Exploring Mathematics- Maths Trail Design - Assignment Example

Name Course Lecturer Date EXPLORING MATHEMATICS- MATHS TRAIL DESIGN INTRODUCTION Mathematics trail can be defined as stop sequences along a pre-determined path or route where pupils or students can examine mathematics in a given area. These trails are very important in the life of a pupil in that it offers the best experience for learning mathematical concepts obtained in class or school syllabus/curriculum. These trails can be designed in such a way that, it fits well with certain topics depending on the grade of the pupil. In choosing these trails, it should be noted that, critical consideration has to be taken so that the pupils mathematical thinking is improved. Not only is the mathematical skills of the pupil is enhanced but also the observational skills because the questions developed give the children the opportunity to solve numerous problems. Further more this trails can serve in exploration of various topics in mathematics on how they are intertwined and how it relates to various disciplines. Maths trails has been found fit in aiding revision of work learned previously and concept reinforcement of ideals learned in class. Children, who undergo trails, have a good reasoning, observing, predictive analyzing and reporting skills. Therefore, when designing these trails, work at each activity station should be structured to cover all levels of ability of the child so that it offers a challenging environment or simplify the task. Language used in the design of this trail is of utmost importance as it enhances easy understanding and clarity. ESSAY Abbotsleigh, Wahroonga, NSW, 2076, is among the best performing schools in Sydney. The school is a pure sex girls school and is located in Wahroonga and has got the highest enrolment of students standing at about 1367 as per the year 2012 statistics. Notably the school has had a strong tradition of excellence in all fields including sporting and importantly academics where mathematics was graded the highest. . The secret to the best results in mathematics and numeracy is mainly due to class and out of class practices. These include designs of mathematical trails so that pupils can be in a position to articulate what she learned in class and the real practical of it. Therefore, here is one hour mathematical trail designed for grade five and six children. The trail involved five activities conducted in five different venues to test counting, Locating, Measuring, Designing, Explaining and playing in classroom, around the soccer field, basketball court, swimming pool and the a hundred meter athletics tract. For the success of this trail, each group should have a clipboard, Pencil, compass, measuring tape, string, magnifying lens and the digital camera. Maths on the field Activity 1: Data handling/Numbers Theme: Gauging use of numbers Venue: classroom Walk and look around the classroom windows and furniture C: Nicholle and Liz are arguing over the number of window panes that exist in the classroom. If one window has got 18 panes with the class having 326 panes. a) What is the total number of windows making up the class? - - - - - - - - - - - - - b) What is the length and the width of each window pane? - - - - - - - - - - - - - - - - L: The class room and the library lie at an angle of 1800 north of the dinning hall a) Who can tell the position of the staff room which is 600 from the classroom? - - - - - - - b) What shape does it make? - - - - - - - - M: If an average desk in the room measures 1.5 meters long and there are 50 desks available. a) Say the total length of all the desks in the classroom. - - - - - - - - - b) Measure the length and the width of the white board and find its approximate area- - - - - - - - - c) Measure the length and the width of the building blocks visible and estimate the total number used in constructing the class.- - - - - - - - - D: Lynn and Avril would like to design a room to accommodate 200 pupils attending a local symposium. Their normal class of 50 has got 25 tables each measuring 3*2 a) What would be the length and the width of the class? - - - - - - - - - - - b) c) Assuming the children are of symmetrical shapes, make different symmetrical patterns that would fit into the rectangle: d) Draw a sketch to redesign the class room to accommodate the dais - - - - - - - E: Explain how to estimate the number of floor tiles used during the construction of the classroom. a) What are the shapes of the tiles used? - - - b) In your personal opinion, what is the significance of the shape you choose? - - - - - c) Calculate the area of your chosen shape - - - - - - - - - - - - P: Estimate the number of leaves in of the flower pot located in the classroom. a) Show the efficient method of arriving