TEACH210 Assignment 1 - Worthwhile tasks in geometry and measurement PDF

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Worthwhile tasks in geometry and measurement...

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TEACH210 - Mathematics

Assignment 1

Artefact One: How Maui Slowed the Sun [ CITATION Gos08 \l 5129 ]

Worthwhile Task: After reading the picture book "How Maui Slowed the Sun" by Peter Gossage", students look particularly at the pictures on the rafters of the wharenui, the tukutuku in the middle of the wharenui and the tukutuku in the middle of the picture and on the walls of the whare. Students are asked 'what do they notice about these?' The red, black and white patterns have symmetric elements to them. Students are given different panels like the ones given (see activity one below). The students are asked to see if the designs given have reflectional symmetry. If the patterns do have reflectional symmetry students draw a line to represent the line of reflection. For each image, students must make a statement based on what the image is showing. e.g. The tukutuku panel has two lines of symmetry. One horizontal, one vertical. A second activity is where students are given a half pattern like the top of the whare in the book. (see activity two below for reference) students create a mirror image of the pattern alongside it.

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Activity One:

Activity 2:

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“Describe the transformations (reflection, rotation, translation, or enlargement) that have mapped one object onto another.”[ CITATION Min07 \l 5129 ] This achievement objective has best reflected the aim of the task chosen. The task looks specifically at reflections in the patterns of the panels of the whare, tukutuku panels inside the house. Reflection can be seen in the panels in up to two ways. The patterns given to draw the line of symmetry on has up to four lines of symmetry which reflect an identical pattern in the mirror.

Reading 1: The article "Engagement with mathematics: what does it mean and what does it look like?" talks about what engagement in the classroom looks like for mathematics, how to Page 2 of 6

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create an engaging lesson and student’s opinion of engaging lessons. The article notes on a year six perception of what makes a 'good' lesson. In this case, engagement is the result of a lesson being 'good'. The students noted the lessons were 'good' because they involved physical activity, active learning involving materials and activities with a game involved. Another aspect of the lessons being 'good' brought us was the link between mathematics and the real world. The task being complete by students involves the history of Māori people and the Māori legend of how Maui raised the sun. The lesson also incorporates the traditional layout of a whare by looking at the tukutuku panels on the walls of the whare and the patterns of the kowhaiwhai along the top of the whare.

There is currently more focus on the importance of transformational geometry, such as symmetry in the curriculum (Sinclair & Bruce, 2015). By incorporating elements of symmetry and New Zealand myths and legends in education, there can be more knowledge about the legends as well as incorporating symmetry into the curriculum. Once students begin to understand the incorporation of symmetry in the New Zealand Marae and Whare designs, they will see how much symmetry is used in the ‘real’ world

The key mathematical ideas branching off this activity is the idea of the idea of transformations. This term “describe actions on shapes that result in some form of pattern”[ CITATION TeK19 \l 5129 ]. The students in this activity should be able to look at the original image or shape and describe what happened to the shape after it went through the transformation. Students at level three should be able to describe what happens to the shape e.g. the second activities description would state: The pattern has been reflected in a mirror image of horizontal symmetry. In the next level of the curriculum, the students will begin to learn the properties of the shape which change and do not change. In level two prior to this task, students predict what will happen if a transformative event will occur (Ministry of Education, 2007). For the first activity where students look at how many points of symmetry an object has, the statement written would be along the lines of “This shape has four lines of symmetry. Three horizontal spaced evenly and one vertical line of symmetry.”

