A set of exercises and solutions on the mid-point theorem.
Topic 2 of 20 in the GetMathsFit Junior Geometry series teaches the fundamentals of shape classification by angle and by side. With worked example and diagrams interior and exterior angle facts are explained firstly for triangles before moving on to quadrilaterals in general and parallelograms in particular. Clear & precise diagrams, suggested activities and rudimentary application of arithmetic make this a very amenable introduction as well as revision unit for those students who want to 'see why' to help them remember. The simple calculations but use of 'therefore' make this a a useful step towards deductive logic & proof without formally introducing them. Plenty of exercises and worked out solutions make this ideal for self study or as an in-class resource and because of it's sequential nature a real save the time needed for lesson preparation.
Topic 5 of 20 in the GetMathsFit Junior Geometry series shows students how to construct key geometric diagrams of angles, lines and shapes. Using ruler, compass and set-square the techniques of bisecting angles, drawing perpendicular line bisectors, constructing equal angles and drawing the core angles of 15°, 30°, 45°, 90° & 120 are all illustrated in a sequential manner. Over 60 pages of demonstration, instruction, exercise an model answers provide a wealth of resources for the often neglected skills of construction in geometry. Useful for maths classes but also; art, design technology & science.
Topic 1 of 20 in the GetMathsFit Junior Geometry is what every secondary school maths teacher has at times wanted to have for their students! Without being patronising this allows students to go back to the beginning of what are and how to think of: points, lines and angles? How do they combine and what basic skills will I need to explore further? Over 60 pages of sequential building on understanding with diagram, explanation, worked example, exercise and model answer. Students will either build a solid foundation from scratch or revise what was forgotten or unclear from previous learning. The amount of GCSE students aiming to boost their grades who take a step back to gain a deeper understanding and have said to me; "aah so that's what an angle is, in xxxxx that makes a lot more sense then!". This unblocking of a conundrum for them on a much more advanced part of their mathematical study is always a teacher pleaser!
Topic 10 of 20 in the GetMathsFit Junior Geometry series follows the trusted template of worked exemplar, summary, definitions, visual explanation and precision to bring the knowledge and skills of the first nine topics together. Students are shown how to get stuck in to problems and use their skills to set out proofs and answer questions. Ten pages of model solutions to the exercise questions allow students to feel secure that they will not get lost their exploration!
Bringing together the 1st 10 of 20 Topics in the GetMathsFit Junior Geometry series. This is over 350 pages of worked exemplar, explanation, definition of meaning & concept, exercises and model solutions. The teaching is logical, sequential and thorough without the need to refer elsewhere. From an introduction to points, lines and angles students explore and learn further characteristics, physical skills and reasoning with plane figures, symmetry, parallel lines, Pythagoras, similarity, congruence and finally proofs and problem solving with angles and parallel lines. Use for in-class introductions, group work, plenaries and differentiation as well as a home self study, revision and reference resource.
Topic 3 of 20 in the Junior Geometry series provides an accessible and task rich introduction to shape & symmetry. From identifying solid shapes in common objects, naming common geometric shapes (both regular & irregular) to lots of activities for a student to make shapes before a exploring symmetry (reflective & rotational). A succinct stand alone unit of work that is ideal fro preparatory work, at-home study and in-class resource. As with all GetMathsFit topics there are plenty of worked examples for students to explore before attempting a myriad of exercises and their associated solutions.
Topic 8 of 20 in the Junior Geometry series begins by showing similar shapes and exploring what similarity means in maths so providing students with a definition and framework with which to work. Scale factors of enlargement are then explored by way of exemplar as well as teaching different techniques of drawing enlargements: either by using grid squares or using rays (straight lines) and the importance of the centre of enlargement. Further work demonstrating how to calculate enlargement using scale factors as well as calculating & using ratios leads students to being able to show for themselves that shapes are similar either by being equiangular or tat their sides are in proportion. The 40 pages of illustrations, exemplars, exercises and solutions are structured sequentially making it ideal for the following: differentiation by outcome with self study in-class, small groups exploring different aspects and 'reporting back' as well as for homework setting.
Topic 7 of 20 in the Junior Geometry series begins by showing congruence as an exact fit and then by illustrating this as wholly equal corresponding sides and angles. The conditions for congruence and therefore proving congruence in triangles are shown by way of worked exemplars. SSS, SAS, AAS & RHS are shown in detail before their use in calculating side lengths or chord lengths is demonstrated. At each step students are given an exercise that allows self assessment and fully worked out solutions to explore any gaps in understanding. The 20 pages of illustrations, exemplars, exercises and solutions are structured sequentially making it ideal for the following: differentiation by outcome with self study in-class, small groups exploring different aspects and 'reporting back' as well as for homework setting.
Topic 9 of 20 in the GetMathsFit Junior Geometry series deals with introductions to proofs. This series of lessons is ideal for students to explore how literacy and language are key concepts in maths. The 24 pages show the links and pros and cons of visual reasoning. Inductive & deductive reasoning are explained by way of exemplars before the concept of converses are shown. Exercises with fully worked out solutions using previously taught 'facts' are included for students to fully grasp how proofs and reasoning can lead to further deductions of new 'facts' as well as some of the more obvious pitfalls. Illustrating easy to grasp layouts for writing out a proofs with deductive steps, this is ideal for in-class groupwork, homework and differentiation as well as demonstrating the transferrable skills taught in maths vis-a-vis other school subjects and life in general!
Topic 4 of 20 in the Junior Geometry series provides a comprehensive, thorough & robust introduction to angles and parallel lines. By illustrating the different types of angles i such as: adjacent, complementary, supplementary, vertically opposite in isolation their correct identification is taught as well as the vocabulary needed to explore further into parallel lines. After learning to identify them the properties of the angles formed by parallel lines (corresponding, alternate & co-interior) are clearly and sequentially laid out so that by the end of this topic students have a firm grounding of all the basic angles and can use this firm foundation for later work. As ever there are lots of exercises and fully worked solutions for monitoring progress across the 40 plus pages. An extremely handy summary of the basics for later years and a thorough grounding for the younger students.
Topic 6 of 20 in the Junior Geometry series demonstrates via a series of worked examples the core calculations of Pythagoras Theorem. Moving on to straightforward applications in 2D & 3D this is a self-contained stand alone resource for self-study and practice. The worked exemplars, exercise questions and model solutions make this a very handy plenary, homework or revision resource.