Introducing our New Grade Nine Practice Questions

Quadratic EquationImage: Wikipedia

As mentioned in our blog last week, we recently introduced grade nine practice questions and we may be introducing even more grades in the future. With our grade nine section we have tried to employ the same rigorous structure that our other grades follow, with plenty of questions to vex the most astute of students. The first sections try to give students a solid understanding of radical numbers, beginning with a quick introduction covering what they are and how they work. Logically, we then give children more complex, practical questions to help them use radical expressions proficiently, always using our advanced DDA system. For those who aren’t familiar with how our DDA system works, it basically gives children questions to suit their individual skill level, so they will always be challenged.

The first sections are quite similar to our rational expressions sections in grade eight, although they are designed so that children fully understand square roots; how to add, subtract, multiply and divide various expressions. Having practice with radical expressions is something every student must be comfortable with if they want to progress to other mathematical problems. Although they won’t directly be an element of future sections, the methods used show children how to use radical and rational expressions in the correct way. Having a complex expression without having knowledge about typical math techniques used to simplify and solve them will make progression difficult. But don’t worry, our math problems have been tailored to give each and every child questions they are comfortable with, always progressing at their pace so they should never feel disheartened.

Rational Expressions Image: Wikipedia

The next section in grade nine is quite informative for a few reasons. We start with recognizing and understanding quadratic equations, and they are perhaps one of the most fundamental mathematical processes a student will ever use. Quadratic equations are used for a whole host of practical applications, but we won’t get into that just now. Although they have many uses, they aren’t overly difficult to comprehend (usually); however, we have finished this section with practical word problems to give quadratics some relevance. Normally in a school curriculum the focus is on solving equations and very little is taught about how to use them in the real world, so we’ve dedicated a whole set of questions to this cause. Having lots of practical questions should give children a unique perspective on the purpose of quadratics, which should be highly beneficial in later math sections. We want to teach every aspect of math and ensure children know why they are learning these processes, hopefully keeping them motivated and interested at the same time. Here is an example of such a question:

A government provided $3200 dollars of subsidies for schools in the mountain areas in 2010.  In 2012 the number would have been $4800.  Given the subsidies increased at the rate of x per year, set up an equation to solve for x.

(A) 3200x² = 4800

(B) 3200(1 + x)² = 4800

(C) 3200(1 + x%)² = 4800

(D) 3200(1 + x) + 3200(1 + x)² = 4800

This is one of the easier problems that students will face and the answer is “B”. It’s also another example of what makes BeijingMath better than typical math programs, namely giving children problem solving practice that is believed to be an essential element of the new Core Math Curriculum. Once children are comfortable with quadratic equations they can try the next section, which is an in depth analysis of circles and how they work, but we will cover that in the next blog.

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