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.
Main Curriculum Tie:
Mathematics - 4th Grade
Standard 1 Objective 5
Compute problems involving multiplication and division of whole numbers and addition and subtraction of simple fractions and decimals.
- 7 books
- counters for each pair of students
- 2 stools/chairs exactly the same height
Mental Math in the Middle Grades, Dale Seymour Publications, 1987.
Background For Teachers:
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.”
Intended Learning Outcomes:
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?”
- Students work in pairs. Have each student count out a certain number of
counters and find the total. Determine how many counters would be needed to
make one group a multiple of 10. Move this amount of counters from one group
to the other group. Does this change the total amount? (No) Repeat this activity
several times with different numbers of counters.
- Give the students an addition problem and have them “make tens”
by adding a compatible number to one of the addends. Go back and subtract
the same amount from the other addend to compensate. Then add the two adjusted
- Practice trading off numbers in order to make a nice even group of tens
for easier computation. Problems for practice:
|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?
- Students need to understand renaming subtraction. Write a simple subtraction
problem on the board. Have the students count out the first number of counters
and subtract the second number. (e.g., 6 - 2 = 4).
- Use the same problem and add “1” to each of the numbers.
(e.g., 7 - 3 = 4). What happened to the difference when we renamed the problem
by adding the same quantity to both numbers? (stayed the same). Try adding
“2” to each of the original numbers. Three. Four. Does the difference
stay the same?
- Give students several problems to subtract using the balancing subtraction
strategy. Make sure students understand that we want to “make tens”
with the number we are subtracting (subtrahend), not the one we are subtracting
from (minuend). It is much easier to subtract a nice even group of tens from
another number B no borrowing, etc.
Problems for practice:
|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.
Created Date :
Aug 29 2003 08:52 AM