現実世界の代数

 Review of arithmetic concepts. I’ve noticed many of my math students don’t fully understand why arithmetic works the way it does, so a quick overview of these concepts sets them up for success going forward. This is helpful even with advanced students as they can often be shown a novel perspective on how math works. It is important to make sure everyone is comfortable with how addition, subtraction, multiplication, and division work and can be used to solve word problems. 

 We will then move on to discussing how in some situations we may want to replace some numbers with variables. These situations are the natural origin of the invention of algebra, with examples such as: basic trade for different goods, unit conversions like days into weeks, and ingredients in food recipes. We will practice basic problems and introduce translating these situations into equations. 

 Building on last week, we introduce more examples of situations one may want to use variables and introduce the idea of inequalities. For this we’ll use speed, distance, and time. So as not to go too quickly, we will also practice everything from our previous lessons and include more word problems. 

 Next we’ll practice using variables for spending and budgets. For example ordering at restaurants: calculating total, tax, and tip based on percentages. We’ll also talk about how people create budgets using algebra and percentages. We’ll make tables/spreadsheets where kids can predict how much someone can spend and save, based on percentage of income and expenses.