Millburn Academy. Numeracy Across Learning. Name. Department

Transcription

1 Millburn Academy Numeracy Across Learning Name Department

2 Introduction Aim of this Booklet This booklet has been produced as the first step towards teaching numeracy across the curriculum in a consistent manner. The booklet addresses the outcomes which were regarded as the highest priority outcomes in the in the Millburn Academy Numeracy Audit (Oct 009). Further outcomes will be added in due course. How to Use this Booklet The booklet has been designed for teachers to use as a reference in advance of teaching numeracy skills in their own subject. For any clarification on any of the topics please consult a member of the maths department. Many thanks to the maths department for their help in the production of this booklet. - -

3 Contents Page Number & Number Processes Addition Subtraction Multiplication Division Fractions Equivalent & Simplifying Fraction of a Quantity 8 Mied Numbers & Improper Fractions 8 Addition & Subtraction 9 Multiplication & Division 9 Information Handling Averages & Spread 0 Frequency Tables Bar Graphs Line Graphs & Scatter Graphs Pie Charts - -

4 Addition The following words/epressions are used to indicate that numbers should be added together: add, and, find the sum of, more than, plus, find the total of. We can use a variety of mental strategies for addition. Try putting a question on the board and discuss with the class the methods they use. Eample Calculate + 8 Method Add the tens, add the units then add both answers together = = so + 8 = 90 + = 0 Method Starting with the first number add the tens and units digits from the second number separately. + 0 = = 0 Method Round to the nearest 0, then add or subtract to the final answer = 00 since we rounded down to 0 we need to add, and we rounded 8 up to 0 so we also need to subtract. So = 00 + = 0 = 0 The written method is much more structured. Eample 8 + Line numbers up from the left ie unit below units, tens below tens etc Add the units column. Carry the tens digit into the net column. Add the tens column. Add the hundreds column. Carry the tens digit into the net column. Add the thousands column. - -

5 Subtraction The following words/epressions are used to indicate that numbers should be subtracted: subtract, take away, minus, less than, find the difference between. We can use a variety of mental strategies for subtraction. Try putting a question on the board and discuss with the class the methods they use. Eample Calculate 8 - Method Subtract the tens digit then the units digit. 8 0 = = Method Think about addition, what do we have to add to to make 8? + 0 = + = 8 we have to add 0 and so the answer is Method Round to the nearest 0, then add or subtract to the final answer = 00 since we rounded down to 0 we need to add, and we rounded 8 up to 0 so we also need to subtract. So = 00 + = 0 = 0 Written Method - Decomposition Eample 8 - Line numbers up from the left ie unit below units, tens below tens etc ,can t do. Borrow from the net column. -= -= -,can t do. Borrow from the net column. -= -= Eample SUBTRACT Borrow from Borrow from Borrow from thousands. hundreds. tens.

6 Multiplication The following words/epressions are used to indicate that numbers should be multiplied together: multiply, times, product, lots of. We can use a variety of mental strategies for multiplication. Eamples ) Calculate 8 Split the larger number into tens and units, multiply each part by 8 and add the answers together. 0 8 = 00 8 = so 8 = 00 + = ) Calculate 89 Round the first number to the nearest 0 and multiply by the second. 90 = 0 We need 89 so we subtract from the answer. so 89 = 0 = ) Calculate 8 0 When we multiply a whole number by 0 we add a zero. If we multiply by 00 we add zeros, for 000 we add zeros etc. 8 0 = 80 ) Calculate 0 Split the calculation, multiply by then multiply the answer by 0. =, 0 = 0 ) Calculate 0 To multiply a decimal by 0 move all of the digits place to the left. To multiply by 00 move the digits places, To multiply by 000 move them places etc. H T U t h - -

