What is the changing nature of conflict and co-operation in our world?

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1 The KING S Medium Term Plan [Mathematics Department] Y8 Learning Cycle 4 Programme Module Challenging question Subject Challenging Question Lines of Enquiry Number (fractions, percentages, decimals) and Data (introduction to probability and statistics). What is the changing nature of conflict and co-operation in our world? What are the conflicts of a mathematician when co-operating between x and y values? In the present learning cycle, students will evaluate how to apply their knowledge to algebra (LC2) to solve one and two-step equations, inequalities and calculate the nth term of a sequence. Besides, pupils will learn how to plot and analyse straight-line graphs, studying in depth some of their properties such as the gradient. Week 1: How do we calculate the rule to continue linear sequences? Pupils will recall how to continue sequences and how to calculate the general rule to calculate any term in the sequence using their knowledge of algebra. Week 2: What do we mean by the balancing effect? Students will be taught how to solve one and two-step equations using the balancing method as well as different algebraic techniques. Week 3: What is the role of inequalities? First, pupils will have to understand the meaning of the inequality symbols in order to solve one and two-step inequalities. Then, applying what they learned in Week 2, inequalities will be solved and students will be able to represent their answers graphically. Week 4: How important is the relationship between x and y variables when solving problems? Students will recall how to plot straight line graphs and will analyse how to calculate any point in the line. Week 5: Why do we need such algebraic manipulation and graphical representation? This week, pupils will apply their knowledge of graphs to calculate gradients and mid points of segments. Week 6-7: Assessment followed by gap teaching from assessment analysis.

2 LC4 Overview

3 Progress Objectives Underlined the extension work for certain GP can be seen. By the end of Learning Cycle 3 in Mathematics SWBAT: A) Continue sequences and find missing terms. B) Calculate the general rule to continue a sequence. C) Apply their knowledge of sequences to patterns. D) Solve linear one and two-step equations with the unknown in one side. E) As the previous objective but with the unknown on both sides. F) As the two previous objectives but with fractions.

4 G) Understand the meaning on the inequality symbols. H) Solve one and two-step inequalities using the balancing method. I) As the previous objective but showing the answer graphically. J) As the previous two objectives but including fractions and unknowns in both sides. K) Recognise the equation of a straight-line graph. L) Plot straight line graphs by calculating a few coordinates. M) Understand the meaning of the gradient. N) Calculate the gradient of a straight line graph as well as identifying equations of parallel lines. O) Calculate the mid point of a segment. 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 Hypothesis 1 Everything has a pattern Recall types of numbers through number series. Understand how special types of number are formed. Apply knowledge of special numbers to create patterns Why would a traffic lights programmer need to know about sequences? Today s work will be peer assessed in lesson. Do Now critical thinking task Stand up sequence game Activity to complete and draw diagrams on different sequences

5 on Tuesday evening each Research Activity Where are sequences seen in real life? REACH Fibonacci sequence Assessment of lesson hypothesis Discuss and explain using examples Hypothesis 2 The difference matters Evaluate term-to-term rules of linear sequences Evaluate the Nth term for linear sequences Apply and use nth term to generate sequences from nth term. Knowledge check using a quiz, which will be peer assessed during the lesson. Do Now critical thinking task Activity to state the term to term rule from linear sequences Activity to match the nth to a linear sequence Generate a sequence from an nth term questions REACH - Create questions for peers to answer (Generate sequences and find nth term) Assessment of lesson hypothesis Find an example to respond to the hypothesis Hypothesis 3 - Nth term only works for linear sequences Understand how to use the nth term to find any term in a linear sequence Apply knowledge of BIDMAS to find any term in a sequence (3n 2 + 2) Evaluate Pascal s Triangle and how it works Pupils to mark their own work in green during lesson against the lesson s objectives. Do Now critical thinking task Activity recap of finding the nth term and generating a sequence

6 Questions on how to find the 50 th and 100 th term in a linear sequence Research task What is Pascal s Triangle and where is it used? Assessment of lesson hypothesis use classwork to provide evidence Hypothesis 4 Algebra can be used in numerical series Apply your knowledge of sequences and BIDMAS to linear sequences Analyse the work of Jakow Trachtenburg Create informative displays on special number sequences and how they are formed. Books will be marked so pupils can act on the feedback written on their books following the colour dot system. Do Now critical thinking task Quick BIDMAS recap questions Activity research task What influence did Mr. Trachtenburg have in Mathematics? Produce an informative display on what you have learned about sequences Assessment of lesson hypothesis discuss and write comments 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 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.

7 hour of homework given out on Tuesday each Additional intervention on Tuesday evening each Hypothesis 1 Inverses are useful for all equations. Recall how to solve 1 step equations using inverses. Understand how to solve 2 step equations with an unknown on just one side. Create your own 2 step equations for real life situations and find the solution. Today s work will be peer assessed in lesson. Do Now Critical thinking task. Activity to find missing values using the inverse function. Balancing discussion and activity worksheet. GCSE questions to write down the equation described. Assessment of hypothesis write an evaluation of the hypothesis using examples of today s work Hypothesis 2 Cont. of hypothesis 1. Recall how to solve 1 and 2 step equations. Understand how to solve equations with the unknown on both sides. Apply your knowledge to solve equations including brackets and fractions. How would you use an equation to find the missing height on a triangle knowing its area? Pupils to mark their own work in green during lesson against the lesson s objectives. Do Now Solving easy one and two step equations. Activity: Practice questions to solve linear equations with the unknown in both sides. REACH: Solve equations with brackets and fractions. GCSE questions to write and solve worded problems.

