MATHS DEPARTMENT

YEAR 7

SCHEME OF WORK

SETS 1-3: IMPACT 1R

1R PLAN

AUTUMN TERM – FIRST HALF

Topic 1 / Calculation & Problem Solving / Additional Transition Unit
Topic 2 / Fractions & Ratio / Additional Unit
Topic 3 / Understanding Number / 1R Ch. 2
Topic 4 / Shapes / 1R Ch. 1
Topic 5 / Number Patterns / 1R Ch. 3

TEST 1

AUTUMN TERM – SECOND HALF

Topic 6 / Probability / 1R Ch. 4
Topic 7 / Multiplication & Division / 1R Ch. 5
Topic 8 / Decimals / 1R Ch. 6

TEST 2

SPRING TERM – FIRST HALF

Topic 9 / Measuring / 1R Ch. 7
Topic 10 / Working with Algebra / 1R Ch. 9
Topic 11 / Fractions & Ratio / 1R Ch. 8
Topic 12 / Perimeter, Area & Volume / 1R Ch. 10

TEST 3

SPRING TERM – SECOND HALF

Topic 13 / Formulae & Equations / 1R Ch. 11
Topic 14 / Negative Numbers / 1R Ch. 12
Topic 15 / Graphs / 1R Ch. 13

TEST 4

SUMMER TERM – FIRST HALF

Topic 16 / Angles / 1R Ch. 14
Topic 17 / Handling Data / 1R Ch. 15
Topic 18 / Percentages / 1R Ch. 16

TEST 5

SUMMER TERM – SECOND HALF

Topic 19 / Averages / 1R Ch. 17
Topic 20 / Transformations / 1R Ch. 18

“Optional” Tests

Topic 21 / Fractions, Decimals & Percentages / Additional Transition Unit
Topic / Investigation

AUTUMN TERM A TOPIC 1

Topic: Transition Unit

Calculation & Problem Solving

/ NC Level:
NC Programme of Study:
Ref3agijko: Add, subtract, multiply and divide integers and then any number; multiply or divide any number by powers of 10, and any positive number by a number between 0 and 1. Recall all positive integer complements to 100 ; recall all multiplication facts to 10x10, and use them to derive quickly the corresponding division facts; recall the cubes of 2, 3, 4, 5 and 10. Develop a range of strategies for mental calculation; derive unknown facts from those they know. Use standard column procedures for addition and subtraction of integers and decimals. Use standard column procedures for multiplication of integers and decimals. Use calculators effectively and efficiently: know how to enter complex calculations using brackets; know how to enter a range of calculations, including those involving measures.
Learning Objectives:
  • Understand and use decimal notation and place value
  • Multiply and divide integers and decimals by 10, 100, 1000, and explain the effect
  • Understand negative numbers as positions on the number line
  • Order, add and subtract positive and negative integers in context
  • Consolidate rapid recall of number facts, including positive integer complements to 100 and multiplication facts to 10x10, and quickly derive associated division facts
  • Use standard column procedures to add and subtract whole numbers and decimals with up to 2 places
  • Multiply and divide 3-digit by 2-digit whole number; extend to multiplying and dividing decimals with 1 or 2 places by single-digit whole numbers
  • Enter numbers in a calculator and interpret the display in different contexts
  • Solve word problems and investigate in the context of number
  • Compare and evaluate solutions

Additional Notes: There are 2 Transition Units. Some pupils may have studied the first unit at the end of year 6. (The first unit should not be covered in year 7)
Key Vocabulary:
DIFFERENCE EXPLAIN INTEGER MINUS NEGATIVE PLUS POSITIVE REASONING SUM SYSTEMATIC
Impact Reference:

This unit should be done in isolation but it relates closely to ch.2,3 &5

/ Other references:
See below (pg.24 onwards)
V4 – ch.1,3,4,8 V5 – ch.4,7
Mental & Oral Starters:

