The KING S Medium Term Plan [Mathematics Department] Y8 Learning Cycle 5 Programme. Module

Transcription

1 The KING S Medium Term Plan [Mathematics Department] Y8 Learning Cycle 5 Programme Module Challenging question Subject Challenging Question Lines of Enquiry Number (ratio) and Geometry (unit conversions and transformations). How has the world being affected by changes in shapes? How has the world being affected by changes in shapes? In the present learning cycle, students will evaluate how to apply their knowledge of ratio to convert between units and currency. On top of that, pupils will learn hoe to transform a shape using different techniques. Week 1: How does money affect now our daily life? Pupils will recall the different currencies in the world as well as how to convert between them. Conversion graphs will be studies too, and their accuracy will be questioned. Weeks 2-3: What benefits have arisen due to the development of transformations in our life? Students will be taught about transformations and how they can affect shapes. Week 4: How important is to know algebra in real life? Students will recall their knowledge of algebra an will apply it to decipher codes in real life. Pupils will be able to create their own codes too. Week 5: Why do we need to know how to calculate area in real life? This week, pupils will apply their knowledge shapes to calculate the area of simple and compound shapes as well as drawing constructions accurately. Finally pupils will calculate the area of the constructions they have drawn. Week 6-7: Assessment followed by gap teaching from assessment analysis.

2 LC4 Overview * Topics highlighted in pink will be only delivered to Archimedes and Euclid groups, prior understanding of topics in black.

3 Progress Objectives Underlined the extension work for certain GP can be seen. By the end of Learning Cycle 3 in Mathematics SWBAT: A) Read conversion graphs in order to convert currencies and units of measurement. B) Use ratio to calculate conversions. C) Understand currency and its changes over time. D) Understand what a transformation is. E) Analyse how to reflect a shape using a given mirror line. F) Draw a mirror line to reflect a shape. G) Understand what a rotation is. H) Analyse how to rotate a shape knowing the centre of rotation, clockwise or anticlockwise and how many degrees. I) Given a rotation, calculate how the shape has been rotated. J) Calculate enlargements using positive scale factors. K) Calculate enlargements using negative scale factors. L) Given an enlargement, calculate the scale factor the shape has been enlarged by.

4 M) Translate a shape given a vector. N) Recall BIDMAS and apply it to algebraic simplification. O) Expand single and double brackets. P) Understand how to factorise linear expressions. Q) Recall how to solve equations and inequalities. R) Understand how to calculate probability of single events and from sample spaces. S) Apply their knowledge of percentages to real life. Assessment in week 6 will be against the above objectives. Gap teaching from analysis of assessments in week 7 after the half term. Week 1 4 hours of lessons plus 1 hour of homework given out on Tuesday each Additional intervention on Tuesday evening each REACH (Review & Recap, Evaluate & Endeavour, Attainment & Achievement, Challenge yourself, Hone your skills) Improvement time to be allocated in one lesson every week from week 2 so pupil s can learn from the mistakes they have made the previous Individual feedback will be provided as well as personalised improvement questions depending on what each pupil has done wrong. Hypothesis 1 Graphs can be used to convert between metric and imperial units. Recall how the names of metric and imperial units. Analyse how to convert between different units using graphs. Apply knowledge of ratio to answer questions that cannot be read from the graphs. If you were a broker and you had been paid to invest other people s money, how would the different currencies affect your work? Today s work will be peer assessed in lesson.

5 Do Now complete the table with the units that you remember. Work done on conversion graphs worksheets. GCSE questions will be practice in the lesson. REACH: How would you calculate a value which is not readable from the graph? Assessment of lesson hypothesis Discuss and explain using examples Hypothesis 2 Conversion graphs are better than conversion rates. Recall how to read values from a graph. Understand how to calculate equivalent ratios. Apply your knowledge of equivalent ratios to find conversions between currencies. Knowledge check using a quiz, which will be peer assessed during the lesson. Do Now GCSE question: Can you find the conversions using the graph? Activity to calculate conversions between currencies using ratio. Higher level activity to find currencies from a table and doing the appropriate conversions. Assessment of lesson hypothesis Find an example to respond to the hypothesis Hypothesis 3 - We do not use ratio when converting between metric and imperial units. Recall metric and imperial units. Analyse what the conversion rates between metric units are. Evaluate how to convert between metric and imperial units. Pupils to mark their own work in green during lesson against the lesson s objectives. Books will be marked so pupils can act on the feedback written on their books following the colour dot system.

