Statistics and Probability - Year 6

Introduction

Statistics

and Probability

A learning unit designed for Year 6 Mathematics students in conjunction with the Australian Curriculum. Teachers, please go to the Teacher's page for more information.

Students, welcome to the exciting world of Statistics and Probability. Statistics and Probability is one of the few maths subjects that is not only fun but it actually relates well with the real world.

Evaluation

Statistics and Probability

Assessment

The tasks in this unit are designed so that students complete all work in their maths books and or project paper so it can be used for assessment against the standards set by the Australian Curriculum.

Rubric

	A	B	C	D	E
Description of observation	Highly detailed descriptions of observations	Detailed descriptions of observations	Minimal descriptions of observations	Partial Description of observations	Beginning level descriptions of observations
diagrams	All diagrams are clearly labelled and have excellent attention to detail	All diagrams are labelled and have some detail	All diagrams are labelled, minimal detail	Diagrams present, partial detail	Beginning level or No Diagrams
Scientific language	Excellent use of Scientific language	Some scientific language present	Minimal Scientific Language	Scientific Language used was insufficient	Beginning level use of Scientific Language

Rubric

	A	B	C	D	E
Description of observation	Highly detailed descriptions of observations	Detailed descriptions of observations	Minimal descriptions of observations	Partial Description of observations	Beginning level descriptions of observations
diagrams	All diagrams are clearly labelled and have excellent attention to detail	All diagrams are labelled and have some detail	All diagrams are labelled, minimal detail	Diagrams present, partial detail	Beginning level or No Diagrams
Scientific language	Excellent use of Scientific language	Some scientific language present	Minimal Scientific Language	Scientific Language used was insufficient	Beginning level use of Scientific Language

Rubric

	A	B	C	D	E
Description of observation	Highly detailed descriptions of observations	Detailed descriptions of observations	Minimal descriptions of observations	Partial Description of observations	Beginning level descriptions of observations
diagrams	All diagrams are clearly labelled and have excellent attention to detail	All diagrams are labelled and have some detail	All diagrams are labelled, minimal detail	Diagrams present, partial detail	Beginning level or No Diagrams
Scientific language	Excellent use of Scientific language	Some scientific language present	Minimal Scientific Language	Scientific Language used was insufficient	Beginning level use of Scientific Language

Teacher Page

Mathematics/ Year 6 /Statistics and Probability / Chance / ACMSP146

Australian Curriculum:

Compare observed frequencies across experiments with expected frequencies (ACMSP146)

Mathematical Goal

Predicting likely outcomes from a run of chance events and distinguishing these from surprising results

Proficiency Strand

Reasoning includes explaining mental strategies for performing calculations, describing results for continuing number sequences, explaining the transformation of one shape into another, explaining why the actual results of chance experiments may differ from expected results

This Learning trajectory was designed to support students’ learning in Statistics and Probability strand of the Australian Curriculum with a focus on the reasoning proficiency strand. The design was modelled off the work by Julie Sarama and Douglas H Clements (Sarama. J and Clements. DH 2009).

Unit Outline

Development Path (Levels of Understanding)

1 -Recognise the element of chance in familiar everyday activities

2 -Distinguish possible from impossible events and describe possible outcomes

3 -Introduce and develop the terms of mathematical language including the concepts of frequency (likelihood), chance and the language needed to describe probability

4 -Making prediction based on investigations or observations of outcomes

Development Path	Instructional Tasks
1	Use Prior Knowledge Task
2	Use the concepts of possible and impossible https://www.studyladder.com.au/learn/activity?id=3430
3	Watch Probability Video’s Lesson *Video* Probability lesson 1 https://www.youtube.com/watch?v=zzaMZ4CHWLc Video Probability lesson 2 http://splash.abc.net.au/home#!/media/1589595/probability-of-rolling-a-…
4	Head and Tales Experimentation,; Working by themselves, students predict the likely outcome of 10 coin tosses then through experimentation compare their actual results to their prediction, recording what they think happened. The students can then extend themselves to 30 or 40 coin tosses. Students pair up and predict the outcome of 50 dice rolls. One student then rolls the dice and the other keeps a tally. They both then compare the results with their prediction and write down what they have learnt Revision of previous learning and activities covered Class discussion on converting the data collected the day before from the dice rolls and coin toss activities. Students to convert their own experiments into graphs Students to record down mathematical facts that they notice in their own graphs about the frequency of numbers. Students play any probability math activities from website scootle. Students play probability game to test knowledge.

Student Prior Knowledge / Learning

Students to discuss with a partner of their choosing what they know about what the words Chance, Data and Probability and what they mean. Groups report back to the teacher during a whole class discussion.

Teacher Identification of possible Prior Knowledge / Pre Existing factors impacting on learning

Prior Knowledge;

Students enter year 6 with both formal and informal knowledge learned through experience.

Basic formal and informal knowledge of:

Chance i.e. experience with dice and card games
Collecting frequency data i.e. experience with tallying, creating graphs
Probability and language associated i.e. certain, likely, unlikely, possible and impossible.