Math in Action 2013-2014
Solutions
1.
How many more bricks are there in the larger stack?
2.
The red wall in the picture is made of identical size of bricks.
How many bricks are missing in this wall?
3.
The figure in the picture on the left is built of identical wooden cubes. How
many cubes were used to build it?
4.
Mark always builds figures made up of eight identical wooden blocks. Which of the figures
below was not made by Mark?
5.
The figure shown on the right was made out of identical wooden cubes.
How many wooden cubes were used?
Answer:
5
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Answer:
6
_____________
Answer:
8
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Answer:
C
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Answer:
14
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6.
7.
Ellie makes a large cube from 27 small white cubes. She paints all the faces
of the large cube. Then Ellie removes four small cubes from four of the
corners, as shown on the right. While the paint is still wet, she stamps each
of the new faces onto a piece of paper. How many of the following stamps
did Ellie make?
How many cubes have been removed from the first block to
obtain the second block?
Original block had 2 x 3 x 2 = 12 cubes
The second block had 6 + 2 = 8 cubes
Number of cubes removed: 12 – 8 = 4
8.
Robert made a tunnel using some identical cubes (fig.1).
When he got bored, he rearranged the tunnel into a
complete pyramid (fig.2). How many cubes from the
original tunnel did he not use for the pyramid?
Answer:
4
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Answer:
4
_______________
Answer:
18
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Number of cubes used for the tunnel: 5x5x4 – 3x4x3 = 100 – 36 =64
Number of cubes used for the pyramid: 25 + 9 + 9 + 3 = 46
He did not use 64 – 46 = 18 cubes
9.
How many unit cubes are still needed to fill up the box in the picture
on the left?
Answer:
98
The number of cube needed = 6*5*4 = 120 units
Number of existing units cubes (from the bottom layers to the top) = (6+3+3+2+1) + 4 + 2 + 1 = 22 cubes
Unit cubes needed = 120-22 =98
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Math in Action 2013-2014
10.
Chris constructed the block on the picture on the left using white and
blue cubes of the same size. The outside of the block is completely
white, but all cubes used inside are blue. How many blue cubes did Chris
use?
Answer:
12
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Number of inside cubes: 2(2 x 3) = 12
11. We made a big cube using 64 small white cubes, and then painted five of the sides of the cube
in red. How many small cubes have exactly two sides painted?
Answer:
20
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Don’t forget to add the corner pieces (4)
12.
Picture 1 shows a castle built out of identical cubes.
When you look at the same castle from above it looks
as shown in Picture 2. Every cube lies either on the
ground or on the top of another cube. How many
cubes were used to build the castle?
Answer:
56
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((3 x 8) + (2 x 16) = 24 + 32 = 56
13. The structure shown in the picture is made by gluing together the sides of 10
cubes. Roman painted the entire structure, including the bottom. How many
faces of the cubes did he paint?
Answer:
14.
Answer:
68
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15.
Alice forms four identical numbered cubes using the net shown.
She then glues them together to form a 2×2×1 block, as shown. Only
faces with identical numbers are glued together.
Alice then finds the total of all the numbers on the
surface of the block. What is the largest total that Alice
can get?
Which of the pieces below is needed to make the solid shown to the
right into a complete wall?
36
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Answer:
E
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