Year Nine Non- Calculator Numeracy - Assignment Example

Year Nine Non- Calculator Numeracy Name University Q 6. Kevin made these 2 objects by gluing cubes together face-to-face. Object (k) object (m) He then joined the 2 objects together. Which object below could not be made using Kevin’s 2 objects? With the knowledge of addition, I was confident that if I added 2 cubes and 3 cubes together I would end up with an object that had 5 cubes (Hurst, 2006). Object (k) has two (2) cubes which are stacked together, object (m) has three cubes which are stacked or joined together forming a letter (l).I drew diagrams to visualize all possible objects using my developed understanding skills acquired in primary school. Therefore it is very simple to know that the final object must be a combination of the objects (k and m). Therefore the final object must possess a total of five cubes. All the objects on the answers category have five cubes in total. But the manner in which the cubes are joined together is totally different and it is the critical part in determining which object does not have the combination of the objects (k and m). I was open-minded in my solving strategy. Kelvin therefore had to be dynamic in the understanding of the objects. Every learner should let the mind explore all possible designs of the object that could be created. I felt very impressed when I singled out the object that could not be created using the availed cubes. The diagram that shows the object that could never be constructed is shown below. Q 7. Jack drew this graph to show how attendance at concerts is related to ticket price. Which statement best describes the graph? (a) As the ticket price goes up, attendance goes down. (b) As the ticket price goes up, attendance goes up. (c) As the ticket price goes down, attendance goes down. (d) As the ticket price goes down, attendance stays the same. With the extensive knowledge of graph reading and data interpretation developed from my predecessor years of study at the upper primary school, I was not only confident but also ready to tackle the question. Straight line graphs are usually very easy to read and deduce correct answer (“Data Grapher”, n.d). So I proceeded to reading the graph, every time matching a reading on the X- axis and the Y-axis. Attendance was calibrated on the Y-axis while ticket price was calibrated on the X-axis. The first step was to take the first reading, when the ticket retails at the price of $ 10 the attendance stands at 2500 persons in the stadium. When the ticket retails at the actual price of $ 20, the attendance stands at 2000 persons in the stadium. When the ticket price hits a value of $ 30, the attendance drops to 1500 persons in the stadium. The trend shows that the price of ticket goes up when the attendance is low hence I proceeded to the answers category I choose to the answer that read, “As the ticket price goes up, attendance goes down”. As the attendance increases, then it is obvious that the price of the tickets is low enough to be afforded by many persons. There no difficulties experienced in this question since it is a straight line, every sober graph reader knows that a value on the X-axis is normally matched to value on the Y-axis. I even proceeded to finding the gradient of the straight line and found it as negative and its value is of (-50) units. This was obtained by the help of the gradient formula which normally the change in Y-axis divided by the change in the X-axis (Ball, 1990). Below is the calculation ;{( 2000-2500)/ (20-10)} = -50. This principle of negative slope helps us arrive at the answer that the higher the ticket price, the lower the attendance and the higher the attendance, the lower the ticket price. This can be memorized; negative gradient implies a decreasing value on the Y-axis. Q 8. Five students compared their heights. This diagram shows their results. Anna Belle Eva Con Dedans KEY Means is taller than. Which student is the tallest? Anna With excellent knowledge of arrows I gained in mathematics taught at primary school level, I was ready to begin the digest of the chain diagram. As a visual learner, I had to redraw the diagrams to understand better. So I proceeded to the question and searched for the point where the arrow began to point to the next person (first strategy). From the key, I knew that an arrow meant, “Is taller than”. Statement that Anna is taller than Belle is where I began and continued to the following statements, Belle is taller than Con and Eva but Con is taller than Eva. This is achieved by the study of the arrows and rearranging the heights of the persons in a new manner. So the order of arrangement of their heights (Anna, Belle, Con and Eva) is as follows; Anna Belle Con Eva And then Con is taller than Dedans and Eva. Therefore Anna is the tallest of all the contestants (Anna, Belle, Con, Eva and Dedans) in the particular event under consideration. Hence I rearranged the heights as follows; Anna Belle Con Eva Dedans Therefore it is definitely true to state that Anna is the tallest person and seconded by Belle in terms of height and the shortest person is the Dedans. I was doubtful of who is tallest between Con and Eva, but after I studied the chain diagram intensively again, I found out. Being dynamic in the way I did build my ideas and thoughts was very important. Arrows that sometimes point backward are challenging to understand just like that one that pointed from Con to Eva. My solving strategy was to read the direction pointed by the arrow since it meant is taller than, from There I proceeded to the direction of the arrow, perhaps this kind of question was easy and am always confident that I can score all the marks pertaining to it. Q 11. Elli was playing a video game. In the game she had to collect objects that are worth points. The pictures show how many points she scored in three games. The pictures show how many points she scored in three games. Game 1 Game 2 Game 3 170 points 150 points 120 points Key: Represents a Star Represents a flower Represents an orange In Game 4 she collected these three objects: How many points did she score in Game 4? With extensive knowledge about symbols and interpretation skills developed throughout my education level, I was very confident that I can solve this particular question with minimal difficulties. My solving strategy was to make links between the symbols and thereafter work backwards to obtain the numerical value of the symbols. I assigned each symbol a name to avoid confusion. So I started at the game number two. At game 2; A total of 150 points were gathered in the video game played by Elli, she scored a total of three stars which actually represented the figure of 150 points in total. Therefore each star represented a total of 50 points which is obtained after dividing 150 points by three (3). 