I created these resources to try to help my classes understand the process of factorising quadratic expressions of the form x^2+bx+c. The idea behind them is to first get the class to practise finding the 2 numbers that have a specified product and sum, then to start to apply this to factorisation with some scaffolded questions.
The first resource gets them to focus on finding the 2 numbers that have a specified product and sum. The 4-page worksheet is broken into four sections - both numbers positive, both numbers negative, one positive and one negative, and then a mixed section.
The second resource is a spreadsheet activity where your classes can further practise the skill of finding the 2 numbers that have a specified product and sum. The questions are randomly generated and they get instant feedback on their answers, either telling them it is correct or telling them which requirement (product/sum) has not been met, giving them a chance to try again. It keeps track of how many each student has answered correctly so you can make this into a competitive activity.
The final 4-page resource starts to apply the skill of finding 2 numbers that have a specified product and sum to factorising quadratics. Each section starts with a set of questions asking for 2 numbers with a specified product and sum, then asks the student to complete/write down the related factorisation. Each section concludes with some factorising questions with no scaffolding. Section A is both numbers positive, section B is both numbers negative, section C is one number positive and one number negative. Sections D has almost 50 quadratic expressions to factorise - starting with a few of each type and then moving onto mixed questions.
Answers to both the worksheets are provided.