**Math:** **AGES 15-16**

## Month 1

Aim:

interpret and compare numbers in standard form A x 10n 1≤A<10, where n is a positive or negative integer or zero

Use the resources below to explore these concepts:

Resources:

https://www.khanacademy.org/math/pre-algebra/exponents-radicals/scientific-notation/v/scientific-notation-old

Geometry and Measures

Aim:

understand and use the relationship between parallel lines and alternate and corresponding angles

Aim:

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

Use the resources to explore these concepts:

Resources:

http://www.bbc.co.uk/education/topics/z93rkqt

http://www.bbc.co.uk/education/guides/zrck7ty/revision

http://www.bbc.co.uk/education/guides/zk8j6sg/revision

https://www.khanacademy.org/math/basic-geo/basic-geo-angles/basic-geo-angle-relationships/v/complementary-and-supplementary-angles

## Month 2

Aim:

use inequality notation a<x≤b

https://www.khanacademy.org/math/algebra-basics/alg-basics-linear-equations-and-inequalities/alg-basics-multi-step-inequalities/v/multi-step-inequalities

http://www.bbc.co.uk/schools/gcsebitesize/maths/algebra/inequalitiesrev2.shtml

Use the resource below to explore this concept:

Resources:

Probability

Aim:

generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities.

Use the resource below to explore this concept:

Resources:

https://www.khanacademy.org/math/probability/independent-dependent-probability/basic_probability/a/probability-the-basics

## Month 3

Aim:

appreciate the infinite nature of the sets of integers, real and rational numbers.

Use the resources below to explore these concepts:

Resources:

https://www.khanacademy.org/math/pre-algebra/fractions-pre-alg/number-sets-pre-alg/v/number-sets

(not 1 month)

Statistics

Aim:

describe simple mathematical relationships between two variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs.

Use the resources below to explore these concepts:

Resources:

https://www.khanacademy.org/math/probability/regression

## Month 4

Aim:

use linear and quadratic graphs to estimate values of y for given values of x and vice versa and to find approximate solutions of simultaneous linear equations

Use the resource below to explore these concepts:

https://www.youtube.com/watch?v=80l4_VTkyO0

Geometry and Measures

Aim:

apply angle facts, triangle congruence, similarity and properties of quadrilaterals to derive results about angles and sides, including Pythagoras’ Theorem, and use known results to obtain simple proofs

Aim:

Use Pythagoras’ Theorem and trigonometric ratios in similar triangles to solve problems involving right-angled triangles

Use the resource below to explore these concepts:

Resources:

http://www.bbc.co.uk/education/topics/zkbc87h

http://www.bbc.co.uk/education/topics/zvtnvcw

use linear and quadratic graphs to estimate values of y for given values of x and vice versa and to find approximate solutions of simultaneous linear equations

Use the resource below to explore these concepts:

https://www.youtube.com/watch?v=80l4_VTkyO0

Geometry and Measures

Aim:

apply angle facts, triangle congruence, similarity and properties of quadrilaterals to derive results about angles and sides, including Pythagoras’ Theorem, and use known results to obtain simple proofs

Aim:

Use Pythagoras’ Theorem and trigonometric ratios in similar triangles to solve problems involving right-angled triangles

Use the resource below to explore these concepts:

Resources:

http://www.bbc.co.uk/education/topics/zkbc87h

http://www.bbc.co.uk/education/topics/zvtnvcw

## Month 5

Aim:

find approximate solutions to contextual problems from given graphs of a variety of functions, including piecewise linear, exponential and reciprocal graphs

Use the resource below to explore these concepts:

https://www.khanacademy.org/math/algebra/introduction-to-exponential-functions/exponential-growth-and-decay/v/exponential-growth-functions

Problem Solving

Aim: Systems of equations

Use the resource below to explore these concepts:

https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-systems-topic/cc-8th-systems-overview/v/trolls-tolls-and-systems-of-equations

## Month 6

Aim:

generate terms of a sequence from either a term-to-term or a position-to-term rule recognize arithmetic sequences and find the nth term

Use the resource below to explore sequences:

https://www.khanacademy.org/math/algebra/sequences/introduction-to-arithmetic-squences/v/finding-the-100th-term-in-a-sequence

Problem Solving

Aim: Systems Elimination

Use the resource below to explore systems elimination:

https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-systems-topic/cc-8th-systems-overview/v/king-s-cupcakes-solving-systems-by-elimination

## Month 7

Aim:

recognize geometric sequences and appreciate other sequences that arise.

Use the resource below to explore this concept:

https://www.youtube.com/watch?v=pXo0bG4iAyg

Geometry and Measures

Aim:

use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3-D

Use the resource below to explore this concept:

https://www.youtube.com/watch?v=9yU_Q3qtGKo

## Month 8

Aim:

solve problems involving percentage change, including: percentage increase, decrease and original value problems and simple interest in financial mathematics

Use the resource below to explore this concept:

Resources:

http://www.bbc.co.uk/education/topics/zq7ncdm

Handling Data

Aim:

Investigating types of data and its purposes.

Aim:

Qualitative and quantitative data

Use the resource below to explore this concept:

Resources:

https://vimeo.com/153644992

Write down a few situations in which a researcher would use quantitative data. Write down a few situations in which a researcher would use qualitative data. Write down a few situations in which a researcher would use both.

## Month 9

Aim:

solve problems involving direct and inverse proportion, including graphical and algebraic representations

Use the resource below to explore these concepts:

https://www.khanacademy.org/math/algebra2/rational-expressions-equations-and-functions/direct-and-inverse-variation/v/direct-and-inverse-variation

Problem Solving

Aim:

Investigating Shapes in real-life contexts

Use the resource below to explore this concept:

Resources:

http://www.bbc.co.uk/education/topics/zbpfb9q

solve problems involving direct and inverse proportion, including graphical and algebraic representations

Use the resource below to explore these concepts:

https://www.khanacademy.org/math/algebra2/rational-expressions-equations-and-functions/direct-and-inverse-variation/v/direct-and-inverse-variation

Problem Solving

Aim:

Investigating Shapes in real-life contexts

Use the resource below to explore this concept:

Resources:

http://www.bbc.co.uk/education/topics/zbpfb9q

## Month 10

Aim:

use compound units such as speed, unit pricing and density to solve problems.

Use the resources below to explore these concepts:

Resources:

http://www.bbc.co.uk/education/topics/z28jmp3

http://www.bbc.co.uk/education/topics/zcf3cdm

Geometry and Measures

Aim:

Interpret mathematical relationships both algebraically and geometrically.

Use the resource below to explore these relationships:

https://www.youtube.com/watch?v=Muba9-W2FOQ

## Month 11

Aim:

Pythagorean Theory

Use the resource below to review and explore this concept:

Pythagorean Theory Review

https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-pythagorean-theorem/v/the-pythagorean-theorem

Pythagorean Proof Review

https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-pythagorean-proofs/v/garfield-s-proof-of-the-pythagorean-theorem

Pythagorean Theory

Use the resource below to review and explore this concept:

Pythagorean Theory Review

https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-pythagorean-theorem/v/the-pythagorean-theorem

Pythagorean Proof Review

https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-pythagorean-proofs/v/garfield-s-proof-of-the-pythagorean-theorem

## Month 12

Aim:

Review all number targets

Go back through any lessons you have trouble with and review.

Or, look on this website for more to try

http://www.analyzemath.com/middle_school_math/grade_8/problems.html

Review all number targets

Go back through any lessons you have trouble with and review.

Or, look on this website for more to try

http://www.analyzemath.com/middle_school_math/grade_8/problems.html