6 Do Now Classify which units are metric and which ones are imperial. How do you know it? Activity converting between metric units. VIF s written to show the main conversion rates between metric units and between metric and imperial. Activity using ratio to convert between metric and imperial units. Assessment of lesson hypothesis use classwork to provide evidence in books Home learning: Given on Tuesday each week and due in the following Tuesday. REACH: More challenging activities will be given to those pupils making extraordinary progress in lessons. SUPPORT: Consolidation activities will be given to those pupils struggling with the topic. Extra support will be offered after school. Week 2 4 hours of lessons plus 1 hour of homework given out on Tuesday each Additional intervention on Tuesday evening each REACH (Review & Recap, Evaluate & Endeavour, Attainment & Achievement, Challenge yourself, Hone your skills) Improvement time to be allocated in one lesson every week from week 2 so pupil s can learn from the mistakes they have made the previous Individual feedback will be provided as well as personalised improvement questions depending on what each pupil has done wrong. Cognitive acceleration lesson Pupils will also take part today in a CA task to develop their deep thinking skills. The symmetry challenge This CA task deepens pupils ability to create, identify and understand symmetry, reflection and rotational symmetry. They each have a number of square grids all the same size. They have to shade in squares to find as many symmetrical designs as possible. This then develops on to creating designs with a given order of rotational symmetry and even drawing designs with no lines of symmetry but with rotational symmetry of order 2. Pupils then discover how larger designs can be made by reflecting some of their designs on a set of axes using the x and y axis and the lines y=x and y=-x (extension task for higher GP).

7 Hypothesis 1-2 We need a real mirror to reflect shapes. Recall what a reflection is. Understand how to plot straight lines as mirror lines. Analyse how to reflect a shape given a mirror line. If you were an artist, why would reflections and rotations be important for you? Pupils to mark their own work in green during lesson against the lesson s objectives. Do Now Discuss what you consider a reflection is. Activity plotting straight lines such as x=3, y=-5. REACH: Plot lines with equations in the form y=mx+c Reflect shapes using a mirror line. GCSE questions to practice. REACH: How has the shape been reflected? Assessment of hypothesis Write the answer to the hypothesis in books after discussion.

8 Hypothesis 2--3 There is only one way of rotating a shape Recall rotational symmetry in shapes. Understand the rules to follow when rotating shapes. Analyse how a shape has been rotated. Knowledge check using a quiz, which will be peer assessed during the lesson. Books will be marked so pupils can act on the feedback written on their books following the colour dot system. Do Now Calculate the rotational symmetry of the given shapes. Task to rotate a variety of shapes on a grid give and write full instructions for a variety of rotations Rotate shapes from a certain centre. GCSE questions to practice. REACH: How have the following shapes been rotated? Centre, angle and direction needed. Assessment of hypothesis Write the answer to the hypothesis in books after discussion. Home learning: Given on Tuesday each week and due in the following Tuesday. REACH: More challenging activities will be given to those pupils making extraordinary progress in lessons. SUPPORT: Consolidation activities will be given to those pupils struggling with the topic. Extra support will be offered after school. Week 3 4 hours of lessons plus 1 hour of homework given out on REACH (Review & Recap, Evaluate & Endeavour, Attainment & Achievement, Challenge yourself, Hone your skills) Improvement time to be allocated in one lesson every week from week 2 so pupil s can learn from the mistakes they have made the previous Individual feedback will be provided as well as personalised improvement questions depending on what each pupil has done wrong.

