6.4: Weighing Weights
Guidance
In order to solve the problem above, use the problem solving steps.
- Start by describing what information is given.
- Then, identify what your job is. In these problems, your job will be to figure out the weight of each individual block.
- Next, make a plan for how you will solve. In these problems, find the weight of the block using the scale that shows only one type of unknown block first.
- Then, solve the problem.
- Finally, check your solution. Make sure that your solution causes each scale to have the correct weight.
Example A
Figure out the weights of the blocks.
Solution:
We can use the problem solving steps to help.
Describe: There are three scales, D, E, and F, with blocks. Scale D has a blue block and a 6 pound weight. Scale E has 3 red blocks. Scale F has one red block, one blue block, and one yellow block.
My Job: Figure out the weights of the blocks.
Plan: Start with D and find the weight of the blue block. Write the weight of the blue block on the pictures. Next, find the weight of the red block and write the weight of the red block on the pictures. Finally, find the weight of the yellow block.
Solve: Scale D tells us that , so the blue block is 3 pounds. Scale E tells us that 3 red blocks weigh 15 pounds, so each red block weighs 5 pounds. Finally, Scale F tells us that one red block, one blue block, and one yellow block together weigh 10 pounds. This means so the yellow block weighs 2 pounds.
Check: Replace each block with its weight. Scale D: 6+3=9. Scale E: 5+5+5=15. Scale F: 3+5+2=10.
Example B
Figure out the weights of the blocks.
Solution:
We can use the problem solving steps to help.
Describe: There are three scales, G, H, and I, with blocks. Scale G has a yellow block and an 8 pound weight. Scale H has a red block and a yellow block. Scale I has 2 red blocks and one blue block.
My Job: Figure out the weights of the blocks.
Plan: Start with G and find the weight of the yellow block. Write the weight of the yellow block on the pictures. Next, find the weight of the red block using scale H and write the weight of the red block on the pictures. Finally, find the weight of the blue block using scale I.
Solve: Scale G tells us that , so the yellow block is 7 pounds. Scale H tells us that one yellow block and one red block weigh 10 pounds, so the red block must weigh 3 pounds. Finally, Scale I tells us that 2 red blocks and one blue block weigh 10 pounds. This means so the blue block weighs 4 pounds.
Check: Replace each block with its weight. Scale G: 8+7=15. Scale H: 7+3=10. Scale I: 3+4+3=10.
Example C
Figure out the weights of the blocks.
Solution:
We can use the problem solving steps to help.
Describe: There are three scales, J, K, and L, with blocks. Scale J has a red block and a 10 pound block. Scale K has 2 red blocks and a blue block. Scale L has one red block, one blue block, and one yellow block.
My Job: Figure out the weights of the blocks.
Plan: Start with Scale J and find the weight of a red block. Write the weight of the red block on the pictures. Next, find the weight of the blue block using Scale K and write the weight of the blue block on the pictures. Finally, find the weight of the yellow block using Scale L.
Solve: Scale J tells us that , so the red block is 5 pounds. Scale K tells us that 2 red blocks and one blue block weigh 16 pounds, so and the blue block must weigh 6 pounds. Finally, Scale L tells us that one red block, one blue block, and one yellow block together weigh 15 pounds. This means so the yellow block weighs 4 pounds.
Check: Replace each block with its weight. Scale J: 10+5=15. Scale K: 6+5+5=16. Scale L: 6+5+4=15.
Concept Problem Revisited
We can use the problem solving steps to help.
Vocabulary
In math, an unknown is a letter that stands for a number that we do not yet know the value of. In this concept, when you figured out the value of the individual blocks you were solving for unknowns .
Guided Practice
Figure out the weights of the blocks.
1.
2.
3.
Answers:
1. The red block is 8 pounds, the yellow block is 6 pounds, and the blue block is 4 pounds.
2. The yellow block is 8 pounds, the blue block is 5 pounds, and the red block is 7 pounds.
3. The blue block is 7 pounds, the yellow block is 5 pounds, and the red block is 8 pounds.
Practice
Figure out the weights of the blocks.
Image Attributions
Description
Learning Objectives
Students determine the individual weights of three different blocks given information about the weights of multiples or combinations of blocks. Students use problem solving steps to help.