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Molehill Maths

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Lessons and Diferentiated Resources to reduce the planning mountain

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Lessons and Diferentiated Resources to reduce the planning mountain
Recurrence Relations
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Recurrence Relations

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Examining the language and use of recurrence relationships. Looks at linear then geometric sequences. Worked examples, questions and match-up activities follow. Then extends to include relations with more then one operation or more than one term leading to Fibonnaci-style sequences and Square Numbers. All answers included.
Prisms: Volume and Surface Areas
jchowelljchowell

Prisms: Volume and Surface Areas

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Starter reviewing areas of 2D shapes. Examples of volume calculations looking at areas of cross-sections leading to volume. Surface area found by through finding areas of each face. Worked examples and questions on all ideas. All answers included.
Circles: Mensuration Review
jchowelljchowell

Circles: Mensuration Review

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Lesson reviewing lengths and areas involving circles. Starter involves naming parts of a circle. Examples and Questions cover circumferences using diameter or radius, area, lengths of arcs, areas of sectors. All topics have worked examples and questions. All answers included.
Similar Shapes - Area and Volume
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Similar Shapes - Area and Volume

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Using similarity to find areas of 2D shapes and volumes of 3D solids. Starter explores multiplicative relationships. Worked examples and table looking at 2D shapes to find relationship between side scale factor and area scale factor. Similar format extending to volume. Questions on all skills included. All answers included.
Algebraic Fractions - Simplifying
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Algebraic Fractions - Simplifying

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Starter looks at separate skills of simplifying numerical fractions and factorising algebraic expressions. Looks first at algebraic fractions which don’t need factorising, worked examples, questions. Then extends to look at fractions requiring factorising (including difference of two squares). Questions on all skills. All answers provided.
Algebraic Fractions: Add and Subtract
jchowelljchowell

Algebraic Fractions: Add and Subtract

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Lesson splits skill into 3 parts A: Fractions with numerical denominators B: Fractions with single expression denominators C: Fractions with multiple expression denominators Worked examples and questions on each skill. Problem Solving question using vector lengths. All answers included.
Quadratics -  Properties Algebraically
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Quadratics - Properties Algebraically

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Explores the properties of Quadratic Curves using an algebraic approach. Looks at roots, turning points, intercept and the line of symmetry around the turning point. Questions on factorising to find roots, finding the line of symmetry and the turning point through substitution. Worked examples and questions on all skills. All answers included.
Quadratics-Find Properties Graphically
jchowelljchowell

Quadratics-Find Properties Graphically

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Explores the properties of Quadratic Curves using a graphical approach. Looks at roots, turning points, intercept and the line of symmetry around the turning point. Starter looks at identifying quadratics, Multiple Choice questions on the properties. Moves on to questions asking pupils to plot a curve and then find the properties. Worked examples and all answers included.
Non-Linear Simultaneous Equations: Graph
jchowelljchowell

Non-Linear Simultaneous Equations: Graph

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Multiple Choice starter identifying linear and quadratic functions. Reminder of solving linear simultaneous equations graphically. Follows similar process to solve quadratic and linear simultaneous equations. Also looks at styles of questions and manipulations of equations to find which graphs to plot.
Equation of A Circle
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Equation of A Circle

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Starter using Pythagoras to find diagonals of quadrilaterals. Use of Pythagoras to explain equation of a circle based on the origin. Extends to look at circles not centred on the origin. Plenary looks at an example of simultaneous equations with a circle. Worked examples and question slides. All answers included.
Using the nth term - Linear Sequences
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Using the nth term - Linear Sequences

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Starter asks pupils to describe number patterns from pictures. Then examining the properties of Linear Sequences from term-to-term rules, pictures, straight line graphs. Examples of how the general rule is used: finding terms, finding positions of terms, seeing if a number belongs in a sequence, finding common terms in two sequences. Worked examples and question slides on each topic. All answers included.
Geometric Sequences
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Geometric Sequences

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Lesson looks at the differences between arithmetic and geometric sequences through the them to term rule. Explains using a term to term rule to find the next terms. The General Rule is then explored. How to find terms from the General Rule is explained. All ideas also have question slides and all answers are included.
Quadratic Sequences- Nth term
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Quadratic Sequences- Nth term

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Using differences and second differences to find the general rule for quadratic sequences. Lots of examples with n^2 , 2n^2, 3n^2 etc. Worked examples and questions on all skills. All answers included.
The Pattern in Quadratic Sequences
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The Pattern in Quadratic Sequences

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Using the Term-to-Term Rule to generate quadratic sequences. Exploring differences and second differences to investigate the similarities between sequences. Worked examples of all skills. All answers included.
Exponential Functions - Graphs
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Exponential Functions - Graphs

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Explores connection between exponential graphs and geometric series in the starter. The shape of exponential functions is explored and the common features. Plotting these graphs is demonstrated. Questions based on two coordinates are explained. Questions and answers included.
Frustums- Volume
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Frustums- Volume

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Starter looks at using the formulae for volume and surface areas for 3D shapes. Explanation of frustum as shape created when top removed from cone or pyramid. Examples of finding volume of a frustum with lengths of whole cone/pyramid included. Extends by looking at using similarity to find volume when given only frustum. Worked examples and questions for all skills. All answers included.
Similar Triangles - Missing Sides
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Similar Triangles - Missing Sides

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Starter looks at multiplicative relationships to use for calculating Scale factors. Similarity of shapes explained. Worked examples of finding missing lengths in triangles and quadrilaterals given. Questions reinforcing learning. All answers included.
Algebraic fractions: Multiply/Divide
jchowelljchowell

Algebraic fractions: Multiply/Divide

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Method relates to numerical fractions and reemphasizes canceling common factors. Worked examples for both numerical and algebraic fractions. Looks at single expressions and complex expressions requiring factorisation. Question slides for all skills. All answers included.
Forming Simultaneous Equations
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Forming Simultaneous Equations

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Looks at how we know what equations to write to solve problems. Starter includes solving equations and substitution. Examples written to trigger a structured method. Full worked examples and questions. Extension slide includes non-linear example, an example where one answer is nonsensical and one example using ratios. All answers included.
Frequency Trees
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Frequency Trees

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Starter look at two-way tables. Links made to similarities and differences between two-way tables and frequency trees. Worked examples including finding probabilities. Worksheet includes questions finding frequencies from proportions of the whole and extends to larger trees. All answers included. Worksheet answers provided on ppt.