1
Level: 4
Standard Targeted: 4.G
Math Focus: Geometry - Angle Building and Recognition
Directions:
A) Take six to nine rods and connect them using any connectors you wish. The shape
should be 2-D and irregular. Sketch your shape below and label each angle as one of the
following;
right, acute, obtuse, straight, reflex
B) Construct a regular hexagon using any rods you wish. Sketch your hexagon below.
What type of angles are inside your hexagon?
Use as many rods and connectors as you wish to construct the following figures:
C) Construct a shape that has all acute angles. Sketch your shape.
D) Construct a shape that has all right angles. Sketch your shape.
E) Construct a shape where half of its angles are acute and half are obtuse. Sketch your
shape.
F) Construct a shape that has at least one right angle. Sketch your shape.
Extension:
A) Which figures above are symmetrical? Add lines of symmetry to your sketches above.
2
Answers:
A) Answers Will Vary
B) Obtuse
C) Answers Will Vary
D) Answers Will Vary
E) Answers Will Vary
F) Answers Will Vary
Extension:
A) Answers Will Vary
3
Level: 4
Common Core Standard Targeted: 4.MD & 4.G
Math Focus: Area and Perimeter
Directions:
Use the following measurements for the questions in this activity:
Orange = 12
Yellow = 8
Purple = 6
Red = 4
Green = 3
A) Without using connectors, form a triangle that has a perimeter of 14.
A1) What type of triangle is this?
B) Without using connectors, form a triangle that has a perimeter of 24.
B1) What kind of triangle is this?
C) Without using connectors form a different triangle that has a perimeter of 24.
C1) What type of triangle is this?
D) Construct a square using red rods. What is the perimeter and area of this square?
E) Construct a rectangle using red and green rods. What is the perimeter and area of this
rectangle?
F) Construct a rectangle with a perimeter of 36. If orange rods are used for one pair of
parallel
sides, what color is the other pair a of parallel sides made of?
F1) What is the area of this rectangle?
G) The area of a rectangle is 36. What color are the rods that make up this rectangle?
G1) What is the perimeter of this rectangle?
4
Extension:
A) Without using connectors, form an isosceles trapezoid that has a perimeter of 26.
Sketch
this trapezoid in color.
B) Can you estimate the area for the trapezoid above?
Answers:
A) 1 purple rod + 2 red rods OR 1 yellow rod + 2 green rods = Isosceles Triangle
B) 3 yellow = Equilateral
C) 1 orange rod + 2 purple rods
C1) Isosceles
D) Perimeter = 16
Area = 16
E) Perimeter = 14
Area = 12
F) Purple
F1) Area = 72
G) Orange and green; Perimeter = 30
Extension:
A) 2 yellow, 1 purple, 1 red
B) About 40
5
Level: 4
Common Core Standard Targeted: 4.OA & 4.MD
Math Focus: Multiplication, Area, Perimeter, Extrapolation
Directions:
A) Using 24 rods of the same color and 16 square connectors, construct the shape below:
B) For the following questions, assume that the shape you created represents one side of a
Rubik’s Cube.
1) How many sides are there in any cube?
2) If you were to construct a hollow Rubik’s Cube, how many rods and connectors would
you need to use in all?
3) If each of your rods has a value of 3, what is the perimeter and area of each of the
smaller squares that make up a face of the cube?
4) What is the perimeter and area of this entire face of the cube?
5) What is the volume of your cube be?
C) If you were to construct a non-hollow cube, how many rods and connectors would you
need to use?
6
Extension:
A) If you were to build the same shape with a rod that was twice the length of the one
that you used (value of 6), would the perimeter and area of one of the new faces also
double?
Show your thinking.
B) Based on your answer above, can you predict what would be the perimeter and area of
the same face built using rods with a length of 9 would be?
C) We have been calling the connectors "square connectors," and "hexagonal
connectors."
What would you call them if you could rename them?
Answers:
B)
1) 6
2) 108 rods and
3) Perimeter = 12
4) Perimeter = 36
5) 9 x 9 x 9 = 729
C) 120 rods
and
56 connectors
Area = 9
Area = 81
64 connectors
Extension:
A) The perimeter would double, but the area would quadruple
B) Perimeter = 108 (36 x 3) Area = 729 (81 x 9)
* If a side is doubled the perimeter of a square will also double, but the area will
increase 4 times the original. Since the side is squared to find the area, 22 = 4.
* Likewise, if the side is tripled, the perimeter will be tripled, but the area will increase
by 32, which is 9.
C) Answers Will Vary
7
Level: 4
Common Core Standard Targeted: 4.NF
