Week 10 Activity) Statistics

MATHEMATICAL CONTENT KNOWLEDGE -

Statistical literacy is needed by all students to interpret the world. Statistics is distinct from

mathematics, as one key difference is focus on variability of data in statistical reasoning.

Doing statistics involves a four step process: formulating questions, collecting data, analyzing

data and interpreting results. Data are gathered and organised in order to answer questions

about populations from where the data came from. There are different types of graphs and

other representations to provide different information about the data and the population the

data was taken from. Measures that describe data with numbers are called statistics. Both

graphs and statistics can provide a sense of shape of the data.

PEDAGOGICAL CONTENT KNOWLEDGE -

The four steps of doing statistics is a useful approach in teaching the concept to primary level
students.

1. Formulate questions: Students are able to choose topics of their interest, and ones that can be easily answered by the population in their classroom E.g. favourite movie, games, ice-cream flavours
2. Collect data: Help students design a plan to collect appropriate data, whether it is visiting another classroom to compare their results to their own classroom, or surveying teachers or family members 
3. Analyze data: Students have the flexibility to learn and create different graphical methods to represent their data. E.g. bar graphs, tally charts, circle charts, picture graphs, line plots, stem and leaf plots, histograms, line graphs, scatter plots, etc.
4. Interpret results: ask students questions on what they have learnt through this data, or what the data tells them. Focus on mathematical questions that are statistical in nature.

Reference: (Van et al., 2015)

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Activity - Interpreting Data

Year Level - 5

Classroom Context -

For students of diverse cultural backgrounds, ensure there is a culture for respect in the classroom.

Ensure objects and materials around the classroom and school are geared to include diverse cultural
backgrounds of all students. Provide opportunities for students to share their cultural stories and be

open to different ideas (if they wish to include some culturally diverse ideas into their assignment

projects such as this one). Stay mindful and sensitive to these children to create a safe environment

and to reduce communication difficulties.

Content Descriptor -

Pose questions and collect categorical or numerical data by observation or survey (ACMSP118)

Learning Objectives -

This learning activity allows students to develop skills in in collecting, representing, analysing

and evaluating information, using both digital and non-digital tools to demonstrate their

understanding.

Resources -

Key Mathematical Language:

Statistics, surveys, data, excel, spreadsheet,

Materials:

Computers, Microsoft Excel, poster paper, glue, scissors, pens, tally data collecting sheet

Use of ICT:

The use of computers and Microsoft Excel are included in this activity. Excel is an important

program to understand, as it plays a key role in many sectors such as spreadsheet programs in

business activities, classwork and even personal data organisation. Using computers to design

their project is also an engaging and visual approach in learning.

Prior Knowledge -

Justifies data collection methods to fit the context

Interprets and uses structural elements in data displays (labels, symbols)

Displays information using real objects or photographs

Instructions -

• Explain to the class that statistics involves a four-step process: formulating questions, collecting data, analyzing data, and interpreting results. Ask the class to copy these notes down.
• Begin with a simple demonstration
• Formulating questions: Write the key question on the board - e.g. What is your eye colour?
• Draw a table on the board with a list of common eye colours and an ‘other’ option
• Collecting Data: Go around the class asking for each student’s answer and draw tallies in the table to record results
• Analyzing Data: Select graphical method - e.g. using a bar graph to represent data. Log into Microsoft Excel to give a tutorial on how to create graphs using collected data
• Interpret Results: Relate interpretation to original question - e.g. write 2 to 3 sentences on your findings, such as the most common answer, least common, any interesting findings.
• Explain to the class that they must conduct their own survey by choosing a topic of their choice, collect data from a group of individuals, analyze this data by creating a graph on Microsoft Excel, interpret their findings, and create a poster including the above information to present to the class. 
• Hand out the tally (data collecting sheet) to all students and help each student with their topic/question ideas to ensure it is reasonable
• Provide extra assistance and time for students to practice making different graphs in the computer rooms
• Ensure you allow students to print their graphs so they can glue it onto their posters
• Either organise time for the class to conduct their surveys within their own classroom, or organise a time to visit another classroom (whichever grade) to survey

Questions to ask -

What do these results and findings tell us about our class?

What is the most common eye colour?

What is the least common?

Do you think these results will differ with other grades or populations?

Enabling Prompts -

Instead of asking students to survey an entire grade, allow them to survey a small group

of people to begin with.

Extending Prompts -

Encourage students to practice making multiple graphs using the same data they collected

and observe which graph is most suitable for their particular topic.

Images -  

 A student example of their data collecting (tally) sheet and their chosen question.

 Students will use Microsoft Excel to create their representation models.

A student example of what graph model they choose to use and the collected data.

