Maths solving problems
Producing a numeracy booklet to solve problems for a group of four individuals that completed the work book was produced within a group of three people. On studying questions to add into the booklet it was decided to do a mixture of questions with or without a calculator. Multiplication, subtraction, division, fractions and addition were used within this booklet. These questions were produced with thirty questions for the group to work through. With each question each individual had to show the working out for each question. It showed which parts were to be used with a calculator and which to be without a calculator. The questions within the numeracy workbook that had been completed showed that some of the students found that division is still an issue. It seemed that the questions on division were not fully understood on how to work out the problem. This caused some of the marks to be low compared to another student who got nearly all division questions wrong. Having received completed workbooks from four students. It showed that some of the questions were just too complicated without the use of a calculator. All four students found these questions 21-25 particularly hard to complete without the use of a scientific calculator. With the students struggling with these questions the probability of these questions seem to be at the wrong level within this paper. On marking these papers two students did quite well with the questions although the other two students got less marks they all still found the questions difficult to answer. All four students did show good working out for each of the questions that did not require the use of a calculator. Each student used methods of working out that had been learnt over the weeks of numeracy lessons that was attended. On researching each question in both sections with and without calculator it found that some questions were easier than others. If a workbook was to be produced again it would be best to evaluate each question carefully before selecting it to be placed within the workbook.
References
www.cumbria.ac.uk/Public/LISS/Documents/skillsatcumbria/ReflectiveCycleGibbs.pdf [Accessed 23/04/2016]
www.mathswatchvle.com/ [Accessed 23/04/2016]
Appendix
Maths solving questions
Portfolio task 1
Solve these maths problems 1-25 (non-calculator)
1) 497+531=
2) 3549+794=
3) 96521+92561=
4) 22000+10542=
5) 475.62+639.1=
6) 4931- 374=
7) 2563 – 792=
8) 97714 – 3295=
9) 596 – 6723=
10) 348 – 1738 =
11) 325 x 374 =
12) 8751 x753 =
13) 59.67 x 37.2 =
14) 63.9 x 26.8 =
15) 59.47 x 28.9 =
16) 256 ÷ 12 =
17) 550 ÷ 15 =
18) 2703 ÷ 42 =
19) 100 ÷ 20 ÷ 5 =
20) 236 ÷ 9 =
21) 5/6 + 7/3 =
22) 3/8 x 40 =
23) 5/7 of 35 =
24) 2 ¾ ÷ ¾ =
25) 7/9 – 3/8 =
Solve these problems (please show working out) calculator allowed
26) Roger earns £825.00 per month and has been awarded a pay rise of 5% what are his new monthly earnings?
27) If the amount of £80.00 is increased by 30% what is the new amount?
28) If a hospital supplier produces 63,000 syringes in the first half of the year then they produce 55,000 syringes in the final half of the year what is the percentage decrease?
29) If the respiratory rate is 12 breaths per minute, how many breaths are taken in 1 hour?
30) If a man weighs 75kg and 60 % of his body weight is water, how many kg of water does he have?
End of maths solving problem
Portfolio Task 2
Physical Measurements Analysis
A collection of data has been taken from 22 students within the group, the height, weight, head circumference, ankle to knee measurement, forearm length, hand span, eye width and foot length measurements where all taken as part of this physical measurement analysis. A table has been produced to show the analysis of this data as long with a table with the calculations showing the mean, mode, median and range of the readings that were taken from the group of 22 students.
The following graph shows the analysis of data taken from height measurements. This graph shows that there are a number of students that are around the similar height. There is an average of 20cms from the smallest of the group to the tallest.
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The graph below shows the waist circumferences from the 22 students within the group. This graph shows that the student’s waist varies between 60cm and 120cm.
There are weaknesses with the measurements as they may not be accurate measurements to calculate the overall accounts of the group’s results. The theory is if the tape measure that was used may have not been straight to have an accurate reading. The measure could have also been inaccurate due to the individual carrying out the measurement themselves; it most likely would have had a more accurate reading if the measurements were done by another person to give a more accurate reading.
The clothes that the individual was wearing may have also affected the measurement results. Did the individuals stand in the correct position to carry out the height reading or was that person slumped slightly in any way. This can be done if the person is measuring themselves. Two or three readings of each measurement could have been taken to give a more accurate reading to ensure that the readings evaluated to the same measurement.
Measurement table analysis for date collected from the group.
Height Weight (KG) Head Circumference Leg Length Arm Circumference Waist Circumference Ankle to Knee Forearm Length Hand Span Arm Span Eye Width Foot Length
155 45 52.5 62 21 63 32 20 14 145 3 20
156 50.9 53.5 63 25.5 66 33 22 14 145 3 21
160 55 54 75 26 68 35 23 14 150 3 22
161 58.5 54 75.5 27 73 35 23 15 156 3.5 23
162 60 54.5 76 28 75 36 23 16 158 3.5 23
162 65 55 78 28 75 38 23.2 16 160 3.5 24
164 66.8 55 78 28 75 38.1 24 16 160 3.5 24
164 67.3 55 80 28.3 75 39 24 16.5 160 3.5 24
164 68.2 55 83 29 77 40 25 17 160 3.8 24
164 68.2 55 89.5 29 78 40 25 17 162 4 24
165 69 55 91 29.5 80 42 25 17.8 162 4 24
165 71.2 56 92 30 81.5 42 25 18 164 4 24.5
166 73.1 56 93 31 82 43.5 25 18 164 4 25
167 76 56 93 32 84 44 25 18 166 4 25
168 76.3 56 94 33 85 44 25 18 166 4 25
168 77 56 96 33 86 44.5 25.5 18 166 4 25
170 85.9 56.5 96 34 89 45 26 18.5 167 4 25
170.2 89.1 56.5 97 35 94 45 26 19 170 4 25
171 89.5 57 98 35 99 45 26.5 20 170 4 25
172 91 57 99 36 104 46 27 20 172 5 26
172 95.2 57.5 101 36 106 48 27 21 180 5 26
175 105 58 103 40 120 48 28 21 190 6 26.1
The table below is the measurements taken from the group, these measurements have been converted into mean, mode, median and range.
