The orange circle on the right looks bigger, but in fact both are the same size. The deception is based on the additional sensory input.
Similarly, the prerequisites for taking algebra are often considered to be basic skills. This is largely an illusion. I routinely encounter students who are referred to me for help as they have been caught in an infinite loop of working on basic math such as number operations (adding, subtracting, multiplication, and division) before moving on to algebra, with limited progress. I am not suggesting basic math skills are not important but am focused on the context of prerequisites needed to engage algebra. Many of the students I have helped who were in this situation. We worked to quickly move them into algebra where they were successful.
One student worked on half a year of 4th grade math during her 7th grade year. During the spring of that 7th grade year and the subsequent summer, I worked with her on algebraic thinking and algebra topics. She successfully completed algebra 1 during her 8th grade year.
The Common Core of State Standards (CCSS) for Math maps out the prerequisites as seen in the CCSS math domains (below). Throughout elementary school, Operations and Algebraic Thinking topics are covered. The Algebraic Thinking standards establish for the students a foundation for algebra taught in middle and high school. A focus of algebra is to model or represent patterns or relationships in real life situations using equations, tables, and graphs. These include quantities modeled by variables.
Below is a break down of this foundation in elementary school. If you are supporting a student in middle or high school who is taking algebra and has major gaps in his or her math education, look to these standards for the essential prerequisite skills.
First Grade: represent situations in word problems by adding or subtracting, and introduce equations (and equal sign).
Second Grade: Represent, solve word problems, introduce multiplication as groups of objects.
Third Grade: represent, solve word problems, explain patterns
Fourth Grade: Solve word problems, generate and analyze patterns
Fifth Grade: Write expressions (equations are 2 expressions with an = in between), analyze patterns and relationships