# Measurement and Geometry

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Measurement and Geometry

## 1. measurement

### 1.1. attributes

1.1.1. length

1.1.2. mass

1.1.3. temperature

1.1.4. capacity

1.1.4.1. connect to volume

1.1.5. teaching sequence (Jorgensen, 2015j; Kanasa, 2015d)

1.1.5.1. 1. identify the attribute

1.1.5.2. 2. compare and order

1.1.5.3. 3. using non-standard units

1.1.5.4. 4. using standard units

1.1.5.4.1. Measurement Olympics

1.1.5.5. 5. derive the formula from first principles

1.1.5.6. 6. application and problem solving

### 1.2. units

1.2.1. measure and compare using

1.2.1.1. scaled instruments

1.2.1.1.1. trunfle wheel

1.2.1.1.2. laser

1.2.1.1.3. ruler

1.2.1.1.4. analog and digital scales

1.2.1.1.5. thermometer

1.2.2. choose

1.2.2.1. appropriate

1.2.2.1.1. length

1.2.2.1.2. volume

1.2.2.1.3. capacity

1.2.2.1.4. mass

1.2.2.1.5. area

1.2.2.2. estimating strategies

1.2.2.2.1. referents - using a known quantity such as your own height to estimate another person's height (Cathcart, 2006, p. 325)

1.2.2.2.2. chunking - estimating the area of a room by first breaking it into several workable parts (Cathcart, 2006, p. 325)

1.2.2.2.3. unitizing - estimating the volume of a pitcher by mentally dividing it into smaller, equal parts such as glassfuls of 250 mL (Catchcart, 2006, p. 325)

1.2.3. convert between

1.2.3.1. metric

1.2.3.1.1. measurement prefixes important to understand

1.2.3.1.2. Length Metric Conversion Rap

1.2.3.1.3. mass - g

1.2.3.1.4. length - m

1.2.3.1.5. capacity - l

1.2.4. connect

1.2.4.1. decimals to metric system

### 1.3. time

1.3.1. am/pm

1.3.1.1. solve problems

1.3.2. conversions

1.3.2.1. conversion tree (design pictorial representations for conversion processes) (Kanasa, 2015d)

1.3.2.1.1. larger to smaller unit requires multiplication - smaller to larger unit requires division

1.3.2.1.2. the numbers divide and multiple by remain the same the whole time

1.3.3. 12hr/24hr

1.3.4. timetables

1.3.4.1. transport i.e. bus, train, plane

1.3.4.1.1. authentic learning from real world contexts supports engagement and makes learning seem more purposeful (Harman & Edelsky, 1989; Shaw & Blake, 1998; Siraj-Blatchford, 1999)

1.3.4.2. school timetable

1.3.4.3. timelines, history

### 1.4. calculate

1.4.1. perimeter

1.4.1.1. rectangles

1.4.2. area

1.4.2.1. 1. Perceive the attribute

1.4.2.1.1. wrapping parcels, colouring in, cutting and pasting, covering items, tessellations with pattern blocks and other materials (Jorgensen, 2015j)

1.4.2.2. 2. Compare and order

1.4.2.2.1. direct comparison using overlaying (Jorgensen, 2015j)

1.4.2.2.2. indirect comparison by covering shapes, cutting them up, reassembling, jigsaws, tessellations, pattern blocks, tangrams (Jorgensen, 2015j)

1.4.2.3. 3. Use non-standard units

1.4.2.3.1. tessellate with shapes

1.4.2.4. 4. Use standard units

1.4.2.4.1. m2, cm2, km2, hectares

1.4.2.5. 5. Derive formulae from first principles

1.4.2.5.1. Students actively engaged in knowledge construction through interaction with concrete manipulative and dialogue with more experienced other (Blakemore & Frith, 2005; Shaw & Blake, 1998; Siraj-Blatchford, 1999; QSA, 2006). Supports students agency in own learning and depth of understanding by allowing them to come to the conclusions through their own supported inquiry (McCuaig & Nelson, 2012; Sorin, 2005; QSA, 2006). Technology a useful tool to engage student interest and to support cross-curriculum priority of multimodal literacy (ACARA, 2015; Seely Flint, 2014)

1.4.2.5.2. Geoboard App - rectangle: reocgnise that it is an array -> apply multiplication concept to work out area -> see that this is the same for all rectangles -> leads to formulae understanding

1.4.2.5.3. Years 7, 8, 9

### 1.5. comparison

1.5.1. qualitative

1.5.2. quantitative

## 5. shape

### 5.1. compare (2D)

5.1.1. regular

5.1.1.1. square

5.1.1.2. traingle

5.1.1.3. rectangle

5.1.1.4. pentagon

5.1.1.5. circle

5.1.1.6. informal means

5.1.2. irregular

5.1.2.1. organic

5.1.3. compound shapes i.e. oval, rectangle, traingle

5.1.3.1. with and without dividing lines

### 5.2. describe (2D)

5.2.1. properties

5.2.1.1. number of sides, corners

5.2.1.2. symmetry

5.2.1.3. length of sides

5.2.1.4. size of angles

5.2.1.5. parallel and perpendicular sides

5.2.1.6. convexitiy and concavity

5.2.1.7. altitude (height e.g. triangle)

