Math Proficiency by 3rd Grade

Since 2000, a research test known as PISA (Program for International Student Assessment) has been used to make international comparisons of math, reading, and science achievement for 15-year-olds.    In 2015,  the U.S. ranked 35th in the world in math achievement – not so great.   Now, this is not the fault of the children’s brains:  research convinces us differently.  The first federally-mandated testing of students is at the end of third grade, when children are usually from 8-10 years old.   If we show respect for the innate math thinking abilities of our youngest citizens and use these precious years to share with them the foundations of important mathematical ideas, then 100% math proficiency by third grade is a reasonable goal.  The first step is to believe it’s both important and possible for our U.S. students to accomplish it. 

So what does math proficiency in third grade look like?

I present for you on this page a list of ten world-class but attainable goals for third graders.  Each one describes math ideas they are capable of understanding and skills they should possess to be prepared for higher levels of math study — fourth grade and beyond —  and thus, make our nation proud on a world-class test like PISA in high school.

A Top-Ten List of Power-Start Math Goals for U.S. Third Graders (August 2018)

  1. Order and compare numbers up to 1000.   Read, interpret, and construct visual displays of number order.  Construct mental representations of number order as well.
  2. Know from memory all one-digit addition and multiplication facts along with related facts for subtraction and division. Use these facts along with number properties and mental arithmetic to solve problems.
  3. Understand place value    This understanding includes meanings of the ones place, tens place, and hundreds place for numbers up to 1000. Use place value and strategies other than calculators to add, subtract, multiply, and divide. multi-digit numbers.
  4. Solve arithmetic problems.   Select the appropriate operation — addition, subtraction, multiplication, and division — and be able to use spoken and written words, numbers, and symbols to explain your solution method. write a math sentence  to solve problems and equations within 1000.
  5. Use tabular information    Use information from a table or diagram to work with data; to think algebraically; and to solve problems. Construct a scaled bar graph to organize up to five categories of data.
  6. Acquire life skills with time and money   Tell time to the nearest minute, using analog and digital clocks, as well as a.m. / p.m. distinctions.  Read and use a monthly calendar appropriately.   Solve word problems about money involving dollar bills and coins.
  7. Classify shapes and partition them into fractional parts.    Partition circles and rectangles into halves, thirds, fourths, and smaller equal portions. Know that each portion represents a part of the whole — one-half, one-third, one-fourth, etc. and that 2/2 = 4/4 = 3/3 = 1 or one whole circle or rectangle.
  8. Measure lengths.    Estimate, and compare lengths with commonly used measuring devices scaled in inches, feet, centimeters, and meters.  Be familiar with one-foot rulers marked off in fractional parts of inches and centimeters.
  9. Distinguish between area and perimeter (a length measure).   Solve arithmetic problems involving area and perimeter.
  10. Select appropriate units of weight, temperature, and capacity.   Measure, estimate, and compare quantities with commonly used units of these measurable attributes.

So, there it is — a list of ten math topics we can start talking about as soon as children seem interested.  I implore you to use the early years, when children are most inquisitive and eager, to build deep and flexible understandings of these big ideas for number and operations; for geometry; for measurement; and for working with data.   Goals 1 – 4 on this list are the most important and require the earliest start.  In thinking about Goal #1,  begin with deep understandings of order and size for the numbers 1 – 10; and then 1 –100.   Goal #2 — the near-instantaneous recall of the one-digit facts — is essential knowledge, and fact mastery by the end of third grade is a giant step for staying on track toward math proficiency by eighth grade and into high school.  With regard to Power-Start Goal #6, I grouped time and money together because clocks, calendars, and monetary units represent such pervasive structures for our daily lives.  So, don’t forget to include time and money in conversations with young children whenever you have the opportunity.  For the much-needed concrete experiences start with coins.

In closing, I remind you that this list, updated on August 17, 2018 is a working draft.  Now, go to my blog, which discusses world-class, third-grade test questions one at a time. (Go to “High Expectations and World-Class Tests” for an introduction to this blog.)  In following my blog and considering these problems, I challenge you to use your math lenses which will help you to focus on deep understandings for the math you already know; to zoom-in and connect math to a child’s interests; and to zoom-out for glimpses of previous steps in this math journey, as well as steps that lie ahead.

Leave a reply if you have questions about my top-ten list or suggestions for revisions.

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