Preparation:

• Interactive TV/Smart Board - with PowerPoint visible
• Activity worksheets- enough for the whole class
• Floor space

Resources:

• Interactive PowerPoint - Activity 1 Powerpoint.pdf
• Worksheet -Picture Graph activity - powerpoint.pdf (Appendix 4)

Activity 1 Description:

This activity begins with an introduction using direct instruction (Siemon et al., 2015) about collecting and organising data according to outcomes MA1-DATA-01 (NESA, 2024) by engaging students in an interactive PowerPoint. As a class, students engage in discussing a mind map (Appendix 1) of their prior knowledge about data, as students have limited experience exploring data in early stage 1, discuss essential vocabulary, definitions and interpretations of data based on what students may have misconceptions or subjective thinking like "Apples are the most popular fruit in our class because me and my friend like it the best". The students think about what they know, discuss it with a peer, and then put their hand up to share what they discussed about the data (Think, Pair, Share) (Samsuriadi et al., 2019). Following students' understanding of data, discuss with students the importance of collecting data and when we might need to collect data, for example, the number of boys and girls in schools or favourite sports (Anthony et al., 2009). Following your conversations about what data is, continue with the next slide and, as a group, explain to students that they are going to collect data about the most popular type of fruit that is eaten at the fruit break in their class (Appendix 2) (Serow et al., 2019). Discuss ways to record the data of fruit in the classroom, introduce students, and explicitly teach students how to use tally marks to represent data (Doabler et al., 2013). As a class, collect data on students' favourite fruits: "Put your hand up if your favourite fruit is an apple", and record the tally of the given fruits on the PowerPoint; discuss with students ", Why might you need the option of 'other' when collecting data?". After collecting data, discuss how you can represent your class's most popular fruit in a graph, and teach students that each picture can represent one piece of fruit per student. Show students our favourite fruit picture graph on the PowerPoint (Appendix 3), discuss the axes showing the different types of fruit and the quantity of fruit, demonstrate how you refer to the tally recordings, and enter them into your graph. After this, provide students with a worksheet to apply their understanding of the topic. In the worksheet (Appendix 4), students will be required to think critically about the order of events in relation to collecting data and interpreting data. In conclusion, reinforce the concept of outcomes and ask students, "How can you use collecting and representing data in everyday situations?".

Differentiation:

Additional support: Display PowerPoint data collection table and graph as concrete material for students. Give students counters to use as a representation of tally marks for data collection and visual representation to represent the data on the graph (Appendix 1 & 2).

Extension: Introduce students to more advanced terminology and concepts to stretch their understanding. Challenge students to modify the unit/picture representation of more than one value. Allow students to use one picture to represent two or three students' favourite fruits, then adjust the data display accordingly.

Activity 2:Using Concrete Blocks to Represent Different-Coloured Cars

Preparation:

• Student work/exercise books
• Grey led Pencil & Rubber per student
• Multilink cubes 15 per student - Colours- White, Black, Red, Blue, Yellow (Appendix 5)
• Print Data collection/ Picture Graph Worksheet Template -(Appendix 6)
• Have student's desk set up

Resources:

• Multilink cubes (Appendix 5)
• Worksheet(Appendix 6)

Activity 2 Description:

After students reengage and explore data and data collection, they use their prior knowledge and understanding to successfully complete their own investigation and interpretation of data collection in activity 2. This activity is designed to build upon their initial exploration of collecting data and representing data with drawings using a structured opportunity for students to strengthen their understanding using hands-on, concrete materials (Reys, R. E, et al., 2017). As a class, briefly discuss students' prior knowledge in a think, pair, share between students and discuss some understandings as a class as per outcome MA1-DATA-01 (NESA, 2024). Begin to discuss and explain to the students that they are going to be given 15 multilink blocks to use to represent different colour cars. Have conversations with students about how using different materials can sometimes represent different objects. Hold up to show the class each colour block and discuss with students, "This block is the colour?" Engage students by answering "Red" and "Which would represent a red colour car?" and continue to do so with the black, white, yellow and blue blocks. Discuss with students that once they get their 15 blocks, they will need to organise their blocks to interpret their data; they will then need to represent their data collection using tally marks and then interpret their data into a picture graph (Serow et al., 2019). Use the student's worksheet to display on the interactive TV and begin to show students what the expectation is for them to complete this task (Doabler et al., 2013). Start by shorting your 15 blocks in front of them and categorising them into colours; discuss with student strategies how you may do this, e.g., putting them into colour groups or rows. Then, chat with students about how they will tally this into their given table and, as a class, record your data into the table. Then, continue to look at how they will represent this data in their picture graph, discussing where they put their title, numbers, and pictures. After explicit instruction, settle students down into their set desk seating arrangements (Ngware et al., 2013) and hand them their 15 multilink blocks and data collection sheets to work through independently. In the worksheet, students will be required to think critically about the order of events in relation to collecting data and interpreting data. They will need to represent data with objects and drawings.