7 Division The following words/epressions are used to indicate that numbers should be divided: divide, share, split. Eamples ) Calculate ) Calculate To divide by we can half the number then half it again. = = 8 ) Calculate 0 0 When we divide a whole number by 0 we remove a zero. If we divide by 00 we remove zeros, for 000 we remove zeros etc. 0 0 = ) Calculate 8 0 If the whole number does not end with zeros we have to move the digits place to the right. We move the digits places to the right when we divide by 00, places to the right when we divide by 000 and so on. =, 0 = 0 H T U t h

8 FRACTION MIXED NUMBER NUMERATOR DENOMINATOR EQUIVALENT IMPROPER FRACTION SIMPLIFYING FRACTION MIXED NUMBER NUMERATOR DENOMINATOR EQUIVALENT IMPROPER FRACTION SIMPLIFYING FRACTION MIXED NUMBER NUMERATOR DENOMINATOR EQUIVALENT IMPROPER FRACTION Many fractions are equal in value. Fractions Numerator The number on the top of the fraction. Denominator The number on the bottom of the fraction. Equivalent & Simplifying We can see that = =. There are an infinite number of fractions which are equal to. We can make equivalent fractions by multiplying the numerator and denominator of a fraction by the same number. This is useful when we want to add or subtract fractions. i.e. starting with the fraction. X Multiplying the numerator and denominator by we get =. Therefore =. We can simplify fractions in a similar way. If the numerator and denominator have a common factor then divide them both by the highest common factor to simplify the fraction. i.e. starting with the fraction the numbers and have the common factors, and. If we divide the numerator and denominator by the highest common factor,, we can simplify the fraction. = FRACTION MIXED NUMBER NUMERATOR DENOMINATOR EQUIVALENT IMPROPER FRACTION - - X

9 FRACTION MIXED NUMBER NUMERATOR DENOMINATOR EQUIVALENT IMPROPER FRACTION SIMPLIFYIN FRACTION MIXED NUMBER NUMERATOR DENOMINATOR EQUIVALENT IMPROPER FRACTION SIMPLIFYIN FRACTION MIXED NUMBER NUMERATOR DENOMINATOR EQUIVALENT IMPROPER FRACTION Fraction of a Quantity A unitary fraction is a fraction with a numerator of. To find a unitary fraction of a quantity we divide the quantity by the denominator of the fraction. i.e. to find ½ we divide by, to find ⅓ we divide by, to find ¼ we divide by etc. e.g. ¼ of 8 = ( 8 = ) If the fraction is not unitary we divide by the denominator and multiply by the numerator. e.g. To find ¾ of we start by finding ¼ of. ¼ of = = 8 ¾ of = 8 = Mied Numbers & Improper Fractions When a fraction has a value greater than it can be written as either a mied number or an improper fraction. e.g. = A mied number has whole number and fraction parts. In an improper fraction, or top heavy fraction, the numerator is greater than the denominator. To change a mied number into an improper fraction: Multiply the whole number part by the denominator this tells us how many fifths are in wholes. Add the answer to the numerator to get the numerator of the improper fraction. The denominator of the improper fraction is the same as the denominator of the mied number. To change an improper fraction into a mied number: Divide the numerator by the denominator this tells us the 0 whole number part of the mied number. The remainder is the numerator of the fraction part of the mied number. The denominator is the same as the improper fraction. FRACTION MIXED NUMBER NUMERATOR DENOMINATOR EQUIVALENT IMPROPER FRACTION - 8 -

