Transcript Collection of Patternsx

Jacob’s Birthday Party
Jacob’s family was setting up tables for his birthday party. They didn’t
want any of the kids to feel left out, so they decided to push all of the
small tables together to make one long table for everyone.
How many tables does Jacob need for 54 guests?
I am having a party, and I want to give 2 Peeps
to each of my guests as part of a party favor
bag. Because the Peep rush has ended, Haribo
is having a special promotion. For each
package of Peeps that you order, you get 2
Peeps as a gift.
How many packages of Peeps should I order
for my 84 guests?
How many Peeps will I be paying for and how
many will be free?
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All of the bridges in this part are built with yellow rods for spans and red rods for
supports, like the ones shown here. This is a 2-span bridge. Note that the yellow rods
are 5 cm long.
Now build a 3-span bridge.
How many yellow rods did you use?
How long is your bridge?
How many red rods did you use?
How many rods did you use altogether?
Try to answer the questions without building a 5-span bridge.
How many yellow rods would you need for a 5-span bridge?
How long would your bridge be?
How many red rods would you need?
How many rods would you need altogether?
Write a rule for figuring out the total number of rods you would need to build a bridge
if you knew how many spans the bridge had.
In the diagram below, the shaded hexagons are flower beds, and the white
hexagons are white paving stones. Marco figures out how many white paving
stones are needed around different numbers of flower beds.
Draw a diagram to show how many white stones are needed around 5 flower
beds.
Marco says that 28 white stones are needed around 13 flower beds. Without
drawing the flower beds, explain how you know that Marco is not correct. How
many white stones are needed around 13 flower beds?
Tom uses toothpicks to make the shapes in the diagram below.
How many toothpicks make shape 3?
Draw shape 4 next to the diagram above.
Tom says, “I need 36 toothpicks to make shape 12.” Tom is not correct. Explain
why he is not correct. How many toothpicks are needed to make shape 12?
How many seats fit around a row of triangular tables?
INPUT
Number of Δ tables
RULE

INPUT
(Number of tables)
What patterns do you see?

