Even and Odd Numbers: Investigate patterns with the 4 operations

The purpose of these resources is to explore patterns in our number system through one of the most fundamental classification of numbers - even and odd.

Recognising even and odd numbers is first seen in Grade 2, and this builds on work covered here. See the resource  Recognising even and odd numbers with and without objects.    

Having accomplished this, a natural extension is to investigate whether there  are any patterns when even and odd numbers are added, subtracted, multiplied or divided. So, as well as looking for patterns pupils are practicing and applying the 4 basic number operations in a math  investigation

There are two fundamental approaches to this investigation:

• Using visual aids: Students can get visual clues when even and odd numbers of objects are displayed in an orderly fashion, which is always a good starting point. Addition and Subtraction are covered here with worksheets and digital teaching resources. Multiplication has a digital teaching resource.
  
  The range of numbers used are between 1 and 28 for addition, and 1 to 14 for division
  For the multiplication the examples go from 2 x 2 to 6 x 7
  

No visual aids: students apply the idea learnt in the Grade 2 resource that whatever the size of the number, in the end only the last (unit) digit matters when deciding if a number is even or odd. Addition, subtraction, multiplication and division are all covered here.

The range of numbers used here are:
- Addition: 2-digit plus a 2-digit number up a total of 30, 50 or 100
- Subtraction: Two 2-digit numbers with the first number a maximum of 30, 50 or 100
- Multiplication: From 2 x 2 to 12 x 12
- Division: Dividend a maximum of 100, Divisor up to 12.

The work is broken down into modules so that a step by step approach can be taken. This prepares your students to:   

• 
  - Independently investigate and recognise any patterns or consistently repeated results  when performing the 4 operations with even and odd numbers.
  - Make  generalizations from the work carried out.
  - Make predictions and test them.

How many worksheets are in each set ?

Lots and lots and virtually unlimited on some of them. At the click of a button all numbers are randomised, so the questions change every time which allows you to create new worksheets for extra practice or revision throughout the year or even give groups of pupils in your class different sets of questions.

Answers can be found on the second page of every worksheet, automatically generated when you create a new worksheet.

Interactive Teaching Resources 

These are designed  for whole class teaching with an Interactive Whiteboard or on a computer for one to one tuition with instant feedback to help introduce the content of the worksheets. As with the worksheets numbers can be randomized giving you almost unlimited examples to work with.

Note
These resources are PDF documents and work with the official  Adobe Acrobat Reader on Windows or Mac computers with the randomising buttons also working via a touchscreen (PC or Mac)or on an Interactive Whiteboard.

Common Core State Standards 

CCSS3.OA.D.9

Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

Australian Curriculum

Year 4:
Investigate and use the properties of odd and even numbers (ACMNA071)

Explore and describe number patterns resulting from performing multiplication (ACMNA081)

For more foundational work on Even and Odd Numbers have a look at:
Recognising & Identifying Even & Odd Numbers