I taught in a range of schools for many years before moving into FE, where I found creative and imaginative approaches just as rewarding with adults. Most of my resources are concerned with giving control to the learner, through a range of methods. Some are great for just giving them experience of examination questions, and the chance to discuss these with other learners. I now concentrate on spreading the range of creations from UK KS1 to KS4, and across the Common Standards.
I taught in a range of schools for many years before moving into FE, where I found creative and imaginative approaches just as rewarding with adults. Most of my resources are concerned with giving control to the learner, through a range of methods. Some are great for just giving them experience of examination questions, and the chance to discuss these with other learners. I now concentrate on spreading the range of creations from UK KS1 to KS4, and across the Common Standards.
All you need for a lesson covering:
derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon, and to derive properties of regular polygons.
A simple example of a triangle sum proof, an investigation into angle sums in both PowerPoint and Word, for classwork or individual work, and plenty of questions for learners to try. Plus a PowerPoint illustrating a variety of tessellation for learners to consider the geometry involved, and hence deduce necessary angle properties.
Common Core Standards
Define trigonometric ratios and solve problems involving right
triangles
6. Understand that by similarity, side ratios in right triangles are
properties of the angles in the triangle, leading to definitions of
trigonometric ratios for acute angles.
Everything you need to deliver a full lesson (or two) to introduce trigonometry through similar triangles and the tangent function. Presentation, activities, worksheets, along with answers, covering all aspects of the Common Core Standards.
Please leave comments, suggestions or corrections.
A PowerPoint presentation to explore the nature of Scientific notation, deriving the methods. Simple worksheet on conversions and another on calculations. Plus card matching activity and pair-matching activity. Everything to teach and explore the subject. Grade 8 – Multiple resources for teaching powers of 10 and scientific notation. Presentation, worksheets and activities.
3. Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.
4. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.
A great lesson for getting the learners to work together and do it for themselves. A matching card activity to get them started on a discussion of inequalities. A poster and a PowerPoint display are provided to remind learners of the symbols. An animated PowerPoint presentation of the solutions allows learners to say what they have before the answer pops up. A worksheet provides for consolidation of learning. And finally a quiz is provided for plenary, or recap at the start of the next lesson.
This whole lesson always goes down very well in my classroom! And no work for teacher, after preparing the materials that is!
Two ways of approaching recognition and identifying properties of 3D shapes at Kindergarten and Grade 1. Either match the shape from the description, or name and identify the properties of the shape. I've split them into the Year 1 and Year 2, and done one with the solids required in both years. Some can be simply given out, and some could be printed on card and cut out for a matching activity. All in Word or PDF. Plus a word search with two versions.
Plus a PowerPoint for class sharing and a PowerPoint showing real examples of each. UK common standards say, for Kindergarten and Grade 1 equivalent:
'Pupils handle and name a wide variety of common (…) 3-D shapes including: (…) cuboids, prisms and cones, and identify the properties of each shape (for example, number of sides, number of faces). Pupils identify, compare and sort shapes on the basis of their properties and use vocabulary precisely, such as sides, edges, vertices and faces.'
Year 4 - Geometry – properties of shapes
Two separate bundles of activities covering (a) triangles and (b) quadrilaterals, all for the new KS2 specifications. Specifically written for Year 4, they can easily be used at any level. In Word for editing or PDF for clear copies. Activities, worksheets and assessments, plus a short presentations on triangles and quadrilaterals. The presentations are included as PowerPoints and PDFs, to ensure at least one will open on any computer.
Statutory requirements
Pupils should be taught to:
• compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes
Notes and guidance (non-statutory)
Pupils continue to classify shapes using geometrical properties, extending to classifying different triangles (for example, isosceles, equilateral, scalene) and quadrilaterals (for example, parallelogram, rhombus, trapezium).
Pupils compare and order angles in preparation for using a protractor and compare lengths and angles to decide if a polygon is regular or irregular.
Everything needed for tree diagrams for probability - a presentation on probability rules for addition and subtraction, a PowerPoint on drawing tree diagrams, and a worksheet for the learners to answer questions on tree diagrams.
All photographs (c)2015 Colin Billett
Math Grade 7
Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
a. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.
b. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.
Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.
Card matching activity with rectangles in algebraic form, answers with and without brackets or parentheses.
PowerPoint presentation with solutions for class checking. Worksheet of twelve questions each of expanding and factorizing using same method, with boxes. Second PowerPoint for starter or checking learning. Three more short worksheets of mixed questions. Plus ‘objectives’ slide. All you need for this straightforward topic, and lots of opportunity for discussion.
Grade 8 – ‘Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3–5 = 3–3 = 1/33 = 1/27.’
PowerPoint to introduce the rules of integer exponents, using number and with lots for the learners to do, and which can be used as a prelude to algebraic manipulation of exponents and radicals. Refresher activity on Grade 6 powers and radicals, plus a worksheet on more complex examples for high schools.
And a single page 'matching' activity in PowerPoint or PDF.
Common Core Standards
Define trigonometric ratios and solve problems involving right triangles
6. Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
Everything you need for a full lesson or two to develop trigonometry from the tangent ratio to sine and cosine.
Presentations, worksheets, activities and solutions, covering all aspects of the Common Core Standards.
Please leave comments, suggestions or corrections.
A full set of resources for developing transformations ready for higher grades. The introduction consists of a revision of the two simple transformations, which can be done by children on an interactive board. Then a full presentation of the four common ones, with rotations, reflections, translations and enlargements, with lots for the learners to try. Plus a worksheet with eight questions to complete. These can be followed by a review of learning worksheet or a quiz to do for assessment of learning - great fun too. An exciting lesson that reviews and builds upon existing knowledge. All images copyright Colin Billett
Clear and simple examples of constructions for geometry, and loci questions from exams.
An identical PowerPoint to the activity to talk the learners through the processes. All tried and tested, and successful with learners.
Answers provided for learners to check their own solutions.
All images (c)2015 Colin Billett
Practical activity using perimeter of shapes to introduce algebraic concept:
Simplify and manipulate algebraic expressions to maintain equivalence by collecting like terms
Simplify and manipulate algebraic expressions by collecting like terms
Hands-on card matching activity for collecting like terms – great for pair work and discussion – with a full set of solutions in PowerPoint. Two similar worksheets – one for classwork and one for homework or recap the following lesson. Plus an extension activity with an investigation and more involved questions.
Hands on activities for generating deeper thinking and discussion of probability questions. Learners consider one or more experiment cards and cards with real data to predict the probability of an event. Is a new baby more likely to be a boy? Look at the data. Are all scores on two dice equally likely? Try it and see. An extensive worksheet to consolidate learning, and some true/false cards to get deeper into the questions, which are also in a PowerPoint presentation.
All photographs (c)2105 Colin Billett
