6.1: Boxes and Boxes
Look at the pictures of the pan balances below. What do you see? If all boxes have whole number weights, can you figure out the weight of box m? Can you say anything about the weight of box r? In this concept, we will learn how to use problem solving steps to help us to describe the relative weights of objects given in pan balances.
Guidance
In order to determine the relationship between the balance pans like the one above, use the problem solving steps to help you.
- First, describe what you see and what information you are given.
- Next, identify what your job is and what you are trying to solve. In all of these problems, your job will be to figure out the relative weights of the two boxes that have letters on them.
- Third, make a plan for how you will solve. Figure out what information each pan balance gives you.
- Fourth, solve the problem.
- Last, check your answer.
Example A
What could be the weights? Tell how you figured it out. All weights are whole numbers of pounds.
Solution:
We can use problem solving steps to help.
Example B
What could be the weights? Tell how you figured it out. All weights are whole numbers of pounds.
Solution:
We can use problem solving steps to help.
Example C
What could be the weights? Tell how you figured it out. All weights are whole numbers of pounds.
Solution:
We can use problem solving steps to help.
Concept Problem Revisited
We can use problem solving steps to help.
Vocabulary
To be equal means to be the same. When pans are balanced then the weights of the two pans are equal . To be greater than means to be bigger. To be less than means to be smaller. When two pans are not balanced then the weight of one pan is greater than the weight of the other pan.
Guided Practice
For each problem, what could be the weights of the two lettered boxes? Tell how you figured it out. All weights are whole numbers of pounds.
1.
2.
3.
Answers:
1. From J, , so pounds. From K, since is heavier than and So, pound.
2. From L, and . So or pounds. From M, Since or or pounds.
3. From N, so pounds. From P, so Then or pounds.
Explore More
For each problem, what could be the weights of the two lettered boxes? Tell how you figured it out. All weights are whole numbers of pounds.
Image Attributions
Description
Learning Objectives
Students determine the relative weights of objects from the relationships displayed in pan balances. Students use problem solving steps to help them.