9 Tuesday each Additional intervention on Tuesday evening each Hypothesis 1-2: Enlargements always increases the size of a shape. Understand what an enlargement is. Understand how to enlarge a shape using integer scale factors Hippocrates, Herodotus and Aristotle. Analyse how to enlarge a shape using scale factors such as 0.5 Archimedes and Euclid Evaluate how to use and find the centre of the enlargement and the scale factor. REACH: evaluate what happens when using negative scale factors Today s work will be peer assessed in lesson. Do Now enlarge simple shapes using different scale factors. Enlargement activity with a variety of shapes, integer and fractional scale factors Activity to use ray lines and find the centre of enlargement, then enlarge shapes from a centre of enlargement Pupils who are capable of further challenge will enlarge shapes using negative scale factors GCSE questions to find the centre of enlargement and the scale factor. Assessment of hypothesis Write the answer to the hypothesis in books after discussion using knowledge of fractional scale factors Hypothesis 2-3: Translation is only used for speaking foreign languages. Understand what a mathematical translation is. Analyse how to translate shapes on a grid or axes. Evaluate how to find the vector of a given translation. If you were a photographer or a computer filmmaker, why would you be interested in transformations? Would you se enlargements in your work? Knowledge check using a quiz, which will be peer assessed during the lesson. Books will be marked so pupils can act on the feedback written on their books following the colour dot system.

10 Do Now Review of all transformations done so far Discussion on the rules for translating shapes e.g. you cannot translate diagonally Activity to practice using vectors when doing translations GCSE activities doing translations and finding the vector given a translation. REACH: pupils will do questions where more than 1 transformation is used. Mid term assessment will de done at the end of week 3. Home learning: Given on Tuesday each week and due in the following Tuesday. REACH: More challenging activities will be given to those pupils making extraordinary progress in lessons. Week 4 4 hours of lessons plus 1 hour of homework given out on Tuesday each Additional intervention on Tuesday evening each SUPPORT: Consolidation activities will be given to those pupils struggling with the topic. Extra support will be offered after school. REACH (Review & Recap, Evaluate & Endeavour, Attainment & Achievement, Challenge yourself, Hone your skills) Improvement time to be allocated in one lesson every week from week 2 so pupil s can learn from the mistakes they have made the previous Individual feedback will be provided as well as personalised improvement questions depending on what each pupil has done wrong. First half of the REACH lesson: This week, improvements will be done based on the result from the mid term assessment done on week 3. Second half of the lesson: Activity linked to Science as described in the Numeracy plan below:

11 Hypothesis 1 We do not used BIDMAS when expanding brackets and simplifying expressions. Recall how to use BIDMAS. Herodotus, Hippocrates and Aristotle. Understand how to expand single brackets. Archimedes and Euclid Understand how to expand double brackets. Analyse how simplify an algebraic expression after expanding brackets. Pupils to mark their own work in green during lesson against the lesson s objectives.

12 Do Now Do you remember what BIDMAS mean? Solve the questions using BIDMAS. Activities expanding brackets depending on GP. Activities recalling how to simplify algebraic expressions. GCSE questions to master brackets, BIDMAS and simplification through problem solving activities. Assessment of lesson hypothesis discuss and explain using examples Hypothesis 2 The code says Maths is fun. Herodotus, Hippocrates and Aristotle. Recall how to substitute positive numbers in simple expressions. Analyse how to substitute negative numbers in algebraic expressions. Evaluate how to substitute values in more difficult expressions. Euclid and Archimedes. Recall how to substitute positive numbers in expressions including brackets and powers. Analyse how to substitute negative numbers in algebraic expressions. Evaluate how to factorise linear expressions. Why do you think a video games designer would need to know about substitution? Knowledge check using a quiz, which will be peer assessed during the lesson. Do Now activity substituting positive numbers in expressions. As before, but using negative numbers. REACH: Activity factorising linear expressions. GCSE questions to practice exam technique. Activity cracking real life codes. Assessment of hypothesis Answer the hypothesis using the sentence starters.

