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WS02 - Statistical investigation

Mathematics, Year 7

By the end of Year 7, students represent natural numbers in expanded form and as products of prime factors, using exponent notation. They solve problems involving squares of numbers and square roots of perfect square numbers. Students solve problems involving addition and subtraction of integers. They use all 4 operations in calculations involving positive fractions and decimals, choosing efficient calculation strategies. Students choose between equivalent representations of rational numbers and percentages to assist in calculations. They use mathematical modelling to solve practical problems involving rational numbers, percentages and ratios, in financial and other applied contexts, justifying choices of representation. Students use algebraic expressions to represent situations, describe the relationships between variables from authentic data and substitute values into formulas to determine unknown values. They solve linear equations with natural number solutions. Students create tables of values related to algebraic expressions and formulas, and describe the effect of variation. 

 

They apply knowledge of angle relationships and the sum of angles in a triangle to solve problems, giving reasons. Students use formulas for the areas of triangles and parallelograms and the volumes of rectangular and triangular prisms to solve problems. They describe the relationships between the radius, diameter and circumference of a circle. Students classify polygons according to their features and create an algorithm designed to sort and classify shapes. They represent objects two-dimensionally in different ways, describing the usefulness of these representations. Students use coordinates to describe transformations of points in the plane. 

 

They plan and conduct statistical investigations involving discrete and continuous numerical data, using appropriate displays. Students interpret data in terms of the shape of distribution and summary statistics, identifying possible outliers. They decide which measure of central tendency is most suitable and explain their reasoning. Students list sample spaces for single step experiments, assign probabilities to outcomes and predict relative frequencies for related events. They conduct repeated single-step chance experiments and run simulations using digital tools, giving reasons for differences between predicted and observed results. 

Statistics

AC9M7ST01

acquire data sets for discrete and continuous numerical variables and calculate the range, median, mean and mode; make and justify decisions about which measures of central tendency provide useful insights into the nature of the distribution of data

Statistics

AC9M7ST02

create different types of numerical data displays including stem and leaf plots using software where appropriate; describe and compare the distribution of data, commenting on the shape, centre and spread including outliers and determining the range, median, mean and mode

Statistics

AC9M7ST03

plan and conduct statistical investigations involving data for discrete and continuous numerical variables; analyse and interpret distributions of data and report findings in terms of shape and summary statistics

Annotations

 

1. Represents collected class data in a stem-and-leaf plot.   

 

2. Uses the stem-and-leaf plot to interpret the data and respond to given questions. 

 

3. Demonstrates understanding of measures of central tendency and spread. 

4. Recognises that the stem of the given plot is not appropriate and creates a stem-and-leaf plot to represent collected data. 

 

5. Interprets the collected data and describes measures of central tendency and spread. 

 

6. Compares the data sets and describes the findings

Annotations

 

1. Interprets the research question and predicts the expected average for the sample being investigated. 

 

2. Identifies possible factors that may influence results. 

 

3. Describes the process undertaken to collect data. 

 

4. Represents collected data in a table. 

5. Constructs stem-and-leaf plots to represent and interpret the data. 

6. Calculates the measures of spread and central tendency, and records them in a table. 

 

7. Interprets results, considering and describing potential reasons for variation between trials. 

 

8. Draws conclusions based on the findings from the data. 

 

9. Describes the effect of outliers on the measures of central tendency. 

 

10. Describes the shape of data, including outliers. 

 

11. Reasons statistically that a larger sample size would provide different results.