150/3 =50 points (Ball, 1990). So I proceeded to game number three to obtain the value of the flower symbol. At game 3; A total of 120 points were scored when played the video game, in this particular event, the end results included a total of two stars and a flower. From game 2, I had earlier found that a star implied or generally represented a total of 50 points. Therefore the two stars will accumulate a total of 100 points in that video game played by Elli. Hence from the results under consideration, I find that a flower symbol represents a total of 20 points (120-100= 20 points) (Hurst, 2006), this is the value that the flower symbol represented in the video game played. Still working backwards, I proceed to game number one. At game 1; A total of 170 points were scored by the player of the video game. The end results of this particular video game included two oranges and a flower. I know that a flower from the previous game represents a total of twenty points (20 points). Therefore when I consequentially subtract 20 points from 170 points I actually obtain a total of 150 points which are then represented by the two oranges. Therefore two oranges represent 150 points hence a single orange represent 75 points (150/2 = 75 points) (“Fraction Models”, n.d), this is the actual value that is represented by the orange symbol in the video game under consideration. So now I want to find the score in game number four. At game 4; When Elli played the forth video game, she scored an orange, a flower and a star. When I have an orange, a flower and a star and their underlying values, then it is possible to calculate the number of points that were scored in the forth video game. A flower is equal to 20 points, a star represents a total value of 50 points and an orange represents a total value of 75 points. So at the video game number four (4), she scored a total of one hundred and forty five points. This actual value was obtained through addition mathematics I was taught at primary school level as shown below; 75+20+50 = 145 points, the results in points of the 4th video game played by Elli. Working backward is the strategy to remember but do not memorize the steps of a particular question since they can easily confuse you since questions can be different, be open-minded but remember the main ideas and concepts just as I did while solving this question. Q 13. Voula spins the arrow 100 times. Which table is most likely to show her results? The below table best represents the results that Voula scored after spinning the arrow for 100 times. This decision was arrived at after observing and consideration certain valuables. There are four elements of consideration in this particular event. Shape score symbol 25 plus 10 Triangle 25 Circle 40 square With excellent knowledge of shapes, angles and their relations, all obtained from the years of study at the elementary school (“Fraction Models”, n.d), I was ready and perhaps more confident to solve this particular question. I had developed enough and sound skills to make links and work from approximations to deduce a correct or near correct acceptable answer. So I first assigned each symbol a name to prevent the occurrences of confusion there was a circle, a square, a triangle and a plus symbols. From the diagram in the question, I could easily comprehend that a plus and a circle symbol represented the same score since they are subtended by same angle (900). The triangle symbol represents a value that is half of what is represented by either the plus or circle symbol. I was very right in my judgment since the plus and circle symbol each share 90 degrees while the triangle symbol share just 45 degrees. The square symbol share 135 degrees hence it represented a value that is thrice of what is represented the triangle symbol. My solving strategy was first to determine the value of the angles shared by each symbol and then look for a relation between them, this was an easy task since at octagon is eight sided and can be divided into eight section with each being subtended by an angle of 45 degrees. I proceeded to the answers table and choose the answer shown above my making approximations which were fair enough to say. Making the approximation was the trickiest part of the question since the angle factor had to be considered precisely. It is always good to make fair enough approximation since the art of approximation is in use in most daily activities hence I found it an easy task. Q 16. In a gym class, 29 students took turns jumping. Pete recorded the height each student jumped. Height (cm) 3 2 4 4 1 5 6 5 2 4 4 8 9 6 1 1 3 4 5 6 6 8 9 7 2 2 5 7 8 8 3 5 5 9 1 2 Key: 5 2 means 52 As having studied the upper primary school, I have developed numerous skills and attained extensive knowledge about statistics which are normally in use in every day of our lives, elements such as a mean, mode, median are some of the easy basics of statistics (Kemp & Hogan, 2000), this question was very easy and I was very impressed and confident that it is one of my areas of specialization in mathematics. The strategy to this question was to first read the key and write down the