## Mathematics

Ages 11-12

Month 1

Aim:

understand and use place value for decimals, measures and integers of any size

Lesson/Activities:

- Revise this concept here
- Do the activity here.
- Revise your learning by doing these questions.
- Watch the video about place value from Kahn Academy.
- Click on ‘Practice this Concept’ and do the activity.
- Do the other decimal videos and activities at the same website (look on the left).

Aim:

order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, ≠, <, >, ≤, ≥

Lesson/Activities:

- Negative numbers
- Watch the video about negative numbers from Kahn Academy.
- Click on ‘Practice this Concept’ and do the activity.
- Do the other negative numbers videos and activities at the same website (look on the left).

- Decimals
- Watch the video about comparing decimals from Kahn Academy.
- Click on ‘Practice this Concept’ and do the activity.
- Do the other decimals videos and activities at the same website (look on the left).

- Fractions
- Watch the video about comparing fractions from Kahn Academy.
- Click on ‘Practice this Concept’ and do the activity.
- Do the other fractions videos and activities at the same website (look on the left).

## Month 2

Aim:

use the concepts and vocabulary of prime numbers, factors (or divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation property

Lesson/Activities:

use the concepts and vocabulary of prime numbers, factors (or divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation property

Lesson/Activities:

- Finding factors.
- Watch the video about finding factors from Kahn Academy.
- Click on ‘Practice this Concept’ and do the activity.
- Do the other finding factors videos and activities at the same website (look on the left).

- Prime numbers
- Watch the video about prime numbers from Kahn Academy.
- Click on ‘Practice this Concept’ and do the activity.
- Do the other prime numbers videos and activities at the same website (look on the left).

- Take the test on this topic here!

## Month 3

Aim:

use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative

Lesson/Activities:

use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative

Lesson/Activities:

- Positive and negative numbers
- Long Division
- Watch the video about long division from Kahn Academy.
- Click on ‘Practice this Concept’ and do the activity.
- Do the other long division videos and activities at the same website (look on the left).

- Dividing fractions

- Watch the video about dividing fractions from Kahn Academy.
- Click on ‘Practice this Concept’ and do the activity.
- Do the other dividing fractions videos and activities at the same website (look on the left).

- Decimals
- Watch the video about adding decimals from Kahn Academy.
- Click on ‘Practice this Concept’ and do the activity.
- Do the other dividing fractions videos and activities at the same website (look on the left).

## Month 4

Aim:

use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals

Use all of the resources below to explore conventional notation:

Resources:

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

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

https://www.khanacademy.org/math/pre-algebra/order-of-operations/order_of_operations/v/introduction-to-order-of-operations

https://www.khanacademy.org/math/pre-algebra/order-of-operations/order_of_operations/e/order_of_operations_2

https://www.khanacademy.org/math/pre-algebra/order-of-operations/order_of_operations/v/more-complicated-order-of-operations-example

Geometry and Measures

derive and apply formulae to calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) and other prisms (including cylinders)

Resources:

http://www.bbc.co.uk/education/topics/zrf3cdm

https://www.khanacademy.org/math/basic-geo/basic-geo-area-perimeter/basic-geo-area-perimeter-polygon/v/perimeter-and-area-basics

http://www.bbc.co.uk/education/guides/zj76fg8/revision

## Month 5

Aim:

recognise and use relationships between operations including inverse operations

Use the website below to explore inverse operations:

Resources:

Inverse operations addition

Inverse operations multiplication

Probability

record, describe and analyse the frequency of outcomes of simple probability experiments involving randomness, fairness, equally and unequally likely outcomes, using appropriate language and the 0-1 probability scale

Aim:

understand that the probabilities of all possible outcomes sum to 1

Resources:

http://www.bbc.co.uk/education/topics/zgf3cdm

recognise and use relationships between operations including inverse operations

Use the website below to explore inverse operations:

Resources:

Inverse operations addition

Inverse operations multiplication

Probability

record, describe and analyse the frequency of outcomes of simple probability experiments involving randomness, fairness, equally and unequally likely outcomes, using appropriate language and the 0-1 probability scale

Aim:

understand that the probabilities of all possible outcomes sum to 1

Resources:

http://www.bbc.co.uk/education/topics/zgf3cdm

## Month 6

Aim:

use and interpret algebraic notation, including: ab in place of a × b 3y in place of y + y + y and 3 × y a2 in place of a × a, a3 in place of a × a × a; a2 b in place of a × a × b b a in place of a ÷ b coefficients written as fractions rather than as decimals brackets

Use the resource below to explore algebra:

Resources:

https://www.khanacademy.org/math/algebra/introduction-to-algebra/variable-and-expressions/v/what-is-a-variable

Statistics

describe, interpret and compare observed distributions of a single variable through: appropriate graphical representation involving discrete, continuous and grouped data; and appropriate measures of central tendency (mean, mode, median) and spread (range, consideration of outliers)

Open the link and watch the videos

Write down information information about; mean, median, mode,

More Resources:

Analyzing data

Statistics

## Month 7

Aim:

substitute numerical values into formulae and expressions, including scientific formulae

Use the resource below to explore numerical values:

Resources:

https://www.khanacademy.org/math/on-sixth-grade-math/on-patterning-algebra/on-variables-expressions/e/one_step_equation_intuition Geometry

Aim:

draw and measure line segments and angles in geometric figures, including interpreting scale drawings

https://www.khanacademy.org/math/basic-geo/basic-geo-lines/basic-geo-lines-rays-angles/v/lines-line-segments-and-rays

substitute numerical values into formulae and expressions, including scientific formulae

Use the resource below to explore numerical values:

Resources:

https://www.khanacademy.org/math/on-sixth-grade-math/on-patterning-algebra/on-variables-expressions/e/one_step_equation_intuition Geometry

Aim:

draw and measure line segments and angles in geometric figures, including interpreting scale drawings

https://www.khanacademy.org/math/basic-geo/basic-geo-lines/basic-geo-lines-rays-angles/v/lines-line-segments-and-rays

## Month 8

Aim:

understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors

use the resource below to explore these concepts:

Resources:

https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-expressions-and-variables/cc-6th-parts-of-expressions/v/expression-terms-factors-and-coefficients

Aim:

derive and use the standard ruler and compass constructions (perpendicular bisector of a line segment, constructing a perpendicular to a given line from/at a given point, bisecting a given angle); recognise and use the perpendicular distance from a point to a line as the shortest distance to the line

use the resource below to explore these concepts:

https://www.khanacademy.org/math/early-math/cc-early-math-measure-data-topic/cc-early-math-measuring-length/e/measuring-lengths-with-different-units

## Month 9

Aim:

simplify and manipulate algebraic expressions to maintain equivalence by: collecting like terms multiplying a single term over a bracket taking out common factors expanding products of two or more binomials

understand and use standard mathematical formulae; rearrange formulae to change the subject

Resources:

https://www.khanacademy.org/math/algebra/introduction-to-algebra/variable-and-expressions/v/what-is-a-variable

Handling Data

Aim:

Averages

Aim:

Collecting, organising data

Resources:

http://www.bbc.co.uk/education/topics/z3nygk7

http://www.bbc.co.uk/education/topics/zbsvr82

## Month 10

Aim:

work with coordinates in all four quadrants

Use the resource below to explore coordinates:

Resources:

https://www.khanacademy.org/math/basic-geo/basic-geo-coordinate-plane/copy-of-cc-6th-coordinate-plane/v/quadrants-of-coordinate-plane

https://www.khanacademy.org/math/basic-geo/basic-geo-coordinate-plane/copy-of-cc-6th-coordinate-plane/e/coordinate-plane-word-problems

https://www.khanacademy.org/math/basic-geo/basic-geo-coordinate-plane/copy-of-cc-6th-coordinate-plane/e/identifying_points_1

Geometry and Measures

Aim:

calculate and solve problems involving: perimeters of 2-D shapes (including circles), areas of circles and composite shapes

Use the resource below to revise these concepts

Resources:

https://www.youtube.com/watch?v=O-cawByg2aA

http://www.bbc.co.uk/education/guides/zc9wxnb/revision

work with coordinates in all four quadrants

Use the resource below to explore coordinates:

Resources:

https://www.khanacademy.org/math/basic-geo/basic-geo-coordinate-plane/copy-of-cc-6th-coordinate-plane/v/quadrants-of-coordinate-plane

https://www.khanacademy.org/math/basic-geo/basic-geo-coordinate-plane/copy-of-cc-6th-coordinate-plane/e/coordinate-plane-word-problems

https://www.khanacademy.org/math/basic-geo/basic-geo-coordinate-plane/copy-of-cc-6th-coordinate-plane/e/identifying_points_1

Geometry and Measures

Aim:

calculate and solve problems involving: perimeters of 2-D shapes (including circles), areas of circles and composite shapes

Use the resource below to revise these concepts

Resources:

https://www.youtube.com/watch?v=O-cawByg2aA

http://www.bbc.co.uk/education/guides/zc9wxnb/revision

## Month 11

Aim:

change freely between related standard units [for example time, length, area, volume/capacity, mass]

Use the resources below to explore standard units:

Resources:

http://www.bbc.co.uk/education/guides/zthsgk7/revision

https://www.youtube.com/watch?v=mDh-8n2REwU

http://www.homeschoolmath.net/worksheets/measuring-customary.php

Aim: Solve mathematical problems expressed in words

Use the resource below to explore word problems:

https://www.khanacademy.org/math/in-sixth-grade-math/algebra-in/using-expressions-practically/v/writing-basic-expressions-from-word-problems-examples

change freely between related standard units [for example time, length, area, volume/capacity, mass]

Use the resources below to explore standard units:

Resources:

http://www.bbc.co.uk/education/guides/zthsgk7/revision

https://www.youtube.com/watch?v=mDh-8n2REwU

http://www.homeschoolmath.net/worksheets/measuring-customary.php

Aim: Solve mathematical problems expressed in words

Use the resource below to explore word problems:

https://www.khanacademy.org/math/in-sixth-grade-math/algebra-in/using-expressions-practically/v/writing-basic-expressions-from-word-problems-examples

## Month 12

Aim:

Express one quantity as a fraction of another, where the fraction is less than 1 and greater than 1

Use ratio notation, including reduction to simplest form

Use the resource below to use explore ratio notation:

https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-ratios-prop-topic/cc-6th-ratios-intro/v/ratios-as-fractions

Problem Solving Activities

Aim: linear problems

Use the resource below to explore this concept:

https://www.khanacademy.org/math/in-sixth-grade-math/algebra-in/using-expressions-practically/v/interpreting-linear-expressions-example-2

Express one quantity as a fraction of another, where the fraction is less than 1 and greater than 1

Use ratio notation, including reduction to simplest form

Use the resource below to use explore ratio notation:

https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-ratios-prop-topic/cc-6th-ratios-intro/v/ratios-as-fractions

Problem Solving Activities

Aim: linear problems

Use the resource below to explore this concept:

https://www.khanacademy.org/math/in-sixth-grade-math/algebra-in/using-expressions-practically/v/interpreting-linear-expressions-example-2