OUTPUT
Number of Seats
OUTPUT
(Number of seats)
If you know how many degrees are in a triangle, how many are in this
figure?
Complete the table.
What do you notice? Write a rule to describe the pattern.
Blocks are used to build the staircases shown below (1 for the first, 3 for the
second, 6 for the third, etc). How many blocks will be used for the 100th stair?
Can you generate a rule that could be used to find the number of blocks used for
any number of stairs?
How many blocks would be
required to build 100 stairs?
What is a general rule that
could be used to find the
number of blocks to build any
number of stairs?
1 Stair
2 Stairs
3 Stair
Describe a pattern you see in the cube buildings.
Use your pattern to write an expression for the
number of cubes in the nth building, where n is
an integer.
Use your expression to find the number of cubes
in the fifth building.
4 cows
5 cows
The pens above show how much fencing
is required to contain 4, 5, and 6 cows.
Each square represents 1 length of fence.
How many lengths would be required to
contain 100 cows? What is a general rule
that could be used to determine how
many lengths are required for any
number of cows
6 cows
Case 1
Case 2
Case 3
How is the above pattern growing?
Represent the pattern in a t-table, a graph, in words, and with an algebraic
rule.
How many squares would be in Case 100?
Term 1
Term 2
Draw Term 3. Create a table, graph, and equation to
represent the pattern you see.
How many squares would be used to build Term 50?
Term 1
Term 2
Draw Term 3. Create a table, graph, and equation to
represent the pattern you see.
How many squares would be used to build Term 50?
Does the shading help you to see the pattern?
Below is a 10x10 grid with the border shaded in. Generate a rule that could be
used to determine the number of shaded border squares for any square grid
The numbers of dots in the figures below are the first four rectangular
numbers. Assume the the pattern continues.
1) Write down everything you observe about the patter.
2) What are the first four rectangular numbers?
3) How do the numeric values relate to the picture?
4) Describe the picture of the 10th rectangular number?
5) Use words, diagrams, or symbols to generalize the pattern. How do you know your
generalization is true?
Find the number of cubes in the tenth tower.
How many cubes would be in the Zero-th building?
What is the rate of change?
How could the pattern be described symbolically? Or, if you know the
pattern number, can you write a formula that will give you the height of
any tower?
#1 #2 #3 #4
Find the number of cubes in the tenth tower.
How many cubes would be in the Zero-th building?
What is the rate of change?
How could the pattern be described symbolically? Or, if you know the
pattern number, can you write a formula that will give you the height of
any tower?
#1 #2 #3 #4
Find the number of cubes in the tenth tower.
How many cubes would be in the Zero-th building?
(Think of it as underground/in the basement)
What is the rate of change?
How could the pattern be described symbolically? Or, if you know the
pattern number, can you write a formula that will give you the height of
any tower?
#1 #2 #3 #4
Find the number of cubes in the tenth tower.
How many cubes would be in the Zero-th building?
(Think of it as underground/in the basement)
How could the pattern be described symbolically? Or, if you know the
pattern number, can you write a formula that will give you the height of
any tower?
#1 #2 #3 #4
How many toothpicks will you need for 4 sections?
What patterns do you see? Explain.
How about 30 sections?
How did you decide? Explain.
100 sections?
5 sections?
How many toothpicks will you need for a square with a side length 4?
What patterns do you see? Explain.
How about a side length of 20?
How did you decide? Explain.
Side length 100?
5?
How many toothpicks will you need for 4 squares?
What patterns do you see? Explain.
How about 30 squares?
How did you decide? Explain.
100 squares?
5 squares?
How many toothpicks will you need for 4 wiggles?
What patterns do you see? Explain.
How about 30 wiggles?
How did you decide? Explain.
100 wiggles?
5 wiggles?
How many square will you need for figure 4?
What patterns do you see? Explain.
How about figure 10?
How did you decide? Explain.
Figure 30?
Figure 5?
How many sides will show in a 4-long?
5-long?
What patterns do you see? Explain.
How about a 20-long?
How did you decide? Explain.
100-long?
How many triangles will you make for 4-high?
What patterns do you see? Explain.
How about a 30-high?
How did you decide? Explain.
100-high?
5-high?
How many squares will you need for Figure 4?
What patterns do you see? Explain.
How about Figure 20?
How did you decide? Explain.
Figure 50?
Figure 5?
How many squares will you need for Figure 4?
What patterns do you see? Explain.
How about Figure 20?
How did you decide? Explain.
Figure 50?
Figure 5?
How many squares will you need for Figure 4?
What patterns do you see? Explain.
How about Figure 10?
How did you decide? Explain.
Figure 30?
Figure 5?
How many squares will you need for Figure 4?
What patterns do you see? Explain.
How about Figure 10?
How did you decide? Explain.
Figure 30?
Figure 5?
How many squares will you need for Figure 4?
What patterns do you see? Explain.
How about Figure 10?
How did you decide? Explain.
Figure 30?
Figure 5?
Square tiles were used to make the pattern above.
a. Write an equation for number of tiles needed to make the nth figure. Explain.
b. Find an equivalent expression for the number of tiles in part a. Explain why they are
equivalent.
c. Write an equation for the perimeter of the nth figure.
d. Identify and describe the figure in the pattern that can be made with exactly 420 tiles.
e. Describe the relationship represented by the equation in parts a and c.
Draw the next figure.
Explain how you knew what figure would come next. What is the pattern that you
see?
How many circles would be in the next term?
How many circles would be in the 25th term? How do you know? What is a general
rule that would allow you to find the number of circles in any term?
Mrs. Ramirez is tiling her back walk and has designed
her own hexagon mosaic tiles. They consist of:
trapezoids, rhombi, and triangles. The perimeter of the
space she has outlined is 106 ft., and she only wants
one tile across.
Each mosaic tile contains:
-6 trapezoids
-2 rhombi
-2 triangles
The cost for each individual tile is:
Trapezoids - $3/tile
Rhombi - $2/tile
Triangles - $1/tile
How much will it cost to tile her back walk?