values of the heights of the students. I first read the key, wrote down the heights and arranged the heights, then I had to understand what median is since it is very crucial. Therefore from the above table, the heights of the students were; 32, 34, 41, 45, 46, 52, 54, 54, 58, 59, 61, 61, 63, 64, 65, 66, 68, 69, 72, 72, 75, 77, 78, 83, 85, 85, 91, 92. All the heights were recorded in centimeters. From the basics of the elementary school level mathematics especially those studied in the upper levels, I arranged the heights in an ascending order so as to obtain the median value. The median value is the value that is usually centered between the other values. For example in the numbers; 1,2,3,4 and 5, the median value is the number 3.Therefore from the above results, the arranged heights of the 29 students were in ascending order; Heights: 32, 34, 41, 45, 46, 52, 54, 54, 58, 59, 61, 61, 63, 64, {65}, 66, 68, 69, 72, 72, 75, 77, 78, 83, 85, 85, 91 and 92. The median height value lies at the 15th height value which is 65 cm. Hence the median is 65 cm. As a student I should memorize the definitions of the elements of statistics such as mean, mode, median so that I can always tackle their question in the examinations. Q 25. The area of the rectangle in this diagram below is 10 cm2. B C A D With great knowledge about geometry which is branch of mathematic that deals with triangles, rectangles, trapezium, circles, squares and many more shapes, I knew I would obtain the area of the trapezium as long as I let my ideas be dynamic. I know that the area of the rectangle is obtained by multiplying the length and its width (“Fraction Models”, n.d), this is what I was taught in my elementary school mathematics and in my case its area is equal to 10cm2. I even draw a rectangle to visualize my concept better. Length * width = 10cm2 Width Length I proceeded to the trapezium and deduced that the lengths numbered AE, EB, CF and FD are related by the following principle; AE= EB= CF= FD. That principle implies that all those lengths are equal. I soon realized a solving strategy which is a trick set by the examiner, “Trick: since lengths AE= EB= CF= FD are equal, they also form another rectangle above the first one”. I proceeded to drawing another diagram that showed the merged rectangle. Therefore from that accepted notation of length equableness, we will have the following kind of modified diagram. I felt relaxed once I realized the trick, hence students should study keenly the properties of various shapes used in mathematics so that they can be able to solve mathematical problems that pertain to such shapes, if possible they should memorize the properties of the those shapes. Therefore the actual area of the trapezium figure will be the summation of the areas of the two rectangles which in turn give a total area of 20 cm2. This was an easy task and am always confident that I can score all marks of this kind of question. Q 30. This design is drawn inside a regular hexagon. What is the size of the angle marked (a)? Having been through the upper primary school or the elementary school, I had already studied the trigonometry. This is trigonometry question; you are definitely dealing with angles, triangles and a hexagon as the particulars of the question. Using my trigonometry skills obtained in the mathematics class, I knew the properties of a hexagon which are essential in solving the question. Hexagon is defined as a figure that is regular and six sided figure. The tiresome part was obtaining the exterior and interior angles of the hexagon. Therefore the exterior angle of hexagon I obtained it using the assistance of the following formula, (360/n-1), where, “n” represents the number of sides of the figure. In my case, it was a hexagon and hence the value of “n” is equal to six “6”. So the exterior angle was, (360/ 6-1 = 1080). From the formula I obtained that the value of the exterior angle as 1080. And since a straight line makes an angle of 1800, then the interior angle is 720 which is obtained by subtracting 72 from 180.I proceeded to drawing the diagrams and showing the angles to prevent confusion since I am a visual learner. Angle labeled “a0” 720 Equilateral triangles 1800 Inside the regular hexagon, there exist two regular equilateral triangles. An equilateral triangle is an equal sided triangle with all interior angles being equal. Each of the interior angle amounts to sixty degrees (600) which is obtained by diving 180 by 3 angles. (600). From that principle of understating the equilateral triangle properties. I found out that the value of angle labeled “a” was equal to 240 which was obtained by subtracting 60 from 108 and dividing the answer by 2. My solving strategy was first to understand the properties of the shapes, use the conventional formula and make links between the hexagon, straight line and the equilateral triangle to obtain the answer. This otherwise could never be realized if I did not have the knowledge of the trigonometry. References Hurst, C., (2006). Numeracy in action: Students connecting mathematical knowledge to a range of contexts. In J.Watson&K.Beswick (Eds).Proceedings of the 30th annual conference of the Mathematics Education Research Group of Australasia.Retrieved from http://www.merga.net.au/documents/RP392007.pdf Illuminations (n.d.). Data Grapher.Retrieved from (http://illuminations.nctm.org/ActivityDetail.aspx?ID=204) Kemp, M. & Hogan, J. (2000). Planning for an emphasis on numeracy in the curriculum. Canberra, Australia: Commonwealth Department of Education, Training and Youth Affairs. Retrieved from http://teamat.oxfordjournals.org.dbgw.lis.curtin.edu.au/content/26/2/79.full.pdf+html Ball, D. L. (1990).Prospective elementary and secondary teachers’ understanding of division.Journal for research in mathematics education, 21(2), 132-144. Retrieved from http://www.jstor.org/stable/749140 Illuminations (n.d.). Fraction Models. Retrieved from http://illuminations.nctm.org/ActivityDetail.aspx?ID=11 Read More

