Year 8 Scheme of Work Shirebrook Academy
Year 8 Scheme of Work Shirebrook Academy Overview: The premise behind the new SoW for Year 8 is that they will continue to secure the underlying philosophies and skills that are needed to ensure success in mathematics. At the beginning of each new unit all students will attend a lecture in the theatre. These lectures are designed to promote mathematical concepts, enjoyment of mathematics and foremost to address the conception that many students have about mathematics. Units will be taught for the appropriate length of time and will not stick to term duration, therefore if one unit needs nine weeks then it will run for nine weeks. For each unit teachers will be given the objectives, main activities / resources should be saved in the appropriate folders on the network. At the end of every unit students will complete an assessment. Students will have one exercise book. Key pieces of work and Assessments will be stuck into the front of the student’s books and marked. Practise work and day to day workings will be done in the back of the student’s book which will be turned upside down. It will be left to the discretion of the teacher as to what and when to mark the practise work. Technicalities: All presentations will be in the same format. No underlining, italics or block capitals. The date, title and objective will be in bold. The font size will be the font recommended for Dyslexia students (dysle+iefont.com) and the font size will be 12 – 14 point.
Unit 1
The World of Number
Lesson 1: lecture on number, looking at primes and triangular numbers, and the patterns that are found in everyday life. Types of Number Do now task foci: properties of shapes Objectives
Old GCSE Grade To be able to calculate squares and square roots (with F and without a calculator) To be able to calculate cubes and cube roots E To be able to use function keys when using a calculator E to solve problems with powers and roots To be able to use the terms square, square root, D negative square root, cube and cube root. To be able to recall integer squares from 2 x 2 up to 15 x D 15 and their square roots. To be able to recall cubes of 2,3,4,5 and 10 D
New Number Grade 2 3 3 4 4 4
Unit 1b Indices Do now task foci: simple area and compound area
Objectives
Old GCSE Grade To be able to evaluate expressions involving different D indices To be able to use laws of indices to multiply and divide C numbers or expressions written in index notation To be able to understand and use index notation in D calculations To be able to simplify algebraic expressions involving B index laws (ext for higher ability)
New Number Grade 4 5 4 6
Unit 1c Standard Form Do now task foci: angle facts and missing angles Objectives
Old GCSE Grade To be able to write very large and very small numbers in B standard form To be able to convert freely between standard form and B ordinary numbers To be able to perform simple calculations with numbers B written in standard form
New Number Grade 6 6 6
Final lesson:
Objectives
Old GCSE Grade To be able to have an understanding of rational, natural, A imaginary and irrational numbers (Plus Notation)
New Number Grade 7
Unit 2 Negative numbers Do now task foci: negative numbers Lesson 1: lecture on negative numbers, looking at real life applications and their impact on society. What would the world be like if we had no negative numbers. Objectives
To be able to use negative numbers in context To be able to order negative numbers
Old GCSE Grade G F
New Number Grade 1 2
To be able to add and subtract negative numbers To be able to multiply and divide negatives To be able to use BIDMAS involving negatives To be able to calculate sums with powers of negative numbers To be able to use a calculator to evaluate sums involving powers and negative numbers
F E
2 3
F
2
F
2
Unit 3 Algebra Do now task foci: Number of the day Lesson 1: students will understand that an unknown is used in a mathematical way in everyday life. Objectives
Old GCSE Grade E G F G F E D
New Number Grade 3 1 2 1 2 3 4
Old GCSE Grade To be able to state and plot coordinates in all four G quadrants. Extend to finding the midpoint of two coordinates within all four quadrants. To be able to draw straight lines that are parallel to the F axis. Such as x = 3 and y = -5. To be able to draw straight lines given a table of values E for lines such as y = x + 7 or y = x + 3 or y = x - 1. To be able to solve one linear inequality and represent it C
New Number Grade 1
To be able to form and rewrite formulae from diagrams To be able to use a formula written in words To be able to use simple formula To be able to form equations To be able to substitute numbers in to a formula To be able to collect like terms To be able to solve one and two step equations Unit 3b Algebra unseen Do now task foci: types of number and venn diagrams Objectives
2 3 5
on a number line. Write down the integers that satisfies that inequality. To be able to solve two linear inequalities Write down the integers that satisfy both inequalities using a number line if necessary. To be able to identify arithmetic sequences and to continue sequences. To also be able to state the 10th term of a sequence or the difference between the 9th term and 12th term. Extend sequences to square, cube, triangular, and Fibonacci sequences. Identify number patterns that are not standard.