Portfolio task 3
Five items have been chosen for this portfolio task that is within the home. These items have been measured to get the information for the perimeter, surface area and the volume.
Item one
Television remote control, this shape is a rectangle.
Width = 5cm
Length = 25cm
Depth = 2.5cm
Diameter
Length + width + length + width = 25cm +5cm + 25cm + 5cm = 60cm
Surface area
Length x Width = 25cm x 5cm = 125cm²
Volume
Length x width x depth = 25cm x 5cm x 2.5cm = 312.5cm³
Item two
Chocolate bar this shape is a rectangle.
Length 22cm
Width 10cm
Depth 2cm
Perimeter
Length + width + width + length = 22cm + 10cm + 10cm + 22cm = 64cm
Surface area
Length x width = 22cm x 10cm = 220cm²
Volume
Length x width x depth = 22cm x 10cm x 2cm =440cm³
Item three
Book this shape is a rectangle
Length 23cm
Width 15cm
Depth 2cm
Perimeter
Length + width + length + width = 23cm + 15cm + 23cm + 15cm = 76cm
Surface area
Length x width = 23cm x 15cm = 345cm²
Volume
Length x width x depth = 23cm x 15cm x 2cm = 690cm³
Item four
Mirror this shape is square
Length = 30cm
Width = 30cm
Depth = 3cm
Perimeter
Length + width + length + width = 30cm + 30cm + 30cm + 30cm = 120cm
Surface area
Length x width = 30cm x 30cm = 900cm²
Volume
Length x width x depth = 30cm x 30cm x 3cm =2700cm³
Item five
Door mat – This item is a rectangle
Length = 75cm
Width = 50cm
Depth = 2cm
Perimeter
Length + width + length + width = 75cm + 50cm + 75cm + 50 cm = 250cm
Surface area
Length x width = 75cm x 50cm = 3750cm²
Volume
Length x width x depth = 7500cm³
Portfolio Task four
Explanation of charts and graphs
This portfolio task is to discuss the three types of graphs or charts that are to be used. Three different sets of data will be collected to produce a pie chart, bar chart and a scatter graph. With having these three sets of data that is used it will then be discussed the positives and negatives of the charts. Looking to see if the graphs produce a good form of information and whether the graph is continuous or discrete. Continuous data is information that can be measured on a scale that can have any numeric value (bitesize, 2014). Continuous data can be recorded in length, size, width, time. Discrete data can be taken from values; this data can be counted where continuous data is measured.
Pie chart
Pie charts are a visual way of displaying how the total data is distributed between different categories. Pie charts should only be used for displaying nominal data that is classed into different categories. They are best for showing information that is grouped into a small number of categories and are a graphical way of displaying data that might otherwise be presented as a simple table.
Bar chart
The bar chart is to record and compare data. Bar charts also show discrete data. Graphs can show different information of data produced (statistics, 2016). To construct a bar chart then all the information should be listed with the categories that are being used first before producing a chart. The following table shows a survey of nine male and females heights to be recorded onto a bar chart.
female male
1 165 165
2 164 193
3 165 169
4 168 182
5 168 183
6 167 164
7 160 190
8 167 195
9 157 189
This bar chart shows the information given by nine male and females for the height. This bar chart includes discrete data as it shows the number of individuals counted for each height taken in survey. Bar charts are quite useful for displaying data that is classified as nominal or ordinal (The University of Leicester, 2015). With nominal data, arranging the categories so that the bars grade from the largest category to the smallest category helps the reader to interpret the data. However, this not being appropriate for ordinal data as the categories already has an obvious data. Bar charts are also useful for displaying data that include categories with negative values; it is possible to position the bars above and below the x-axis (The University of Leicester, 2015). Bar charts are one of the easiest charts used as they can easily show the data that has been recorded. Bar charts are also simple to create for the data that is provided. Bar charts are also a flexible chart type there are several variations of the bar chart including stacked bar charts, grouped or component charts and horizontal bar charts.
Scatter Graph
Average Height of males in 1836
Age Average height of
males in Factories
9 115
10 120
11 125
12 130
13 135
14 142
15 159
16 152
Scatter graphs are used to show a relationship between pairs of quantitative measurements made for an object or individual. The paired measurements are the age and height of children in 1836 (ceu.hu/, 2015). In a scatter plot a dot represents each individual or object. Within in the scatter graph there it is located with reference to the x-axis and y-axis, each of which represents one of the two measurements. Analysing the pattern of dots that make up a scatter graph it is possible to identify whether there is any systematic or causal relationship between the two measurements. It is clear from the trending pattern that children's height increases with age. Lines can also be added to the graph and used to decide whether the relationship between the measurements can be explained or if it is due to chance.