8 Assessment of hypothesis write an evaluation of the hypothesis using examples of today s work Hypothesis 3 Equations help calculate missing information in any mathematical problem. Recall how to solve one and two step equations. Understand how to write a worded problem as an equation. Create your own problem for your partner to solve it. 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 critical thinking task Activity solving real life problems using equations. Pupils will create a question that will be later solved by their peers. REACH Expressing a worded problem as an equation using two variables. Assessment of hypothesis explain the answer with an example to the hypothesis. 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 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 given out on Tuesday each Additional intervention on Tuesday evening each Hypothesis 1 - The alligator always eats the biggest number Recall inequality symbols and use in simple cases Understand how to solve simple 1 and 2 step inequalities Apply knowledge of substitution to check solutions How would you find the area in a garden where all the conditions are good for harvesting? Pupils to mark their own work in green during lesson against the lesson s objectives. Do Now Critical thinking task Substitution starter to link to inequalities. Balancing activity worksheets solving 1 and 2 step inequalities. REACH: What happens if you have to divide or multiply by a negative number? Assessment of hypothesis Answer hypothesis in books Hypothesis Number lines are useful when solving inequalities Recall how to calculate the values inequalities can represent Understand how to represent 1 step inequality solutions on a number line Apply knowledge to represent 2 step inequalities on a number line Knowledge check using a quiz, which will be peer assessed during the lesson. Do Now What ranges of values are represented on the number lines? Match up activity to link inequalities to number lines. Activities solving one and two step inequalities representing the answers on a number line. Assessment of hypothesis Discuss and answer the hypothesis in books. Hypothesis 3 X always has a unique value.

10 Recall how to represent both 1 and 2 step inequalities on a number line Analyse how to write inequalities using a number line Create number lines to demonstrate a range of inequalities with 1 and 2 variables Books will be marked so pupils can act on the feedback written on their books following the colour dot system. Do Now critical thinking task Activity solving one and two step inequalities using a number line. Create your own inequality given the range of values that are the answer. REACH: Solve inequalities with brackets and fractions. Assessment of hypothesis Use a probability tree to reflect on the hypothesis 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 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 lesson REACH: 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 intervention on Tuesday evening each Hypothesis 1 Lines are just input and output machine Recall how to substitute values in an algebraic expression. Understand that the equation of a straight line is y=mc + c Analyse how to plot a straight line graph given the equation. Today s work will be peer assessed in lesson. Do Now substitute positive and negative values in the expressions given. Activity to plot coordinates on a set of axis.

12 Activity to complete tables of values given the equation of the graphs. Activity plotting the graphs of several straight lines. Assessment of lesson hypothesis discuss and explain using examples Hypothesis 2 The gradient indicates the point where the line crosses the X axis. Recall what the equation of a straight line is. Analyse what happens when the coefficient of X changes in the equation gradient. Evaluate how to calculate the gradient of a straight line graph. Understand what the Y-intercept is. Why do you think a F1 driver would need to analyse graphs? Knowledge check using a quiz, which will be peer assessed during the lesson. Do Now match the graphs with their equation. Given a set of graphs and equations, what happens when the coefficient of X changes? Different questions to calculate the gradient and Y intercept of several graphs. Assessment of hypothesis Use a probability tree to reflect on the hypothesis Hypothesis 3 Parallel lines have the same Y intercept. Recall the meaning of gradient and Y intercept. Understand the relationship between parallelism and gradient. Analyse how to plot vertical and horizontal straight line graphs. Books will be marked so pupils can act on the feedback written on their books following the colour dot system. Do Now What are the equations of the graphs? Given a few parallel lines, write down their equation. What do you notice?

13 Activity to plot several vertical and horizontal lines. Given a few horizontal and vertical lines, what would you say are their equations? 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 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 We must use a ruler to calculate the mid point of a segment. Recall how to plot in all 4 quadrants Understand how to calculate the mid-point of a line Apply knowledge of coordinates to plot vertical and horizontal lines. Why would a runner want to calculate the midpoint of the itinerary? Pupils to mark their own work in green during lesson against the lesson s objectives. Do Now Plotting coordinates and segments. Activity to calculate the mid point of several segments with different gradients. REACH: Reverse question to calculate one of the ends of the segment knowing the mid point. Assessment of lesson hypothesis discuss and explain using examples

14 Hypothesis 2 Inequalities can be shown on a graph Recall how to plot inequalities on a graph Analyse the inequalities shown on a variety of graphs Evaluate the inequalities and match them up to the correct graph Knowledge check using a quiz, which will be peer assessed during the lesson. Do Now Plotting straight line graphs using just the equation (no table of values) Activity to find the common region on a garden given different conditions. Worded questions for pupils to identify the inequalities described on the question and find the shaded areas. Hypothesis 3 Coordinates will help you check correct regions Recall how to calculate the inequalities using a graph Apply knowledge draw a graph using the inequalities Create graphs from sets of inequalities and find the correct region showing the solution set Books will be marked so pupils can act on the feedback written on their books following the colour dot system. Do Now Plotting different graphs using the equation only. GCSE questions to find the shaded area. Activity using coordinates to check that the shaded region is correct. 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

16 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.

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