F
2
To be able to find the nth term of a linear sequence.
C
5
Unit 4
Fractions
Do now task foci: rounding Lesson 1: lecture on fractions Fractions Objectives
Old GCSE Grade Write fraction of shape a shaded/unshaded. Simple G equivalent fractions. Which fractions from a list aren't equivalent.
New Number Grade 1
Use of LCM to find common denominator.
D
4
Addition and subtraction using LCM for denominators. Extending to mixed numbers.
C
5
Convert between improper and proper fractions Add, subtract. This is to include functional problems.
D
4
Fractions of an amount
E
3
Unit 4 B
Fractions Decimals and Percentages
Do now task foci: worded number problems Lesson 1: lecture on fractions, decimals and percentages FDP Objectives
Building from shading to finding equivalent fractions and simplifying fractions. Ordering fractions. Extending to equivalence between Fractions, Decimals and Percentages. Ordering Fractions, equivalence between Fractions, Decimals and Percentages.
Old GCSE Grade D
D
New Number Grade 4
4
Unit 5 Ratio and Proportion Do now foci: negative numbers Lesson 1: come dine with me Ratio and Proportion Objectives Express a multiplicative relationship between two quantities as a ratio or a fraction. Relate ratios to fractions and to linear functions
Old GCSE Grade C
New Number Grade 3
Putting ratios in simplest form. Divide simple quantities by a given ratio such as dividing £30 in a ratio of 2:3. Use the bucket method.
D
4
Divide a given quantity into two parts in a given ratio. Apply ratio to real life contexts and problems (The different types of ratio questions should be covered). Understand and use proportion as equality of ratios e.g. recipe questions
D
4
Solve and construct problems involving direct proportion. (involving graphical and algebraic representations) Level 6 only
A
9
Unit 6 Percentages Do now task foci: collecting like terms and solving simple algebra Lesson 1: students will look at the place of percentages in context to life Objectives
Old GCSE Grade Understand that % means out of 100, the line means F divide Work out a percentage of a given quantity E Increase or decrease a quantity by a given percentage D Express one quantity as a percentage of another Work out a percentage decrease or increase C
New Number Grade 2 3 4 5
Unit 1
The World of Number
Lesson 1: lecture on number, looking at primes and triangular numbers, and the patterns that are found in everyday life. Types of Number Do now task foci: properties of shapes Objectives
Old GCSE Grade To be able to calculate squares and square roots (with F and without a calculator) To be able to calculate cubes and cube roots E To be able to use function keys when using a calculator E to solve problems with powers and roots To be able to use the terms square, square root, D negative square root, cube and cube root. To be able to recall integer squares from 2 x 2 up to 15 x D 15 and their square roots. To be able to recall cubes of 2,3,4,5 and 10 D
New Number Grade 2 3 3 4 4 4
Unit 1b Indices Do now task foci: simple area and compound area
Objectives
Old GCSE Grade To be able to evaluate expressions involving different D indices To be able to use laws of indices to multiply and divide C numbers or expressions written in index notation To be able to understand and use index notation in D calculations To be able to simplify algebraic expressions involving B index laws (ext for higher ability)
New Number Grade 4 5 4 6
Unit 1c Standard Form Do now task foci: angle facts and missing angles Objectives
Old GCSE Grade To be able to write very large and very small numbers in B standard form To be able to convert freely between standard form and B ordinary numbers To be able to perform simple calculations with numbers B written in standard form
New Number Grade 6 6 6
Final lesson:
Objectives
Old GCSE Grade To be able to have an understanding of rational, natural, A imaginary and irrational numbers (Plus Notation)
New Number Grade 7
Unit 2 Negative numbers Do now task foci: negative numbers Lesson 1: lecture on negative numbers, looking at real life applications and their impact on society. What would the world be like if we had no negative numbers. Objectives
