With many thanks to Don Steward for inspiration on Saturday 16 March 2019 at ATM London, IoE, UCL, London. Cross links to ratio, sequences and gradient. Square dotty paper is set as back ground for slides; so you can build your own or print and ask your pupils to create their own. I’m certain you have access to more than enough questions on adding fractions. This merely provides pupils with a different means to answer them; visually/geometrically.

Takes a bit of effort to imagine when simultaneous equations may come in handy. Partly inspired by the new fashion of publishing the tax returns of persons in "positions in influence" (with a view to identifying enemy agents: with "foreign" income sources), these questions will hopefully awaken pupils' interest in simultaneous equations and how/when/why they might (just might!) become useful in "real life"... [now with, step-by-step, solutions]

Folllowing the timeline for the Spring term I have provided on this website, this breaks each objective into four steps: consolidating; developing; securing; mastering. Each objective is taken directly from the "new" UK National Curriculum for Key Stage 3 [where an objective is given for each bullet point (from page 5): https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/239058/SECONDARY_national_curriculum_-_Mathematics.pdf ] . Consolidating - is generally pitched for the weakest pupils: who are revisiting key stage 2 material that may have been first taught before year 6. Mastering - will generally pitched to stretch at or beyond expectations for key stage 3. Problem solving exercises will need to be set within and around material each week. Three hours per week has proven enough to deliver the material to the very most committed and able pupils (when accompanied with sufficient homework); however, five hours per week (and some looping back to earlier objectives if/when later objectives prove inaccessible) may suit pupils who would benefit from such an approach.

From days at Primary; animated & adjusted to work for -ve powers of 10 as well as +ve. Kibel [pp34-40 Miles T.R., Miles E. (2004)Dyslexia é mathematics] has +ve story to tell about Dienes blocks. Worth remembering that their use can be scaled up é down. Hence BETTER version will be made by someone with time é 3D ICT kit. It’ll ZOOM in é out to enable pupils to view (é correctly name - for US é Brit purposes!) numbers as big as a Googol é as small as... It'll use techniques like those in these slides; but combined with ZOOMING as seen in this: http://www.youtube.com/watch?v=I-Tym_6YLUI

Place Bearing Point on ground and calibrate to magnetic north using compass/GPS. Pupil stands on Bearing Point with trundle wheel. Giant scale map-making/diagram-drawing begins. Corners/Vertices can be marked using cones. Bearing point can be lifted and replaced with cone at each vertex to aid taking further bearings. £4.50 IKEA Mat: http://www.ikea.com/gb/en/catalog/products/40239429/ Chalk pen: http://www.amazon.co.uk/s/ref=nb_sb_noss?url=search-alias%3Daps&field-keywords=pens+chalkérh=i%3Aaps%2Ck%3Apens+chalk [might work with Tippex pen]