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The Doorbell Rang, by Pat Hutchings, ISBN978-0-688-09234-4 Reys, R. E., Suydam, M. N., and Lindquists, M. M. (1995).
Helping Children Learn
Mathematics, 4th ed. Needham Heights, MA: Allen and Bacon.
Background For Teachers:
The more partitions the whole is divided into, the smaller the pieces. The size of the partitions also depends on the size of the whole.
Students should realize that every fraction has an infinite number
of names. It should also be understood that when a whole is
partitioned, the numerator and the denominator are increased by the
same factor. Students should be familiar with equivalent fractions
and feel comfortable adding and subtracting fractions with the same
Intended Learning Outcomes:
Play “Multiples Game”. Have all students stand around the room. Call out a number from 1 to 12. When the number is called, students must get into groups the size of the number that was called and lock arms. Any one not in a group stands out. A different number is called each round. Call out numbers that are factors of 12 (2, 3, 4, 6, 12) to begin. Then call out a number that is not a factor of 12 (e.g. 5, 7, 8). Discuss with students why when you called out 5, why did classmates have to stand out. Why did no one leave the game when you called out 2 or 3 or 4 or 6 or 12? Everyone got into a new sized group but no one was eliminated. What could we deduce from this? Lead the discussion to multiples and what numbers divide evenly into 6, 8, 9 & 12.
When denominators are DELIGHTFULLY DIFFERENT (like apples & oranges), you must find a common denominator before you can add or subtract the fractions. This is like mixing the fruit together in a fruit salad!
Jensen, E. (1999). Teaching with the Brain in Mind. Association for Supervision and Curriculum Development, Alexandria, VA.
To our brain, we are either doing something we already know how to do or we are doing something new. Repetition of previous learning is likely to make the neuron pathways more efficient and therefore makes the brain more efficient. Reviewing what students already know on a regular, daily basis has great benefits. Reviewing and assessing what students already know about a concept helps them make more connections.
Memory is the only real evidence of learning. Lasting learning seems to be a function of the repeated electrical stimulations of a neuron. Quality education will provide multiple and varied explorations of concepts for increased connections and advanced memory.
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