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11Chess Cubes Unit
2 . Learn two methods of counting stacked cubes.
Find the number of cubes. Have students learn the methods of counting stacked 2. Have students learn two methods of
counting stacked cubes.
cubes. They can either count the cubes in each layer,
Method 1: Count the cubes in layers.
Method 1 or in each column. Students need to visualize each layer and
then count the cubes. Students who have
Count the cubes in each layer. a. 1+3+3 problems imagining layers may want to
sketch each layer on paper. The number of
7 cubes cubes is determined by adding up the cubes
in each layer.
b. 2+6 Top layer: 1
Number of cubes: 1 3 5 = 9 (cubes) 8 cubes Middle layer: 3
Bottom layer: 5
Method 2 c. 1 3 5 9 cubes
Count the cubes in each column.
Method 2: This is done the same way as
7 cubes Method 1, only instead of counting cubes by
layers, the cubes are counted in columns.
1212 1 Which is the best way to count cubes?
Both ways are good.
d. What is the advantage of counting cubes
both way? They prevent students from
missing cubes that are hidden from view.
23 12
Number of cubes: 3 2 2 1 = 8 (cubes) 123 23 11 cubes
11. Chess Cubes 99
Counting Cubes Serves Several Functions
1. It helps students visualize things which may be hidden from view.
2. It helps reinforce math concepts, such as the basics of addition and subtraction to the more complicated
such as determining an orderly progression of numbers.
3. It introduces students to working with three dimensions, which will be used in more advanced math
lessons such as figuring out the mass of an object when you know its height, width, and length.
4. It teaches students there is more than one way to arrive at the solution to a problem. For example, one
student adds four blocks to three blocks, another combines six blocks with one block, and a third adds
two blocks to five. Each student ends up with seven blocks, and all of the ways used to achieve this were
correct.
5A Unit 11 161
2 . Learn two methods of counting stacked cubes.
Find the number of cubes. Have students learn the methods of counting stacked 2. Have students learn two methods of
counting stacked cubes.
cubes. They can either count the cubes in each layer,
Method 1: Count the cubes in layers.
Method 1 or in each column. Students need to visualize each layer and
then count the cubes. Students who have
Count the cubes in each layer. a. 1+3+3 problems imagining layers may want to
sketch each layer on paper. The number of
7 cubes cubes is determined by adding up the cubes
in each layer.
b. 2+6 Top layer: 1
Number of cubes: 1 3 5 = 9 (cubes) 8 cubes Middle layer: 3
Bottom layer: 5
Method 2 c. 1 3 5 9 cubes
Count the cubes in each column.
Method 2: This is done the same way as
7 cubes Method 1, only instead of counting cubes by
layers, the cubes are counted in columns.
1212 1 Which is the best way to count cubes?
Both ways are good.
d. What is the advantage of counting cubes
both way? They prevent students from
missing cubes that are hidden from view.
23 12
Number of cubes: 3 2 2 1 = 8 (cubes) 123 23 11 cubes
11. Chess Cubes 99
Counting Cubes Serves Several Functions
1. It helps students visualize things which may be hidden from view.
2. It helps reinforce math concepts, such as the basics of addition and subtraction to the more complicated
such as determining an orderly progression of numbers.
3. It introduces students to working with three dimensions, which will be used in more advanced math
lessons such as figuring out the mass of an object when you know its height, width, and length.
4. It teaches students there is more than one way to arrive at the solution to a problem. For example, one
student adds four blocks to three blocks, another combines six blocks with one block, and a third adds
two blocks to five. Each student ends up with seven blocks, and all of the ways used to achieve this were
correct.
5A Unit 11 161
