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Level Four > Number and Algebra

Number in Statistics

Achievement Objectives:

Achievement Objective: NA4-2: Understand addition and subtraction of fractions, decimals, and integers.
AO elaboration and other teaching resources

Purpose: 

These exercises, activities and games are designed for students to use independently or in small groups to practise number properties. Some involve investigation (see Related Resources) and may become longer and more involved tasks with subsequent recording/reporting. Typically an exercise is a 10 to 15 minute activity.

Specific Learning Outcomes: 

find the midpoint between two numbers
find the mean of two numbers
find the mean in a group of related numbers

 

Description of mathematics: 

Addition and subtraction, AM (Stage 7)

 

Required Resource Materials: 
Practice exercises with answers (PDF or Word)
Balance Beam
Calculator
Activity: 

Prior Knowledge

Add two and three digit numbers

Background

The mean is a very important concept in many disciplines. In physics it is the understanding behind the centre of gravity as “moments about the origin” in 1, 2 and 3 dimensional bodies and indeed the definition of E(X) is this exact equation. In statistics the mean represents many other numbers in a very democratic fashion. The moving means of time series data link to graphing and trends. The mean is often confused with average. An average is a number that will represent others as a typical value of which mean, mode, and median are all examples. The median estimates the mean and in certain circumstances is a very good estimator. These exercises develop an understanding of the mean, and uses number and geometrical properties to calculate the mean.

Comments on the Exercises  

Exercise 1
Asks students to use different methods to find the number exactly midway between two numbers.

Exercise 2
Asks students to find the number exactly halfway between two numbers.

Exercise 3
Asks students to find the mean using addition and subtraction methods. For example, 6 + 9 = 15, 15 ÷ 2 = 7.5,  and 9 - 6 = 3, 3 ÷ 2 = 1.5, 9 - 1.5 = 7.5.

Exercise 4
Asks students to explore the concept of the midpoint or mean using a balance beam model.

Exercise 5
Asks students to use the balance beam model to balance two weights against one weight. 

Exercise 6
Asks students to use the balance beam model to balance more than two weights against multiple weights. 

Exercises 7, 8 and 9
Asks students to find the mean of a regularly spread sequence of numbers e.g. 4, 8, 12, 16, 20.

AttachmentSize
NumberInStatisticsSheet.pdf29.92 KB
NumberInStatisticsSheet.doc107.5 KB