These** proficiency strands** are addressed in this unit of work: Year Level 6:

**understanding**includes describing properties of different sets of numbers, using fractions and decimals to describe probabilities, representing fractions and decimals in various ways and describing connections between them, and making reasonable estimations**fluency**includes representing integers on a number line, calculating simple percentages, using brackets appropriately, converting between fractions and decimals, using operations with fractions, decimals and percentages, measuring using metric units and interpreting timetables**problem-solving**includes formulating and solving authentic problems using fractions, decimals, percentages and measurements, interpreting secondary data displays and finding the size of unknown angles**reasoning**includes explaining mental strategies for performing calculations, describing results for continuing number sequences, explaining the transformation of one shape into another and explaining why the actual results of chance experiments may differ from expected results.

The * Content Descriptions *involve:

#### Chance

Describe probabilities using fractions, decimals and percentages (ACMSP144)

Conduct chance experiments with both small and large numbers of trials using appropriate digital technologies (ACMSP145 )

Compare observed frequencies across experiments with expected frequencies (ACMSP146)

(Australian Curriculum, n.d.)

(These are explained in the Evaluation section)

This website provides students with opportunities to fulfill the proficiency strands. **Understanding: **students are experimenting with fractions and decimals using a rang of media. **Fluency: **students solve problems using fractions and decimals, part of a whole. They are exposed to problem-solving data methods online. **Reasoning: **The website delves into calculations, prediction and comparing results of experiments.

**Learning Trajectory process**

* Students build on their prior knowledge and justify choices of likelihood by referring to past experience.

* Students enhance this knowledge and scaffold through the use of the website/lesson plans

* Students use their past learning about likely events and make predictions about probability experiments

* Students use decimals and fractions to answer problems

* Students compare their answers to the outcomes

* Students use data to compare events within their experience/knowledge and using the resources

* Students design a probability game to develop and demonstrate their understandings

**Answers to Worksheets:**

Fair Die Worksheet: (1,2,3,4,5,6), 1/2, 1/2, 1/2, 1/6.

Fair Coin Worksheet: (H,T), 1/2, 1/2, 1, 0

Probability of Numbers Worksheet: 1/10, 1/2, 1/2, 9/50, 12/25

Probability Worksheet (Days of the week): 1/7, 2/7, 2/7, 2/7, 1/7

Probability Worksheet (boys and girls): 3/5, 2/5, 3:2, 2:3, yes

Independent and Dependent: 1/13, 1/17, 4/52*4/51 = 4/663, 4/52*4/52=1/169, 8/52*8/52=4/169

Pair of Dice Worksheet: (1,1), (1,2), (1,3), (1,4), (1,5), (1,6)

(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)

(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)

(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)

(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)

1/4, 1/2, 1/2, 1/4, 1/6

Balls in a container: 1/3, 1/6, 13/24, 5/8, 17/24, 0

Deck of Cards Worksheet: 1/2, 1/2, 1, 1/13, 3/13

Probability - Spinner: 5/8, 3/8, 9/16, 8/16, 5/16

**Cross Curriculum Ideas: ***Visual Arts* - making a spinner: Develop and apply techniques and processes when making their artworks

*Design and Technologies Processes and Production Skills - *making a spinner: Generate, develop and communicate design ideas and processes for audiences using appropriate technical terms and graphical representation techniques

*Digital Technologies Processes and Production Skills* - Plan, create and communicate ideas and information, including collaboratively online, applying agreed ethical, social and technical protocols

*HASS* - Present ideas, findings, viewpoints and conclusions in a range of texts and modes that incorporate source materials, digital and non-digital representations and discipline-specific terms and conventions

*English* - Identify and explain how analytical images like figures, tables, diagrams, maps and graphs contribute to our understanding of verbal information in factual and persuasive texts

**References**

Australian Curriculum. (n.d.). Mathematics: Understanding how Mathematics works. Year 6. Retrieved from https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics/

Education Services Australia Ltd. (2013). Dice Duels Bike Race. Retrieved from http://www.scootle.edu.au/ec/viewing/L2637/index.html

Maths Worksheets 4 Kids. (2019). Redefining the word math. Retrieved from https://www.mathworksheets4kids.com/probability.php

Nussbaum Education Network, LLC. (2020). Probability Fair Online Game. Retrieved from https://mrnussbaum.com/probability-fair-online-game

Youtube. (2017, January 18). *Probability Word Problems (Simplifying Math)*. Retrieved from https://www.youtube.com/watch?time_continue=601&v=vGcmjINp1x8&feature=em b_title

* images from Pinterest https://www.pinterest.com.au