 An example of how a student may choose to present their poster.

Reflection -

For our final activity plan, our topic was statistics; including representing data, displaying data,
analysing data and the importance of using graphs. Graphs are mathematical models that
children learn to use in order to tell stories, misinform and persuade. Statistics are everywhere
in our daily lives, hence it is important to equip our students with the skills to understand and
interrogate figures so they can understand what they really mean and represent. I remember
learning about collecting data and creating surveys during my time in primary school. These
activities usually consisted of looking at characteristics such as hair colour, eye colour, and
siblings. The activity I created above represents a fun, engaging and practical way to allow
students to learn about data, statistics and representational modelling. It incorporates social
interaction with other groups of people, as well as using ICT to create graphs. In the future, I
think it would be a great idea to allow students to use more real-world application of statistical
analysis - which can be done by exploring statistics from online resources and researching real-
world articles on everyday issues.

References -

Van, D. W. J. A., Karp, K. S., & Bay-Williams, J. M. (2015). Elementary and middle

school mathematics: teaching developmentally, global edition. Retrieved from

https://ebookcentral-proquest-com.ezproxy.library.uq.edu.au

Week 9 Activity) Measurement

MATHEMATICAL CONTENT KNOWLEDGE -

Measurement is a process that shows how much there is of something, but prior to this, there

are considerations that include which attributes will be measured, what objects (non-standard)

or standard tool will be used to measure it, and which unit of measure will be used. Finally, the

measurement will be taken, which is the distance between two endpoints. When measuring,

estimation skills will become helpful, as well as ensuring there is comparative language,

repeated units of measure, and no gaps or overlaps. Measurement concepts include geometric

or spatial measure such as length, area, volume and capacity. It also includes physical attributes

such as mass, weight, time and money. Units of measurement include everyday units, non-

standard units and standard units. Measurement is important to teach and learn as it provides

many life applications, transfers to other mathematical topics, transfers to other curriculum areas,

requires active learning, and flows from problem solving.

Common misconceptions:

Mass poses particular problems for some students as they confuse it with volume, size or

quantity. A common misconception is that the bigger the size of an object, the greater the mass.

This occurs when judgement is made based on sight rather than on feel (which is a transfer from

learning about length).

For example -

Students might think a tennis ball is heavier than a gold ball because it is larger.

Students may think that 5 ping-pong balls weigh more than a basketball because there are

more of them.

Other misconceptions include:

Measuring from the wrong end of the ruler or beginning at 1 rather than 0, counting the hash

marks rather than the space (units), not aligning two objects when comparing them

PEDAGOGICAL CONTENT KNOWLEDGE -

Strategies in teaching measurement can include the ‘sequence of experiences.’

Step 1, students make comparisons E.g. which object is heavier/lighter? taller/shorter?

Step 2, students use models of measuring units E.g. use physical models to fill, cover,

match or make the desired comparison of the attribute with the unit (paper clips or pieces

of string)

Step 3, students use measuring instruments E.g. use these in comparison to actual unit

models to see how the measurement tool performs the same function as the individual units

Reference: (Van et al., 2015)

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Activity - What’s the Length?

Year Level - 2

Classroom Context -

For students who may speak English as a second language (ESL) in the classroom, ensure

to make each instruction visual. Write instructions on the board, use diagrams, model the steps

of a process and give further assistance to them during individual working time. Build in more

group work to ensure ESL students are practicing the English language and socially engaging

with their peers.

Content Descriptor -

Measure, order and compare objects using familiar metric units of length, mass and capacity

(ACMMG061)

Learning Objectives -

Students will be able to estimate and measure lengths using centimetres and metres

Resources -

Key Mathematical Language:

Units, length, centimetres (cm), metres (m), width, measurement, estimation

Materials:

Metre rulers, centimetre rulers, measurement recording sheet, everyday objects in the classroom

Prior Knowledge -

Identifies the attribute of length (using gestures)

Identifies the longest object using direct comparison

Compares the length of two objects by aligning the ends

Uses everyday language to describe attributes that can be measured

Compares objects and explains how they have been ordered using comparative

language (shorter, longer, lighter, heavier)

Using informal units of measurement

Instructions -

• Show the class a 30cm ruler and a 1 metre ruler, discuss and question the students asking them what they think each one can be used for. Ensure students know that there is 100 cm in a metre. 
• Explain that they will be measuring the length of different objects. Show the students what they must do to correctly measure length with these rulers
• Explain to students how to estimate the length of an object - E.g. Is my coffee mug more likely to be 10 centimetres or 10 metres? Explain that an estimation is an educated guess
• Walk around the classroom to demonstrate by measuring different objects with both the centimetre ruler (e.g. pencils, books) and the metre ruler (e.g. one side of the classroom floor)
• Give all students a recording sheet for measuring, where they must look at the object they need to measure the length of, make an estimation, measure it, and record all their details in the sheet
• Make each student have a partner to work with as they walk around the classroom/outside the room to measure objects
• To close the activity, gather all pairs back into the room to share their measurements (as some may not get to measure all of them) and share any items they found difficult to measure or if they were unsure of which sized ruler to use
• Explain that certain objects can be measured in both centimetres and metres (E.g. desk)

Questions to ask -

Is 1 centimetre or 1 metre longer?

