Maths Program
- 1. Achievement Targets (AC): By the end of Year 5, students solve simple problems involving the four operations using a range of strategies. They check the reasonableness of answers using estimation and rounding. Students identify and describe factors and multiples. They explain plans for simple budgets. Students connect three-dimensional objects with their two-dimensional representations. They describe transformations of two-dimensional shapes and identify line and rotational symmetry. Students compare and interpret different data sets. Students order decimals and unit fractions and locate them on number lines. They add and subtract fractions with the same denominator. Students continue patterns by adding and subtracting fractions and decimals. They find unknown quantities in number sentences. They use appropriate units of measurement for length, area, volume, capacity and mass, and calculate perimeter and area of rectangles. They convert between 12 and 24 hour time. Students use a grid reference system to locate landmarks. They measure and construct different angles. Students list outcomes of chance experiments with equally likely outcomes and assign probabilities between 0 and 1. Studentspose questions to gather data, and construct data displays appropriate for the data. English Program: Number and Algebra Measurement and Geometry Statistics and Probability General capabilities and cross-‐curriculum priorities Content description Create simple financial plans Elaborations • creating a simple budget for a class fundraising event • identifying the GST component of invoices and receipts Code ACMNA106 Content description Use estimation and rounding to check the reasonableness of answers to calculations Elaborations • recognising the usefulness of estimation to check calculations • applying mental strategies to estimate the result of calculations, such as estimating the cost of a supermarket trolley load Code ACMNA099 Content description Identify and describe factors and multiples of whole numbers and use them to solve problems Elaborations • exploring factors and multiples using number sequences • using simple divisibility tests Code ACMNA098 Content description Use efficient mental and written strategies and apply appropriate digital technologies to solve problems Elaborations • using calculators to check the reasonableness of answers Code ACMNA291 Content description Describe translations, reflections and rotations of two-dimensional shapes. Identify line and rotational symmetries Elaborations • identifying and describing the line and rotational symmetry of a range of two-dimensional shapes, by manually cutting, folding and turning shapes and by using digital technologies • identifying the effects of transformations by manually flipping, sliding and turning two-dimensional shapes and by using digital technologies Code ACMMG114 Content description Apply the enlargement transformation to familiar two dimensional shapes and explore the properties of the resulting image compared with the original Elaborations • using digital technologies to enlarge shapes • using a grid system to enlarge a favourite image or cartoon Code ACMMG115 Content description Use a grid reference system to describe locations. Describe routes using landmarks and directional language Elaborations • comparing aerial views of Country, desert paintings and maps with grid references • creating a grid reference system for the classroom and using it to locate objects and describe routes from one object to another Code ACMMG113 Content description Connect three-dimensional objects with their nets and other two-dimensional representations Elaborations • identifying the shape and relative position of each face of a solid to determine the net of the solid, including that of Content description Construct displays, including column graphs, dot plots and tables, appropriate for data type, with and without the use of digital technologies Elaborations • identifying the best methods of presenting data to illustrate the results of investigations and justifying the choice of representations Code ACMSP119 Identify and describe the general capabilities and cross-‐curriculum priorities that will be targeted in the unit. Delete those that do not apply. • Literacy Word Walls and Glossaries will be built for all main concept areas. • Numeracy Being a Maths program it predominantly focuses on Numeracy acquisition. • Critical and creative thinking A problem solving approach and ongoing questioning and encouragement of • Personal and social capability Working in groups for puppet theatre will encourage communication and the ability to work as a team. • Intercultural understanding Incorporating Indigenous and Asian perspectives in the program will broaden children’s understanding of numeracy to include intercultural perspectives • Aboriginal and Torres Strait Islander histories and cultures Aboriginal Mapping paintings shown to link to maths mapping and coordinates. • Asia and Australia’s engagement with Asia Shadow Puppetry developed in Asia-‐ Use videos from this region MATHS This Unit Plan describes the school requirements and integrates these with history, art and science where possible. Maths skills are useful in a wide variety of human endeavours; including science, art and history. Year Level: 5
- 2. prisms and pyramids • representing two-dimensional shapes such as photographs, sketches and images created by digital technologies Code ACMMG111 Content description Calculate the perimeter and area of rectangles using familiar metric units Elaborations • exploring efficient ways of calculating the perimeters of rectangles such as adding the length and width together and doubling the result • exploring efficient ways of finding the areas of rectangles Code ACMMG109 Content description Choose appropriate units of measurement for length, area, volume, capacity and mass Elaborations • recognising that some units of measurement are better suited for some tasks than others, for example kilometres rather than metres to measure the distance between two towns • investigating alternative measures of scale to demonstrate that these vary between countries and change over time, for example temperature measurement in Australia, Indonesia, Japan and USA Code ACMMG108 Content description Estimate, measure and compare angles using degrees. Construct angles using a protractor Elaborations • measuring and constructing angles using both 180° and 360° protractors • recognising that angles have arms and a vertex, and that size is the amount of turn required for one arm to coincide with the other Code ACMMG112 Prior Knowledge Resources, Programs and Texts Students have been engaged in whole school programs so theoretically are ready for the material in the identified whole school programs. There are a number of students who do “maths Olympiad” and a number of students who struggle with learning. My aim is to provide diverse learning experiences which will engage all students and ensure there is more scaffolding for some and extension activities for others. Most lessons begin with the basic and become progressively more challenging. Specific challenges can be set for the more capable students as they complete the easier tasks. These tasks can be set discreetly for particular students instead of confusing the rest of the class with too many instructions. Whole School Programs Signpost Mental Maths Books Signpost Maths Books and teacher books Elementary Maths Mastery : Mental Maths program Angle Dance Video http://thekidshouldseethis.com/post/49936880302 Maths Greek Geometry video http://thekidshouldseethis.com/post/79866139523 3D objects
