The transition to algebra is a transition to abstract reasoning. And while students may not always utilize algebraic equations later in life, they will certainly depend upon the analytical and problem-solving skill sets that accompany the subject. The following concepts are central to building a foundation in algebraic skills, and they are crucial areas to assist in your child’s mathematics development.
The addition of variables like x and y intimidates many students, but this anxiety can be lessened with practical experience in solving problems where one or more parts are unknown. A great example, and one that occurs frequently in middle school and high school, is the Pythagorean theorem: a2 + b2 = c2. Pythagorean theorem questions are well suited to hands-on learning (for example, "How tall is our house?" or, "How long is the pool diagonally?"), and they can help students increase their comfort with variables.
Try getting your child to help you plan a furniture rearrangement on paper, or help plan and execute a construction project. Another option for practicing number forms is to combine with a budgeting life lesson: Ask your child to pay all the bills for the month, and whatever is left over (or half of it) can be their allowance for the month.
Before beginning algebra, students should understand all forms of numbers, including whole and negative numbers, fractions, decimals, percentages, exponents and square roots. Fraction and percentage problems are another wonderful way to address solving for unknown variables, and recognizing that numbers have different forms is a good step toward abstract thinking and analysis.
Functions are a second abstraction that students can start to explore by recognizing and describing patterns. Being able to predict the next number in a sequence helps build the ability to identify functions. A function is a relationship between an input and an output; in other words, if the function is defined as subtracting 5, an input of 1 has an output of -4. Likewise, an input of 7 has an output of 2. The function is the relationship between the input and the output.
One of the easiest ways to practice functions is by cooking. By asking students to halve or double recipes, they’ll have to multiply and divide fractions ahead of time, and after a few times, they’ll understand the function of halving, doubling or tripling fractions.
Young students are often asked to visually represent numbers through charts. Bar graphs, flow charts, pie graphs and X/Y axes assist students in visualizing the concepts behind mathematics problems, and again, moving toward abstraction. But another, subtler way students are challenged to visualize is via word problems. Producing a familiar equation from a problem in paragraph form helps students use equations as visual aids and as descriptions of functions.
Games are fun ways to build skill sets in visualization and graphing without it feeling like "work." One great example is Algebra vs. the Cockroaches, which asks students to identify the algebraic functions of cockroaches walking across a graph, and provides a satisfying squish when successful. Wuzzit Trouble is a game specifically designed by a Stanford mathematician to "secretly" teach math, but more popular games like Minecraft are still visually building skills in 3-D axes and problem solving. Try to identify some math-based video games and ask your student to put them into rotation over the summer.
For more tips and strategies to help your student succeed in school, visit www.varsitytutors.com.
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