5.2.2. relationship between shapes

5.2.2.1. congruency

5.2.2.2. similarity

5.2.2.3. transformation

5.2.3. classification schemes

5.2.3.1. triangles

5.2.3.1.1. by sides (equilateral, scalene, isosceles)

5.2.3.1.2. by angle (acute, right, obtuse)

5.2.3.2. rectangles

5.2.3.2.1. parallelogram, rhombus, trapezoids, squares, rectangles/oblongs

5.2.4. Create a stained glass window

5.2.4.1. students applying knowledge about how to describe shapes (properties, classifications) as well as how to transform them to create a singular image. This activity targets range of levels of Blooms taxonomy from recalling and describing shapes using information about their properties to synthesising this knowledge to create a stained glass window (Bloom et al., 1956; Krathwohl, 2002; Robertson, 2009). Students are also actively engaged with concrete materials to develop understandings (QSA, 2006; Shaw & Blake, 1998; SIraj-Blatchford, 1999).

### 5.3. 3D objects

5.3.1. connect

5.3.1.1. nets

5.3.1.1.1. prisms

5.3.1.1.2. pyramids

5.3.1.1.3. Create opportunities for students to predict what a net of a shape might look like before making one and vice versa.

5.3.1.2. 2D representations

5.3.2. construct

5.3.2.1. Information, teacher and student resources - great information on language to use to describe and therefore communicate about constructions.

5.3.2.2. Skeletons - using toothpicks, PlayDoh, blutac etc. Ensure students are recording their observations and learning during construction phase.

5.3.2.2.1. By transforming information into different forms (physical construction, dialogue with peers into written anchor chart or notes) students are demonstrating higher order thinking and therefore engaging in deeper levels of meaning making (Robertson, 2009)

5.3.3. Test about 3D shapes (maybe use as a diagnostic pre-assessment or periodic formative assessment to gauge students level of understanding to inform instruction) http://www.bbc.co.uk/bitesize/ks3/maths/shape_space/3d_shapes/activity/ http://www.bbc.co.uk/bitesize/quiz/q44861627

## 6. location and transformation

### 6.1. location

6.1.1. interpret

6.1.1.1. basic maps

6.1.1.1.1. simple scales (alpha numeric)

6.1.1.1.2. legends

6.1.1.1.3. directions

6.1.2. use grid references

6.1.2.1. describe location

6.1.2.1.1. UBD

6.1.2.1.2. Battleship

6.1.2.1.3. How Does Your Garden Grow?

6.1.2.1.4. Grid References with Nerf Guns

6.1.3. describe

6.1.3.1. routes

6.1.3.1.1. landmarks

6.1.3.1.2. directional language

6.1.4. cartesian plane - X, Y axis, Quadrant 1 - 4

6.1.4.1. creating a picture from designated coordinates

6.1.4.1.1. Maths can be fun!

### 6.2. transformations

6.2.1. symmetry

6.2.1.1. create

6.2.1.1.1. patterns

6.2.1.2. identify

6.2.1.2.1. line

6.2.1.2.2. rotational

6.2.2. describe (2D shapes)

6.2.2.1. translation

6.2.2.1.1. slide

6.2.2.2. reflection

6.2.2.2.1. flip

6.2.2.3. rotation

6.2.2.3.1. turn

6.2.2.4. enlargement

6.2.2.4.1. reduce, make smaller, decrease

6.2.2.4.2. increase, grow, magnify, make bigger

6.2.2.5. tessellations

6.2.2.5.1. Students actively playing with shapes in a purposeful way at the same time learning about names, transformations and using mathematical language to describe their actions and thoughts building connections with other geometry content knowledge (i.e. properties, transformations etc) (Ebbeck, Yim & Lee, 2013; Perry & Dockett, 2007; Siraj-Blatchford, 1999; Van Oers, 2010;

6.2.2.5.2. Game

6.2.2.5.3. Generator

6.2.2.6. ICT Transformations Activity

6.2.2.6.1. Teaching with technology important in modern society (TTF, n.d.; Koehler, n.d). Promotes multimodal literacy and supports engagement by encouraging learning through a mode students relate to and recognise as purposeful to their lives (Seely Flint et al., 2014).

6.2.3. investigate combinations

## 7. geometric reasoning (angles)

### 7.1. compare

7.1.1. < >90

7.1.1.1. Types of Angles Song

7.1.1.1.1. Learning through range of sensory inputs supports deep learning (Kanasa, 2015a; Jensen, 2005; QSA, 2006)

### 7.2. construct

7.2.1. protractor

7.2.1.1. Online Protractor

7.2.1.1.1. Teaching with technology important in modern society (TTF, n.d.; Koehler, n.d.). Promotes multimodal literacy and supports engagement by encouraging learning through a mode students relate to and recognise as purposeful to their lives (Seely Flint et al., 2014).

### 7.3. investigate

7.3.1. straight line

7.3.2. point

7.3.3. vertically opposite