Differentiation:

Additional support:Step-by-step Guidance: Allow students to complete their worksheet with step-by-step guidance in a small group under teacher or TA guidance (Doabler et al., 2013). Break down each step into smaller tasks and more manageable steps and guide students through each process with clear explanations. Encourage students to ask questions and seek clarification; for example, provide prompts and cues to help students organise and tally their data.

Extension: Students are given ten more blocks that represent coloured cars and are to draw their table and graph into their math exercise book. Students are to construct a table and show their tally marks that represent the number of colours. They are to use equal spacing and same-sized pictures to represent their data collection in a picture graph.

Activity 3: I Can Describe My Results

Preparation:

• Student work/exercise books
• Grey led Pencil & Rubber per student
• Data collection/ Picture Graph Worksheet Template from students' workbooks complete -(Appendix 6)
• Have student's desk set up
• Data Interpretation Worksheet - enough for each student - (Appendix 8)
• Interactive TV with PowerPoint Presentation- (Appendix 7)

Resources:

• Completed Worksheet from Activity 2(Appendix 6)
• PowerPoint (Appendix 7)
• Data Interpretation Worksheet (Appendix 8)
• Whiteboard

Activity 3 Description:

Following the exploration of collecting data by using concrete materials that represent colour cars, students in this activity further their learning by engaging in concepts of reasons of representations of data (MA1-DATA-02) (NESA,2024), describing their results and focusing on analysing and interpreting data through counting (Serow et al., 2019). As a class, display the Analysing and Representing data PowerPoint presentation (Appendix 7) to students on interactive TV/Smartboard. Begin asking students, "What are the steps in collecting data?" allow students to Think, Pair and Share (Samsuriadi et al, 2019) and explicitly teach the steps in teaching data; explain to students it starts with a question, "Like how many Colour cars?" then the data is collected into "our tally table" we then represent that data into the picture graph "but what happens after this?" (Siemon et al., 2015). Continue onto the next slide in the presentation and begin to look at the type of pets in the classroom graph; discuss with the students what they can see by looking at the graph; give them time to Think, Pair and Share; propose questions to students like Which Pet was the favourite? Which Pet was the least favourite? After explicit discussions, answer the question on the slide: "Write three sentences representing the data of types of pets in the class". Model the sentence for the question on the whiteboard, taking ideas and discussion from students (Serow et al., 2019) (Heyd-Metzuyanim, E. 2019). Following class explicit teaching, instruct students to go back to their set desks and to get their math expertise book (Ngware et al., 2013). Using their Colour Cars Picture Graph, they will analyse and represent the data they collected. Hand out the "Let's Interpret the Data" worksheet (Appendix 8) to students and talk them through each question and where they will need to write their responses. Once they have answered the given questions about their data on the worksheet at the bottom, they are to create three sentences summarising their findings. In the worksheet, students will be required to think critically about the order of events in relation to representing and anayalysing data. Students may base outcomes on their own beliefs rather than results, and it is possible that students may not fully grasp the concept of findings of the initial car colours but rather be more interested in colours not listed (Doabler et al., 2013). Therefore, students should be encouraged to expand their understanding and share strategies and observations to increase their representation and description of interpreting data results (MA1-DATA-02)(Siemon et al., 2015).

Differentiation:

Additional support:Provide students with more straightforward terminology to help them create a better understanding of what interpreting data is. Explain to students that they are just going to tell you what they see in the graph and answer questions with visual concrete material like the multilink blocks (Doabler et al., 2013). Allow students to create their graph using the blocks and have them answer prompts through comparison, like how many Colours Blue cars you have. This supports students in counting and analysing data and allows them to answer this in their Maths exercise book and continue to do so with all other colours (Doabler et al., 2013).

Extension:To add more complexity to this activity, students will work more independently to compose information or questions from their picture graph and pose their own questions that can be answered using information from their graph. Students can ask questions like What information can you get from this picture graph? What information can you not get from this picture graph? Why? Composing more in-depth responses like these examples allows students to deepen their thinking and interpretation of data analysis (Serow et al., 2019).

