# Logic-Based Problem Solving Math Competition (first week of prep)

This week, I introduced the children to the Noetic Learning Math Competition (NLMC) which is taken by over 25,000 student from 602 schools nationwide. The NLMC will test them in binary operations, geometry, algebra, probability and logical thinking. This past fall, I entered my 3rd grade class at The Sage School for the first time and this team came in third in the country and first in Massachusetts. This test is the antithesis of MCAS; the NLMC is based on logic word problems that challenge the children beyond mere calculation.

This week, I introduced the children to practice problems in grades below, at, and above their grade level. I also gave them a full-length test to take over the next two weeks at their grade level (with the exception of the first graders who will take a second grade test). Please encourage them to take the 20-question test in pencil, if they receive parent help, they should use pen and when they complete the test should again use pen to self-grade using the answer keys provided (these also have explanations). They should come prepared the week of March 14th will questions.

The practice problems we worked on in class included:

• 2nd Grade — Paige was in line 4th from one end and 8th from the other end; how many students were in that line? My process with the children was to let them know not to fall into the “its so obvious trap.” Most wanted to add 4 + 8 which of course is wrong. I encourage them to draw a picture with circles representing each student on either side of Paige which they can represent with a P.
• 2nd Grade — Each day, Julie picked 10 apples and ate 3; she saved the rest. How many apples did she have by the 4th day? Many answered 7 forgetting that it was for four days not one. Some answered 40 forgetting that she does not have the apples she ate. One best approach would be 10 - 3 = 7 x 4 = 28.
• 3rd Grade — How many three digit numbers can you make from the digits 0, 2, and 9 if each digit is used exactly once? Many students answered 6 because they believed that 029 and 092 are three digit numbers (they are still 2 digit numbers). I encouraged a systematic approach to recording these numbers. I pushed them to answer the same question if the digits are 1, 2, 4, and 9 (the answer is 24 but they should only have to write down 6 numbers and multiply by 4).
• 3rd Grade — Jeff left home March 1999 and travelled for 40 months. In what month did he return. This is simply a matter of dividing 40 by 12 and using the remainder of 4 to add to March to reach July. I showed them how to write out this problem by looking at March 2000, 2001, and 2002 and putting a 12 to the right of each date, adding this up to 36. The extension question was what if he travelled for 150 months (150/12 is 12 remainder 6 so September).
• 4th Grade — How many two digit numbers are even? First identify the first and last (10 and 98). In the teens, there are 5 even numbers (10, 12, 14, 16, and 18) and there are nine rows of these numbers. 9 x 5 = 45.
• 5th Grade — There are 18 students in a class. Each student must take at least one foreign language and the school only offers Spanish and French. If 9 student are taking Spanish and 11 are taking French, how many are taking both? Since the same of 9 and 11 is 20, if you subtract 18 you get the 2 students who are taking both. Using a Venn Diagram is the best way to approach this problem.
• 5th Grade — Two girls went to the orchard to pick apples. Vicki picked two more than half as many as Amy.  Together they picked 98 apples. How many apples did Amy pick? Using guess and check (the algebra is too difficult here), the answer is Vicky 34 and Amy 64. Many answered 34, the number of apples Vicky picked, not reading the question.

The key to success here is underlining key words in the problem, drawing pictures or tables to help organize your thoughts, and starting somewhere. A student can spend 5 minutes staring at a problem when the best way to approach it is to start writing down some numbers; if it is wrong, cross it out and take a different approach. The right approach is usually evident when first taking the wrong path. It is like taking the wrong path in a maze. If you hit a wall, back out and try an different road.

The attached pdfs will be sample problems and the other pdf will be at grade level full-length tests they should take and self-grade.

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