments in the silent conversations and revisit on a regular basis to see if opinions have changed Investigation Students have been as the new ice-cream inventor at Miss/Mrs/Mr Insert your name here School Creamery. FISH problem solving kit TOPIC CONTENT DESCRIPTOR KEY IDEA Pre-ASSESS ASSESSMENT INVESTIGATION STUDENT JOURNAL RESOURCES 5.1.19 ACMMG114 Describe translations, reflections and rotations of shapes. Identify line and rotational symmetries Tessellations are created by transforming two shapes to make a pattern with no gap or overlay. Discuss how the patterns were made - draw out the mathematical language needed – rotation, flip, transform, etc. Option 1 - Use one pattern block repeatedly to tesselate. Take a photo and describe the pattern using the terminology learnt. Option 2 - Create an irregular and demonstrate how it can be tessellated without leaving gaps. Describe the pattern by reminding students that: rotating lengths, areas, angles do not change but orientation does. internet templates of 2D shapes to cut out grid paper, dot paper, paper tracing paper cardboard scissors pictures of tessellations in - eg. brick wall, tiled floor, scales on a fish, mosaics, honeycomb etc.