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Estimation & Measurement Rounding Addition, Subtraction, Multiplication & Division

NUMERACY. Estimation & Measurement Rounding Addition, Subtraction, Multiplication & Division Scientific Notation / Standard Form Fractions Percentages Proportion Time Algebraic Expressions, Equations & Formulae Co-ordinates Data & Analysis. Estimation & Measurement.

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Estimation & Measurement Rounding Addition, Subtraction, Multiplication & Division

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  1. NUMERACY • Estimation & Measurement • Rounding • Addition, Subtraction, Multiplication & Division • Scientific Notation / Standard Form • Fractions • Percentages • Proportion • Time • Algebraic Expressions, Equations & Formulae • Co-ordinates • Data & Analysis

  2. Estimation & Measurement • Estimate / measure height and length in mm, cm, m and angle sizes in degreeseg. length of pencil ≈ 10cm width of desk ≈ 0.5m diameter of 1p coin ≈ 15mm • Estimate / measure weight in g and kg, area in cm2, m2 and hectares and volume / capacity in cm3, m3 and l eg. bag of sugar ≈ 1kg area of window ≈ 4m2 volume of drinks can ≈ 300ml

  3. Estimation & Measurement • Learn equivalences100mm = 1cm1000mm = 100cm = 1m1cm3 = 1ml1000cm3 = 1000ml = 1l10000m2 = 1 hectare

  4. Rounding • Round to the nearest whole number, 10 or 100eg. 74 to the nearest 10 = 70 347.5 to the nearest whole number = 348 • Round to any number of decimal places or significant figureseg. 7.51 = 7.5(1dp) 3.14159 = 3.142 (3dp) = 3.14 (3sp) 0.00231 = 0.002 (1sf)

  5. Rounding When the next number is a 5 always round up Always round your final answer to the same level of accuracy as your starting values  Never round as you go along – just at the end  Watch out for necessary roundingeg. If 90 children and 4 teachers go on a trip, how many 40-seater coaches would be needed ? 94  40 = 2.35 coaches which has to be rounded up or some people will be left behind !

  6. Addition, Subtraction, Multiplication & Division • Subtract using decomposition (as a written method)eg. 271-38 233 Do not borrow and pay back • Calculate using alternative mental methods when appropriateeg. 478-99 = 379 by subtracting 100 then adding 1eg. 1+2+3+ ……… +8+9+10 = 11 x 5 = 55

  7. Addition, Subtraction, Multiplication & Division • Use correct order of operationsRemember BODMAS (or BOMDAS) BracketsOrderDivideMultiplyAddSubtract eg. 18 – 7 x 2 = 18 – 14 = 4 eg. (14 + 12)  (6 – 4) = 26  2 = 13

  8. Scientific Notation or Standard Form • Write large or small numbers in standard form and vice versaeg. 24500000 = 2.45 x 107 0.000988 = 9.88 x 104Write as a x 10n where a is between 1 and 10 • Use a calculator to carry out calculations involving standard formeg. To avoid confusion do not use 10x on calculator Different calculators have different displays - learn how yours works

  9. Fractions • Find simple fractions of a quantityeg. 1/5 of 70 eg. 2/3 of 120 = 70  5 = 120  3 x 2 = 14 = 80Divide by the denominator, multiply by the numerator • Use equivalence of widely used fractions and decimalseg. 3/10 = 0.3 eg.

  10. Fractions • Add and subtract fractions Common denominator for adding and subtracting  Never use decimals in a fraction question

  11. Fractions • Multiply fractions

  12. Fractions Cancel numerators and denominators first if possible to simplify figuresAlways write final answer as a mixed numberAlways give your answer in its simplest formNever cancel two numbers on the top/or bottomNever use a common denominator when multiplying

  13. Divide Fractions To divide, invert second fraction and multiplyDon’t use a calculator for calculations involving fractions

  14. Percentages • Find 50%, 331/3%, 10% and 1% without a calculator and use addition to find other amounts eg. 50% of £240 eg. 15% of £360 = ½ of £240 = 10% of £360 + 5% of £360 = £120 = £36 + £18 = £54 • Express some fractions as a percentage without a calculatoreg.

