Mathematics

Pearson enVision Mathematics 2020 Common Core covers the following topics:

__Strategies for Addition Facts__

__Counting all__

This is a particularly straightforward strategy: to solve 7 + 8, for example, the student gets 7 of something and 8 of something and counts how many there are altogether. The “something” could be beans or chips, or marks on paper. In any case, the student counts all the objects to find the sum. This is perhaps not a very efficient method, but it is effective, especially for small numbers, and is usually well understood by the student.

__Counting on__

This is a natural strategy, particularly for adding 1, 2, or 3. Counters such as beans or chips may or may not be used. As an example with counters, consider 8 + 3. The student gets 8 beans, and then 3 more, but instead of counting the first 8 again, she simply counts the 3 “new” beans: “9, 10, 11.” Even if counters are not used, finger gestures can help keep track of how many more have been counted on. For example, to solve 8 + 3, the student counts “9, 10, 11,” holding up a finger each time a number word is said; when three fingers are up, the last word said is the answer. There are efficient finger techniques you can teach your students if you wish, or you can let them use their own intuitive methods.

__Doubles__

Facts such as 4 + 4 = 8 are easier to remember than facts with two different addends. Some visual imagery can help, too: two hands for 5 + 5, a carton of eggs for 6 + 6, a calendar for 7 + 7, and so on.

__ ____Making a 10__

Facts with sum 10, such as 7 + 3 and 6 + 4, are also easier to remember than other facts. A ten frame can be used to develop imagery to help even more. This sort of visual imagery helps the students remember, for example, that 8 + 2 = 10.

__Using a 10__

Students who are comfortable partitioning and combining small numbers can use that knowledge to find the sums of larger numbers. In particular, there are many strategies that involve using the number 10. For example, to find 9 + 7, we can decompose 7 into 1 + 6 and then 9 + 7 = 9 + 1 + 6 = 10 + 6 = 16. Similarly, 8 + 7 = 8 + 2 + 5 = 10 + 5 = 15.

__Reasoning from known facts__

If you know what 7 + 7 is, then 7 + 8 is not much harder: it’s just 1 more. So, the “near doubles” can be derived from knowing the doubles. This is an example of reasoning from known facts.

__Strategies for Subtraction Facts__

__Using counters__

This method consists of “acting out” the problem with counters like beans or chips. For example, to solve 8 – 3, the student gets 8 beans, removes 3 beans, and counts the remaining beans to find the difference. As with the addition strategy of “counting all,” this is a relatively straightforward strategy that may not be efficient but has the great advantage of usually being well understood by the student.

__Counting up__

The student starts at the lower number and counts on to the higher number, perhaps using fingers to keep track of how many numbers are counted. For example, to solve 8 – 5, the student wants to know how to get from 5 to 8 and counts up 3 numbers: 6, 7, 8. So, 8 – 5 = 3. Special finger-counting techniques may be helpful, but this strategy seems to be a natural for most students.

__Counting back__

Counting back works best for subtracting 1, 2, or 3; for larger numbers, it is probably best to count up. For example, to solve 9 – 2, the student counts back 2 numbers: 8, 7. So, 9 – 2 = 7.

__Using a 10__

Students follow the pattern they find when subtracting 10, e.g., 17 – 10 = 7 and 13 – 10 = 3, to learn “close facts,” e.g., 17 – 9 = 8 and 13 – 9 = 4. Since 17 – 9 will be 1 more than 17 – 10, they can reason that the answer will be 8, or 7 + 1. In this strategy, 10 is a part in the whole-part-part scenario.

__Making a 10__

Knowing the addition facts which have a sum of 10, e.g., 6 + 4 = 10, can be helpful in finding differences from 10, e.g., 10 – 6 = 4 and 10 – 4 = 6. Students can use ten frames to visualize these problems. These facts can then also be used to find close facts, such as 11 – 4 = 7. In this strategy, 10 is the whole in whole-part-part scenario.

__Using doubles__

The addition doubles, e.g., 8 + 8 = 16 and 6 + 6 = 12, can be used to learn the subtraction “half-doubles” as well: 16 – 8 = 8 and 12 – 6 = 6. These facts can then be used to figure out close facts, such as 13 – 6 = 7 and 15 – 8 = 7.

"Arithmetic is being able to count up to twenty without taking off your shoes."

Mickey Mouse