How Do Cluster Problems Help Children Learn Multiplication?
Cluster problems are sets of problems that help children use what they already know to solve a more difficult problem. They progress in order from the simple to the complex, as in the following example: • 4 x 6 • 4 x 10 • 4 x 20 • 4 x 26 Students do the simpler problems first and use their answers to solve the most difficult problem which comes at the end of the set. The first two problems in this set are multiplication facts which most children will “just know:” document.getElementById(‘adsense_placeholder_2’).innerHTML = document.getElementById(‘adsense_ad_2_hidden’).innerHTML; • 4 x 6 = 24 • 4 x 10 = 40 • 4 x 20 = ? • 4 x 26 = ? If students know that 4 x 10 = 40, it is easy to solve the third problem, 4 x 20, just by doubling. • 4 x 6 = 24 • 4 x10 = 40 • 4 x 20 = 80 • 4 x 26 = ? Now students can solve the final problem, 4 x 26, by breaking it into two smaller problems: 4 x 26 = (4 x 20) + (4 x 6). Solving the last problem in the cluster is now just a matter of addition: • 4 x 6 = 24
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