Basic Operations1b.ppt

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Helping Children Master the Basic Facts
 Mastery of basic fact means that a child can give a quick response (in about 3 seconds) without resorting to nonefficient means, such as counting. Work towards mastery of addition and subtraction facts typically begins in the first grade. Most books include all addition and subtraction facts for mastery in the second grade, although much additional drill is usually required in grade 3 and even after. Multiplication and division facts are generally a target for mastery in the third grade, with more practice required in grades 4 and 5. Unfortunately, many children in grade 8 and above do not have a complete command of the basic facts.
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A Three Step Approach to Fact Mastery
Help children develop a strong understanding of the operations and of number relationships.
Develop efficient strategies for fact retrieval through practice.
Then provide drill in the use and selection of strategies once they have been developed
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One-More-Than and Two-More-Than Facts
Each of the 36 facts highlighted in the chart has at least one addend of 1 or 2. These facts are a direct application of the one-more-than and two-more-than relationships.
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Join or part-part-whole problems in which one of the addends is a 1 or 2 are easy to make up. For example: When Tommy was at the circus, he saw 8 clowns come out in a little car. Then 2 more clowns came out on bicycles. How many clowns did Tommy see in all?
Can you think of a word problem using this method?
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Facts with Zero
Nineteen facts have zero as one of the addends. Though such problems are generally easy, some children over generalize the idea that answers to addition are bigger. Word problems, involving zero will be especially helpful. In the discussion, use drawings that show two parts with one part empty.
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Doubles
There are only ten doubles facts from 0 + 0 to 9 + 9, as shown here. These ten facts are relatively easy to learn and become a powerful way to learn the near-doubles (addends one apart). Some children use them as anchors for other facts as well.
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Near Double
Near Doubles are also called the “doubles-plus-one” facts and include all combinations where one addend is one more than the other.
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Make-Ten Facts
These facts all have at least one addend of 8 or 9. One strategy for these facts is to build onto the 8 or 9 up to 10 and then add on the rest. For 6 + 8, start with 8, then 2 more make 10, and that leaves 4 more for 14.
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Generic Task
If you did not know the answer to 8 + 5 what are some really good ways you can use to get the answer? 
“Really good” means that you don’t have to count and you can do it in your head.
See if you can come up with more than one way.
Share your ideas in your group of three.
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Other Strategies and the Last Six Facts
Doubles Plus Two, or Two-Apart Facts
 Of the six remaining facts, three have addends that differ by 2: 3 + 5, 4 + 6, and 5 + 7. There are two possible relationships that might be useful here, each depending on knowledge of doubles. Some children find it easy to extend the ideas of doubles. Some children find it easy to extend the idea of the near doubles to double plus 2. For example, 4 + 6 is double 4 and 2 more. A different idea is to take 1 from the larger addend and give it to the smaller. Using this idea, the 5 + 3 fact is transformed into the double 4 facts- double the number in between.
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Make-Ten Extended
 Three of the six facts have 7 as one the addends. The make-ten strategy is frequently extended to the facts as well. For 7 + 4, the idea is 7 and 3 more makes 10 and 1 left is 11. You may decide to suggest this idea at the same time you initially introduce the make-ten strategy. It is interesting to note that Japan, mainland China, Korea, and Taiwan all teach an addition strategy of building through 10 and do so in the first grade.
Counting On
 Counting on is the most widely promoted strategy. It is generally taught as a strategy for all facts that have 1, 2, or 3 as one of the addends and thus, includes the one and two-more-than facts. For the fact 3 + 8, the child starts with 8 and counts three counts, 9, 10,11. There are several reasons this approach is downplayed in this text. First, it is frequently applied to facts where it is not efficient, such as 8 + 5.
It is difficult to explain to young children that they should count for some facts but not others. Second, it is much more procedural than conceptual. Finally, if other strategies are used, it is not necessary.
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Ten-Frame Facts
 The ten-frame model is so valuable in seeing certain number relationships that these ideas cannot be passed by in thinking about facts. The ten-frame helps children learn the combinations that make 10: 5 + 6, 5 + 7, and 5 + 8 are quickly seen as two fives and some more when depicted with these powerful models. 
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Strategies for Subtraction Facts
Subtraction as Think-Addition
 Students are encouraged to think, “What goes with this part to make the total?” When done in this think-addition manner, the child uses known addition facts to produce the unknown quantity or part.
 Think-addition is most immediately applicable to subtraction facts with sums of 10 or less. These are generally introduce with a goal of master in the first grade. Sixty-four of the 100 subtraction facts fall into this caegory.