13 Hypothesis 3 The answer to 3x + 5 = 14 is 19/3. Herodotus, Hippocrates and Aristotle Recall the rules of inverses to solve equations. Understand how to solve one and two step equations. Analyse how to solve equations with the unknown on both sides. Euclid and Archimedes Understand how to solve one and two step equations. Analyse how to solve equations with the unknown on both sides. Apply your knowledge of equations to solve inequalities. Today s work will be peer assessed in lesson. Books will be marked so pupils can act on the feedback written on their books following the colour dot system. Do Now Activity solving one and two step equations. GCSE questions solving longer equations. Real life activities where pupils will have to write an equation and solve it. GCSE problem solving questions about equations and inequalities. REACH: Activities solving inequalities from GCSE questions. Assessment of lesson hypothesis discuss and explain using examples Home learning: Given on Tuesday each week and due in the following Tuesday. REACH: More challenging activities will be given to those pupils making extraordinary progress in lessons. SUPPORT: Consolidation activities will be given to those pupils struggling with the topic. Extra support will be offered after school. From the mid term assessments extra intervention will be planned accordingly. Week 5. 4 hours of lessons plus REACH (Review & Recap, Evaluate & Endeavour, Attainment & Achievement, Challenge yourself, Hone your skills) Improvement time to be allocated in one lesson every week from week 2 so pupil s can learn from the mistakes they have made the previous Individual feedback will be provided as well as personalised improvement questions depending on what each pupil has done wrong.

14 1 hour of homework given out on Tuesday each Additional intervention on Tuesday evening each Hypothesis 1 To calculate probability we need to grow trees. Recall how to calculate probability of mutually exclusive events. Understand how to calculate the probability of two events using sample spaces. Herodotus, Hippocrates and Aristotle Apply your knowledge to use sample spaces applied to real life situations. Euclid and Archimedes Analyse how to calculate probability using probability trees. Does probability affect sports? Would it affect you if you were a footballer? Pupils to mark their own work in green during lesson against the lesson s objectives. Do Now Calculating probabilities of single events. Activity to completing sample spaces and answering questions about probability, REACH: Activity to apply probability in real life. Activity completing GCSE questions about probability. Tree diagrams drawn and probabilities calculated. Assessment of lesson hypothesis discuss and explain using examples Hypothesis 2 To calculate 10% we divide by 100. Recall how to calculate simple percentages of amounts. Understand how to calculate more difficult percentages such as 36%, 72%... Analyse how to solve real life problems involving discounts and VAT. Knowledge check using a quiz, which will be peer assessed during the lesson. Do Now Calculate simple percentages. Activity to find more difficult percentages. Real life applications using VAT and discounts.

15 REACH: Calculate 14.5%, 36.2%... Real life application: have these prices been reduced correctly? GCSE questions to practice exam technique. Hypothesis 3 To draw a triangle accurately we only need a ruler. Recall how to calculate the area of compound shapes. Understand how to bisect and angle and a line accurately. Analyse how to draw triangles SSS, SAS, ASA. Books will be marked so pupils can act on the feedback written on their books following the colour dot system. Today s work will be peer assessed in lesson. Do Now Calculating areas of triangles and rectangles. GCSE questions to find the compound area. Activity bisecting angles and lines. Activity drawing triangles accurately and calculating their area after. GCSE and real life questions to practice. Home learning: Given on Tuesday each week and due in the following Tuesday. REACH: More challenging activities will be given to those pupils making extraordinary progress in lessons. SUPPORT: Consolidation activities will be given to those pupils struggling with the topic. Extra support will be offered after school. From the mid term assessments extra intervention will be planned accordingly. Week 6 Revision using levelled booklets followed by assessments. Gap Analysis Reinforcement

16 Week 7 Gap Reinforcemen t As seen in the lesson activities each week, gap teaching will not just be at the end of the Learning Cycle after exam analysis has taken place. Gap teaching is an integral part to each unit of work and will consist of summary sheets, minitests and tasks where gaps can be filled and REACH activities can be delivered. Extended Learning (This is not part of the timed schedule but is seen as additional support) Extended learning will in a variety of forms. During home learning pupils may be asked to use the following sites where they complete quick quizzes, CIMT tasks, GCSE style questions and more open ended tasks. 1) Levelled quizzes 2) Lots of maths online help and activities as well as mini tests 3) This link is useful for additional revision and practice on all areas of maths. For semester 4 pupils should click on the Geometry areas for practice questions. 4) this link will provide good revision and extended learning opportunities on the semester 5 project 5) in depth links to maths and sport Extended learning will also be in lesson plans where links are made to the history theme of historical changes. During Tuesday and Thursday enrichment pupils will have the chance to strengthen skills and develop them further. We will look at UKMT challenges, levelled tasks, GCSE questions and build a Kings Maths Team ready to enter competitions in year 8.

17