at this problem. b) Calculate the height of the flower and estimate the age of the flower - - - - - - - Hint: place uprightly an isosceles right angled triangle such that the equal sides lie parallel to the ground and the other side is perpendicular to the ground. The height of the flower will be equal to your own height plus the distance you are standing away from the flower. While in finding the age of the flower, the girth of the flower is measured by use of string 150cm from the ground the divide the answer by 2.5 Activity 2: Multiplication of fractions Theme: Gauging multiplication skills From the classroom and straight to the school fields C: If the school has 100 acres and one building covers ¼ of an acre; a) Estimate the proportion occupied by buildings in the school compound - - - - - - - - - b) What percentage does the basketball court holds of all the play fields in the compound? - Walking directly to the assembly ground, look around and locate the flag mast L: Taking the flag mast as your point of reference, the class president makes ½ turn of the masts perpendicular angle in a clockwise direction and then moves straight for a length of 10 meters, a) Where does she land? - - - - - - - - - - - - - - - - b) Estimate the angle of turn - - - - - - - From the assembly grounds turn on your left through the car park on your way to the football pitch M: The car park holds 200 vehicles. Assuming that the parking bay is increased by 50%, a) Estimate the number of vehicles that will be parked in the parking bay after the increase. (Measure the Length and with of a single vehicle parked) b) What is the fraction of the park that remains unused? - - - - - - - - - - c) Identify the models of the vehicles in the park and represent them in a graph - - - - - D: By looking at the chapel from the football pitch, Use 3D shapes to construct the model of the chapel and; a) Calculate the fraction occupied by the chapel in the compound. - - - - - - - - - - b) Design a door of your own choice suitable for the chapel and calculate the area of the door E: For every 10m of 100m track, Lynn uses 5 secs, whereas for every 1m of the same track, Jones uses 2 secs. a) Who among the two ran the fastest race? Explain. - - - - - - - - - - - - b) If Lynn were to run twice as fast as Jones , estimate the time used by Lynn to complete - - - - - - P: Jerry, Jayne and Marianne each have got a ball. Jerry holds a football ball; Jayne holds a tennis ball while Marianne holds one for basketball. a) What are the fractions of the circumference of each ball in relation to the volleyball ball? - - - - - - - - - - b) If the basketball ball cost five times the cost of both the tennis ball and the football ball, form equations to indicate the cost of the basketball ball. - - - - - - - - - - - - - - c) Find the surface area of each of the balls. Hint: C=2πR, π is 22/7 Tennis football basketball Activity 3: Geometry Theme: Geometrical skills analysis. Venue: Basketball and football pitch Turn back and walk straight to the goal area of the opposite goals C: Divided in groups; a) Each group is check to identify the different angles made in the field and the goal posts._ - - - - - b) State the number of the different shapes and sketch them on the rectangle provided -- - - - - - -. c) What angles does the rear slanting bars makes with the horizontal? - - - - - - - - Goal post L: Taking the penalty spot as the point of reference, Cynth is a goalkeeper in a soccer match and she is perpendicular to the ball; a) Locate the angle of the ball from the posts of the goal posts. Give your answer in degrees - - - - - - - penalty spot b) Estimate the angles between the following: i. The swimming pool and the basketball court -- - - - - - - - - ii. The basketball court and the triple jump field- - - - - - - - - - iii. The triple jump field and the swimming pool -- - - - - - - - - - M: Each of the children is required to measure the angle made by each of the corners of different fields. a) Give the answer to the nearest degree and sketch. - - - - - - - - - - - - - - - b) Measure the line joining the upper and the lower side of the field and give the angle it makes at the point of joint. - - - - - - - c) Measure the diameter and the circumference of the basketball ring - - - - - D: Grade 5 children are required to construct a model of the library similar to the one next to the swimming pool a) Estimate the angles the roof makes to the horizontal. - - - - - - - - - - - - b) Sketch the different types of shapes the likely to feature in the design E: A tent is set at the edge, of the basketball court. Grade 5 and six pupils argue on the shapes making up the tent. a) Can the class presidents come up with a rough sketch of the tent and explain which shape is it - - - - - -- - -- - - b) What