Mathematical Mindset Algebra
This 4-week curriculum unit we have developed is one that can be used to introduce algebraic concepts at any grade level. It draws upon algebraic research showing that it is more helpful for students to learn algebra through studying pattern growth where a variable represents a case number, and can vary, before learning about “solving for x.” When students start learning algebra by solving for x they come to believe that a variable stands for a single number and does not vary. Later when they need to understand that variables can vary, they meet a conceptual barrier, and many do not ever get past that barrier. We recommend that students learn first about pattern growth and see that algebra can be useful for describing growth. Later, when they encounter situations when the variable stands for one missing number, they see this as a subset of their broader learning about variables and there is no confusion.
Algebra Big Ideas
We have designed some activities to help build a culture of multi-dimensional mathematics and equitable group work. We recommend that you start with these 3 days of activities, as they will help the rest of the school year. If you have already set up this culture you could move to the algebra lessons instead.
Students in a class will describe the border growth in different ways, they then move to writing about the growth and finally they can be helped to use variables and to create different algebraic expressions.
Students will see the visual nature of algebra and make connections between written descriptions, coordinate graphs, tables of values, visual patterns and algebraic expressions.
Students will visualize how a pattern grows before they determine how many are in any case. After describing the different ways they see the pattern growing they will generalize the different ways into words, followed by algebraic expressions.
In the first week we focused on visualizing patterns of linear functions. This investigation includes linear and non-linear patterns.
Students will build and find patterns in 3-D cubes while making connections to area, volume, linear, quadratic and cubic functions.
Students will explore a mathematical object called the Cantor Set in order to become familiar with exponential patterns, as well as come up with their own questions to investigate.