Activity 4: Let us get into Creating - IT

Preparation:

• Student work/exercise books
• Grey led Pencil & Rubber per student
• Have student's desk set up
• Interactive TV with Data Poster- (Appendix 9)
• iPad or Chromebooks- for students
• SeeSaw logins for each student- (Appendix 10)

Resources

• Data question poster- (Appendix 9)
• SeeSaw- Tally and Graph (Appendix 10)

Activity 4 Description:

After exploring collecting, displaying, and interpreting data, students look at this activity,asking open questions to collect a range of information to create and interpret a data display on a chosen topic of their choice using technology. Students think mathematically and make connections of prior knowledge in previous activities to follow the steps of conducting and collecting data (Siemon et al., 2015). Students will apply their understanding in organising, gathering and displaying data in tables and picture graphs (MA1-DATA-01) and discussing reasons for the representation of data and their interpretation and analysis of data (MA1-DATA-02) (NESA,2024). Begin with the class recapping prior lessons and activities, allowing students to contribute their knowledge (Heyd-Metzuyanim, 2019). Following group discussions as a class, start to revisit what was spoken about in the last activity, asking students, "What are the steps in collecting data?" allow students to Think, Pair, Share, and discuss as a class (Samsuriadi et al., 2019). Explicitly, a step-by-step look at the process of collecting data is more in-depth, with the idea that students are going to do this independently (Doabler et al., 2013). Begin discussing the first step of picking a suitable topic to collect data; look at the Data Collection Poster (Appendix 9) on the interactive Smartboard/TV and discuss with students that they need to pick a sensible topic that will be suitable for them to collect a relevant amount of data (Siemon et al., 2015). Continue to examine the next steps in the data collection, where students use tally marks and the representation of data where students create a picture graph (Siemon et al., 2015). Following discussions about the steps, students will begin creating their data collection using the SeeSaw online program. The students log into SeeSaw and will find the document they need to complete their work (Appendix 10). Discuss with students; they will start with a blank page where they will put their data investigation question and draw up their tally table. Once all students have completed their table, they will leave their devices, and the students will go around to each other's desks and draw their tally marks to the appropriate question. Students will then continue to complete their picture graph, drawing all relevant headings and sub-headings (Siemon et al., 2015). In this activity, studentswill be required to think critically about the order of events in relation to collecting, representing and analysing data. Students may generalise their interests rather than the appropriate data to be collected and the time to complete the collection and representation of the data, making it more of a contest or boy vs girl thing. Continue to reinforce the continuum of learning so that students can gather, display, and represent data as opposed to given outcomes (MA1-DATA-01) (MA1-DATA-02) (NESA,2024) (Reys et al., 2017).

Differentiation:

Additional support:Guided Practice???Support students in completing the task using more straightforward, more manageable steps(Doabler et al., 2013). Guide students through each task as you do (model) they do expectations(Doabler et al., 2013). Allow students to work with the teacher or TA on the SeeSaw program on the TV/Smartboard so that they can see clearly and follow instructions well.

Extension:To extend students further, introduce them to creating a new task or page using SeeSaw; they can then independently begin to create their own suitable questions, where answers from categories can predict a likely response(Doabler et al., 2013). For example, which school sport is the most popular in our class? Students then need to follow the process of collecting data, create a tally and picture graph template, and pose relevant questions about the representation of data.

Assessment 2 Part B: Analytical Report:

Analysis of key S&P concept(s):

For which the sequence of learning activities has been designed. Discuss their importance within the continuum of learning and identify key learning indicators to explain how each activity fits into a coherent learning sequence to build deeper conceptual understanding.

Identify students' prior knowledge before completing these activities and the knowledge and skill progression as students complete each sequenced activity. Refer to the 'Table of objectives and outcomes' (NESA, 2022), provided within the 'Resources/Assessment 2 Resources' folder. Also consider what the next logical knowledge or skill acquisition, following on from the third activity, should be.

Consider reviewing the numeracy progression for ideas (pdf also provided within the 'Resources/Assessment 2 Resources' folder):

https://www.australiancurriculum.edu.au/resources/national-literacy-and-numeracy-learning-progressions/national-numeracy-learning-progression/

For example: UnC1 (understanding chance): Describing chance:

• Describes everyday occurrences that involve chance

Justification for:

1. For the design of sequenced activities:
2. Targeting possible student misconceptions:

in which you reference, based on educational literature:

1. Pedagogical models and practices for primary mathematics.
2. Provision of a list of stage-relevant possible student misconceptions, detailing how and why the sequence of learning activities would support children in redressing the identified misconceptions (i.e. identify and provide reasons regarding which possible student misconception(s) this sequence of activities will address), as well as develop students conceptual knowledge and understanding of the identified concept, encouraging students to develop and apply their working mathematically skills.
3. An analysis of how the sequence of three (EMM209) and four (EMM418) learning activities supports children in meeting their cognitive, social, cultural and/or aesthetic needs, particularly through literacy and/or numeracy practices.

Considersomeof the major elements of mathematics pedagogy when preparing your learning activities and report, such as: children's misconceptions; working mathematically; higher order thinking; social constructivism; authentic tasks; problem-based learning; cooperative learning; student-centred learning; making connections; literacy and numeracy practices; and modelling and thinking mathematically.

A possible resource: Top Drawer (AAMT):https://topdrawer.aamt.edu.au/