Should you measure this object in centimetres or metres?

What is the best way to measure this object?

How did you find out the length of this?

What is your estimation of the length of this object?

How many centimetres are there in a metre?

Enabling Prompts -

Have students measure 5 objects of the list rather than 10 OR allow students to begin

with informal units such as fingers or string. Once confident, move towards using rulers.

Extending Prompts -

Challenge students with larger measurement tasks - e.g. measure the length of our

entire classroom.

Images -  

  A 30cm ruler that students would use to measure smaller items with.

 A metre ruler to measure larger items with.

The worksheet that students must fill out by measuring the correct objects.

Reflection -

In week 9, our focus topic was on promoting conceptual understanding of measurement
concepts and relationships. For students to become proficient with measurement, they must
experience a variety of measuring tools. Such experiences should be in contexts that are
meaningful to students and give them a sense of accomplishment and appreciation of the
usefulness of measurement. Measurement is significantly connected to other concepts in
mathematics and with other key learning areas. Examples of real-world contexts in relation
to measurement skills include using thermometers, scales, and measurement tools to measure
how tall we are, how hot we are, how heavy we are, etc. In the above activity, the students were
given the opportunity to measure everyday items around the classroom to experience the
importance of measurement in everyday life. I hope I get to plan practical and useful
measurement activities like this one in my future classroom.

References -

Van, D. W. J. A., Karp, K. S., & Bay-Williams, J. M. (2015). Elementary and middle

school mathematics: teaching developmentally, global edition. Retrieved from

https://ebookcentral-proquest-com.ezproxy.library.uq.edu.au

Week 8 Activity) Geometry

MATHEMATICAL CONTENT KNOWLEDGE -

MCK of geometry includes properties of 2D and 3D shapes, classification including hierarchical

thinking, transformations, relationships between 2D and 3D figures/objects, representations,

visualisation, and location.

Shapes:

• 3D shapes are categorised into curved surfaces, flat surfaces, and curved and flat surfaces.
• Polyhedrons are 3D solid shapes with flat faces
• Prisms have two identical parallel faces joined together by rectangles
• Pyramids have one face with at least 3 straight edges which are joined together by triangles meeting at one centre point (apex)
• Spheres have no vertices and no edges
• Cones are solid with one face and one vertex that is not on the face
• Cylinders have two congruent, parallel face
• Platonic solids are a special type of polyhedron, where all faces are identical in shape, size, length of edges, angles and vertices

Location and mapping: There needs to be an understanding of the representation of position

including the use of coordinates. Additionally, the use of positional language with distance/

measurement is a crucial skill for location and mapping.

Transformation and symmetry: Ensure to understand change of position, orientation, size

and shape. It is appropriate to understand symmetry in shapes and arrangements. The focus

in transformations is on the process by which the original shape is transformed into a new one.

The two focuses in symmetry include bilateral symmetry and rotational symmetry.

PEDAGOGICAL CONTENT KNOWLEDGE -

When teaching 2D shapes, students must be able to recognise examples and non-examples

of shapes, as well as models for real objects. They must learn the names of common shapes

and common vocabulary. Teachers are to give opportunities to students to explore the properties

or solve problems. Look at different shapes in the classroom and go through each property such

as it’s number of sides and corners, symmetry lines or reflections, lengths of sides, sizes of angles,

parallel and perpendicular sides, convexity and concavity, and altitude. Teachers can use tangram

puzzles, mosaic puzzles, and geoboards to teach composing and decomposing shapes. With 3D

shapes, examine objects with curved surfaces (spheres) , flat surfaces (prisms), and those with

flat and curved surfaces (cones). Many educators choose to do describing and sorting games,

such as ‘Who am I?’ where students must identify the shape with information about its edges,

vertices and faces.

Reference: (Van et al., 2015)

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Activity - Creating Composite Shapes

Year Level - 4

Classroom Context -

As this lesson is made up of multiple small activities and ICT tools, students with learning difficulties

or special needs may experience some challenges with keeping up to task. Using iPads and

hands-on materials can be distracting or cause students to fall off-track. For students with

learning disabilities, the teacher should plan for the student to complete the activity in a

desk away from distractions. The teacher should also provide explicit individual scaffolding

for these learners to reduce frustration or anxiety.

