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2 class periods of 30 minutes each
In this lesson students will use the mental math skill of adding and subtracting by making multiples of ten and adjusting (compensation). These suggested strategies should be discussed in two separate lessons.
Mental Math in the Middle Grades, Dale Seymour Publications, 1987.
Calculating in your head is a practical life skill. Many types of everyday computation problems can be solved mentally. Mental calculation provides the cornerstone for all estimation processes, allowing a variety of alternative nonstandard techniques or strategies for finding answers. Mental computation encourages students to think about numbers and number relationships developing strong number sense and mathematical confidence. A survey from the National Assessment of Educational Progress in mathematics found that most children were unaware that a mental calculation is often the most convenient method to find a solution. Most students claimed that either a paper and pencil or calculator was needed to determine solutions.
It would be helpful if students have had prior experience with compatible numbers, in this case, pairs of numbers that make ten.
1. Demonstrate a positive learning attitude toward mathematics.
2. Become mathematical problem solvers.
3. Reason mathematically.
4. Communicate mathematically.
5. Make mathematical connections.
6. Represent mathematical situations.
Lesson One:Trading Off (Compensation)
Invitation to Learn
Give one student 4 books and another student 3 books. Ask: If you take part of the books from one student and give it to the other student does it change the total amount of books? How can this idea help you to add numbers?
|29 + 62||37 + 69|
|28 + 45||43 + 49|
|49 + 26||55 + 19|
Lesson Two:Balancing Subtraction (Compensation)
Invitation to Learn
Have two students of different heights help to demonstrate the idea that if you add the same amount to both the number you are subtracting and the number you started with, the difference will be the same.
Ask who is taller and approximately what is the difference in height? Give the shorter student a small stool/chair to stand on. (This student should now be taller). Many of the students will pick up on the idea that the difference changed when the shorter student had something to stand on. In order to keep the difference the same, the taller student would need something the same size to stand on. How can you use this idea to help you subtract numbers?
|65 - 49||44 - 28|
|43 - 19||81 - 58|
|72 - 29||71 - 47|
Use these strategies to find the sum and difference of 3 and 4 digit numbers.
Homework & Family Connections
Have students teach a member of their family a new way to mentally add or subtract and return a note indicating the shared mathematical experience between the family member and the student.
Have students write instructions for how to perform the skill they have just learned in their journals.