- 3. Protractors Painting Country – Forms of Mapping – Cross Curriculum Priorities http://aso.gov.au/titles/documentaries/painting-‐country/clip3/ Online Kids Maths Dictionary and ipad app http://www.amathsdictionaryforkids.com/dictionary.html Symmetry Video https://www.youtube.com/watch?v=6qNB2LsgC8Y (See more resources below in resource sections) Links to other learning areas Geometry exercises will link with art making curriculum. Coordinates will be explored through maths, mapping and choreography of puppet theatre. Measurement and translations will be explored through shadow puppet project. Unit Overview Context/Intent Deep Knowledge and Understandings Skills Processes/Values/Attitudes This Unit Plan describes the school requirements and integrates these with history, art and science where possible. Using coordinates to map local places of historical significance can aid both numeracy, history and geography learning. Understanding and creating maps are important skills for general numeracy and literacy. The specialist science teacher is working on light this term. Maths activities will include translating and enlarging figures to appropriate sizes using grid paper and using coordinates to measure and choreograph puppet performance. Translations, reflections and rotations will be explored through the students own art and design work as well as the art of Escher. Literacy learning will be integrated with all of these activities through journal writing, word walls, mind maps, word sleuths and cross words. Maths skills are useful in a wide variety of human endeavours; including science, art and history. Different people solve problems in different ways. Working together can achieve the most positive results. Maths can be used to enhance learning and understanding in all the other key learning areas. People may have different ways of solving the same problem. Working as a team can solve problems faster. Maths can be creative and fun and help us solve problems in science. Asking questions and coming up with ways to test and try out our ideas is a good way of approaching maths problems as well as science and history problems. Program Activities There are three whole school Maths programs that must be completed on a daily basis. These include Signpost Maths, Signpost Mental Maths and Elementary Maths Mastery: Mental Maths. Students at the more competent level of maths also attend extension maths : “Maths Olympiad” once a week. The mental maths sessions are conducted from Elementary Maths Mastery : Mental Maths and Signpost Maths :Mental Maths as well as using individual laminated white boards to practice with chanting tables and basic facts. Overall Assessment Systems Formative and Summative There is a maths test every Friday which covers material from mental maths as well as assessing material covered in the signpost maths. Work sheets, maths books, art works and literacy work associated with the language of each maths topic will also be assessed and noted. Feedback given as soon as possible after work to the student. And outcomes used to plan next phase of learning. The first activity in any concept will be reviewed promptly as diagnostic assessment in order to choose the next activity and prepare the following lessons with the appropriate differentiated activities. Differentiation All lessons will include a number of different activities. Whole class activities will begin the lesson and then different activities beginning with the easiest and building to the more complex. Once students have finished an activity and it has been checked for
- 4. accuracy another activity which is slightly more challenging will be given. In this way everyone covers the same material and some are offered further extension than others. Some students second activity may be easier rather than harder depending on how easily they completed the first task. Students will where practicable be given choices as to the order in which they complete thins and the difficulty level in order to increase engagement. Concepts Space and Geometry reflection, rotation, translations • Learning Activities • Signpost Maths Activities expanded • Watch Escher Videos • Use physical actions to demonstrate: Translation – Slide Reflection – two people face each other – two hands held up. Rotation – a turn around with one arm in the air. • Show Arrow example on the board. • Hand out photocopies • Students cut out images • Trace around and create diagrams of reflection, rotation and translations. • Complete worksheet • Questions • What do you see when you look in the mirror? • Is it the same as what you actually look like/ what you see in a photograph? • How else do we use the word rotation? • What else rotates? Group Structure Whole Class Individual Resources Escher Videos Photocopies of Escher designs Maths books Pencils, scissors, glue Assessment Note : There will be a maths test every Friday in which work from both the EMMS mental maths and Signposts maths work and all work included in this program will be assessed. Assessment will also take place constantly during lessons to check for understanding before moving to the next phase. …………………………………………………………………….. Worksheet marked and clued into maths book. Diagram drawn in Maths book marked. Feed back given as close as possible to completion. Ongoing questioning in the classroom using named paddle pop sticks so that all children remain accountable for their learning. Space and Geometry 3D shapes and Nets • Show students weetbix box. • Ask students if they know what a net is. • Ask them what the shape of the box would be if you pulled it apart. • Instruct them to individually draw their answers on the white boards – allow them to chat and share with a partner. • Get them to share their diagram answers. • …………….. • Questions • “Is there only one answer?” • “Which answers do you think would make a box. • ……………… • Pull apart the weetbix box and show them the net shape. • Hand out an assortment of templates of 3D nets on coloured cardboard • Differentiation If students finish offer a challenge to those who finish. How could they use a 3D shape (from the maths kits) to create a net? IE trace around the item – moving the shape around to create a net. Weetbix box Scissors Assorted photocopied nets on coloured cardboard Scissors 3D shapes plane coloured cardboard glue sticky tape Made shapes – checklist of completed objects. Anecdotal notes on how children complete tasks.