Content Descriptor -

Compare and describe two dimensional shapes that result from combining and splitting common

shapes, with and without the use of digital technologies (ACMMG088)

Learning Objectives -

This learning activity is designed for students to further their knowledge on geometric shapes.

The lesson is made up of three different activities. First, students will dive into their pre-existing

knowledge on two-dimensional shapes and demonstrate what they know. Second, students will

learn and demonstrate their skills on identifying and re-creating composite shapes. Finally, students

will learn to create composite shapes from written/verbal instruction. This lesson is important because

when students reach the older grades, they will begin to look at measuring areas of shapes, which

is often done by breaking down the individual common shapes.

Resources -

Key Mathematical Language:

2-dimensional, 2D, shapes, geometric, composite, sketch, graph, symmetry/symmetrical,

rotational

Materials:

Notebooks, pencils, sheet of composite shapes, grid paper, iPads

Use of ICT:

The use of iPads and software in this lesson will allow students to learn how to create geometric

shapes using online tools. Use of these resources will help engage students in their learning.

It is also beneficial for their future classes where they may be presented the opportunity to create

more shapes in subject areas such as Graphics, Science or Art.

Prior Knowledge -

Uses everyday language to describe and compare shapes and objects

Finds similar shapes or objects in the environment

Identifies and describes features of shapes and objects

Represents shapes and objects (sketching, model building, digital drawing packages)

Instructions -

• Ask the students to find things that represent 2D shapes around the classroom or school (can step outside the classroom) and list/draw as many they can find in their notebooks
• Write these up onto the whiteboard and discuss the properties these shapes have (similarities and differences)
• Provide each student with a sheet of composite shapes and explain that these shapes are results of the combining and splitting of common shapes (like the ones listed on the whiteboard)
• Using grid paper, allow each student to re-create these composite shapes by individually sketching the common shapes first. Ensure they label each common shape
• Once finished, hand out iPads to each student and ask them to access ‘Sketchometry,’ a digital tool for creating geometric constructions
• Ask students to create composite shapes responding to your verbal instructions. E.g. ‘Can everyone please sketch a composite shape using 2 triangles and 1 rectangle,’ etc.
• Give students time and further assistance if needed, allow students to work together if they wish to, as particular students can also provide learning support to others

Questions to ask -

Is this a 2D shape or a 3D shape? How can you tell?

What are some 2D shapes around the classroom?

Can you tell me some properties of a 2D shape?

What is a composite shape?

How can these 2D shapes join together to form a composite shape?

Enabling Prompts -

Have students practice identifying and drawing common basic shapes on grid paper.

Once confident, encourage them to join these basic shapes together.

Extending Prompts -

Challenge students to research or list names of composite shapes that has not yet been

studied during this activity. Encourage them to draw these on the digital tool.

Images -  

The sheet of composite shapes they must recreate and label

An example of how they would sketch/label the composite shape on grid paper

Using iPads, students must go onto this website to digitally sketch composite shapes

An example of how they would use Sketchometry to sketch their new shapes

Reflection -

In week 8, our focus topic was geometry and how students can develop shape awareness

and knowledge, as it promotes visual thinking and communication skills. Research on the

teaching and learning of geometry indicates that physical experience, especially physical

manipulation of shapes, is important at all ages, that a wide variety of geometrical experiences

are necessary in order for children to gain a solid understanding of geometrical relationships

(Jones and Mooney, 2003).

Children need many opportunities to learn about shapes and to identify their different parts,

as they are exposed to shapes everyday in their environment, as well as interact with them

everywhere. They must be able to recognise shapes, verbalise what they see, and understand

why they are there. For example, we want a child to have the ability to make the connection of

knowing that the wheel of a car is a circle. As children learn each geometric concept, they will

develop into further stages of understanding to learn more complex geometry concepts later.

This is why the above activity/lesson plan allows the students to observe the shapes they see

around their classrooms and school. This is then followed by an activity where they must construct

shapes with a digital tool. In the future, I would like to help my students develop an understanding

of shapes by encouraging questions and having discussions about them. This can be done simply

just by allowing a child to share with the class about shapes they see in their environment. It is

important to make fun and engaging geometry activities daily in maths lessons and play times.

References -

Jones, K., & Mooney, C. (2003). Making space for geometry in primary mathematics.

Enhancing primary mathematics teaching, 3-15.

Van, D. W. J. A., Karp, K. S., & Bay-Williams, J. M. (2015). Elementary and middle
school mathematics: teaching developmentally, global edition. Retrieved from https://ebookcentral-proquest-com.ezproxy.library.uq.edu.au