Rules for Arithmetic – What students need to know

07 Aug

With the new common core standards, students are being asked to learn a large number of math rules in a single year.  Math rules can be very daunting for students.  If you think about how they change for every little thing.  When we multiply with decimals we add up decimal points to figure out number of decimal points in the answer, when we add and subtract with decimals, we line up decimal points, when we divide with decimals we have different rules depending on whether or not the the divisor is a decimal (then we move the decimal point) or not, then we just mark the spot and divide normally.  This is just for decimals, fractions are even more difficult, especially when you deal with mixed numbers.  Adding and subtracting always have different rules than multiplying and dividing!  Almost nothing is ever just intuitive.  No we can’t take 1/2 + 1/3 and just add the tops and bottoms and say the answer is 2/5!  How are students supposed to keep all these rules straight and at the same time, we want them to conceptually understand fractions, decimals, percents, geometry, algebra, patterns, and more!

I suggest flash cards.  On one side is the type of problem such as addition of fraction with unlike denominators and the other side contains the steps for performing it or the rules.  The student reviews the flash cards and practices a problem similar to the type on the flash as he reviews that rule, this process continues until all the rules are solid.  So, what are the rules that you should make sure your child knows?  Here they are:

  1. Adding decimals
  2. Comparing decimals
  3. Subtracting decimals (include the case such as:  4.1-.27)
  4. Multiplying decimals (I have students count the decimal places, put that number in a circle off to the side, remove decimals, multiply regularly, and then put decimal in at end.)
  5. Dividing decimals when divisor is a whole number and dividend is a decimal (4.46 / 2)
  6. Dividing decimals when divisor is a decimal and dividend is a decimal and also case of whole number (2.46 / .2 or 246 / .2)
  7. Adding fractions with unlike denominators (denominators have no factors in common and denominators do have a factor in common)
  8. Finding the LCM or LCD (lowest common denominator)
  9. Reducing a fraction to simplest form
  10. Adding mixed numbers
  11. Subtracting mixed numbers (when you need to borrow and not borrow)
  12. Multiplying fractions (where you can and cannot cross cancel)
  13. Dividing fractions
  14. Multiplying mixed numbers
  15. Dividing mixed numbers
  16. Finding GCF
  17. Writing a prime factorization
  18. Evaluating a number with an exponent
  19. Order of operations (remember that multiplication and division are on the same level and addition and subtraction are on the same level)
  20. Finding multiples of a number
  21. Converting from a mixed number to an improper fraction
  22. Converting from an improper fraction to a mixed number
  23. Divisibility Rules for (2, 3, 6, 5, 9, and 10)
  24. Knowing vocabulary of Sum, product, quotient, difference
  25. Rules for rounding numbers (include rules for rounding when you have 34.399, rounding to hundredth place)
  26. Key words for problems (Each means multiply or divide; of means multiple; How many more/fewer – means subtract)
  27. Rules for scientific notation
  28. Adding positive plus a negative
  29. How to approach subtraction with integers (switch / change approach)
  30. Multiplying negative times negative
  31. Multiplying with opposite signs (pos X neg or neg X pos)
  32. How to convert fractions to percents
  33. How to convert fractions to decimals
  34. How to convert decimals to percents
  35. How to solve percent word statements (is/of = %/100)

There are also many Geometry terms that can be added.  I realize some of these are not in the correct order (finding LCM, should be in card order before adding fractions when applied).  Most of these up through #26 are appropriate for students who have finished the 5th grade.  $27-#35 include 6th grade concepts.  There are additional concepts that can be added for 6th graders that start to include rules for algebra such as combining like terms, distributive property, etc.  However, if you want your child to be a strong math student – don’t just practice random problems, have them communicate the actual rules first and study these in the same way they might study a spelling list or science vocabulary for a test.  I have made some flash cards that you can print at:

Lynne Gregorio, Ph.D.


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