# 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 eight or so 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.

### (May 2019)

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. Understand place value   This understanding includes meanings of the ones place, tens place, and hundreds place, etc.
3. Know from memory all one-digit addition and multiplication facts along with related facts for subtraction and division. Use memorized facts, place value, and a variety of strategies other than calculators to add, subtract, multiply, and divide larger numbers.
4. Solve arithmetic problems.   Select the appropriate operation — addition, subtraction, multiplication, and division. Use facts, number properties, and mental arithmetic. Be able to use spoken and written words, numbers, and symbols to explain your solution method.
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 problems about money involving dollar bills and coins.
7. Classify shapes by their properties 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; then 1 –20; and then 1-100.   Goal #2 –understanding place value — can be realized by using a 100-grid. Learn not only how to count to 100 by ones and tens but also make friends with these numbers.  Making friends with the number 43 means knowing things about it. For example,

• 42 comes just before and 44 just after, and
• 43 is 4 groups of 10 and three ones.

Goal #3, 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.  Goal #4 solving arithmetic word problems combines the student’s math knowledge with reading skills, and critical thinking.

Goal #5, using tabular information, is more of a math practice than piece of information.  In today’s world of technology, children are exposed to tabular information at very young ages.  Why not start using simple tables in preschool for group discussion purposes.   For 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. Goals  #7 through #10 focus on geometry and measurement, and third-grade knowledge can remain at the introductory level.  In geometry, begin introducing basic shapes before age 3 — circle, triangle, square, rectangle, pentagon, hexagon, octagon, etc. And, let children find these in the real world and pages of books.   For measurement, only introductory knowledge is needed by third graders, but always look for real-world opportunities to introduce measurement to children.

In closing, I remind you that this list, updated on May 20, 2019 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.