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Number Sense Using Base Ten

Developing number sense is a critical skill that students need to learn.  When teaching Place Value manipulatives can be very powerful in developing this skill.


Do you see the pattern that is shown using the MasterPieces?

First, look at the unit cubes. You will see that from the top that each cube makes the shape of a square. Then the ten-bar makes the shape of a rectangle and the Hundred-block makes the shape of a square again.  What if this pattern continued?  What would the shape of 1,000 be?

Well, there are actually two different shapes that 1,000 could take!

Shape 1 is a CUBE.  This would be the representation of a 3-dimensional shape with length, width, and height. This would be a good example of 10x10x10 or 10 to the third power.  It is a great shape for older students learning more complex applications of mathematics.  However, it is not the best example for developing number sense.

Shape 2 would be a RECTANGLE. This shape is a good shape for developing number sense in younger students because it continues the pattern already started with the units (ones), tens, and hundreds places.

Using the MasterPieces we can help students develop number sense of much larger AND smaller numbers!

Each unit cube is 1/2"x 1/2" (Square) Each ten-bar is 1/2" x 5" (Rectangle)

Each hundred-bar is 5" x 5" (Square)

Each thousand-bar would be 5" x 50" (a big long rectangle - explains why we don't make a thousand-bar)

Each ten-thousand-bar would be 50" x 50" (big square)

Each hundred-thousand-bar would be 50" x 500"  (HUGE Rectangle) For perspective, 500" is 41'-8" long! That is as high as a four-story building!

Place Value on the Playground! Herfurth Elementary - Garland, TX

Now lets change the perspective a bit to show Place Values lower than 1.

Let's make the 10,000 square (since it is a square) our unit block.  So the big 50" x 50" square is now the unit block.

Now follow to the right...

The 5" x 50" rectangle is now one-tenths place.  It is one-tenth the size of the unit block.

The next block that is 5" x 5" is now the one-hundredths place. It is 100 times smaller than the unit block.

The next block that is 1/2" x 5" is now the one-thousandths place. It is 1,000 times smaller than the unit block.

And finally the block that is 1/2" x 1/2" is not the ten-thousandths place!  It is 10,000 times smaller than the unit block!

Now that is developing number sense!