10 FRACTION MIXED NUMBER NUMERATOR DENOMINATOR EQUIVALENT IMPROPER FRACTION SIMPLIFYING FRACTION MIXED NUMBER NUMERATOR DENOMINATOR EQUIVALENT IMPROPER FRACTION SIMPLIFYING FRACTION MIXED NUMBER NUMERATOR DENOMINATOR EQUIVALENT IMPROPER FRACTION Fractions Addition & Subtraction When adding or subtracting fraction we must have a common denominator. If we have a common denominator we add the numerators. e.g. + = If the fractions do not have a common denominator we must change one or both of them so that they have a common denominator. e.g. + multiply the first fraction by to give a common 8 denominator or = = e.g. - multiply first fraction by and the second by to give a common denominator of = = Change mied numbers into improper fractions before adding or subtracting. e.g. + = + = + = = Fractions Multiplication & Division To multiply fractions we multiply the numerators and the denominators e.g. = simplify the answer by dividing the numerator 8 0 and denominator by. = Alternatively we can cancel either numerator with either denominator before we multiply. = = 8 To divide we keep the st fraction the same, change divide to multiply and invert the nd fraction. = = Change mied numbers into improper fractions before multiplying or dividing. e.g. = = = = FRACTION MIXED NUMBER NUMERATOR DENOMINATOR EQUIVALENT IMPROPER FRACTION

11 Averages The mean is the total of all of the values divided by the number of values. The median is the middle value when the data is listed in numerical order. If there is an even number of data values then the median is the mean of the middle values. The mode, or modal value, is the value which has the greatest frequency. The mode is useful for non-numerical data i.e. we can find the modal car colour of the cars in the car park. Spread The range is a measure of the spread of the data. The range is the highest value lowest value. Eample Find the mean, median, mode and range for the set of class test marks:,,,,,,,,,,,, 8, 8, 8, 9, 9, 9, 0, Mean = = =. Median -,,,,,,,,,,,, 8, 8, 8, 9, 9, 9, 0, 0 The median is between and, therefore it is.. Mode the most frequently occurring value is. Range = highest lowest = 0 = 8-0 -

12 Frequency Tables A frequency table is used to organise a set of data. Frequency tables can be used for numerical or non-numerical data. No of Siblings Tally Frequency 0 Eye Colour Tally Frequency Blue Brown 8 Green When numerical data has a large range we use a frequency table with class intervals. % Prelim Mark Tally Frequency

13 Number of Pupils Number of Days Bar Graphs A bar graph is a graph consisting of parallel, usually vertical bars with lengths proportional to the frequency with which the quantities occur. Graphs MUST have a TITLE. Number of Hours of Sunshine in January Each AXIS MUST be LABELLED. 0 0 Hours of Sunshine. Method of Travelling to School 0 Walk Bus Car Cycle Method of Travel When the horizontal ais shows categories rather than numerical values we usually leave gaps between the bars. The gaps between different bars MUST be the same width. - -

14 Height (cm) Line Graphs Line graphs have sets of points which are plotted and joined by straight lines. Graphs MUST have a TITLE. Height of Sunflower after Planting Each AXIS MUST be LABELLED Week after planting When asked to find the trend of a graph we are looking for a general description of it. The trend of the graph above is increasing. Scatter Graphs A scatter diagram is used to establish a connection between variables. eg Plot a scatter graph to show the Maths and Physics test marks for a group of pupils. Maths Physics The first line of the table is plotted on the horizontal ais, the second line of the table is the vertical ais. The graph shows a positive correlation between the Maths test marks and the Physics test marks i.e. as the Maths test marks increase the Physics marks increase. A negative correlation means that as one variable increases the other decreases. Negative correlation is shown by a downward trend on the graph. - -

15 Pie Charts A pie chart is a circular diagram used to display data. The pie chart shows the eye colour of 80 first year pupils. Eye Colour Looking at the angles we can see that 90 or 0 have brown eyes, or have green eyes and or have blue eyes. 0 Blue 0 Brown 0 Green So pupils have brown eyes, 0 pupils have green eyes and 0 have blue eyes. 80 pupils were asked to name their favourite game console. The results are: Wii 8, X-bo, Playstation 8, Nintendo DS - 0 Show this information on a pie-chart. Find the fraction of the pie-chart required for each game console. Use the fraction to find the angle required for each game console. Fraction Angle Wii = X-bo - 0 = Playstation = Nintendo DS = Favourite Game Console Nintendo DS ⁰ Playstation 8⁰ ⁰ 08⁰ Wii Remember the Title X-bo - -

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