When I pose this problem to teachers in professional learning sessions, many mental strategies get revealed. Here are just a few that are often shared. We want students to think as flexibly about numbers and operations as these teachers do. Students need to demonstrate flexibility when performing mental calculations. For this multiplication problem and many others, knowing how to double efficiently is a great strategy.
Doubling is a strategy that people of all ages frequently use. Young children first learn doubles as an addition of two groups. What multiplication facts can be used by using a doubling strategy? If you said the twos , fours , and eights facts then you are correct! The word double comes from the Latin word duplus.
Use images that help students visualize the quantities by displaying them in an array structure. The card below shows the mental picture we want students to have of two groups of six, or double six. If students have been working with ten-frames, they might see the quantity as a ten and two more!
These arrays can be expanded to show the relationship between the twos, fours, and eights multiplication facts. Be sure to emphasize how the pictures show the doubling that is occurring.
The turnaround facts e. Draw the diagram shown below on the board. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page. Videos and songs to help Kindergarten and Grade 1 kids learn to add and subtract within 20, demonstrating fluency for addition and subtraction within 10 by creating equivalent but easier or known sums e.
Common Core: 1. Using derived fact strategies comes after learning counting strategies to solve addition and subtraction problems. A derived fact strategy means that there are some number combinations that the child knows and has memorized, and he or she uses those combinations to figure out derive other number combinations.
Children often memorize double facts fairly early on, so learning how to use doubles to figure out near-double facts is one of the first derived fact strategies children are able to use. Before children can use doubles to solve other problems, they must first learn some of the doubles. Building pictures for doubles by using symmetry is one way for children to learn doubles, especially for doubles of numbers to 5.
For example, children can place counters on either side of a symmetry line to show the double facts:. As suggested in the Teaching Student-Centered Mathematics text, you can also make pictures or flash cards with common objects that show doubles.
Unfortunately, it's rather hard to find good examples for some of the larger doubles:. One strategy is well illustrated by a double Cuisenaire rod staircase. Of course, once children have good ways of figuring out double facts, then it's time to practice so that at least some of them are memorized. Practice can be just flash cards, or it can be in the form of songs or rhymes or games.
A lot of games can be modified to practice double facts--just provide one sided die, and make the rule that you double the number on the die and go forward that many spaces, or collect that many points or tokens. An introductory lesson using a word problem Let's think about a class where the children have talked about and practiced doubles a little bit each day for several days perhaps weeks and all of the children know at least some of the double facts.
The teacher wants to introduce the idea of using double facts to solve facts that are near doubles. She might ask the class to think about the problem:. After waiting for children to think and figure out a solution, she asks: who would like to share how they solved this problem?
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