1R folder: pg. 24-25,44-46,76-78

101 Starters: pg.2-6, 14-17, 24-27, 39, 41, 47-51, 58

FOR DETAILED LESSON PLANS SEE:
“TRANSITION FROM Y6 TO Y7: MATHS – UNITS OF WORK” BOOK
Time: 5 lessons

AUTUMN TERM A TOPIC 2

Topic: Fractions & Ratio

/ NC Level:
NC Programme of Study:
Learning Objectives:
  • Use fraction notation to describe parts of shapes and to express a smaller whole number as a fraction of a larger one
  • Simplify fractions and identify equivalent fractions
  • Calculate simple fractions of quantities; multiply by an integer
  • Understand percentage as the ‘number of parts per 100’
  • Recognise the equivalence of percentages, fractions and decimals
  • Calculate simple percentages
  • Understand the relationship between ratio and proportion; use direct proportion in simple contexts; use ratio notation and divide a quantity into 2 parts in a given ratio; solve simple problems about ratio and proportion using informal strategies
  • Consolidate and extend mental methods of calculation to include decimals, fractions and percentages, accompanied where appropriate by suitable jotting; solve simple word problems mentally
  • Check a result by considering whether it is of the right order of magnitude and by working the problem backwards
  • Represent problems mathematically, making correct use of symbols, words and diagrams
  • Present and interpret solution in the context of the original problem; explain and justify methods and conclusions, orally and in writing.

Key Vocabulary:
OPERATOR MULTIPLIER INCREASE DECREASE FRACTION IMPROPER MIXED NUMBER NUMERATOR
DENOMINATOR EQUIVALENT RATIO PROPORTION
Impact Reference: / Other references:

SEE FRACTIONS & RATIO MINI-PACK FOR FURTHER GUIDANCE

Time: 6 lessons

AUTUMN TERM A TOPIC 3

Topic: Understanding Number

/ NC Level: 2 - 4
NC Programme of Study:
Ref2a: Use their previous understanding of integers and place value to deal with arbitrarily large positive numbers and round them to a given power of 10.
Ref3agijko: Add, subtract integers and then any number. Recall all positive integer complements to 100. Develop a range of strategies for mental calculation; derive unknown facts from those they know. Use standard column procedures for addition and subtraction of integers and decimals. Use calculators effectively and efficiently: know how to enter complex calculations using brackets; know how to enter a range of calculations, including those involving measures.
Ref4c: Use a variety of checking procedures, including working the problem backwards, and considering whether a result is of the right order of magnitude.
Learning Objectives:
  • Consolidate rapid recall of number facts, including positive integer complements to 100
  • Round positive whole numbers to the nearest 10, 100, 1000
  • Understand addition and subtraction as they apply to whole numbers
  • Make and justify estimates and approximations of calculations
  • Use standard column procedures to add and subtract whole numbers
  • Solve simple word problems mentally
  • Check a result by considering whether it is of the right order of magnitude and by working the problem backwards
EXT – Recall known facts, including fraction to decimal conversions (1R-6.6,6.7,6.8)
Round positive numbers to any given power of 10 (1R-6.11)
Key Vocabulary:

DIGIT PLACE VALUE ORDER MENTAL ADDITION SUBTRACTION ROUND ESTIMATE

Impact Reference:

Book 1R – ch. 2

/ Other references:

V4 – ch.1, 3, 4

Mental & Oral Starters:

1R folder: pg. 24-25

101 Starters: pg. 2-6, 14-17, 41, 47, 58

Discussion opportunities:
Emphasise the importance of discussing different methods / Pair / Group Work:
Set each other sets of problems
ICT Links:

Many internet games

Spiritual/Moral/Citizenship Links:
We all have different ideas and methods – it is important that we respect each other’s
Investigation:

Different methods for different calculations

Time: 10 lessons

AUTUMN TERM A TOPIC 4

Topic: Shapes

/ NC Level: 2 - 4
NC Programme of Study:
Ref2cdfjk: Use parallel lines. Use angle properties of equilateral, isosceles and right-angled triangles. Recall the essential properties of special types of quadrilateral, including square, rectangle, parallelogram, trapezium and rhombus. Explore the geometry of cuboids (including cubes), and shapes made from cuboids. Use 2D representations of 3D shapes and analyse 3D shapes through 2D projections and cross-sections, including plan and elevation.
Ref3ab: Understand that reflections are specified by a mirror line. Recognise and visualise reflections, including reflection symmetry of 2D and 3D shapes, and rotation symmetry of 2D shapes.
Learning Objectives:
  • Identify parallel and perpendicular lines
  • Begin to use angle, side and symmetry properties of triangles and quadrilaterals
  • Use 2D representations to visualise 3D shapes and deduce some of their properties
EXT – Classify quadrilaterals by their geometric properties (1R-1.7)
Key Vocabulary:
SHAPE SYMMETRY REGULAR IRREGULAR REFLECT TRIANGLE PARALLEL PERPENDICULAR SOLID PRISM PYRAMID
Impact Reference:

Book 1R – ch. 1

/ Other references:

V4 – ch.14 V5 – ch.20 V6 – ch.14,15

Mental & Oral Starters:

1R folder: pg. 4-5

101 Starters: pg. 73-78

Discussion opportunities:
Compare the symmetry properties of shapes, sorting shapes, etc. / Pair / Group Work:
Classify shapes into a number of categories
ICT Links:

LOGO

Maths Mansion programmes 33 & 34
Spiritual/Moral/Citizenship Links:
We need to look at 3-D shapes from all angles – similar to conflicts / confrontations – consider everyone’s opinion.
Investigation:

Activities Book 1R pg.3

Time: 6-7 lessons

AUTUMN TERM A TOPIC 5

Topic: Number Patterns

/ NC Level: 2 - 4
NC Programme of Study:
Ref6abc: Generate common integer sequences. Find the first terms of a sequence given a rule arising naturally from a context; find the rule (and express it in words) for the nth term of a sequence. Generate terms of a sequence using term-to-term and position-to-term definitions of the sequence; use linear expressions to describe the nth term of an arithmetic sequence, justifying its form by referring to the activity or context from which it was generated.
Learning Objectives:
  • Generate and describe simple integer sequences
  • Generate terms of a simple sequence, given a rule
  • Generate sequences from practical contexts and describe the general termin simple cases
  • Express simple functions in words
EXT – Generate terms of a linear sequence using term-to-term and position-to-term definitions of the sequence (1R-3.6)
Begin to use linear expressions to describe the nth term of an arithmetic sequence (1R-3.6)
Key Vocabulary:

PATTERN NUMBER MACHINES SEQUENCE RULE

Impact Reference:

Book 1R – ch. 3

/ Other references:

V4 – ch.8 V5 – ch.8 V6 – ch.6

Mental & Oral Starters:

1R folder: pg. 44-46

Discussion opportunities:
Discuss the rule which produces the next term / Pair / Group Work:
Develop different sequences – partner has to identify the rule
ICT Links:

EXCEL produces number patterns when programmed

C4 Video “Primes & powers”
Spiritual/Moral/Citizenship Links:
Each term in the sequence follows the same rule – links to the rules followed at school
Investigation:

Number patterns in real life – e.g. Fibonacci numbers

Time: 4-5 lessons

AUTUMN TERM B TOPIC 6

Topic: Probability

/ NC Level: 2 - 4
NC Programme of Study:
Ref4cde: Understand and use the probability scale. Understand and use estimates or measures of probability from theoretical models, including equally likely outcomes, or from relative frequency. List all outcomes for single events, and for two successive events, in a systematic way.
Ref5hij: Use the vocabulary of probability in interpreting results involving uncertainty and prediction. Compare experimental data and theoretical probabilities. Understand that if they repeat an experiment, they may and usually will get different outcomes, and that increasing sample size generally leads to better estimates of probability and population characteristics.
Learning Objectives:
  • Use vocabulary and ideas of probability, drawing on experience
  • Understand and use the probability scale from 0 to 1
  • Find and justify probabilities based on equally likely outcomes in simple contexts
  • Identify all the possible mutually exclusive outcomes of a single event
  • Collect data from a simple experiment and record in a frequency table
  • Estimate probabilities based on this data
EXT – Know that if the probability of an event occurring is p then the probability of it not occurring is 1-p (1R-4.9)
Find and record all possible mutually exclusive outcomes for 2 successive events in a systematic way using diagrams and tables
Key Vocabulary:

CERTAIN IMPOSSIBLE POSSIBLE LIKELY UNLIKELY EVEN CHANCE SCALE EVENT OUTCOME EXPERIMENTAL

Impact Reference:

Book 1R – ch. 4

/ Other references:

V4 – ch.22 V5 – ch.28,29 V6 – ch.20

Mental & Oral Starters:

1R folder: pg. 62-63

Discussion opportunities:
Discuss the probability of real life events / Pair / Group Work:
Probability experiments
ICT Links:

Random number generators. Internet games

Spiritual/Moral/Citizenship Links:
Morality of gambling, Lottery
Investigation:

Investigate probabilities within the class – e.g. the probability of having blue eyes in the class

Time: 5-6 lessons

AUTUMN TERM B TOPIC 7

Topic: Multiplication & Division

/ NC Level: 3 - 5
NC Programme of Study:
Ref2ab: Use the concepts and vocabulary of factor (divisor), multiple, common factor, highest common factor, least common multiple, prime number and prime factor decomposition. Use the terms square, positive and negative square root, cube, cube root; use index notation for small integer powers and index laws for multiplication and division of positive integer powers.
Ref3agik: Multiply and divide integers and then any number; multiply or divide any number by powers of 10, and any positive number by a number between 0 and 1; find the prime factor decomposition of positive integers. Recall all multiplication facts to 10x10, and use them to derive quickly the corresponding division facts; recall the cubes of 2, 3, 4, 5 and 10. Develop a range of strategies for mental calculation; derive unknown facts from those they know. Use standard column procedures for multiplication of integers and decimals.
Ref4c: Use a variety of checking procedures, including working the problem backwards, and considering whether a result is of the right order of magnitude.
Learning Objectives:
  • Multiply and divide integers by 10, 100, 1000 and explain the effect
  • Consolidate the rapid recall of number facts, including multiplication facts to 10x10, and quickly derive associated division facts
  • Enter numbers into a calculator and interpret the display in different contexts
  • Know how to use the laws of arithmetic and inverse operations
  • Multiply and divide 3-digit by 2-digit whole numbers
  • Recognise and use multiples, factors, common factor, HCF, LCM in simple cases and primes (<100)
  • Use simple tests of divisibility
  • Use the square root key
  • Recognise the squares of numbers to at least 12x12
EXT – Recall known facts including fraction to decimal conversions (1R-6.6,6.7,6.8)
Use known facts to derive unknown facts including products such as 0.7 and 6, 0.03 and 8
Multiply and divide integers and decimals (1R-6.8,6.9)
Find the prime factor decomposition of a number (1R-5.5)
Use squares and positive and negative square toots
Key Vocabulary:

MULTIPLY DIVIDE MULTIPLE FACTOR SQUARE ROOT CUBE PRIME HALFWAY POWER

Impact Reference:

Book 1R – ch. 5

/ Other references:

V4 – ch.3,4,8 V5 – ch.4,7

Mental & Oral Starters:

1R folder: pg. 76-78

101 Starters: pg.24-27, 39, 48-51

Discussion opportunities:
Different ways of learning times tables (e.g. using the fingers for the 9 times table). / Pair / Group Work:
Set each other problems
ICT Links:
Many internet games
Maths Mansion programmes 23 & 24
Spiritual/Moral/Citizenship Links:
Discuss how different factors play a part in our lives each day
Investigation: Number patterns produced.