  15. Percentages • Find percentages with a calculator eg. 23% of £300 = 0.23 x £300 = £69 • Express fractions as percentages using a calculatoreg.A caravan was bought for £3000 and sold for £3250 What was the profit as a percentage of the cost price ? Profit = £3250 - £3000 = £250

  16. Percentages • Carry out calculations involving percentage increase and decrease eg. Increase £350 by 15% 1.15 x £350 = £402.50 Always change percentages to decimals when using a calculator  Never use the percentage button your calculator

  17. Proportion • Use the unitary method (ie. find the value of one first, then multiply by the required value) eg. Direct If 5 bananas cost 80p, what do 8 bananas cost ?  3 bananas cost 48p eg. Inverse The journey time at 60km/h is 30 minutes, so what is the journey time at 50km/h ?  The journey time at 50km/h is 36 minutes

  18. Proportion Always communicate answer Don’t round until the last stage

  19. Time • Convert between 12 and 24 hour clockeg. 2327 = 11.27pm Do not write 2327pm • Calculate duration in hours and minutes by counting up to the next hour then on to the required time, including pm  am times Remember the cross-eyed frog ! Never use the percentage button your calculator

  20. D S T Time • Change minutes to hours and hours to minuteseg. 27 mins = 27  60hrs = 0.45hrs eg. 0.2hrs = 0.2 x 60 mins = 12 mins • Use the link between time, speed and distance to carry out related calculationsSpeed = 42 km/h Distance = 800km

  21. Algebraic Expressions, Equations & Formulae Solving Equations • By balancing / using the flag method • Performing the same operation to each side of the equation • Doing ‘undo’ operations eg. undo ‘+’ with ‘-’ • Using statements like “multiply both sides by …”

  22. Algebraic Expressions, Equations & Formulae One equal sign per line, written underneath each otherWork down the pageWrite the letter ‘x’ differently from a multiplication signNever change side, change signDo not write ‘nonsense’ statements, such as 2x = 6 = 3

  23. Algebraic Expressions, Equations & Formulae Formulae • Write down the formulae first • Substitute clearly • Simplify the expression • Communicate answer fully  Always show all steps in workingAlways substitute first, then re-arrange as necessary to solve the equation

  24. Co-ordinates • Cartesian Co-ordinates are pairs of numbers separated by a comma and enclosed in brackets. Each pair of numbers gives the position of a point relative to an origin O, eg. (3,4) is 3 units to the right along the x-axis and 4 units in the positive y-direction and (-3, -2) is 3 to the left and 3 down.  The points are marked where the lines cross, and not in the spacesThe order matters in that (3, 4) is not in the same place as (4, 3) (Remember: along the corridor then up (or down) the stairs !)

  25. Data and Analysis Use a pencil and ruler Give the graph a title Label lines Label the frequency up the side Label on lines, not on spaces

  26. Bar Graph • Construct and interpret bar graphseg. Make sure each bar has equal width Label each bar in its centre

  27. Line Graph • Construct and interpret line graphsThe distance a gas travels over time has been recorded in the table below Distance travelled by a gas over time Plot points neatly using a cross or dot If the lower point of a graph has beenmissed out, use a jagged line to show this

  28. Scatter Graph • Construct and interpret scatter graphs Draw a line of best fit when there is a correlation

  29. Pie Charts • Construct pie charts involving simple fractions, decimals or percentages eg. 30% of pupils travel to school by bus 10% by car, 55% walk and 5% cycle Bus 30% of 360° = 108° Car 10% of 360° = 36° Walk 55% of 360° = 198° Cycle 5% of 360° = 18°360°  check

  30. Pie Charts • Construct pie charts of raw data eg. 20 pupils were asked “what is your favourite subject?” Replies were Maths 5, English 6, Science 7, Art 2 Maths 5  20 x 360° = 90° English 6  20 x 360° = 108° Science 7  20 x 360° = 126° Art 2  20 x 360° = 36°360°  check

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