This principle of negative slope helps us arrive at the answer that the higher the ticket price, the lower the attendance and the higher the attendance, the lower the ticket price. This can be memorized; negative gradient implies a decreasing value on the Y-axis. Q 8. Five students compared their heights. This diagram shows their results. Anna Belle Eva Con Dedans KEY Means is taller than.

Which student is the tallest? Anna With excellent knowledge of arrows I gained in mathematics taught at primary school level, I was ready to begin the digest of the chain diagram. As a visual learner, I had to redraw the diagrams to understand better. So I proceeded to the question and searched for the point where the arrow began to point to the next person (first strategy). From the key, I knew that an arrow meant, “Is taller than”. Statement that Anna is taller than Belle is where I began and continued to the following statements, Belle is taller than Con and Eva but Con is taller than Eva.

This is achieved by the study of the arrows and rearranging the heights of the persons in a new manner. So the order of arrangement of their heights (Anna, Belle, Con and Eva) is as follows; Anna Belle Con Eva And then Con is taller than Dedans and Eva. Therefore Anna is the tallest of all the contestants (Anna, Belle, Con, Eva and Dedans) in the particular event under consideration. Hence I rearranged the heights as follows; Anna Belle Con Eva Dedans Therefore it is definitely true to state that Anna is the tallest person and seconded by Belle in terms of height and the shortest person is the Dedans.

I was doubtful of who is tallest between Con and Eva, but after I studied the chain diagram intensively again, I found out. Being dynamic in the way I did build my ideas and thoughts was very important. Arrows that sometimes point backward are challenging to understand just like that one that pointed from Con to Eva. My solving strategy was to read the direction pointed by the arrow since it meant is taller than, from There I proceeded to the direction of the arrow, perhaps this kind of question was easy and am always confident that I can score all the marks pertaining to it. Q 11. Elli was playing a video game.

In the game she had to collect objects that are worth points. The pictures show how many points she scored in three games. The pictures show how many points she scored in three games. Game 1 Game 2 Game 3 170 points 150 points 120 points Key: Represents a Star Represents a flower Represents an orange In Game 4 she collected these three objects: How many points did she score in Game 4?

With extensive knowledge about symbols and interpretation skills developed throughout my education level, I was very confident that I can solve this particular question with minimal difficulties. My solving strategy was to make links between the symbols and thereafter work backwards to obtain the numerical value of the symbols. I assigned each symbol a name to avoid confusion. So I started at the game number two. At game 2; A total of 150 points were gathered in the video game played by Elli, she scored a total of three stars which actually represented the figure of 150 points in total.

Therefore each star represented a total of 50 points which is obtained after dividing 150 points by three (3). 150/3 =50 points (Ball, 1990). So I proceeded to game number three to obtain the value of the flower symbol.

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