- 5. Space and Geometry Angles and Protractors The language of Geometry – Angle Glossary • Show Video Angle Dance: https://www.youtube.com/watch?v=tqIki33mTgs&feature=kp • Ask Students to note down all the words they hear that are related to Geometry. • Ask students individually to come up to board and write words up on board • Once all the words are up-‐ if there are any left out fill them in. • Ask children to rule up a page in their maths book and write down words to create a glossary. • Use a literacy lesson to fill in the definitions of the words. • Introduce protractors. • Name the important elements of a protractor. • Base line, centre point, • Define steps to measuring an angle using interactive white board. Use Prezi (Like powerpoint) to do this as a warm up • Students write steps in their maths book. • Practice measuring angles with prepared angle sheets. • Practice measuring angles by creating angles for each other in pairs using a protractor. • Use a clock to describe angles. • Use compasses to explore degrees and directions. • Set a compass quest with degrees and directions. • Origami folding paper and identifying angles. Whole Class Individual Pairs Video Angle Dance: https://www.youtube.com/watch?v=tqIki33mT gs&feature=kp Maths books White Boards. Pencils Protractor Sets Compasses Clock Sheet with angles to measure. Steps : Measure angles steps Step one – Line up centre point AMSI site information http://www.amsi.org.au/ESA_middle_years/Ye ar5/Year5_md/Year5_1a.html#stucon-‐2 Origami angles http://www.arvindguptatoys.com/arvindgupta/ sastrymath.pdf Folding angles and making an equilateral triangle http://nrich.maths.org/5372 Angle Game Online http://nrich.maths.org/1235 Good way of explaining online http://www.amblesideprimary.com/ambleweb /mentalmaths/angleshapes.html Glossary created in maths book. Angle Worksheets. Angle section in Friday maths test. Coordinates • Introduce coordinate grid using 3D object chart. Signpost maths. Work as a whole class with exercise on the electronic board • Use coordinate grid for shadow puppet choreography – students work in teams to create a short shadow puppet play • A version of Battleship on the Electronic white board with coordinates • Practice with the signpost maths worksheet • Use coordinates for mapping exercise in History and with white board / laminated map • Use tarp coordinates to explicitly teach how to map shadow puppet choreography • Incorporate into the Friday test Whole Class Individual Groups Signpost activities for white board White board /laminated map of Australia Tarp with coordinates marked on with masking tape (see Science Program Resources) Indigenous Art /Mapping country/Cross cultural perspectives on knowledge of space http://aso.gov.au/titles/documentaries/paintin g-‐country/clip3/ Coordinates added to weekly Friday Maths test Signpost Maths activity sheets glued in to books Addition and Subtraction of money/decimals Simple Budgets Understandings ( Taken from https://www.moneysmart.gov. • Elicit current knowledge by asking students questions about budgets and money. • What words do we need to understand in order to communicate about money and learn about how to manage budgets? Begin to create a word wall and budget glossary: budget, addition, subtraction, multiply, divided by • Talk about something they might want but don’t have the money for. Ask them to think of something and to give an estimate of how much it might cost. • Ask students to consider whether they get pocket money or not – or birthday/ Christmas money. Whole Class Pairs Individual Electronic White Board active inspire. Pictures of desirable objects-‐ Loom band kits Bicycles Skateboards Problem sheets glued into Maths books and marked.
- 6. au/media/391824/5_3_mst_pr imary_maths5_unit.pdf) Budgets are a way to plan and manage spending Expenditure can be classified as essential or optional, and choices made have a financial impact Estimation and rounding can be used to check the reasonableness of answers Accurate calculations are important when planning and amending a budget • Do an example on the electronic white board of a new skateboard • Frame it as a word problem (see literacy program) How long will it take to save up for a particular item • Do one together. Then get them to do one themselves – check with partner -‐ and then write one for each other. Perimeter and Area Being able to calculate perimeter and area have many practical applications for students and their families. • Use the front student desk to demonstrate the idea of perimeter. Get a volunteer to come up and measure the sides. • Remind them of angles as the diagram and number sentence is written on the board. • Talk about different measurements. Why do we need different measurements-‐ could we measure an oval in centremetres? When is it useful to be able to work out perimeter and area? Explicitly teach language necessary for actvities • Use a selection of worksheets and problems. Start with the easy ones get students to put up their hand when they have finished. Allow them to choose the next tasks level of difficulty as long as the first task shows understanding. Whole Class, Individual Formative assessment of each activity before moving on to the next one. Add maths terms to the weekly spelling words. Activities posted in to Maths books. Perimeter and area activities included in weekly test.