Prior Knowledge
- Adding basic facts
- Subtracting basic facts
- Naming cubes, spheres, and cylinders
Introducing the Activity
Draw the picture of the two weight scales shown in Weight Problem 1 on the board. Label the scales A and B, as shown.
Weight Problem 1
Tell the students that these are scales and that they show the weights of the blocks that have been placed on them. Ask the following questions:
- (Point to scale B.) What is on scale B? [A sphere] How much does it weigh? [Six pounds]
- (Point to scale A.) What is on scale A? [A cube and a sphere] How much do the objects weigh all together? [Nine pounds]
- Figure out the weight of the cube. How did you do it? [The sphere is 6 pounds, so the cube weighs 9 - 6, or three, pounds.]
Next, draw the two scales for weight problem 2 on the chalkboard or on poster board.
Weight Problem 2
As in problem 1, the weight of one block is given in this problem. But unlike in problem 1, to find the weight of a cube, two operations must be performed. First the total weight of the cubes must be determined. Then the weight of each cube must be found. Ask the following questions:
- What block is on scale A? [A sphere]
- How much does the sphere weigh? [Four pounds] How do you know? [The scale shows four pounds.]
- (Point to scale B.) What is on scale B? [One sphere and two cubes]
- How much do the blocks weigh all together? [Fourteen pounds]
- (Point to the sphere on scale B.) How much does this sphere weigh? [Four pounds]
- How can you figure out how much each cube weighs? [The sphere is four pounds. So the two cubes are 14 - 4, or ten, pounds. So each cube weighs five pounds.]
Point out to the students that the blocks of the same shape have the same weight. So since the sphere on scale A weighs four pounds, the sphere on scale B must also weigh four pounds. In like manner, the cubes weigh the same number of pounds.
Present weight problem 3 to the students. Unlike in the first two weight problems, in this problem the weight of one of the blocks is not given
directly. The students have to decide which scale to consider first. The scale with two identical blocks is the best place to begin because, through guess and check or the recall of the addition of doubles, the students can find the weight of one sphere.
Weight Problem 3
Ask the following questions:
- Which blocks are on scale A? [A sphere and a cube.] How much do they weigh all together? [Eleven pounds]
- Do you know how much the sphere weighs? [No, we can't tell.]
- Do you know how much the cube weighs? [No, we can't tell.]
- Which blocks are on scale B? [Two spheres]
- How much do they weigh all together? [Twelve pounds]
- Do you know how much each sphere weighs? [Yes, each weighs six pounds.]
- How did you figure it out? [6 + 6 = 12, so half of 12 is 6.]
- Can you figure out the weight of the cube? [Yes]
- How will you do that? [The sphere weighs 6 pounds, so the cube is 11 - 6, or five, pounds.]
Distribute copies of the Block Pounds Activity Sheet for students to complete individually or in pairs. Encourage the students to record the weights on the blocks as they are determined. Once the students have completed the problems, have them talk about how they solved them.
Note that the problems on "Block Pounds" are ordered by difficulty. Problem A gives the weight of one of the blocks directly. Problem B requires a knowledge of a doubles addition fact to find the weight of one block before the weight of the other can be computed. Problems C and D show three scales with three different types of blocks. In problem C, the weight of the sphere is given directly and the students have to replace the sphere on each of the other two scales with its weight to find the weights of the cylinder and cube. In problem D, no weight of a block is given directly.
