Lots of everyday objects can be fun, whether it’s buttons, beans, or LEGO blocks. But just because objects are fun to play with, doesn't mean they can't teach something, too! By creating patterns with objects, students begin to develop their algebraic thinking skills.
Here’s an activity that uses coins to build problem-solving strategies. With practice, students can use these “manipulatives” to discover lots of key mathematical concepts such as the commutative and associative properties, which will underly addition and multiplication work for years to come.
What You Need:
- Pennies
- Nickels
- Dimes
- Quarters
- Table or other flat surface
What You Do:
- Model a repeating pattern using pennies and nickels. You can show a series of two pennies, 1 nickel, or a similar pattern. Ask your child to name your pattern.
- Ask your child to extend your pattern by adding what comes next. If your pattern shows two pennies, one nickel, two pennies, one nickel, two pennies; then one nickel comes next. Allow your child to place the nickel after the two pennies.
- Add to the challenge. This time set up a repeating pattern showing pennies, dimes, and quarters. Place the coins on the table to show the first two repetitions. You might try something like penny, penny, dime, quarter, quarter. This series shows an ABC pattern, which is a bit more challenging. Ask your child to name the pattern you created. Now have your child extend this pattern by placing the coins on the table to show the next repetition.
- Explore some more. Set this series of coins in a row on the table - one nickel, two pennies, one nickel, three pennies, one nickel, four pennies. Discuss this pattern with your child. Ask him what part of the pattern remained the same (the nickel). Ask him what part changed (the number of pennies).
- Let your child experiment! Set her to work independently. Ask an open-ended question like, “How could you use these four types of coins to make a different pattern?” Encourage her to show you the patterns.
All mathematics is based on patterns, and because generations of mathematicians have clarified their observations, we also know that patterns can even become formulas that underly much more complicated mathematics work in grades to come. There’s a danger, though, in learning the formulas without anchoring them in hands-on discoveries like this exercise: kids may do math “by the rules,” but have no idea how or why. Any time you let your kid practice sequences, make new ones, and think it all over, you are building habits and ways of thinking that can support math success for years to come.
By Sally Ann Stanley
Sally is an experienced educator, with over 14 years of teaching experience. In addition to teaching, she has also created educational materials, including ancillary, textbook, and test items, for Grades K-8 for major educational publishers.
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