are the angles of the joints making up the tent? - -- - - - -- - -- - -- P: In groups two, each child should make the maximum possible stride and with the help of her colleague. a) Find the maximum angle of stretch by each pupil. - - - - - - - - - - b) Construct shapes of different kinds and measure the corresponding angles. - - - - - - - - - Activity 4: Measurement Theme: Measuring skills Venue: Athletic track Walking out of the football and onto the opposite end, you will the similarity of the athletic track on both ends C: If eight children from grade five and six are set to compete over 50m of 100m track. By use of stop watch and tape measure; a) Estimate the time used by each of the eight children - - - - - - - Hint: D=S*T b) Construct and calibrate the finish line. - - - - - - - - -- -- L: By use of the protractor and the pair of compass, a) Locate the dinning hall which lies at 750 clockwise on the starting point of 100m track. - -- --- b) Draw and estimate the length of the line joining the dinning hall -- - - - - - - - - . M: By use of readily available measuring tools: a) Estimate the width of the 100m track lane. - - - - - - - - -- b) If there are 8 lanes in the tract, what is the total area covered by the 8 lanes. -- - - - - - D: Design the model of the athletic track and by use of established figures: a) Measure the semi circle part of the track and estimate the area of the track - - - - - - - - . b) Calibrate the starting points of all athletes in a 400m race - - - - - - - - - -- - E: Beryll and Rodrigo are set to compete. Beryll is on the first lane whereas Rodrigo is on the eighth lane and both start at the same point. a) Why do you think Beryll finished much earlier than Rodrigo? - - - - -- - -- b) What ought to have been done? -- - -- - -- - P: At a triple jump field event, Merkel’s Jump is three times that of Jessica. If Jessica made a jump of 3m; a) What is the distance of jump made by Merkel? - -- -- - - - - -- . b) What is the range difference of jump between the two - - - - - - - - - Activity 5: Capacity and volume with whole numbers Theme: Application of formulas Moving past the school chapel , on your left is the fence further across is a busy highway and traffic lights. Turn to your left and move past the statue of the schools founder along Wahroonga lane straight to the swimming pool. C: If there are 30 columns in the swimming pool mounted to provide sitting for fans. a) Count the number of seats in a column and the estimate the sitting capacity of the swimming pool. b) At the edges of the swimming pool along lengths, there are numerous circular life saving devices, i. Estimate the radius of one of them and find its area - - - - - - - - ii. Find the total available life rafts found in the swimming pool- - - - - - iii. If one life raft, cost £ 5, what is total cost spent in purchasing all the rafts in the swimming pool? - - - - - - - L: The swimming pool is located at 300 West of the flag mast. a) What is the location of the classroom located 450 from the swimming pool. Sketch - - - - - b) If the class room is located 30m perpendicular and west of the statue, i. Draw a sketch joining the classroom, the statue and the swimming pool. - - - - - - - ii. Using the sketch, calculate the distance between the classroom and the swimming pool. M: By use a tape measure and a chalk, the children with the help of the swimming pool Stewarts sought to obtain the length, width and depth of the swimming pool. a) Using the figures of the measurement estimate; i. The area of the swimming pool - - - - - -- ii. The volume of the swimming pool. - - - - - -- b) Make a sketch of the swimming pool disregarding the deep and the shallow end - - - - D: Using the estimated volume, each group to design a 3 dimensional cylindrical model such that, all models capacity of each group is equivalent to the swimming pool capacity. Hint: V=L*W*H Also volume of a cylindrical shape is, V=1/2Bah .Obviously assuming each group get an equal share of the total volume of the swimming pool capacity P: Using volume obtained in part M, the water tap at the swimming pool uses 60 secs to fill an ordinary 3 litre container. I. Estimate the time used by the tap to fill an empty swimming pool , assuming that the outlet is closed- - - - II. If the outlet jet can fill a 3 litre container in 120secs. How long will the swimming pool be filled if both jets were running at the same time? - - - - - - - III. Calculate the rate of flow of the inlet tap and the outlet tap - - - - - - - - - IV. Pythagoras theorem states that, a2 + b2 = h2 .Estimate the diagonal length of the swimming pool Work cited Bishop, Alan J, Ken Clements, and Christine Keitel. International Handbook of Mathematics Education. Pt. 2. Dordrecht: Kluwer Academic, 1996. Print. Read More