I am very excited about a Pi day today. We love math in our house and we do a lot to supplement a school math curriculum at home. I am delighted to join with several other kid bloggers in We Love Math blog hop and share some ways to play with math at home. I planned a geometry post originally but decided to go instead with my “first love” – logic problems for children.
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Math Is Not Only About CalculationsI went to school in the former Soviet Union where math was valued and respected. We were taught to think of math not only as the world of numbers, but as the world of shapes, the world of natural laws, and the world of logical thinking. A lot of real math problems are logic problems that require deep reading comprehension, thinking through different scenarios, evaluating options and selecting the right way forward. Both my husband and I enjoy this kind of math and we started to introduce simple logic problems to our daughter since she was a preschooler. We really stepped up our efforts now when she is in the second grade.
Examples of Logic Problems for Grade 1-2I am going to give a few examples of logic math problems we tried with our daughter when she was in the first and now in the second grade. She couldn’t do all of them, and it’s OK. We don’t always walk her through the answer leaving the problem unanswered and waiting for its time to come.
1. A lateral thinking problem. Two children are born on the same day of the same year to the same set of parents, but they are not twins. Who are they to each other?
2. A spatial thinking problem. Move two matches two different places to make 4 squares out of these 5:
3. Reading for clues. We use books from Creative Thinking Mind Benders series to introduce our daughter to classic “matrix” logic problems. She is surprisingly good at those (same cannot be said about spatial problems)
4. Stretching existing arithmetic and algebra knowledge. A student bought 4 books. 3 books without the first one cost 42 cents, 3 books without the second one cost 40 cents, 3 books without the third one cost 38 cents, 3 books without the last one cost 36 cents. How much is every book?
5. Logical problems that can be helped by physical setup. Many logic problems can be helped by having a physical set up to work through them. One famous problem is “fake coins” problem. In fact, there is a whole set of fake coin problems out there, but we started with the easiest one. We have 15 coins, and one of them is fake. We don’t know whether the fake coin is easier or lighter than other coins. We have a balance scale and two chances to weigh coins. We need to find out whether a fake coin is lighter or heavier than true coins.
Setting Up a “Fake Egg” Problem
I gave Smarty this coin problem as mental math, but it proved to be too difficult for her. She simply couldn’t visualize fake coins and couldn’t even start designing a solution. I decided to set up this problem for her with Easter eggs. I told Smarty that I made one of the eggs “fake” and that she is not allowed to touch them. She can direct me to weigh them on the scale to find whether the fake egg is heavier or lighter. I made it heavier by putting a chocolate candy inside.
Having something “real” to work with really helped our daughter to work through 15 coins problem. She tried different scenarios and was able to figure out the solution. We tried a more difficult problem later – we have now 12 eggs, one of which is fake (this time it was lighter, but this fact is unknown in the beginning). You have 3 chances to weigh your eggs, and you need to find a fake egg. She could solve a generic case for this one, but, to her credit, my husband spent a lot of time trying to convince me that this problem is not solvable for all combinations (he was wrong).
More Math and Logic Problems?
- Math is Fun site
- Enriching Mathematics from University of Cambridge
- Russian math problems for elementary school (in Russian)
- 100 Ways to Have Fun with Math at Home