MOORE PUBLIC SCHOOLS
Marshmallows, and
Toothpicks, and
Equations, Oh My!
Common Core Ready
Andrea Brock, M.Ed.
OSSM Summer Conference 2013
Name: _________________________________
Common Core Links:
6th Grade:
7th Grade:
8th Grade:
Mathematical Practices:
4. Model with mathematics
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
Name: _________________________________
Marshmallows and toothpicks and equations, Oh my!
1. Predict how many toothpicks it will take to build 9 squares that are touching each other in 3 rows?
2. Do you think you will need the same amount of toothpicks to build nine squares in a row going
across? If you think you will need a different amount then please record that number below.
3. When you have your supplies, build both figures one square at a time. Complete the tables below
as you build.
Table 1: 3 rows of 3
# of squares
# of toothpicks
(x)
(y)
0
1
(x, y)
Table 2: 9 squares going across
# of squares
# of toothpicks
(x)
(y)
(x, y)
0
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
1
4. Were your predictions right?
3 x 3:
9 across:
5. Draw both constructions below. How many squares do you see in the first construction you built?
(There are more than 9 )
6. Is there a pattern for the number of squares and number of toothpicks? If yes, describe it.
Name: _________________________________
Table 1:
Table 2:
7. Based on your answers above, which table has a constant rate of change?
8. For data to be linear it needs a constant rate of change.
Which table is linear? __________ Which table is nonlinear? ___________
9. Looking at your answer in number 8, if you graphed those points and connected them with a line,
which of these would it look like?
10. Use the graph paper provided to graph each function. Use one side for Table 1 and one side for
Table 2.
11. Use the chart below to record the slope between the points.
Table for Graph 1
Slope
Table for Graph 2
Point
Point
First
Second
Second
Third
Third
Fourth
Point
First
Second
Third
Point
Second
Third
Fourth
Fourth
Fifth
Fourth
Fifth
Fifth
Sixth
Fifth
Sixth
12. Which table has the same slope for each point (constant rate of change)?
13. Does this match your answer for problem 9?
14. Is the slope positive or negative? Why?
15. Which quadrant contains all of the points?
16. What does the ordered pair (1, 4) represent in the problem?
17. What does the ordered pair (2, 7) represent in the problem?
*Bonus: How many toothpicks would you need to build 18 squares for Table 2?
*Bonus: How many triangles do you see in the model below?
Slope
Name: _________________________________
Extend
18. What is the y-intercept for your line?
19. What is the slope of your line?
20. Using slope intercept form write your equation
m=
y=___________
b=
21. Now build 9 triangles side by side. Complete the table below as you build.
# of
triangles
(x)
0
# of
toothpicks
(y)
(x, y)
1
1
2
3
4
5
6
7
8
9
22. Use the graph paper provided to graph the function.
23. Use the chart below to record the slope between the points.
Point
First
Second
Third
Point
Second
Third
Fourth
Fourth
Fifth
Fifth
Sixth
Slope
24. What is the y-intercept for your line?
25. What is the slope of your line?
Name: _________________________________
26. Using slope intercept form write your equation
m=
y=___________
b=
27. Compare the two linear functions that you graphed.
a. What do you notice about the y-intercepts?
b. What do you notice about the slopes?
c. Which shape produced a greater slope? Why do you think this occurred?
d. Do you think these lines will ever intersect? Why or why not?
Name: _________________________________
Marshmallows and toothpicks and equations, Oh my!
1. Predict how many toothpicks it will take to build 9 squares that are touching each other in 3 rows?
2. Do you think you will need the same amount of toothpicks to build nine squares in a row going
across? If you think you will need a different amount then please record that number below.
3. When you have your supplies, build both figures one square at a time. Complete the tables below
as you build.
Table 1: 3 rows of 3
# of squares
# of toothpicks
(x)
(y)
0
1
(x, y)
Table 2: 9 squares going across
# of squares
# of toothpicks
(x)
(y)
(x, y)
0
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
1
4. Were your predictions right?
3 x 3:
9 across:
5. Draw both constructions below. How many squares do you see in the first construction you built?
(There are more than 9 )
6. Is there a pattern for the number of squares and number of toothpicks? If yes, describe it.
Name: _________________________________
Table 1:
Table 2:
7. Based on your answers above, which table has a constant rate of change?
8. For data to be linear it needs a constant rate of change.
Which table is linear? __________ Which table is nonlinear? ___________
9. Looking at your answer in number 8, if you graphed those points and connected them with a line,
which of these would it look like?
10. Use the graph paper provided to graph each function. Use one side for Table 1 and one side for
Table 2.
11. Use the chart below to record the slope between the points.
Table for Graph 1
Slope
Table for Graph 2
Point
Point
First
Second
Second
Third
Third
Fourth
Point
First
Second
Third
Point
Second
Third
Fourth
Fourth
Fifth
Fourth
Fifth
Fifth
Sixth
Fifth
Sixth
12. Which table has the same slope for each point (constant rate of change)?
13. Does this match your answer for problem 9?
14. Is the slope positive or negative? Why?
15. Which quadrant contains all of the points?
16. What does the ordered pair (1, 4) represent in the problem?
17. What does the ordered pair (2, 7) represent in the problem?
*Bonus: How many toothpicks would you need to build 18 squares for Table 2?
*Bonus: How many triangles do you see in the model below?
Slope
Name: _________________________________
Extend
18. What is the y-intercept for your line?
19. What is the slope of your line?
20. Using slope intercept form write your equation
m=
y=___________
b=
21. Now build 9 triangles side by side. Complete the table below as you build.
# of
triangles
(x)
0
# of
toothpicks
(y)
(x, y)
1
1
2
3
4
5
6
7
8
9
22. Use the graph paper provided to graph the function.
23. Use the chart below to record the slope between the points.
Point
First
Second
Third
Point
Second
Third
Fourth
Fourth
Fifth
Fifth
Sixth
Slope
24. What is the y-intercept for your line?
25. What is the slope of your line?
Name: _________________________________
26. Using slope intercept form write your equation
m=
y=___________
b=
27. Compare the two linear functions that you graphed.
a. What do you notice about the y-intercepts?
b. What do you notice about the slopes?
c. Which shape produced a greater slope? Why do you think this occurred?
d. Do you think these lines will ever intersect? Why or why not?