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Artefact Two: Astronaut Chris Hadfield and Chef Traci Des Jardins Make a Space Burrito

https://www.youtube.com/watch?v=f8-UKqGZ_hs Astronaut Chris Hadfield and Chef Traci Des Jardins Make a Space Burrito (May, 2013) Worthwhile Task: NASA uses cubes as storage space for food (seen in the background of the clip). Each cube holds of one week worth of food. • Each cube must be sealed on each edge • Which net will cost NASA the least? Each square of the net costs NASA $10. The parcels will need to be 1 cube total to 4 cubes total. For each new parcel shape, students must: • Draw a diagram of the 3D shape and a net of the shape • In a table include, ○ Number of weeks the package is being used for ○ Total amount of squares used ○ Total cost of the net ○ Total cubes on the base of the pattern ○ Total cubes high the pattern is ○ Total cubes deep the pattern is. After creating the 3D models and filling out the table, explain in a statement what you have found out and why (using evidence) Represent objects with drawings and models." [ CITATION Min07 \l 5129 ] The achievement objective for this task is as said above. Each cube of food is drawn and created by the student showing a 2D net and a 3D model. Students figure out how these come together. Each cube represents one week worth of food. The students will be making physical models of the cubes alongside a 2D net. Beryfogle and Williams explain what makes a task worthwhile in their article "Designing and Implementing Worthwhile tasks"(2008), they determined four questions one should ask themselves when designing a worthwhile task. The most question I focussed on was "Does it Page 4 of 6

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[the worthwhile task] allow for multiple solution methods or approaches?" (Page 277). In this task, students have many different approaches to completion. The students can create the nets first, fill out the table with the dimensions of the shape and fill out the table using the diagrams they draw as reference, or draw diagrams fist followed by nets and data. The task asks students to find out five different net shapes for the initial single cube. This gives students a different perspective on how to approach the following shapes once there are more cubes added in (Beryfogle & Williams, 1986). Fitzgerald & Shroyer created a book called "Mouse and Elephant: Measuring Growth" (1986). The book gives an outline on what students should have as a goal (unknown to them). They are learning in the lesson about volume and surface area using the terminology in the story. The terminology used for volume is weeks' worth of fool. Surface area is number of squares used. Students also learn about dimensions of a shape (base, height and depth). Mentioned in the introduction of the book was the Instructional model. The idea is to launch, explore and summarise the lesson plan. The 'launch' is pitching the challenge to students to design a structure for NASA to hold food. The exploration is done by asking questions, redirecting students should they need it. Summarisation is when at the end of the lesson students come back and talk about their finding and compare notes on what they have found and the results they collected[ CITATION Fit86 \l 5129 ]. When students are summarising and discussing their results, there is a part of the task which could lead to some debate. When students make a net for four cubes of food, they could get the answer is either $180 or $160 as the cost for four cubes to go. This is because two different styles of net can be used[ CITATION Fit86 \l 5129 ].

The key mathematical idea in this task is one three-dimensional shape is made from a net. There are eleven different nets which can form a cube.[ CITATION Fit86 \l 5129 ] The mathematics used in the task is multiplication of the cost of the shape between the number of squares and $10/square. Students in this activity should be able to create the intended shape using the net from another student and vice versa. Another idea which could support children to learn is the need to create a shape based on a drawing[CITATION TeK19 \l 5129 ]. In this task, students draw a diagram of the 3D shape. This is so students can begin to understand the shape in plain view and in a net form. The ability to recognise a shape from a net is a skill which comes in use in finding the surface area of an object which is an achievement objective of stage four[CITATION Min07 \l 5129 ]. See picture below for example of the first shape.

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Attard. C (2012) Engagement with mathematics: What does it mean and what does it look like? Australian Primary Mathematics Classroom, 17(1), 9-13. Breyfogle, L. & Williams, L. (2008). Designing and implimenting worthwhile tasks. Teaching Children Mathemetics, 15(5), 276-280. Fitzgerald, W., & Shroyer, J. (1986). Mouse and Elephant: Measuring Growth. California: Addison-Wesley Publishing Company. Gossage, P. (2008). How Maui slowed the Sun (3rd ed.). Auckland: Puffin Books. Ministry of Education. (2007). The New Zealand Curriculum. Wellington, New Zealand: Learning Media Limited. Ministry of Education. (2019, July 22). GM3-4: Represent objects with drawings and models. Retrieved from TKI: NZ Maths: https://nzmaths.co.nz/ao/gm3-4-represent-objectsdrawings-and-models Sinclair, N., & Bruce, C. (2015). New opportunities in geometry education at the primary school. ZDM, 47(3), 319-329.

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