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Multiplication Facts Using Strategies David McKillop Making Math Matter, Inc. Why should students learn the number facts? They are the basis of all mental math strategies, and mental math is the most widely used form of computation in everyday life Knowing facts is empowering Facilitates the development of other math concepts How is fact learning different from when I learned facts? 1. Facts are clustered in groups that can be retrieved by the same strategy. 2. Students can remember 6 to 8 strategies rather than 100 discrete facts. 3. Students achieve mastery of a group of facts employing one strategy before moving on to another group. General Approach For each cluster of facts that you are going to introduce, start by showing students one of the facts and ask them to put up their hands when they have the answer. Then ask some student(s) to explain how they did it. This can lead to a discussion of a variety of strategies from which you can extract the one you will highlight. Students should understand that they can use whatever strategy makes sense to them and enables them to get an answer in a reasonable time frame. You will be highlighting a specific strategy for each cluster but students may use other ones. Therefore, during the reinforcement activities when you ask students to explain their strategy, you should be open to, and welcome, any strategy that is reasonable. You don’t want to lose sight of the mission to have students be flexible in their thinking. As well, you will have students who know facts automatically without using a strategy, so you should be open to “I just knew it.” when you ask to explain how they did it. In fact, our long-term goal would be automaticity of the facts for all students. General Approach Introduce a strategy using association, patterning, contexts, concrete materials, pictures – whatever it takes so students understand the logic of the strategy Practice the facts that relate to this strategy, reducing wait time until a time of 3 seconds, or less, is achieved. Constantly discuss answers and strategies. Integrate these facts with others learned by other strategies. IT WILL TAKE TIME! Facts with 2s: 2 x ? and ? X 2 Highlighted Strategy: Connect to Doubles in Addition Start with 2 x ? Relate ? X 2 to 2 x ? Practice the Facts Webs Dice games Card games Flash cards Facts with 9s: ? X 9 and 9 x ? Highlighted Strategy: Nifty Nines Strategy: Two Patterns Decade of answer is one less than the number of 9s and the two digits of the answer sum to 9 9 x 9 = 81 8 x 9 = 72 7 x 9 = 63 6 x 9 = 54 5 x 9 = 45 4 x 9 = 36 3 x 9 = 27 Practice the Facts Calculator Facts with 5s The Clock Strategy: The number of 5s is like the minute hand on the clock – it points to the answer. For example, for 4 x 5, the minute hand on 4 means 20 minutes; therefore, 4 x 5 = 20. Practice Strategy Selection Which facts can use The Clock Strategy? Which facts can use the Nifty Nines Strategy? Which facts can use the Doubles Strategy? 3x5 5x9 8x2 9x7 9x2 2x5 7x5 6x9 Facts with 0s Highlighted Strategy: The Tricky Zeros: All facts with a zero factor have a zero product. (Often confused with addition facts with 0s) If you have 6 plates with 0 cookies on each plate, how many cookies do you have? Facts with 1s Highlighted Strategy: The No Change Facts: Facts with 1 as a factor have a product equal to the other factor. If you have 3 plates with 1 cookie on each plate OR 1 plate with 3 cookies on it, you have 3 cookies. Facts with 3s Highlighted Strategy: The Double and One More Set Strategy. For example, for 3 x 6, think: 2 x 6 is 12 plus one more 6 is 18. Facts with 4s Highlighted Strategy: The Double-Double Strategy. For example, for 4 x 6, think: double 6 is 12 and double 12 is 24. The Last Nine Facts 6x6 6 x 7 and 7 x 6 6 x 8 and 8 x 6 7x7 7 x 8 and 8 x 7 8x8 Have students suggest strategies for these. Possible Strategy: Using helping facts: 6x6=5x6+6 7x6=5x6+2x6 6x8=5x8+8 7x8=5x8+2x8 8x8=4x8x2 • • Some know 8 x 8 is 64 because of a chess board What about 7 x 7? Practice the Facts Flash cards Bingo Dice Games Card Games Fact Bee Calculators