NUMBERS AND THE NUMBER SYSTEM - Key Stage 3 Framework Years 7, 8, and 9

Year

Page

Ref

Key Objective Objective

pcMaths package

Place value, ordering and rounding

Pupils should be taught to: Understand and use decimal notation and place value; multiply and divide integers and decimals by powers of 10

7

36

Understand and use decimal notation and place value. Read

and write any number from 0.001 to 1 000 000, knowing what each digit represents

Add & Subtract Decimals 1

(Starter & Plenary)

Multiply Decimals by 10

36

Know the significance of 0 in 0.35, 3.05, 3.50

Add & Subtract Decimals 1

Multiply Decimals by 10

36

Add or subtract 0.1 and 0.01 to or from any number.

Add & Subtract Decimals 1

Add & Subtract Decimals 2

38

Multiply and divide numbers by 10, 100 and 1000.

Multiply Decimals by 10

38

Investigate, describe the effects of, and explain multiplying and dividing a number by 10, 100, 1000, e.g. using a place value board,

Multiply Decimals by 10 (Plenary)

Div by 10 100 1000 (Starter)

38

When a number is multiplied by 10, the digits move one place to the left:

Multiply Decimals by 10 (Plenary

38

When a number is divided by 10, the digits move one place to the right

Div by 10 100 1000

Div by 10 100 1000 (Starter & Plenary)

8

37

Read and write positive integer powers of 10.

Powers of 10

37

Add or subtract 0.001

39

Multiply and divide numbers by 0.1 and 0.01.

Starters & plenaries to:

Multiply Decimals by 10

Equivalent Multiplications

39

In particular, recognise how numbers are increased or decreased by these operations.

Starters to:

Div by 10 100 1000

Multiply Decimals by 10

39

Multiplying by 0.1 has the same effect as multiplying by 1⁄10

Starters to:

Div by 10 100 1000

Multiply Decimals by 10

Equivalent Multiplications

39

Multiplying by 0.01 has the same effect as multiplying by 1/100 or dividing by 100.

Starters to:

Div by 10 100 1000

Multiply Decimals by 10

Equivalent Multiplications

39

Dividing by 0.1 has the same effect as dividing by 1⁄10 or multiplying by 10.

Starters to:

Div by 10 100 1000

Multiply Decimals by 10

Equivalent Multiplications

39

Dividing by 0.01 has the same effect as dividing by 1⁄100 or multiplying by 100.

Starters to:

Div by 10 100 1000

Multiply Decimals by 10

Equivalent Multiplications

9

37

Extend knowledge of integer powers of 10.

Powers of 10

Equivalent Multiplications (Starter & Plenary)

39

Multiply and divide by any integer power of 10.

Equivalent Multiplications

Begin to write numbers in standard form,

Powers of 10

Pupils should be taught to: Compare and order decimals

7

40

Use, read and write, spelling correctly: decimal number, decimal fraction, less than, greater than, between, order, compare, digit, most/least significant digit… and use accurately these symbols: =, ≠≠, <, >, ≤,≥.

Number Vocabulary

40

Know that to order decimals, digits in the same position must be compared, working from the left, beginning with the first non-zero digit

Decimal Scales

40

Identify and estimate decimal fractions on a number line and find a number between two others by looking at the next decimal place.

Decimal Scales

40

Use a computer simulation to zoom in and out of a number line to compare and order decimals to at least 2 d.p.

Decimal Scales (Starter)

8

40

Know that to order decimals, digits in the same position must be compared, working from the left, beginning with the first non-zero digit. Extend to negative numbers

Decimal Scales

41

Identify decimal fractions on a number line and find a number between two others by looking at the next decimal place.

Decimal Scales (Activity 2&3)

41

Use a computer simulation to zoom in and out of a number line to compare decimals to at least 3 d.p.

Decimal Scales (Starter)

Pupils should be taught to: Round numbers, including to a given number of decimal places

7

42

Use, read and write, spelling correctly: round, nearest, to one decimal place (1 d.p.)… approximately…

Number Vocabulary

42

Round positive whole numbers to the nearest 10, 100 or 1000,

Rounding Whole Numbers 1

43

Round positive whole numbers and decimals.

Know that if a measurement is half way between two numbers it is normally rounded up to the next number.

Rounding Whole Numbers 1

Rounding Decimals 1

Round decimals to the nearest whole number or to one decimal place.

Rounding Decimals 1

8

43

Use vocabulary from previous year and extend to: recurring decimal…

43

Round positive whole numbers to a given power of 10

Rounding Whole Numbers 1

45

Recognise recurring decimals.

Recurring decimals contain an infinitely repeating block of one or more decimal digits.

Simple Division 123

45

Round decimals to the nearest whole number or to one or two decimal places.

Rounding Decimals 1

9

43

Use vocabulary from previous years and extend to: significant figures,

45

Round decimals to the nearest whole number or to one, two and three decimal places.

Rounding Decimals 1

46

Understand upper and lower bounds.

Rounding Whole Numbers 1 (Plenary)

Integers, powers and roots

Pupils should be taught to: Order, add, subtract, multiply and divide positive and negative numbers

7

48

Use, read and write, spelling correctly: integer, positive, negative, plus, minus… and know that –6 is read as ‘negative six’.

Number Vocabulary

48

Order integers and position them on a number line.

Decimal Scales

Ordering Decimals (Level 1)

48

Begin to add and subtract integers.

Missing Link 1 & 2

Totally PYRAMIDS 1 2 & 3 4

48

Answer open-ended questions such as:

• The answer to a question was –8.

   What was the question?

• The result of subtracting one integer from another is –2.

   What could the two integers be?

• The temperature is below freezing point.

   It falls by 10 degrees, then rises by 7 degrees.

   What could the temperature be now?

Missing Link 1 & 2

Totally PYRAMIDS 1 2 & 3 4

Subtract Whole Numbers 123 (Plenaries)

8

49

Order positive and negative decimals.

Decimal Scales

Ordering Decimals (Level 1)

49

Add and subtract integers.

Missing Link 1 & 2

Totally PYRAMIDS 1 2 & 3 4

Subtract Whole Numbers 123 (Plenaries)

51

Multiply and divide positive and negative numbers.

+-X div grid 01

51

Link known multiplication tables to negative number multiplication tables

Learning Number Bonds

+-X div grid 01 (Starter B)

51

Write tables, continuing the pattern:

2 x 2 = 4    2 x  –2 =  –4

1 x 2 = 2    1 x  –2 =  –2

0 x 2 = 0    0 x  –2 =   0

+-X div grid 01 (Starter B)

51

Complete a multiplication table. (+ & - results)

Learning Number Bonds

+-X div grid 01

51

Use the sign change key on a calculator to work out:

48 x –53;   –74 x 3 9;   0.2 ÷ –22

Using a calculator 1 (Plenary)

51

Solve puzzles such as:

• Complete (this) multiplication grid. (+&-)

+-X div grid 01

51

Extend to the distributive law.

(Double one) x (Half the other)

Pupils should be taught to: Recognise and use multiples, factors and primes; use tests of divisibility

7

52

Use, read and write, spelling correctly: multiple, lowest common multiple (LCM), factor, common factor, highest common factor (HCF), divisor, divisible, divisibility, prime, prime factor, factorise…

Number Vocabulary

52