The Romsey School Mathematics Faculty - Year 8
Topic 1
Number
Links
All pupils should be able to:
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Squares, cubes
and their roots
recognise square numbers and square roots.
Know all square numbers up to 100, and whole number square roots for the same.
make appropriate use of powers and roots function keys on a calculator.
Use correct methods for approximation
perform simple calculations using the 4 basic operations
http://www.mymaths.co.uk/gold/powers/squareNumbers.swf
Most pupils should be able to:
Estimation &
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Recognise cube numbers and cube roots, and index notation for small positive integer powers.
Approximation
Powers & Roots
Powerpoint presentation "Powers and Roots" can be found in the faculty area.
> know that the square root of any number up to 100 lies between two consecutive integers
> Estimate solutions to calculations by rounding to 1 SF
Some pupils should be able to:
> Know that the square root of any positive number can be positive or negative.
> Express very large and very small numbers using standard index notation.
> Express a number as the product of prime factors (prime factorisation), using a calculator as necessary
for 3 digit numbers.
Possible
Starters:
Possible
Misconceptions
Probing
Questions
Assumed
knowledge
Ma1
opportunities
> Use a demonstration 100 square, and ask for estimates for square roots etc
> The square root of anumber lies between which two consecutive numbers?
Use "E-starters" in the starters & plenaries folder in the general resources folder in the maths
faculty area.
"Pick & Point" starter
〈 Manypupilsbelievethat1isaprimenumber–amisconceptionwhichcanariseifthedefinitionistakenas‘anumber
whichisdivisiblebyitselfand1’
〈 Acommonmisconceptionistobelievethat53=5×3=15
〈 Notethatwhilethesquarerootsymbol(√)referstothepositivesquarerootofanumber,everypositivenumberhasa
negativesquareroottoo.
〈 WhenusingEratosthenessievetoidentifyprimenumbers,whyistherenoneedtogofurtherthanthemultiplesof7?If
thismethodwasextendedtotestprimenumbersupto200,howfarwouldyouneedtogo?Convinceme.
〈 Kennysays’20isasquarenumberbecause102=20’.ExplainwhyKennyiswrong.Kennyispartiallycorrect.Howcould
hechangehisstatementsothatitisfullycorrect?
〈 Always/Sometimes/Never:Thelowestcommonmultipleoftwonumbersisfoundbymultiplyingthetwonumbers
together.
> multiplication tables,
> square and square root notation, rounding to nearest unit, ten, hundreds etc
> Dead Ends, End Digits, Consective cubes, Generating Primes
> explore and explain the shape of quadratic, cubic and square root graphs
> Add consecutive pairs or triangular numbers to make square numbers
> Add cube numbers to make the square of triangular numbers
ICT
opportunites
Assessment
Opportunities
> graphical calculators. Draw graph of y=x2 and y=16 (for example )
> Square number fun http://www.learntables.co.uk/square_numbers/
http://hotmath.com/hotmath_help/games/numbercop/numbercop_hotmath.swf
Level 5
Level 6/7