To be able to use negative numbers in context To be able to order negative numbers
Old GCSE Grade G F
New Number Grade 1 2
To be able to add and subtract negative numbers To be able to multiply and divide negatives To be able to use BIDMAS involving negatives To be able to calculate sums with powers of negative numbers To be able to use a calculator to evaluate sums involving powers and negative numbers
F E
2 3
F
2
F
2
Unit 3 Algebra Do now task foci: Number of the day Lesson 1: students will understand that an unknown is used in a mathematical way in everyday life. Objectives
Old GCSE Grade E G F G F E D
New Number Grade 3 1 2 1 2 3 4
Old GCSE Grade To be able to state and plot coordinates in all four G quadrants. Extend to finding the midpoint of two coordinates within all four quadrants. To be able to draw straight lines that are parallel to the F axis. Such as x = 3 and y = -5. To be able to draw straight lines given a table of values E for lines such as y = x + 7 or y = x + 3 or y = x - 1. To be able to solve one linear inequality and represent it C
New Number Grade 1
To be able to form and rewrite formulae from diagrams To be able to use a formula written in words To be able to use simple formula To be able to form equations To be able to substitute numbers in to a formula To be able to collect like terms To be able to solve one and two step equations Unit 3b Algebra unseen Do now task foci: types of number and venn diagrams Objectives
2 3 5
on a number line. Write down the integers that satisfies that inequality. To be able to solve two linear inequalities Write down the integers that satisfy both inequalities using a number line if necessary. To be able to identify arithmetic sequences and to continue sequences. To also be able to state the 10th term of a sequence or the difference between the 9th term and 12th term. Extend sequences to square, cube, triangular, and Fibonacci sequences. Identify number patterns that are not standard.
F
2
To be able to find the nth term of a linear sequence.
C
5
Unit 4
Fractions
Do now task foci: rounding Lesson 1: lecture on fractions Fractions Objectives
Old GCSE Grade Write fraction of shape a shaded/unshaded. Simple G equivalent fractions. Which fractions from a list aren't equivalent.
New Number Grade 1
Use of LCM to find common denominator.
D
4
Addition and subtraction using LCM for denominators. Extending to mixed numbers.
C
5
Convert between improper and proper fractions Add, subtract. This is to include functional problems.
D
4
Fractions of an amount
E
3
Unit 4 B
Fractions Decimals and Percentages
Do now task foci: worded number problems Lesson 1: lecture on fractions, decimals and percentages FDP Objectives
Building from shading to finding equivalent fractions and simplifying fractions. Ordering fractions. Extending to equivalence between Fractions, Decimals and Percentages. Ordering Fractions, equivalence between Fractions, Decimals and Percentages.
Old GCSE Grade D
D
New Number Grade 4
4
Unit 5 Ratio and Proportion Do now foci: negative numbers Lesson 1: come dine with me Ratio and Proportion Objectives Express a multiplicative relationship between two quantities as a ratio or a fraction. Relate ratios to fractions and to linear functions
Old GCSE Grade C
New Number Grade 3
Putting ratios in simplest form. Divide simple quantities by a given ratio such as dividing £30 in a ratio of 2:3. Use the bucket method.
D
4
Divide a given quantity into two parts in a given ratio. Apply ratio to real life contexts and problems (The different types of ratio questions should be covered). Understand and use proportion as equality of ratios e.g. recipe questions
D
4
Solve and construct problems involving direct proportion. (involving graphical and algebraic representations) Level 6 only
A
9
Unit 6 Percentages Do now task foci: collecting like terms and solving simple algebra Lesson 1: students will look at the place of percentages in context to life Objectives
Old GCSE Grade Understand that % means out of 100, the line means F divide Work out a percentage of a given quantity E Increase or decrease a quantity by a given percentage D Express one quantity as a percentage of another Work out a percentage decrease or increase C
New Number Grade 2 3 4 5
