algebra can be exciting!
Algebra 1 can be exciting and fun for students because they start to feel very "mathematically mature" when using variables (letters) with their math. It is a wonderful thing to see students embrace algebra. I've seen many students use and recite formulas with variables proudly because they feel like they have been introduced to knowledge that is part of a more adult world. Algebra 1 is the gateway to more advanced math.
It is important that students have the skills needed for Algebra 1 so that they can indeed thrive in the class and be motivated to do well in future math classes. While I've taught students who excel in algebra, I've also tutored many students who start Algebra 1 without having the necessary foundational skills. This situation unfortunately makes them struggle and dislike the subject, instead of finding it exciting and reveling in their newfound math skills.
If you have a child who is starting Algebra 1 this fall, now is the time to make sure certain key skills are in place for the class. Let's make sure algebra is embraced and not disliked!
Take a look at my free resource that lists 5 skills that should be mastered before starting Algebra 1. I will go through each of these skills below.
The 5 recommended Skills
1. Exponents
Students are introduced to exponents before starting Algebra 1. Exponents are used to represent repeated multiplication. Make sure your child understands:
how to use exponents with whole numbers, fractions, and decimals
that any number raised to the 0 power is equal to 1
scientific notation, which uses positive and negative exponents
that if a number is raised to a negative exponent (for example, 10 raised to the -1 power), it is really getting multiplied by a fraction, which makes the number smaller
when expressions with exponents can be combined, such as:
2. multiplication and the distributive property
Algebra 1 uses the distributive property with variables frequently. For this reason, it is important that your child feels comfortable with the property when using it with only numbers first. Students need to recognize that it provides a way to multiply numbers together.
In the example provided below, students can use the Order of Operations and solve 6+5 first to get 11 and then multiply 4 by 11 to get the answer of 44. Alternatively, they could get the same answer by applying the Distributive Property and distributing the multiplication of the 4 across the 6 and the 5, then adding those products together to get 44 (see below).
It would also be a good idea to make sure your child knows how to break down a product using the distributive property, for example:
8 x 14 = 8(10 + 4) or 8(7+7) or 8(11+3) or 14(6 + 2) or 14(3 + 5).....or other options
I also suggest that while practicing multiplication techniques, that your child knows factors of numbers well. That means that if a number like 30 is given to your child, the factors of 30 are known: 1, 2, 3, 5, 6, 10, 15, 30. This comes in handy for factoring in algebra.
3. fractions, decimals, and percents
I have spent time with many students on converting percents, fractions, and decimals. This is a critical part of middle school math and I find that it as a topic that is confusing for many of them.
One of the new things introduced to students in Algebra 1 is the way to write expressions and equations with variables. For example, the multiplication sign...poof....goes away! If we want to express "6 times y", we simply write "6y." If we need to divide 4x by 4, we write a line underneath "4x" and write the "4" underneath the line to signify that "4x is getting divided by 4." This will make a lot more sense to a student if it's already understood that fractions are used to represent division.
Once you arrive to Algebra 1, it is expected that you have the flexibility to work with numbers. Students may be asked to solve an equation that includes decimals and fractions, for example. This will present a problem to anyone who doesn't know how to convert one to the other. Word problems will also be presented frequently, sometimes with prices and percents, and there will be a need to translate the facts into an equation that makes sense.
A great game to practice these conversions is BINGO, which I recommended in this blog post.
4. operations using positive and negative numbers
Another key skill to master before starting Algebra 1 is how to use all of the four operations (add, subtract, multiply, and divide) with positive and negative numbers. Algebra problems will combine positive and negative numbers and students will have to solve equations knowing how to work with these kinds of numbers.
For example, does your child know that:
-6 - 13 = -6 + -13 = -19
1/2 - 3.5 = -3
(-5)(-12) = 60
(-3)(5) = -15
60 / (-1/2) = -120
-6.3 / -2 = 3.15
These are just a few examples of problems that use operations with positive and negative numbers. I've seen confusion with the first kind of problem with many students, when a negative number is subtracted from another negative number. Sometimes students think this follows the rule of "two negatives make a positive", when in fact the answer becomes more negative.
Sometimes it helps to have students realize that subtracting is the same thing as adding the opposite of the number. The opposite of a number is the same number, but with the opposite sign in front of it. So if a number is positive, its opposite is negative and vice versa. 6 is the opposite of -6 and -6 is the opposite of 6.
For example, if the problem is 7 - 5, the numbers are positive 7 and positive 5 and positive 5 is being subtracted from positive 7. I could also think of this problem as 7 + (-5) because -5 is the opposite of 5. Likewise, if presented with 10 + (-4), it can be switched to a subtraction problem to say 10 - 4 because 4 is the opposite of -4.
The same holds true when the first number in the problem is a negative number:
-20 - 5 is the same as -20 + (-5). The subtraction problem was turned in to an addition problem where the opposite of 5 was added. This may make it clearer to some students that since you're adding -5 to -20, the answer will be more negative.
5. graphing on the coordinate plane
Graphing is a huge part of algebra and more advanced math. Students who understand how to graph points on the coordinate plane will have a much easier time when they become introduced to linear equations and more advanced topics. Make sure your child can identify the the origin (point (0,0)), the x-axis, and the y-axis correctly. Then make sure your child can correctly graph points in all four quadrants, for example:
The point A (3, 1) in Quadrant I
The point B (-3, 1) in Quadrant II
The point C (-3, -1) in Quadrant III
The point D (3, -1) in Quadrant IV
It is also important to be able to write the coordinates of any point if given the picture of it. In other words, if presented with the picture above and asked the coordinates of Point D, it would be no problem to say, "(3, -1)."
In summary, there are many critical skills to master before entering into the exciting world of Algebra 1. Let's make sure students have the necessary skills needed so that they can appreciate the beauty of algebra! Reach out with any questions or if you think I may be able to help prepare your child for what's ahead.
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Melissa Agocs
melissa@learnwithme123.com