Real Number Nesting Boxes Activity
You are going to make a manipulative that will help you visualize how the various families of numbers work. This activity
will also help you with geometry topics like nets and measurements.
You will have to be very precise in your measurements. Remember when we went over the words precise and accuracy
earlier this year. If you are having trouble “ASK”, however, pay close attention to the explanation the teacher is giving
you before you start.
Step 1
Natural number box (Pink Paper)
1
1
a. Draw 2 rectangles with sides 2 4 by 2 4 inches by measuring them with a ruler.
1
4
b. Measure and draw 4 rectangles that are 2 by 3 inches.
c.
d.
e.
f.
g.
Label one of the rectangles “natural numbers”
Include on one of the sides the definition for natural numbers
Include on the rest of the sides examples of natural numbers
Decorate your rectangles with colors and designs
Cut out the rectangles, form a net, tape the rectangles together then fold the sides to make a box. Seal it up
and set it aside.
Step 2
Whole numbers (White Paper)
a.
1
1
Measure and draw 3 rectangles that are 2 2 by 3 4 inches.
1
1
b. Measure and draw 2 rectangles that are 2 2 by2 2 inches.
c.
d.
e.
f.
g.
Label one of the rectangles “whole numbers”
Include on one of the sides the definition for whole numbers
Include on the rest of the sides examples of whole numbers
Decorate the rectangles
Cut out the rectangles, form a net, tape the rectangles together then fold the sides to make a box. Seal it up
and set it aside.
“HINT-This box will not have a top”
Step 3
Integers (Bright Yellow Paper)
3
1
3
3
a. Measure and draw 3 rectangles that are 2 4 by 3 2 inches.
b. Measure and draw 2 rectangles that are 2 4 by2 4 inches.
c.
d.
e.
f.
g.
Label one of the rectangles “integers”
Include on one of the sides the definition for integers
Include on the rest of the sides examples of integers
Decorate the rectangles
Cut out the rectangles, form a net, tape the rectangles together then fold the sides to make a box. Seal it up
and set it aside. “HINT-This box will not have a top”
Step 4
Rational numbers (Purple Paper)
14
3
14
14
a. Measure and draw 3 rectangles that are 2 16 by 3 4 inches.
b. Measure and draw 2 rectangles that are 2 16 by2 16 inches.
c.
d.
e.
f.
g.
Label one of the rectangles “rational numbers”
Include on one of the sides the definition for rational numbers
Include on the rest of the sides examples of rational numbers
Decorate the rectangles
Cut out the rectangles, form a net, tape the rectangles together then fold the sides to make a box. Seal it up
and set it aside.
“HINT-This box will not have a top”
Step 5
Irrational numbers (Blue Paper)
14
inches.
16
14
14
2 16 by2 16 inches.
a. Measure and draw 4 rectangles that are 1 by 2
b. Measure and draw 2 rectangles that are
c.
d.
e.
f.
g.
Label one of the rectangles “irrational numbers”
Include on one of the sides the definition for irrational numbers
Include on the rest of the sides examples of irrational numbers
Decorate the rectangles
Cut out the rectangles, form a net, tape the rectangles together then fold the sides to make a box. Seal it up
and set it aside.
“HINT-this will be an entire box and will not fit in with the others from above.”
Step 6
Real numbers (Red Paper)
a.
b.
c.
d.
e.
f.
g.
Measure and draw 3 rectangles that are 5 by 3 inches.
Measure and draw 2 rectangles that are 3 by 3 inches.
Label one of the sides “real numbers”
Include on one of the sides the definition for real numbers
Include on the rest of the sides examples of real numbers
Decorate the rectangles
Cut out the rectangles, form a net, tape the rectangles together then fold the sides to make a box. Seal it up
and set it aside.
“HINT-This box will not have a top and all other boxes will fit into it”
Challenge:
The Real Number System is partnered with the Imaginary Number System, like the Rational and Irrational Numbers.
Determine the pattern between the nesting boxes and create the correctly sized Imaginary Number System box (Green
Paper) . These two Number systems reside IN the Complex Number System (Pale Yellow Paper). Create a complex
number system box that holds ALL the nesting boxes. These two new boxes should be decorated, labeled and have
examples similar to the other boxes.
Grading:
Level

1




2




3




4




Description
The boxes are not built to the measurements
given.
There are no decorations.
Most of the examples do not fit into the number
system described.
The definitions are incorrect.
Most of the boxes are not built to the
measurements given.
Some of the boxes are missing decoration.
Some of the examples do not fit into the number
system described.
The definitions are unclear or vague.
The boxes are built to the measurements
described.
All the sides are decorated.
All of the examples are correct for the number
system described.
The definitions are correct.
The boxes are built to the measurements
described.
All the sides are decorated.
All of the examples are correct for the number
system described.
The definitions are correct.
The Challenge was successfully completed.