AUTUMN TERM B TOPIC 8

Topic: Decimals

/ NC Level: 4 & 5
NC Programme of Study:
Ref2d: Use decimal notation and recognise that each terminating decimal is a fraction; order decimals.
Ref3ahijk: Add, subtract, multiply and divide integers and then any number; multiply or divide any number by powers of 10, and any positive number by a number between 0 and 1. Round to the nearest integer and to one significant figure; estimate answers to problems involving decimals. Develop a range of strategies for mental calculation; derive unknown facts from those they know; add and subtract mentally numbers with up to two decimal places; multiply and divide numbers with no more than one decimal digit, using factorisation when possible. Use standard column procedures for addition and subtraction of integers and decimals. Use standard column procedures for multiplication of integers and decimals, understanding where to position the decimal point by considering what happens if they multiply equivalent; solve a problem involving division by a decimal by transforming it to a problem involving division by an integer.
Learning Objectives:
  • Understand and use decimal notation and place value
  • Multiple and divide decimals by 10, 100, 1000 and explain the effect
  • Compare and order decimals in different contexts
  • Use standard column procedures to add and subtract decimals with up to 2 places
  • Consolidate and extend mental methods of calculation to include decimals, fractions and percentages accompanied where appropriate by suitable jottings
  • Solve simple word problems mentally
  • Round decimals to the nearest whole number or one decimal place
  • Know and use the laws of arithmetic and inverse operations
  • Make and justify estimates and approximations of calculations
  • Multiply and divide decimals with 1 or 2 places by single digit whole numbers
  • Check a result by considering whether it is of the right order of magnitude and by working the problem backwards
EXT – Recall fraction to decimal conversions (1R-8.8)
Round decimals to one or two decimal places (1R-6.11)
Multiply and divide integers and decimals including decimals such as 0.6 and 0.06; and understand where to position the decimal point by considering equivalent calculations(1R-6.8,6.9)
Key Vocabulary:

PLACE VALUE DECIMAL POINT PLACE ORDER HALFWAY ROUND NEAREST APPROXIMATE ESTIMATE

Impact Reference:

Book 1R – ch. 6

/ Other references:

V4 – ch.12 V5 – ch.1 V6 – ch.2

Bridging Units lessons 11 – 16 (Fractions, Decimals & Percentages)
Mental & Oral Starters:

1R folder: pg. 98-100 101 Starters: pg. 40-52

Discussion opportunities:
Share different ways of solving problems
Where do decimals occur in real life? / Pair / Group Work:
Posters – shop prices/ discounts
ICT Links:

EXCEL can be used for rounding decimals.

Maths Mansion programmes 21, 22, 29 & 30
Spiritual/Moral/Citizenship Links:
Everything is significant no matter how small
Investigation: Investigate use of decimals in real life. What happens when multiplied/divided?
Time: 8 lessons

SPRING TERM A TOPIC 9

Topic: Measuring

/ NC Level: 3 & 4
NC Programme of Study:
Ref4ad: Interpret scales on a range of measuring instruments, including those for time and mass; know that measurements using real numbers depend on the choice of unit; recognise that measurements given to the nearest whole unit may be inaccurate by up to one half in either direction; convert measurements from one unit to another; know rough metric equivalents of pounds, feet, miles, pints and gallons; make sensible estimates of a range of measures in everyday settings. Measure and draw lines to the nearest millimetre.
Learning Objectives:
  • Know that when comparing measurements they must be in the same units
  • Use names and abbreviations of units of measurement to measure, estimate, calculate and solve problems in everyday contexts involving length, area, mass, capacity, time and angle
  • Convert one metric unit to another
  • Read and interpret scales on a range of measuring instruments
  • Use a ruler to draw and measure lines to the nearest millimetre
EXT – Make simple scale drawings
Know rough metric equivalents of imperial measures in daily use
Key Vocabulary:
MEASURE LENGTH DISTANCE UNIT ORDER WEIGHT READ SCALE TIME TIMETABLE
Impact Reference:

Book 1R – ch. 7