In this lesson, the balance model for subtraction will be demonstrated
using both an actual and a virtual pan balance. If you have only a
balance with hanging weights, please modify the directions given as
Display a pan balance and review with the students how it
operates. Place 5 weights on one side of the balance and 3 weights on
the other side. Discuss with students how to make the scale balance
using take away. Relate this action to the equation 5 – ___ = 3.
Explain that the equals sign is like the middle point of a balance
scale — both sides must be equal. The Pan Balance Overhead can be displayed if you do not have access to a pan balance.
Pan Balance Overhead
Ask how many links need to be taken away so that the scale
balances. Accept and model all student responses. When the correct
response [2.] is given, complete the equation so that it reads
5 – 2 = 3. Repeat by having students place different weights on the
balance, write an equation, and solve. Continue until the students are
comfortable with the process.
Now show students the online Pan Balance- Shapes, and assign some children to work with this tool. Because the different
colored on-screen weights have different values, tell the children that
they should use only one color of weight in a problem. Have students
place an unequal number of weights on each side (for example, 5 on one
side and 3 on the other), then remove some from the heavier side until
the beam balances. Have them write the equation suggested by their
action — in this case, 5 – 2 = 3.
Pan Balance— Shapes
Split the class into two or more groups for center activities.
While some children are using the online balance, others can play
"What’s in the Bag?" To start the game, give pairs of children a pan
balance, a paper bag, and some links. Assign one child to go first,
placing 10 links (or connecting cubes) on the right side of the
balance. The same student then places up to 10 links (or connecting
cubes) in the bag and places the bag on the left side of the scale. The
other child is to take away from the right side until the scale
balances. Then the students write a subtraction equation to describe
the situation. Have them repeat the activity several times, switching
roles each time.
Questions for Students
1. Place 5 weights on one side and 3 weights on the other side of a balance. Which side of the scale is heavier? How do you know?
[The side with 5 weights is heavier because it is lower than the side with 3 weights.]
2. If we want the sides to balance, which side will we have to take weights from? How many weights will we have to take away?
[We have to take 2 weights away from the side with 5, since it is heavier.]
3. Suppose you put 6 links on the left side of the balance and 9 links on the right side. How would you balance the scale? What equation tells what you did?
[Take 3 links away from the side with 9. The equation is 9 – 3 = 6.]
4. How did you find out how many links were in the bag?
[Take weights away until the sides balance.]
- Which students met all the objectives of this lesson? What extension activities are appropriate for these children?
- Which students did not meet the objectives of this lesson? What instructional experiences do they need next?
- When the students worked in pairs, did both children contribute equally?
- Which students are counting to find differences? Which students use known facts to solve balance problems?
- What adaptations did you make for special needs students? Were these appropriate?
Students will be able to:
- Explore the balance model of subtraction.
- Write the subtraction modeled on the balance in equation form.
- Practice subtraction facts from 10.
- Demonstrate understanding of the equals sign (=).
NCTM Standards and Expectations
- Use concrete, pictorial, and verbal representations to develop an understanding of invented and conventional symbolic notations.
Common Core State Standards – Mathematics
-Kindergarten, Measurement & Data
Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.
-Kindergarten, Measurement & Data
Directly compare two objects with a measurable attribute in common, to see which object has ''more of''/''less of'' the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter.
Common Core State Standards – Practice
Use appropriate tools strategically.
Attend to precision.