Recently I have been working with some students getting ready for their End of Grade Testing in North Carolina. This is a couple years into our adoption of Common Core. I have watched Common Core unfold and found both positive and negative things about the new standards. This is not an article about those! However, one of the big negatives is that students are spending more time on “conceptual” understanding and “alternative” (and long winded) approaches to mathematics that are getting further behind on the basics including the ability to do procedural mathematics. In the mathematics education community, there has always been much discussion about the percentage of focus on procedural mathematics vs. conceptual mathematics. Let me quickly summarize the current thought:

Procedural : the ability to perform mathematics and solve actual problems such as 4X3 and 1/3 + 4/5. Procedural mathematics gets a bad wrap, many educators assume that since calculators and computers can do this, our focus needs to be on the concepts behind the procedures and if we do this, the procedural math will come naturally. This DOESN’T happen! So many students can’t do the procedural math steps and we don’t spend enough time on them.

Conceptual: the ability to understand the concepts surrounding the mathematics and the “why.” One cannot solve a word problem involving multiplication if they don’t understand the concept of what multiplication is and how it is different from addition or subtraction. However, one still needs to be able to do the procedural steps to get the answer to the problem and I disagree that the “procedural mathematics” will come automatically if a student knows the concepts. Often, students only get to a partial understanding of the concepts and then they are in a real bind since they can’t do either the procedural or conceptual.

So, how does this apply to YOUR child? Well, most children are just not given enough time practicing the procedures and this is what a parent must make up at home until these steps are automatic and easy. Leave the conceptual teaching for the teachers (or get a tutor if needed for this) but you can do your child a huge service at no cost by having them master procedural mathematics!

This is not an inclusive list but a list of things that one should work on at each grade. If your child is in 6th grade and hasn’t mastered the objectives listed for 4th grade, you need to start there. Start at whatever level your child is not 95% successful at.

Grade 4:

- Knows all multiplication and division facts (0-12)
- Can do multi-digit multiplication
- Can do long division with a single digit divisor
- Can convert between mixed numbers and improper fractions

Grade 5:

- Can add, subtract, multiply, and divide with fractions with unlike denominators (including 3 or 4 in a row)
- Can add, subtract, multiply, and divide with mixed numbers
- Can reduce fractions (including BIG fractions)
- Understands divisibility rules and how to apply them (minimum can do 2, 5, 9, and 10)

Grade 6:

- Can add, subtract, multiply, and divide with decimals
- Can convert between decimals and fractions
- Can solve 1 step algebraic equations
- Can combine like terms in algebra
- Can use distributive property in algebra
- Can solve order of operation problems
- Can find the 5 point summary for a box plot, graph, and interpret
- Understands / memorizes appropriate math vocabulary: mean, median, mode, range, IQR, Q1, Q3, variation, cluster, gap, outlier, MAD, standard deviation, spread, radius, diameter, etc.

Grade 7:

- Can set up and solve ratio and proportion problems
- Can set up and solve percent problems from words
- Can solve 2 step algebraic equations
- Can simplify algebraic expressions that mix distributive property and combing like terms
- Can convert from words to algebraic expressions
- Can solve 2 step algebraic equations that involve fractions and decimals
- Can find volume and surface area of prisms
- Can find area, perimeter, and circumference of mixed figures

Grade 8:

- Can find slope from 2 points
- Can find equation of a line from a slope and point
- Can find equation of a line from 2 points
- Can find equation of a line from a table or graph
- Understands and can apply idea of x and y intercepts graphically and as points
- Can find lines perpendicular to other lines
- Can apply Pythagorean theorem
- Can find the distance and midpoint between two points
- Can solve more advanced algebraic equations including ones with fractions and decimals
- Can solve problems involving the use of all exponent rules including negative exponents

I suggest that each student does 4 problems every night, this way they are not overloaded but they are doing math consistently. They can’t move on until they are getting answers consistently correct and then always revisit old problems with new problems. For example, your child might have mastered addition and subtraction of fractions with unlike denominators and they are working on multiplication and division of fractions now. Some nights they will get all 4 problems of multiplication and division but some nights they will get a mix of old, one of each operation or even older material, one adding fractions, one dividing fractions, one long division (grade 4), and one reducing fractions (application to long division).

This IS the best way to help your child be successful. Always check your child’s work after the first problem, you don’t want them doing all 4 problems wrong, then they are practicing how to do things wrong! If it looks good, they can continue. If they don’t get all answers correct, give them the first chance to fix it, if they can’t, then you can help them out or save up the pages and meet with a tutor and do these problems with a tutor.

Go to sites where they print out worksheets for your child and answers for you! Sites such as math aids and Kuta software.

Lynne Gregorio, Ph.D.

Mathematics Educator