Math Focus: Fractions
Directions:
A) If each orange rod were worth 24, what would be the value of the following:
Purple rod: _____ Yellow rod: ______ Red rod: ______ Green Rod: ______
B) If each yellow rod were worth 6, what would be the value of the three colored rods
below?
Sketch a picture of how you figured this out.
Orange = ______
Red = ______
Purple = ______
C) Fill in the following with an appropriate fraction:
1) The purple rod is _______ of the orange rod.
2) The red rod is _______ of the orange rod
3) The green rod is _______ of the purple rod
4) The green rod is _______ of the orange rod
5) The yellow rod is _______ of the orange rod
6) The red rod is _______ of the yellow rod
7) The purple rod is _______ of the red rod.
8
Extension:
A) If each orange rod were worth 10, what would be the value of the following:
Purple rod: _____ Yellow rod: ______
Red rod: ______
Green Rod: ______
B) The three numbers below represent possible values for the orange rod. Which of these
values would be the most difficult to use if you were then asked to figure out the values
of the remaining rods? Why?
12
20
36
Answers:
A) Purple = 12
Yellow = 18
B) Orange = 9
Red = 3
Purple = 4.5
* Pictures Will Vary
C)
1) ½
5) ⅔
2) ⅓
6) ½
3) ½
7) 1⅓
Red = 9
Green = 6
4) ¼
Extension:
A)
Purple = 5
Yellow = 6⅔
Red = 3⅓
Green = 2½
B) 20 - Explanations Will Vary
EXAMPLE: 20 is not a multiple of three. This will be difficult to find the value of
the yellow and red rods.
9
Level: 4
Common Core Standard Targeted: 4.NF
Math Focus: Addition and Subtraction of Fractions
Directions:
A) Build a square out of red rods. If each rod has a value of ¼, what is the total value of
the square?
A1) If you then built a square using the yellow rods, what would be its total value,
given your answer above?
A2) What should be the value of each yellow rod?
B) Build a square out of green rods. If each rod has a value of ⅓, what would be the
value of the square?
B1) If you then built a square using purple rods, what would be its value, given
your answer above?
B2) What should be the value of each purple rod?
C) The values of the red, yellow, green and purple rods remained the same as above. A
rectangle was built, using two orange and two red rods. The total value of this rectangle is
9/10
C1) What is the total value of both orange rods?
C2) What is the value of each orange rod? Please show your thinking.
D) Using the values above, build a structure with a total value of 2, using any rods you
choose. Prove that your structure has a value of 2.
D1) If each connector has a value of 1/10, what is the total value of your structure now?
10
Answers:
A) 1
A1) 2
A2) ½
B) 1⅓
B1) 2⅔
B2) ⅔
C) View Construction
C1) 4/10 or 2/5
C2) 2/10 or 1/5
D) Answers Will Vary
D1) Answers Will Vary
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Level 4
Most of the exercises are designed to cover the Common Core State Standards
(CCSS) in Math. The Intooba manipulative encourages students to find solutions to
real world problems in three dimensions.
(4.G)
•
Build a right triangle
•
Build an triangle that contains an acute angle
•
After creating a square, find one rod to approximate a line of symmetry. How
many lines of symmetry can you find for your square?
•
Repeat this notion for a rectangle and other various shapes?
•
Create any shape out of rods and connectors. Can you identify a line of
symmetry for your shape?
(4.NF.3)

Make an hexagon with a partner using all the same colored rods.
- How many rods make your hexagon a whole? Express this as a fraction.
(6/6).
- If you took 3 rods out of the hexagon, what fraction are you left with?
(3/6).
- Write a subtraction equation expressing what you just did. (6/6 – 3/6 =
3/6).
- Repeat this notion for various shapes and/or fractions.

Build a 3-D triangle worth 22 if each purple is worth 6/3 and each yellow is
worth 3 ½.
-
If you added another dimension to the triangle, what is its
value now? (Answer = 35)
12

Build a 4-legged square table using yellow rods. If each rod is worth 7 2/3,
what is the value of the table?

(Similar triangles) Start with building one triangle with orange rods. How can
you build a second triangle inside this one using purple? How many triangles
are there now. What other shapes do you see? (Answer: 2 parallelograms).
How much are the parallelograms worth? (Hint: You can slide the connectors
up and down on the rods). If each orange rod is worth 7 ½, and each purple 5
1/4, how much is each triangle worth?

Build three adjoining triangles. If each yellow rod is worth 8 2/3, what is the
value of the figure?